Hybrid and Solar Vehicles - DIMEC

Transcript

International Workshop on
Hybrid and Solar Vehicles
Graphic design: Luciano Statunato - 3D images: Marco Coraggio
November 6, 2006 - University of Salerno, Italy
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Provincia di Salerno
www.acsalerno.it
IFAC TC Automotive Control
Energy Conversion Systems
and their Environmental Impact
Istruzione e cultura
Leonardo da Vinci
International Workshop on
Hybrid and Solar Vehicles
University of Salerno, Italy
November 5-6, 2006
www.dimec.unisa.it/WHSV
Proceedings
Copyright © 2006
PREFACE
The growth of mobility has had a positive effect on prosperity and quality of life, but its
negative impact on the environment and the erosion of non-renewable resources are becoming
more and more visible. As a consequence, the attention toward the sustainable mobility is
rapidly increasing, spreading from specialists to final users and to public opinion. In last
decade, the hybrid electric vehicles have emerged as a valid mid-term solution to reduce fuel
consumption and carbon dioxide emissions. Their integration with photo-voltaic sources may
give a further contribution toward the mitigation of fossil fuels depletion, global warming and
climate changes. Despite these promising perspectives, there is a certain lack of systematic
research on the integration of hybrid vehicle technology with solar sources.
This Workshop is dedicated to hybrid and solar vehicles, with particular emphasis on the
combined use of these two approaches. These proceedings include 13 papers, from Hungary,
France, Italy, Romania, Spain, Turkey and United States. Most of the research presented is
conducted in an academic context, also in cooperation with industry and research centres. The
papers cover several aspects of hybrid and solar vehicles. The actual trends and the
opportunities related to the integration of electric vehicles with photo-voltaic and, more
generally, with renewable sources are presented in the first paper. Five papers deal with
modelling, design and control of hybrid solar vehicles, also caring for profitableness of such
vehicles. Other five papers concern hybrid electric vehicles: hybridization of a small vehicle for
urban transportation and of a 4WD parallel vehicle, control of super-capacitors, HEV real-time
control and performance testing. Other two papers are devoted to photovoltaic sources for
automotive applications, concerning MPPT modelling and power interfaces.
I would thank all the Authors for their dedication in preparing excellent technical papers, the
members of Scientific Committee for their cooperation in paper review and my colleagues at
the University of Salerno for their help in the Workshop organization. We acknowledge the
financial and operative support of University of Salerno to this Workshop, co-sponsored by the
Technical Committee “Automotive Control” of International Federation of Automatic Control
and by SAE Naples Section. We also recognize the significant impulse given to the studies on
hybrid solar vehicles by the European Community in supporting the Leonardo Project “Engine
Conversion Systems and Their Enviromental Impact”, with sponsorship of Automobile Club
Salerno, Lombardini, Saggese and Province of Salerno.
The Workshop Chair
Gianfranco Rizzo
Chair
Prof. Gianfranco Rizzo, DIMEC, University of Salerno (I), [email protected]
Scientific Committee
I.Arsie, DIMEC, University of Salerno (I)
M.Basset, UHA, Mulhouse (F)
J.Bokor, BUTE, Budapest (HU)
E.Chiappini, University of L’Aquila (I)
G.Gissinger, UHA, Mulhouse (F)
L.Guvenç, ITU, Istanbul (TR)
Y.Guezennec, OSU, Columbus (USA)
L.Guzzella, ETH, Zurich (CH)
I.Ionita, Univ. of Galati (RO)
T.Peter, BUTE, Budapest (HU)
C.Pianese, DIMEC, University of Salerno (I)
G.Rizzo, DIMEC, University of Salerno (I)
G.Rizzoni, OSU, Columbus, Ohio (USA)
G.Spagnuolo, DIIIE, University of Salerno (I)
Organizing Committee
I.Arsie, DIMEC, University of Salerno (I)
G.Rizzo, DIMEC, University of Salerno (I)
M.Sorrentino, DIMEC, University of Salerno (I)
G.Spagnuolo, DIIIE, University of Salerno, (I)
CONTENTS
S.E.Letendre
Prometheus Institute for Sustainable Development, Vermont (USA)
USHERING IN AN ERA OF SOLAR-POWERED MOBILITY
1
Zs. Preitl (1), P. Bauer (1), J. Bokor (2)
(1) Budapest University of Technology and Economics, Dept. of Transport Automation, Hungary
(2) Computer and Automation Research Institute, Budapest, Hungary
FUEL CONSUMPTION OPTIMIZATION FOR HYBRID SOLAR VEHICLE
11
P. Bauer (1), Zs. Preitl (1),P. Gáspár (2), Z. Szabó (2), J. Bokor (2)
(1) Budapest University of Technology and Economics, Dept. of Transport Automation, Hungary
(2) Computer and Automation Research Institute, Budapest, Hungary
CONTROL ORIENTED MODELLING OF A SERIES HYBRID SOLAR VEHICLE
19
A.Boyali (1), M.Demirci (1), T.Acarman (2), L.Güvenç (1), B.Kiray (3), M.Yildirim (3)
(1) Istanbul Technical University, Mechanical Engineering Dept., Istanbul, Turkey
(2) Galatasaray University, Fac.of Engineering and Technology, Istanbul, Turkey
(3) Ford-Otosan, Product Development, R&D Department, Kocaeli, Turkey
SIMULATION PROGRAM AND CONTROLLER DEVELOPMENT FOR A 4WD PARALLEL HEV
27
I.Arsie, R.Di Martino, G.Rizzo, M.Sorrentino
DIMEC, University of Salerno, Italy
A MODEL FOR A PROTOTYPE OF HYBRID SOLAR VEHICLE
35
G.Petrone (1), G.Spagnuolo (1), M.Vitelli (2)
(1) DIIIE, University of Salerno, Italy
(2) DII, Seconda Università di Napoli, Aversa (CE), Italy
A MODEL OF MISMATCHED PHOTOVOLTAIC FIELDS FOR SIMULATING HYBRID SOLAR
VEHICLES
43
I.Ionita, D.Negoita, S.Paraschiv, I.V. Ion
University of Galati "Dunarea de Dos", Romania
THE PROFITABLENESS OF HYBRID SOLAR VEHICLES
49
C.Boccaletti (1), G.Fabbri (1), F.M.Frattale Mascioli (2), E.Santini (1)
(1) Department of Electrical Engineering, University of Rome “La Sapienza”, Italy
(2) Department INFOCOM, University of Rome “La Sapienza”, Italy
TECHNICAL AND ECONOMICAL FEASIBILITY STUDY OF A SMALL HYBRID VEHICLE FOR
URBAN TRANSPORTATION
57
D.Paire (1), M.Becherif (2), A.Miraoui (1)
(1) L2ES, UTBM, Belfort (cedex) 90010, France
(2) SeT, UTBM, Belfort (cedex) 90010, France
PASSIVITY-BASED CONTROL OF HYBRID SOURCES APPLIED TO A TRACTION SYSTEM
63
G.Rousseau (1,2), D.Sinoquet (1), P.Rouchon (2)
(1) Institut Français du Pétrole, 92852 Rueil Malmaison, France
(2) Centre Automatique et Systèmes, École des Mines de Paris, Paris, France
HYBRID ELECTRICAL VEHICLES: FROM OPTIMISATION TOWARD REAL-TIME CONTROL
STRATEGIES
71
N.Caccavo, G.Carbone, L.Mangialardi, L.Soria
Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Italy
PERFORMANCE TESTING OF HYBRID VEHICLES IN BARI DOWNTOWN
79
M. Cacciato, A. Consoli, G. Scarcella, A. Testa
Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Catania, Italy
HYBRID VEHICLES WITH ELECTRICAL MULTI ENERGY UNITS
87
A.Cid-Pastor (1,3), L.Martínez-Salamero (2), C.Alonso (1), G.Schweitz (3), R.Leyva (2)
(1) LAAS-CNRS, Laboratoire d’Analyse et des Architectures des Systèmes, Toulouse, France
(2) ETSE Universitat Rovira i Virgili / Dept. Eng. Electrònica, Elèctrica i Automàtica, Tarragona, Spain
(3) EDF R&D / LME Department, Moret sur Loing, France
IMPEDANCE MATCHING FOR PV GENERATOR
93
USHERING IN AN ERA OF SOLAR-POWERED MOBILITY
Steven E. Letendre, Ph.D.
Green Mountain College, Poultney, VT &
The Prometheus Institute for Sustainable Development, Cambridge, MA, USA
[email protected]
Abstract: Modern mobility, for both humans and commodities, relies almost exclusively
on fuels derived from petroleum. At the same time the world is experiencing soaring
demand for mobility, environmental and resource constraints have become increasingly
acute. This article discusses the role that electric drive, initially in the form of hybrid
electric vehicles, can play in addressing the mobility challenge. This article discusses the
opportunity that electric drive vehicles create to use solar and wind power for
transportation. The potential of the emerging vehicle integrated PV concept is discussed,
along with the importance of connecting cars to the electric grid.
Keywords: electric vehicles, solar energy, renewable energy systems, electric power
systems
Today, mobility is a commodity for which demand is
linked closely to income. Specifically, increases in
demand for highway travel and air travel in a country
tracks closely growth in national income. Figure 1
provides data on per capita vehicle miles travelled
(VMT) and per capital air travel from 1960 to 2004
in the US. During this timeframe per capita income
grew from $13,800 to $38,856 while per capita VMT
more than doubled and per capita domestic air travel
quadrupled. Based on the experiences in the US, per
capita VMT took approximately 30 years to double,
while per capita domestic miles flown doubled in just
ten years.
10,000
20
8,000
per capita VMT
Human progress is tied to advances in mobility.
Societies adept at harnessing technology to reduce
the travel times to distant lands successfully gained
access to new resources, allowing wealth creation
opportunities beyond which local resources allowed.
The process accelerated dramatically as fossil fuels
were employed to provide even greater opportunities
to move people and commodities across great
distances.
25
12,000
15
6,000
10
4,000
Per Capita VMT
5
Per Capita Miles Flown
(domestic)
2,000
per capita air travel
1. MOBILITY IN THE 21ST CENTURY
-
0
1960
1965
1970
1975
1980
1985
1990
1995
2000
2004
Year
Fig. 1. Mobility trends in the US: Per capita
vehicles miles travelled and per capita domestic
air travel, 1960 to 2004 (Sources: US Bureau of
Economic Statistics and the US Bureau of
Transportation Statistics)
As incomes in the developing world rise, demand for
mobility likewise increases in these regions. Myer
and Kent (2003) in their book New consumers: The
influence of affluence on the environment highlight
the rapid increase in demand for personal
automobiles occurring in the developing world and in
countries as a new consumer class emerges. They
argue that over 1 billion of these new consumers will
Workshop "Hybrid and Solar Vehicles", November 5-6, 2006, University of Salerno, Italy
1
soon have an aggregate spending capacity, in
purchasing power parity terms, to match that of the
US. Recent data suggests that China is rapidly
expanding its automobile manufacturing capabilities;
annual passenger production grew from 100,000
vehicles in 1991 to 2.3 million in 2004—a 28 fold
increase (Worldwatch Institute, 2006).
We have reached an apex in global mobility. The
shear volume and pace of movement, of both humans
and commodities, on this planet is incomprehensible.
The 3.7 trillion passenger-kilometers of air travel in
2005 equals over four and a half million round trips
from the Earth to the Moon (ICAO, 2005).
What made this level of mobility possible, and how
much longer can it be sustained? This critical
question is addressed in the next section of the
article.
1.1 Petroleum and transportation: resource
constraints, the environment, & supply risks
Petroleum-derived fuels, such as gasoline for
vehicles and jet fuel for modern aircraft, provide
over 97% of primary energy for transportation. Of
the 80 million barrels used globally each day in
2003, approximately one half are consumed for
transportation. The US Department of Energy’s
Energy Information Administrations (EIA) predicts
that global oil consumption will reach 118 million
barrels per day by 2030 (EIA, 2006). In sum,
transportation is entirely dependant on a single
source of energy—petroleum—and its consumption
for transportation purposes is predicted to rise by
47% in twenty-five years. Most of this increase will
come from rising demand for transportation in nonOECD countries (EIA, 2006).
The state of modern transportation systems is
extremely precarious.
Relying exclusively on
petroleum as a source of energy for transportation
creates significant risks, the most important of which
is resource limits. Volumes have been written about
the so called peak oil phenomenon, which suggests
that global oil production peaks and subsequently
enters a prolonged period of decline. While oil does
not “run out” many predict that prices rise
dramatically in the face of rising demand and
declining production (Simmons, 2005). While the
timing of peak oil is the subject of debate, it’s
generally accepted that it will occur within the first
half of this century.
The use of petroleum for transportation is a factor
linked to global climate change. The combustion of
fuels for transportation causes carbon dioxide
emissions, the primary pollutant contributing to
global
warming,
into
the
atmosphere.
Approximately 25% of global emissions of carbon
dioxide come from the transport sector. In addition,
transport related emissions are one of the fastest
growing categories, which is likely to increase the
share of total carbon emissions coming from the
transport sector.
A number of recent scientific studies suggest that
global climate change is occurring more rapidly than
scientists predicted and is already having negative
impact on ecosystems across the globe.
Governments and non-governmental organizations
worldwide are calling for dramatic reductions in
carbon dioxide emissions to minimize further
warming of the Earth and the associated
consequences of rising sea levels, more severe
weather patterns, and negative ecosystem impacts.
Clearly, efforts are needed to reduce the transportrelated emissions of carbon; this can only be
accomplished by either reducing the amount of
travel, increasing the efficiency of the vehicle fleet,
shifting toward alternative fuels, or some
combination there of.
Supply risks are an additional concern linked to the
transport sector’s exclusive reliance on oil as a
primary energy source. Roughly one-third of global
oil production comes from the politically volatile
Middle East (EIA, 2006). Furthermore, this region is
home to the largest known oil reserves, thus the
region will become increasingly important as a
global supplier. The region is currently enmeshed in
several armed conflicts, including the conflict
between the US and Iraq. Terrorist attacks on key
ports and escalating regional violence could cause
significant supply shocks.
2. TOWARD SUSTAINABLE MOBILITY
The scope of the mobility challenge is daunting. The
issue must be addressed on multiple fronts, from
smart planning to reduce the need for travel by
automobiles to the development of new vehicle
technologies.
The remainder of this article focuses specifically on
options to reduce the light vehicle fleet’s dependence
on petroleum-derived fuel sources. This is achieved
through either improving fuel economy and/or using
alternative fuels. Progress has been made in these
areas, but virtually all vehicles commercially
available today run primarily on either gasoline or
diesel fuel.
In the US, the primary mechanism for regulating
vehicle fuel economy is the Corporate Average Fuel
Economy (CAFE) standard, established at the
national level. These standards remain unchanged
since 1985 at 27.5 miles per gallon (mpg). Europe is
further along in addressing the mobility challenge
with more developed mass transit systems and a
much more efficient light vehicle fleet than that
found in the US.
The search for viable alternative fuels has focused on
biofuels, with interest in biofuels surging in recent
years. Brazil is often held up as a successful
example of large-scale biofuel development, meeting
20% of its transport fuel requirements with ethanol
derived from sugar cane. The development of flexfuel vehicles in the US is gaining momentum, which
provides a vehicle owner a choice of energy options
2
to meet their transportation needs. For example,
some automobile manufacturers are building vehicles
that operate on biofuel blends like E85—a blend of
85% ethanol and 15% gasoline.
Biofuels offer the potential to reduce our dependence
on gasoline for the light vehicle fleet, but the
potential is limited. There is much debate about the
energy balance of biofuels and the appropriateness of
using arable land to produce energy crops as apposed
to food. It is unlikely that biofuels will emerge as a
replacement for gasoline as a transport fuel, although
they could serve to displace a small portion of
gasoline and diesel fuel for the light vehicle fleet.
Much effort is being directed at producing fuel cells
for mobile applications, fuelled with onboard
compressed hydrogen. Fuel cell vehicles running on
compressed hydrogen are viewed by some as the
ultimate means to achieve sustainable mobility. In
recent years, however, some have questioned the
over emphasis on research and development in to
fuel cell vehicles and their potential to reduce carbon
emissions in the short-term.
It is becoming
increasingly clear that hydrogen-powered fuel cells
vehicles face a number of technical and economic
challenges that will likely take decades to address
(Morris, 2003).
In a 2004 report prepared by the US-based Center for
Energy and Climate Solutions for the National
Commission on Energy Policy concluded, “We
believe that the most plausible vehicle of the
future is a plug-in hybrid running on a
combination of low-carbon electricity and a lowcarbon biomass-derived fuel.” (Center for Energy
and Climate Solutions, 2004)
2.1 The hybrid electric vehicle revolution
Hybrid electric vehicles (HEV), using both an
internal combustion engine and electric motor,
achieve dramatic improvements in fuel economy.
Commercially available HEVs boast fuel economy
ratings of over 50 mpg. For example, the most
popular hybrid, the Toyota Prius, achieves a fuel
economy rating of 60 mpg highway and 51 mpg city.
Consumers now have several HEV options to choose
from, and their popularity among the car-buying
public is increasing.
Virtually every major
automobile manufacturer is manufacturing, or plans
to in the near future, HEVs. In 2005, HEVs reached
1.2% of new cars sold in the US, more than doubling
the number sold in the prior year. Toyota is the
leading manufacturer of HEVs, globally selling over
50% of all hybrids purchased in the US in 2005.
The evolution of HEVs to allow charging from the
electric grid, so called plug-in hybrids (PHEV), is
assumed by many to be desirable—some may argue
inevitable. Ultimately, the economics of displacing
gasoline with electricity should drive consumer
demand for PHEVs. The cost of electricity to drive a
vehicle the same distance as one gallon of gasoline is
equal to approximately $1—or even less if off-peak
electricity prices are assumed (Denholm and Short,
2006). Furthermore, as discussed later in this article,
PHEVs could potentially generate revenue for the
vehicle owner by providing grid support services.
Combined, these value propositions could serve to
usher in an era of advanced vehicles with dramatic
reductions in gasoline use and tailpipe emissions.
A growing, national movement to bring PHEVs to
the market has emerged in the US, bolstered by the
undeniable economic and national security benefits
that result from displacing gasoline with electricity.
One highly-visible, grass-roots campaign, called
Plug-In Partners, seeks to demonstrate to the major
automobile manufacturers that a national market
exists for flexible-fuel PHEVs; dozens of businesses,
utilities, municipal governments, and environmental
groups have joined the Plug-In Partners campaign.
While there are no commercially available PHEVs
on the market, a number of prototypes have been
built and tested. The most established PHEV
program is housed at the University of California
Davis, where Professor Andrew Frank works with
students designing and building prototype PHEVs. A
second development project involves collaboration
between the Electric Power Research Institute and
DaimlerChrysler. They produced, and are in the
process of testing, several prototype plug-in hybrid
vans using the Sprinter platform. Two start-up firms
plan to offer conversion kits for current generation
hybrid electric vehicles to allow grid charging of the
on-board battery pack. These conversions kits offer
the potential to almost double an HEV’s fuel
efficiency rating to 100+ miles per gallon by
increasing the size of the battery storage system and
installing the hardware and controls to allow
charging from the electric grid.
3. HYBRIDS AND RENEWABLES: EXPLORING
THE POTENTIAL
As the vehicle fleet moves toward electric drive,
initially in the form of HEVs, the opportunity for
renewables, beyond biofuels, to serve as an energy
source for the transport sector emerges. This
opportunity is greatly enhance when vehicles connect
to the grid to charge an onboard battery pack. The
remainder of this article explores this opportunity
from the emerging vehicle integrated concept (VIPV)
to the role that wind can play in powering gridconnected cars.
Hybrids electric vehicles with the capability to
recharge from the electric grid dramatically reduce
the needed liquid fuels for transportation. Studies
have found that most vehicles could meet the vast
majority of their daily commute with a PHEV
designed with a 40 mile all electric range. Thus,
PHEVs can exploit wind and solar as a fuel source
and at the same time dramatically reduce liquid fuel
requirements. It becomes more realistic for biofuels
to meet the lower liquid fuel requirements needed as
3
the vehicle fleet relies to a greater degree on
electricity.
3.1 The Solar Hybrid Electric Vehicle
In 2003, the author presented the vehicle integrated
photovoltaic (VIPV) concept to an American
audience at the annual meeting of the American
Solar Energy Society. The paper titled, Vehicle
integrated PV: A clean and secure fuel for hybrid
electric vehicles argued that HEVs create an
opportunity for PV to serve as an energy source for
the transport sector.
Until recently, PV has not been considered a viable
energy source for vehicles. Some experiments were
conducted using PV for electric vehicle (EV)
charging, but efforts to commercialize have stalled
due to the perceived lack of market acceptance for
these types of vehicles. Other efforts to deploy PV
for transportation have taken place at a variety of
university research centers, where teams of students
and faculty build vehicles powered solely from solar.
These vehicles are designed and built to compete in
solar car races such as the World Solar Challenge,
which began in Australia in 1987. These vehicles
were never intended for commercial production, the
futuristic look and design of these experimental
vehicles would not likely appeal to mass markets.
Since the 2003 conference, the author learned of a
variety of projects to advance the VIPV concept.
Researchers at the University of Queensland in
Australia are developing a commuter hybrid vehicle
with PV integrated in to the body panels. An
engineer in Canada installed a 270 watt solar array
on the roof of his Toyota Prius, increasing the
mileage by approximately 10%. Even the major auto
manufacturers are eyeing the VIPV opportunity, with
both Ford, and its close corporate partner Mazda,
displayed hybrid vehicles with modest amounts of
VIPV at recent auto shows. The author produced a
second article on the topic highlighting recent VIPV
activities, which appeared in the May/June 2006
edition of Solar Today.
In October of this year, the French specialty vehicle
manufacturer Venturi Automobiles announced plans
to offer the first commercially available solar hybrid
sports car called the Astrolab. The company also
produces an urban electric commuter vehicle called
the Eclectic. The 3-seater vehicle has solar PV
integrated on to the roof of the vehicle. Venturi
claims that this is the first energy-autonomous
vehicle available to the public.
Pic. 1. PV integrated Toyota Prius, Lapp
Renewables LTD, 2005
Pic. 2. Venturi Automobiles’ Astrolab, the first
commercially available PV integrated hybrid
Pic. 3. Venturi Automobiles’ Eclectic, the first
energy autonomous electric urban commuter
vehilce
Recently, Taiwan’s PV cell manufacturer E-Ton
Solar announced a joint venture with several
partners, including Yulon Nissan Motor Co., Ltd. to
develop PV products for the car market. The joint
venture began with the manufacturing of PV modules
for car sunroofs.
4
Given current HEV designs, VIPV could serve to
enhance the overall efficiency of the vehicle, but
only provide a small portion of the vehicle’s energy
requirements. In this context, VIPV is similar to
regenerative breaking, which, through converting the
kinetic energy lost in breaking to electrical energy,
serves to enhance the overall efficiency of an HEV.
A number of design and engineering considerations
could serve to increase PV’s role in fuelling a new
generation of solar hybrid vehicles
The key parameters dictating VIPV’s ability to
displace gasoline for transportation are the quantity
of PV in watts integrated on to the body panels and
the efficiency of the vehicle drivetrain. The amount
of PV that can be integrated on to a vehicle is a
function of the available space and the efficiency of
the PV technology deployed. Venturi Automobile’s
Astrolab mentioned above contains 3.6 m2 of PV
integrated on to the vehicle. Measurements of the
available surface area of a number of conventional
vehicles suggest available surface areas of between
3.5 m2 to 5.5 m2 (Letendre et al., 2006). Figure 2
indicates potential PV in watts for three different
scenarios of available surface by PV conversion
efficiencies.
1,200
3.5 m2
watts VIPV
1,000
4.5 m2
5.5 m2
800
600
400
200
20
%
19
%
18
%
17
%
16
%
15
%
14
%
12
%
13
%
11
%
9%
10
%
8%
7%
6%
5%
-
PV Conversion Efficiency
Fig. 2. VIPV watts potential: surface area vs. PV
sunlight to electricity conversion efficiency
As Figure 2 illustrates, the sunlight to conversion
efficiency of the PV technology deployed in VIPV
applications is an important parameter. While flat
plate silicon PV has high conversion efficiencies,
thin film PV may be better suited for VIPV
applications.
Again referring back to Venturi
Automobile’s Astrolab, the vehicle uses high
efficiency monocrystaline PV cells to achieve 600
watts of PV on the available 3.6 m2 of surface area.
Copper indium gallium diselenide (CIGS) solar cells,
which are not yet fully commercial, offer both
advantages of flexibility like other thin film PV
technologies, but with much higher conversion
efficiencies.
One US company, DayStar
Technologies,
is
nearing
commercial-scale
production of a CIGS PV product on flexible steel.
Generally, the US is leading in the development of
the next generation PV technology, which should be
predominantly flexible thin films.
It should be noted that the onboard PV capacity may
not necessarily be constrained by the available
surface area on the vehicle’s body panels, but
flexible PV could be used to design retractable solar
shades that could be deployed when the vehicle is
parked to provide additional PV capacity for daytime
charging.
The efficiency of the vehicle drivetrain determines
the number of solar miles obtained from any given
VIPV system. Current hybrids, like the Toyota Prius
have all electric efficiencies in the 156 watt-hours per
kilometer range. Figure 3 illustrates solar miles for a
500 watt VIPV system in a region with an average of
4 sun hours per day for total annual PV generation of
710 kWh.
250
watt-hours / km
3.2 Design Considerations for Solar Hybrids
SUV
200
Toyota Prius
150
Honda Insight
100
50
-
2,000
4,000
6,000
8,000
10,000 12,000 14,000 16,000
Annual Solar Kilometers
Fig. 3. VIPV watts potential: surface area vs. PV
sunlight to electricity conversion efficiency
Advances in the use of lightweight materials for
vehicles will serve to increase the potential solar
miles delivered from a VIPV system. However, even
today’s commercially available hybrid can benefit
from VIPV. Initial VIPV applications will provide
incremental improvements in vehicle efficiency, but
the future potential is much greater. The Leonardo
Project, sponsored by the European Commission,
aims to train a new generation of engineers in
sustainable transportation focused initially on
designing and building a solar hybrid. This project,
and other like it, will serve to advance knowledge on
these concepts and ultimately achieve advanced
designs that dramatically improve existing
technologies and approaches.
Battery storage devices are a critical enabling
technology for the solar hybrid revolution. While
many advances have been made in battery
technology, reductions in price and improvements in
performance are needed to produce commercially
viable solar hybrid vehicles.
A promising new battery technology was unveiled at
the September 2006 California Air Resources Board
Zero Emission Vehicles Symposium. Navada-based
Altairnano announced a new lithium ion battery
system called NanoSafe™, which replaces graphite
as the electrode materials with nano-titanate
materials (www.altairnano.com).
The company
claims that this new materials solve the thermal
runaway problem with conventional lithium ion
batteries, and offer significant improvements in cycle
life and delivers optimum energy/power balance in
the high power region, which is critical for hybrid
and electric vehicle applications.
5
While both conventional HEVs and PHEVs can
adopt a VIPV strategy allowing for the use of solar
for transportation, only plug-in hybrids facilitate the
use of wind power for transportation purposes.
Wind power is the fasting growing new source of
power generation world-wide. In the US alone the
American Wind Energy Association estimates that
over 3,000 MW of new wind will go on line in 2006.
Globally, estimates of installed wind power capacity
reached 60,000 MW in 2005 (Worldwatch Institute,
2006). Wind power is a clean and renewable source
of power generation that will continue to expand in
the coming years.
The intermittent nature of wind power creates
challenges for developers seeking to integrate wind
into electric grids and wholesale markets. At low
wind power penetration rates intermittency is less of
an issue; however, as wind plays an increasingly
important role in the global supply mix,
intermittency will need to be addressed. The
variability of output from wind farms creates
challenges given the existing electric industry
structure, which is characterized by scheduled flows
of power from sources to sinks. The cost and
environmental
characteristics,
however,
are
sufficiently compelling that regulations have been
devised to facilitate wind power integration in to the
electric supply mix.
The variability of wind power can be understood in
discrete categories based on increasingly longer time
intervals that characterize the market strategy that is
needed to manage the variability as more and more
wind appears on the electric network.
These
categories are:
• Minute to hour variability, addressed
through regulation markets, intra-hour
adjustments, or spinning reserves.
• Hour to day, addressed through operating
reserves (spinning and non-spinning
reserves)
• 1-4 days, dispersion of wind resources with
transmission, operating reserves, load
management, and dedicated storage
(Kempton and Tomic, 2005a)
Recent analyses suggest that the emergence of
PHEVs and other electric vehicles could serve to
address the intermittency challenge associated with
wind and other intermittent resources like solar
(Letendre et al., 2002; Kempton and Tomic, 2005a,
and Denholm and Short, 2006). In one of these
studies Kempton and Tomic (2005a) calculate that
that electric vehicles with onboard battery storage
and bi-directional power flows could stabilize largescale (one-half of US electricity) wind power with
3% of the fleet dedicated to regulation for wind, plus
8–38% of the fleet providing operating reserves or
storage for wind.
At a minimum, the nature of PHEV charging
complements the intermittent nature of wind power.
Given the high periods of non-use of vehicles,
PHEVs represent a new source of load, unlike critical
loads like computers and other information
technologies, which doe not require a constant flow
of power for re-charge. The charging of PHEVs can
be modulated as the power production from a wind
farm varies. This serves to address the first tear of
intermittency (variability) described earlier.
I
envision new power contracts between PHEV owners
and developers of wind farms. The complementary
nature of wind power and PHEVs creates an
opportunity to further enhance the environmental
character of PHEVs through wind power charging.
To address the second and third tiers of wind power
variability described earlier, PHEVs would require
reverse flow capabilities. This concept has become
widely known as the vehicle to grid (V2G) concept,
which is covered extensively in the next section of
this article. Millions of PHEVs connected to the
electric grid would represent a very large aggregate
energy storage resource. Figure 4 indicates the
amount of storage that would be connected to the
grid for PHEVs with various electric only ranges
(from 20 to 60 miles) by the number of vehicles.
Even at small penetration rates in the new car market
PHEVs could offer a significant storage capacity to
address wind power’s longer duration variability.
400,000
350,000
MWh Storage Potential
3.3 Plug-In Hybrids Facilitates the Use of Wind for
the Transport Sector
300,000
250,000
200,000
PHEV60
PHEV40
PHEV30
PHEV20
150,000
100,000
50,000
0
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
Millions of V2G Vehicles
Fig. 4. PHEV energy storage potential
It’s quite possible that VIPV, wind power charging,
and ethanol or biodiesel could create the first mass
market, mobility solution that is 100% renewable.
This mobility system becomes even more attractive
when understood in the context of the emerging
vehicle to grid concept. Next, I turn to this topic and
describe the benefits that are possible as the transport
and electric power sectors converge.
6
4. V2G: INTEGRATING THE TRANSPORT AND
ELECTRIC POWER SECTORS
As the vehicle fleet moves toward electric drive,
initially in the form of HEVs, interesting synergies
can be exploited between the transport and the
electric power sectors when a bi-directional grid
interface is built. In aggregate, grid-connected cars
would represent a potentially large and highly
reliable power resource to the electric power sector.
This opportunity was first explored by Kempton and
Letendre in a 1997 article published in
Transportation Research-D.
The light vehicle fleet and the electric power system
represent two massive energy conversion systems,
which evolved in isolation from each other over the
past century. The electric power system relies on
thousands of generating units which convert stored
energy (chemical [coal, natural gas, oil], mechanical
[hydro and wind], and nuclear) in to alternating
current that flows across a massive interconnected
transmission and distribution grid to final end users.
In contrast, the light vehicle fleet coverts
petrochemical energy to rotary motion and then to
travel. A massive petroleum, refining, and transport
infrastructure exists to support the light vehicle
fleet’s energy needs.
The electric power industry is unique in that the
product, electricity, is produced and consumed at the
same time. There is virtually no storage in the
system; except for pumped hydro in select locations.
Grid operators must continuously match supply and
demand by turning on and off generators in response
to demand. In contrast the light vehicle fleet requires
storage, given that its fuel must be mobile and thus is
carried onboard in a storage container. As the light
vehicle fleet migrates toward electric drive, storage
energy in onboard batteries serves to supplement the
stored energy in the vehicle’s fuel tank.
Electric generators are designed for high duty cycles,
in the US average utilization rates of the nation’s
generating assets reaches 60%. In contrast, as
mentioned above, vehicles are in use approximately
5% of the time. While electric generators can take
minutes or hours to deliver power to the grid, electric
drive vehicles could deliver power to the grid
virtually instantaneously.
In aggregate these complementary characteristics of
the electric power sector and the light vehicle fleet
offer a compelling reason to evaluate the integration
of these systems as vehicle technology migrates
toward electric drive. Through a bi-directional
interface, grid-connected cars could deliver power
when called upon by a central grid operator. Figure
5 illustrates schematically the vehicle to grid (V2G)
concept. Advances and cost reductions in wireless
communications would allow a central operator to
dispatch stored energy in vehicles upon demand. In
Figure 5 the Independent System Operator (ISO) is
delivering a dispatch signal to those vehicles
connected to the grid and prepared to deliver power
at a moments notice.
Fig. 5. Schematic of vehicle to grid concept
(Kempton and Tomic, 2005a)
Even at small fractions of the vehicle fleet, electric
drive vehicles could represent a very large power
resource. At 10 kW per vehicle, one million vehicles
represent 10,000 MW of available V2G power; the
current global vehicle fleet is estimated to be over
600 million vehicles (Worldwatch Institute, 2006).
4.1 V2G Research Finding
The author knows of just one V2G demonstration
project (Brooks, 2002). The demonstration project
was conducted by a California-based electric vehicle
development company AC Propulsion, in
conjunction with the California Independent System
Operator (ISO). AC Propulsion produces the only
V2G capable electric vehicle drivetrain. For the
demonstration project a Volkswagen Beetle was
converted to a pure electric vehicle outfitted with AC
Propulsion’s
bi-directional
charger
and
a
communication link with the California ISO. They
successfully demonstrated the remote dispatch of
power from a parked electric vehicle in response to a
signal from the ISO.
Most of the research to date on V2G involves
modelling and economic analyses.
One
comprehensive study, for which the author was
involved, was funded by the California Air
Resources Board. Although no technical barriers
were discovered in the research, a number of key
issues were identified that bear on the economic
value of V2G power services.
Research on this topic suggests that V2G capable
cars are best suited to provide grid services that
require a rapid response, but our used for a short
duration. The limited onboard energy storage of an
electric drive vehicle is not suited for providing baseload power. The most promising markets for V2G
power fall under the heading of ancillary services—
services purchased by grid operators to maintain
system reliability. The two most valuable ancillary
services in the US are for regulation (frequency
response) and spinning reserves. Economic analyses
demonstrate that a single vehicle can generate
hundreds of dollar annually providing these services
(Letendre and Kempton, 2002).
7
A second important issue for V2G capable cars,
which determines the potential revenue from
providing grid services, is the power output that can
be sustained by a vehicle providing ancillary
services. Kempton and Tomic (2005b) identify three
key factors that limit the amount of power a gridconnected car can deliver back to the grid. These
include the on board vehicle electronics, capacity of
the plug circuit, and energy storage capacity and
state of charge when the vehicle is plugged in to
provide grid services.
A PHEV’s vehicle’s power electronics should not
create a binding limit on the amount of power that
can be exported to the grid. PHEVs require high
power components for acceleration and to optimize
vehicle performance.
The electric drivetrain
developed and manufactured by AC Propulsion
mentioned earlier provides 80 amps in either
direction, allowing 19.2 kW of power output. Thus,
the critical factors dictating the reverse power
potential come down to the capacity of the plug
circuit and the size and state of charge of the PHEV’s
battery pack.
Given the evidence on the V2G potential today, the
next logical step would be a large-scale
demonstration project. A fleet of say 100 electric
drive vehicles equipped with a bi-directional charger
could serve to resolve some issues that would give
the private sector more confidence in pursuing the
V2G business opportunity. In the end, the revenue
that V2G could generate would help to overcome the
price premium for the first-generation plug-in
hybrids or pure electric vehicles, thus ushering in a
new era of clean, flexible fuel vehicles.
As experience is gained and the price of electric
drive vehicles declines, their use in providing peak
power and storage for intermittent renewables is
more likely. Furthermore, an increasingly fleet of
V2G capable vehicles could eventually enhance the
overall reliability of the grid and support a more
environmentally sound electric supply mix.
5. CONCLUSION
As we enter the early stages of the 21st Century,
society has reached an apex in mobility. The global
economy is poised precariously on continues flows
of people and goods, made possible by an abundant
and cheap source of energy—oil! Recent events
suggest that this critical resource is no longer
abundant and cheap. In 2006, petroleum reached
record prices on international exchanges of over $70
per barrel. Some of the world’s most renowned
petroleum geologists are warning that we are quickly
approaching the point at which we have extracted
approximately one half of the existing oil reserves
buried deep in the Earth crust—the so called peak oil
event.
a portion of the mobility we have come to rely upon
in this modern ear. It’s becoming increasingly clear
that electric drive will play a central role in the future
vehicle fleet. Already, today hybrid electric vehicles
(HEVs) have gained commercial success. Many
groups are actively pursuing the logical evolution of
HEVs to allow charging from the electric grid.
Others are focused on hydrogen as the primary
energy carry for transportation, fuelling a future fleet
of fuel cell vehicles. Regardless of the technology
that dominates the future, vehicle will rely
increasingly on electric drive and contain
significantly more onboard battery storage than
today’s fleet of internal combustion engines.
This new era of electric drive vehicles allows for
renewables, beyond biofuels, to serve as an energy
source for the light vehicle fleet. Vehicle integrated
PV and grid-connected cars charging from wind
power become real possibilities as hybrid electric
vehicles emerge as viable alternatives to internal
combustion vehicles.
There is tremendous
momentum in this direction as research
organizations, governments, and private industry
seek to solve our immanent mobility crisis. A French
specialty automobile company plans to offer the first
commercial solar hybrid to consumers. E-Ton Solar,
a major PV manufacturer, has entered a joint venture
to develop products specifically for the car market.
Finally, the V2G concept is the ultimate vision
whereby the transport and electric power sector
converge and reap tremendous efficiencies while
improving reliability, reducing pollution, and
delivering greater energy security to those nations
with the foresight to seize this opportunity.
REFERENCES
Brooks, A. (2002). Vehicle-to-grid demonstration
project: Grid regulation ancillary service with a
battery electric vehicle. Report to the California
Air Resources Board.
The Center for Energy and Climate Solutions. (June
2004) The car and fuel of the future: A
technology and policy overview, Prepared for the
National Commission on Energy Policy,
Washington, DC.
Energy Information Administration (EIA), US
Department of Energy. (2006). International
energy outlook 2006, Washington, DC.
International Civilian Aviation Organization (ICAO).
(28 July 2005). World air passenger traffic to
continue to expand through to 2007, press
release, Montreal.
Kempton, W and J. Tomic. (2005a). V2G
implementation: From stabilizing the grid to
supporting large-scale renewable energy. J.
Power Sources, 144, 280-294.
Kempton, W and J. Tomic. (2005b). Vehicle to grid
fundamentals: Calculating capacity and net
revenue. J. Power Sources 144, 1, 268-279.
These, and other critical geopolitical events, suggest
that society must rapidly pursue the development of
alternative means of transportation to maintain even
8
Kempton, W., J Tomic, S. Letendre, A. Brooks, and
T. Lipman. (2001). Electric drive vehiclesbattery, hybrid, and fuel cell-as resources for
distributed electric power in California,
University of California Davis, ITS-RR-01-03.
Kempton, W., and S. Letendre. (1997). Electric
vehicles as a new power source for electric
utilities. Transportation Research-D, 2, 157175.
Letendre, S. R. Perez, and C. Herig. (May/June
2006). Solar vehicles at last?. Solar Today, Vol.
20, No. 3, 26-29.
Letendre, S., R. Perez, and C. Herig. (2003). Vehicle
integrated PV: a clean and secure fuel for hybrid
electric vehicles. Proceedings of the 2003
American Solar Energy Society Annual
Conference, Boulder, CO.
Letendre, S and W. Kempton. (2002). V2G: a new
model for power?. Public Utilities Fortnightly,
140, 16-26.
Letendre, S., R. Perez, and C. Herig. (2002). Batterypowered, electric-drive vehicles providing buffer
storage for PV capacity value. Proceedings of
the 2002 American Solar Energy Society Annual
Conference, Boulder, CO.
Myers, N. and J. Kent. (2004). The new consumers:
The influence of affluence on the environment,
Island Press, Washington, DC.
Morris, D. (2003). A better way to get from here to
there: A commentary on the hydrogen economy
and a proposal for an alternative strategy, The
Institute for Local Self-Reliance, Minneapolis,
MN.
Simmons, M. (2005). Twilight in the desert: The
coming Saudi oil shock and the world economy,
Wiley & Sons, Inc, Hoboken, New Jersey.
Worldwatch Institute. (2006). Vital signs 2006 –
2007: The trends that are shaping our future,
W.W. Norton & Company, Inc., New York, NY.
9
10
FUEL CONSUMPTION OPTIMIZATION FOR HYBRID SOLAR VEHICLE
Zs. Preitl*, P. Bauer*, J. Bokor**
* Budapest University of Technology and Economics, Dept. of Transport Automation,
H-1111 Budapest, Bertalan L. u. 2., Hungary
Email: [email protected], [email protected], [email protected]
** Computer and Automation Research Institute,
H-1518 Budapest, Kende u. 13-17, Hungary
Abstract: Hybrid electric vehicles (HEVs), having multiple main energy sources, are an
attractive alternative to conventional vehicles. The paper presents a study on minimizing
the energy consumption in a series hybrid solar vehicle (HSV). First a description of the
series HSV is given, after which two control strategies are presented for fuel consumption
optimization. The first control strategy is dynamic programming (DP) which is used to
obtain a global optimum for fuel consumption. The second control algorithm is Model
Predictive Control, using the MPC Toolbox of Matlab. Both strategies are tested through
simulations.
Keywords: hybrid solar vehicles (HSV), control strategies, dynamical programming (DP),
Model Predictive Control (MPC)
1. INTRODUCTION
Hybrid electric vehicles (HEVs), having multiple main
energy sources, are an alternative to conventional
vehicles. More and more importance is dedicated to
research in this field of alternative vehicles. These
energy sources are the conventional fuel tank and a
battery, delivering both chemical and electrical energy.
If a photovoltaic panel is also added, a Hybrid Solar
Vehicle (HSV) is obtained. HSVs can be seen as a
transition from conventional vehicles to fully electric
vehicles. The architecture of HSVs can be different,
depending on the requirements imposed. Basic
drivetrain structures for HSVs are: series, parallel,
series/parallel and complex hybrids. Since the target of
the research is optimization of fuel consumption in case
of urban drive cycles, a series architecture was chosen
for this study, this proving to be optimal in this case. A
basic diagram of the series HSV is depicted in Figure 1.
The first control strategy is based on dynamic
programming (DP), which is actually used to obtain a
global optimum for fuel consumption. The reference
signal consists of several urban cycles.
The result is an input sequence of battery nominal
power values. Since DP is not a feasible solution for
practical implementation due to its computational time,
an alternative control strategy consists in Model
Predictive Control (MPC), implemented using the MPC
Toolbox of the Matlab environment. Simulations were
performed and presented in the paper for both
strategies. To test and compare simulation results,
standardized drive cycles had been defined in the
literature, this paper focuses the simulations mainly on
the so-called New European Driving Cycle (NEDC)
and on the Federal Urban Driving Schedule (FUDS)
which were presented in detail in (Bauer et al., 2002).
Fig.1. Basic diagram of a series HSV
2. FUEL CONSUMPTION MINIMIZATION USING
DYNAMIC PROGRAMMING
Optimal control of the series HSV was first achieved in
this paper with dynamic programming. This is based on
11
Bellman’s principle which says that: “The parts of an
optimal trajectory are all optimal trajectories”.
This allows one to make calculations on a specific
problem backward in time, with the assumption of
optimal trajectory. The result of dynamic programming
calculations is the optimal input sequence applicable to
the system to achieve control goals. Dynamic
programming gives the global optimal solution of the
problem.
Unfortunately this solution needs a priori knowledge of
the reference signal and disturbances on the entire time
horizon considered in the calculations.
This means that, the results of a dynamic programming
solution can mainly be used just as a reference optimal
solution to be compared with other control methods,
such as MPC control in this paper.
The other problem with dynamic programming is the
time consuming calculations which prevent its
application in real time solutions. For the used HSV
model with NEDC drive cycle, the calculation of the
optimal solution on a 1200 sec time horizon needed one
hour on a PC with AMD 64 Athlon 3000+ processor
and 1 GB DDR 400 RAM.
In the following subsections the problem formulation,
solution with dynamic programming and the results of
this global optimal solution are discussed.
2.1 PROBLEM FORMULATION AND DYNAMIC
PROGRAMMING SOLUTION
The control goal of a HSV is the minimisation of fuel
consumption over the whole time horizon considered in
calculations. This can be achieved by proper switching
(balancing) between the energy sources. In a HSV the
electric motor’s (EM) power needs can be satisfied
from the photovoltaic (PV) panel, battery and electric
generator (EG). This means that one can optimize the
use of this three energy sources. The electric power
from PV panel depends on sun insolation and cell
temperature (see Bauer et al. 2006). Unfortunately, one
cannot control these parameters, so PV power cannot be
a control variable, however it can improve the fuel
economy of the vehicle.
Figure 2. System layout for dynamical programming
However, if one gives Pbn , Peg is
determined by
equation 1. So the optimal solution of the control
problem can be generated by the calculation of the Pbn
sequence in time.
In dynamic programming this can be achieved by a
backward calculation from end of the drive cycle and
final value of the battery SOC. The start and end values
of battery SOC must be the same (charge sustaining
strategy).
Of course, the drive cycle for the HSV must be a priori
known. It the paper there were used the NEDC and
FUDS drive cycles, with given constant insolation and
temperature on PV panel.
The charge sustainability gives limits on battery SOC in
time. A diamond shaped limit set can be calculated for
every vehicle and drive cycle as, it is presented in
figure 3.
The system layout used for dynamic programming
solution is depicted in figure 2.
The notations used can also be seen in figure 2. The
fuel consumption optimization can be achieved by the
proper use of the EG and the battery, while satisfying
drive power needs and sustaining battery state of charge
(SOC), considering the whole time horizon. The power
balance of the system is described by the following
equation:
Pe = Peg + Pbn + PPV
(1)
On the right side, Peg electric generator power and Pbn
battery nominal power are the control variables.
Pe electric motor power can be calculated from Pd
drive power need, considering the characteristics of the
EM. The controller can influence Peg and Pbn .
Figure 3. Battery SOC bounds with NEDC drive cycle,
1 kW/m2 insolation and 25°C cell temperature
The calculation are performed considering the possible
SOC values at every time step, which can be achieved
according to the constraint, SOC (0) ≡ SOC (end ) , and
the minimal and maximal allowed SOC values. The
minimal and maximal SOC values are 0.6 and 0.8
respectively, from (Musardo et al. 2005). Both the
upper and lower limits are described with three
sections. These are the following:
12
1.
2.
3.
1.
2.
3.
Upper: the maximum possible SOC value
which can be achieved from SOC(0) using
maximum battery charge
Upper: the maximum allowed SOC value
Upper: the maximum SOC value from which
SOC(end) can be achieved using maximum
battery discharge
Lower: the minimum possible SOC value
which can be achieved from SOC(0) using
maximum battery discharge
Lower: the minimum allowed SOC value
Lower: the minimum SOC value from which
SOC(end) can be achieved using maximum
battery charge
calculated. Finally, the minimum fuel path is selected as
an optimal solution.
In every step k the possible battery SOC range has to be
considered and compared with the next range (step
k+1) calculated in the previous step. For every SOC
value in range k all possible SOC trajectories to range
k+1 have to be calculated (limited with maximum
battery charge and discharge). This is illustrated
schematically in figure 5.
Of course for these calculations the maximum and
minimum nominal battery charge powers have to be
known for every time instant. The minimum power
(discharge power) is given by the limits of the battery.
The maximum power (charge power) is given by the
limits of the vehicle and can be calculated from (1):
Pbnmax = Pe − PPV − Peg max
(2)
In this form, Pbn reaches a negative value (if Peg and
PPV are assumed to be positive) which has to be
considered in the battery calculations. In the presented
example Pe is positive in EM driving mode and
negative in EM braking mode, which fits the
calculations in (2).
The calculated minimum and maximum powers for the
case from figure 3 can be seen in figure 4.
Figure 5. Sketch of dynamical programming solution
After determining the possible charge and discharge
range (considering the limits), it can calculated the ICE
fuel consumption for every trajectory from step k to
k+1. Adding these fuel consumptions to every total fuel
consumption from step k+1 to end, there result the
possible total fuel consumptions from k to end starting
from SOC(k). The minimum of the total fuel
consumptions give the global optimal trajectory from
SOC(k) to SOC(end). In step k these are calculated and
stored for every possible SOC(k) values.
After completing this procedure, in SOC(0) step, the
global optimal total fuel consumption results. The
optimal SOC trajectory can be determined following the
minimum fuel path from SOC(0) to SOC(end). This
results in the optimal Pbn sequence in time.
This optimal input sequence can than be applied to the
Simulink model of the vehicle. Test results are given in
the following subsection.
2.2 CALCULATION AND TEST RESULTS FROM
DYNAMIC PROGRAMMING
Figure 4. Maximum and minimum battery power, with
drive power need (NEDC drive cycle, 1 kW/m2
insolation and 25°C cell temperature)
In figure 4 it can be seen that the maximum charge
power (negative according to (2)) has a minimum point
(in absolute value) where the drive power need is
maximal.
After calculating the possible battery SOC limits, the
solution can be achieved with dynamic programming.
This starts from SOC(end) and Pd (end ) stepping
backward in time. This way in every time step the
optimal fuel use until the end of drive cycle is
Calculations were performed for NEDC and FUDS
drive cycles, considering the whole range of sun
insolation on 25°C cell temperature. Reference results,
without controller (but with battery charge with
regenerative braking) were generated in (Bauer et al.
2006). They are summarized in table 1:
2
1
λ [kW/m ]
SOC
0.7192
total fuel [g] 913.7265
NEDC
2
λ [kW/m ]
SOC
total fuel [g]
FUDS
1
0.7125
499.696
0.8
0.7189
916.015
0.6
0.4
0.7186
0.7183
918.1686 920.4583
0.2
0.7181
922.613
0
0.7178
924.768
0.8
0.6
0.4
0.2
0
0.7122
0.7119
0.7116
0.7113
0.711
502.8127 505.7325 509.5911 513.0373 515.9575
Table 1. Reference results without controller
13
The dynamic programming gave less total fuel
consumption in every case.
Optimal SOC trajectory, fuel consumption and Pbn
sequences are presented in figure 6, 7 and 8 for NEDC
drive cycle, 1 kW/m2 insolation and 25°C cell
temperature. The SOC trajectory lies between the limits
in every time step, moreover, it is near the desired value
(0.7) during the entire time range. In fuel consumption
(figure 7) horizontal sections mean that the ICE was
turned off and no fuel consumption occurred during that
time range. This is the case of regenerative braking or
low power need satisfied from PV power. In Pbn
sequence regenerative braking is strongly used to
improve fuel economy.
Results from dynamic programming are summarized in
table 2, while results from MATLAB Simulink vehicle
model simulations with optimal Pbn sequence are
summarized in table 3 (about the vehicle modelling,
details can be found in (Bauer et al. 2006)).
2
λ [kW/m ]
1
0.8
0.6
0.4
0.2
0
total fuel [g] 811.6438 814.3697 817.516 820.4546 822.6674 835.5047
fuel spare [%] 11.172
11.096
10.96
10.865 10.8329
9.6525
NEDC
2
λ [kW/m ]
1
0.8
0.6
0.4
0.2
0
total fuel [g] 369.0273 374.4629 380.9043 388.4347 393.5668 396.6046
fuel spare [%]
26.15
25.526
24.68
23.77
23.287
23.13
FUDS
Table 2. Results from dynamic programming
2
λ [kW/m ]
1
0.8
0.6
0.4
0.2
0
SOC
0.7004
0.7005
0.7005
0.7005
0.7004
0.7004
total fuel [g] 855.8369 585.2858 858.8072 860.8495 863.4588 872.5427
fuel spare [%]
6.336
6.302
6.4652
6.47
6.4116
5.647
NEDC
2
λ [kW/m ]
1
0.8
0.6
0.4
0.2
0
SOC
0.7009
0.7008
0.7009
0.701
0.7009
0.7008
total fuel [g] 421.7183 426.8949 434.7972 440.241 442.2611 444.2961
fuel spare [%] 15.605
15.098
14.026
13.609
13.796
13.889
FUDS
Table 3. Results from simulations with optimal Pbn
input sequence
Figure 6. SOC trajectory from NEDC drive cycle
As it is presented in table 2, DP results are almost the
same for different insolation values, calculating with
the same drive cycle. In the case of NEDC, the fuel
spare ranges from 9.7 to 11.2 %, while in the case of
FUDS it ranges from 23.13 to 26.15 %. This is mainly
because NEDC needs higher drive power, which means
more intensive battery use and constrained alternator
usability for battery charge. Battery SOC is originally
sustained by DP calculations.
Table 3 shows that in the case of system model
simulation with optimal Pbn input sequence lower fuel
spare values can be achieved. This is due to continuous
dynamics of the battery, in spite of moving between
discrete battery charge level values as it was in the DP
solution. However, overall charge sustainability
requirement is satisfied in each case (see Table 3, SOC
values).
Figure 7. Fuel consumption from NEDC drive cycle
Finally it is worth noting that, these results were
calculated without limitation in changes of battery, EG
and ICE power. So, sudden changes were allowed, as
can be seen in figure 8. In real applications, of course,
the limitation of battery power, EG power and ICE
power derivatives have to be considered. This is the
objective of future research and will decrease the fuel
economy of the vehicle, but it is required for control
strategy feasibility.
3. MODEL PREDICTIVE CONTROL FOR FUEL
CONSUMPTION MINIMIZATION
Figure 8. Optimal Pbn sequence from NEDC drive
cycle
The second control strategy that was applied for the
series HSV architecture is Model Predictive Control
(MPC), as used also for a hybrid vehicle in (Back et al.,
2002). MPC is an advanced control strategy which had
spread significantly during the past years in industry as
14
well, due to its increasing popularity (Camacho and
Bordons, 1999). The main advantages of MPC is that
the basic formulation is extended to MIMO plants with
almost no modification, on the other hand the basic
concept of MPC is relatively easy to understand, and it
is a powerful tool to cope with constraints effectively
(Maciejowski, 2002). Without getting into a detailed
presentation of MPC algorithms, the basic “elements”
that build the problem formulation are the following:
•
Cost function that penalizes the deviations of the
predicted outputs from the reference trajectories;
•
Internal model of the plant;
•
Reference trajectory for the desired closed-loop
trajectory;
•
Possibility of defining constraints;
•
On-line optimization to determine the future
control strategy;
• Receding horizon principle.
For design and simulation of the fuel consumption
minimization for a series HSV, the MPC Toolbox of
Matlab is used. In this sense, the problem formulation
follows the steps and form required by this design tool,
based on the above presented elements.
The first element to be defined is the plant model that is
used in the predictive controller. This model is
presented in detail in (Bauer et al., 2006), based on a
detailed presentation of the components and their
models.
As it can be noted from (Bauer et al., 2006), the model
is non-linear, so in order to apply the MPC tools a
linearization is needed prior to it. This is achieved
through the Matlab function linmod2, which creates a
linear model from the non-linear system using an
advanced method. The advantage is that the state
variables of the system remain the original ones, so the
physical meaning of the chosen state variables is kept.
According to this, the states, inputs and outputs of the
linearized plant are:

MPC
Controller
Figure 9. Bloc diagram of a SISO MPC
Toolbox Application
The numerical values for the linearized and sampled
state-space model are (sampling time of Ts=0.001 sec.
was chosen).
0 ⎤ ⎡ x 1 (k ) ⎤
⎡ x 1 (k + 1) ⎤ ⎡0.3679 0
⎢ x (k + 1)⎥ = ⎢ 0
1
0 ⎥⎥ ⎢⎢ x 2 (k )⎥⎥ +
⎥ ⎢
⎢ 2
⎢⎣ x 3 (k + 1) ⎥⎦ ⎢⎣ 0
0 0.9048⎥⎦ ⎢⎣ x 3 (k ) ⎥⎦
⎡ 3.78 ⋅10 −6
6.321 ⋅10 − 4 ⎤
⎥ ⎡ u (k ) ⎤
⎢
0
+⎢
− 1.517 ⋅10 −11 ⎥ ⎢ 1 ⎥ +
u (k )
⎥⎣ 2 ⎦
⎢2.638 ⋅10 −7
0
⎦
⎣
⎡6.321 ⋅10 −4 ⎤
⎥
⎢
0
(3)
+⎢
⎥ d m (k )
⎥
⎢
0
⎦
⎣
⎡ y1 (k ) ⎤ ⎡800 0 0 ⎤ ⎡ x 1 (k ) ⎤
⎢ y (k )⎥ = ⎢ 0 1 0 ⎥ ⎢ x (k ) ⎥
⎥
⎥⎢ 2
⎢ 2 ⎥ ⎢
⎢⎣ y 3 (k ) ⎥⎦ ⎢⎣ 0 0 100⎥⎦ ⎢⎣ x 3 (k ) + ⎥⎦
The system is both observable and controllable, so
MPC can be applied without problems.
The acting constraints that are defined for the problem
are the following:
⎧0 ≤ u 1 ≤ 93000
⎪− 26000 ≤ u ≤ 14000
2
⎪⎪
40000
y
−
≤
⎨
1 ≤ 58000
⎪0.6 ≤ y ≤ 0.8
2
⎪
⎪⎩0 ≤ y 3 ≤ 7.3
State variables: - x1: ICE power state,
- x2: SOC,
- x3: EM power state;

Inputs: - u1: ICE power,
- u2: Battery nominal power;

Controlled outputs: - o1: Drive power,
- o2: SOC,
- o3: Fuel rate;

Measured disturbance input: - dm: PV panel
power.
The PV power is considered as a measured disturbance
(since it depends on the actual insolation which is an
external factor that cannot be influenced) and treated as
such, both in the modelling phase and in the controller
design phase (Kulcsar and Bokor, 2006), (Maciejowski,
2002).
For a SISO case, the basic idea for designing an
application for the MPC Toolbox is depicted in figure
9, based on (Bemporad et.al., 2006).
Plant
(4)
The next step is the definition of the cost function that
is used for the optimization. The aim is the fuel
consumption minimization for the series HSV. A
quadratic cost function is assumed that has the
following form:
J (k ) =
N2
∑
yˆ (k + i k ) − r (k + i k )
2
Q (i )
+
i = N1
Nu
∑ ∆uˆ(k + i k )
(5)
2
R (i )
i =0
Where yˆ (k + i k ) are the predictions, at time k, of the
output y, r (k + i k ) is the reference trajectory vector,
∆uˆ (k + i k ) are the changes of the future input vector
(this term is necessary to ensure the reference tracking
behaviour).
15
The tuning parameters of the cost function are as
follows:
Prediction horizon: N1 = 1, N 2 = 10
•
Control horizon: Nu=4
•
Penalties:
⎡10 −4
0
0 ⎤
⎡10 −15
0 ⎤
⎥
⎢
Q = ⎢ 0 1000 0 ⎥, R = ⎢
⎥
0
10 −15 ⎦
⎣
⎥
⎢ 0
0
0.01⎦
⎣
x 10
PD reference signal tracking
4
Output
Reference
5
4
3
2
Pd [W]
•
6
1
0
-1
The tuning parameters can be modified to obtain
different performances.
After defining the required parameters, the problem
setup can be transposed into the following Matlab
design tool (GUI of the MPC Toolbox) (figure 10).
With its help, the final adjustments and also parameter
modifications for new setups can be easily performed.
-2
-3
-4
0
200
400
600
Time [sec]
800
1000
1200
Figure 11. NEDC reference tracking
SOC
0.72
SOC
0.7
0.68
0.66
0.64
0
200
400
600
Time [sec]
800
1000
1200
800
1000
1200
Total fuel
1000
mf [g]
800
600
400
200
0
0
200
400
600
Time [sec]
Figure 12. NEDC SOC and total fuel consumption
Figure 10. GUI setup for the given problem
8
ICE power
4
PICE
6
4
2
0
-2
0
2
200
x 10
400
600
Time [sec]
800
1000
1200
800
1000
1200
Battery nominal power
4
1
Pbn
The first simulation was the application of the NEDC
drive cycle, transposed into required reference of drive
power for r1 which is presented in figure 4. Also, for the
SOC the constant reference of r2=0.7 was held, the
third reference was r3=0 (for fuel rate).
The simulation results are depicted in figures 11
(reference tracking), figure 12 (SOC and total fuel) and
figure 13 (control signals ICE power and battery
nominal power).
It can be seen that the reference tracking is ensured by
the predictive controller. The fuel consumption is
between the global optimum value and the value
calculated without controller (see table 1.). The SOC
ensures a lower final value compared to the DP. This
can be taken into account at a later global evaluation.
Secondly, a different standard drive cycle is applied,
namely the FUDS, presented in figure 14, together with
the system output. The tuning parameters of the
controller are the same as in the NEDC case.
x 10
0
-1
-2
-3
0
200
400
600
Time [sec]
Figure 13. ICE power and nominal battery power
The same signals are plotted as in the NEDC case, for
comparison, namely the SOC and total fuel
consumption (figure 15) and ICE power plus battery
nominal power (figure 16).
16
1.5
x 10
7. CONCLUSIONS
PD reference signal tracking
4
Output
Reference
1
0.5
Pd [W]
Based on a brief description of the model of a series
HSV, two control strategies are presented for fuel
consumption optimization.
0
-0.5
-1
0
200
400
600
Time [sec]
800
1000
1200
Figure 14. FUDS reference tracking
SOC
0.71
SOC
0.7
0.69
0.68
0
200
400
600
Time [sec]
800
1000
1200
Total fuel
600
mf [g]
400
0
-200
0
200
400
600
Time [sec]
800
1000
ICE power
4
PICE
1.5
1
0.5
0
0
2
x 10
200
400
600
Time [sec]
800
1000
1200
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the contribution of
Hungarian National Science foundation (OTKA
N:K060767). This work was partially supported by the
Hungarian National Office for Research and
Technology through the project "Advanced Vehicles
and Vehicle Control Knowledge Center" (no: OMFB 01418/2004).
Battery nominal power
4
1
Pbn
The second control algorithm is Model Predictive
Control, implemented using the MPC Toolbox of
Matlab. Simulations were performed for two drive
cycles, namely for the New European Drive Cycle and
for the Federal Urban Drive Schedule. In both cases the
results are satisfactory, both concerning reference
tracking and fuel consumption minimization. The fuel
consumption lies between the global optimum values
(calculated with DP) and values without controller. The
results are very promising, still further research is
needed to improve the methodology.
1200
Figure 15. FUDS SOC and total fuel consumption
x 10
The first control strategy is dynamic programming (DP)
which is used to obtain a global optimum for fuel
consumption. This is not an on-line solution, since it
assumes that the future reference is entirely known. In
the paper a DP solution was given, showing that the
energy management concept is working for pre-defined
drive-cycles.
The test simulations are performed for both strategies
using Matlab/Simulink environment .
200
2
The paper presents two solutions for fuel consumption
optimization of a series Hybrid Solar Vehicle (HSV).
HSVs, having multiple main energy sources, are an
alternative to conventional vehicles.
REFERENCES
0
-1
-2
0
200
400
600
Time [sec]
800
1000
1200
Figure 16. FUDS ICE power and battery nominal
power
It can be remarked that for the case when the FUDS
drive cycle is used, the reference tracking is ensured
acceptably well by the predictive controller. The fuel
consumption is between the global optimum value and
the value calculated without controller (see table 1.).
The SOC ensures a lower final value compared to the
DP.
I.Arsie, M.Graziosi, C.Pianese, G.Rizzo, M. Sorrentino
(2004). Optimization of Supervisory Control
Strategy for Parallel Hybrid Vehicle with
Provisional Load Estimate, AVEC ’04 (Department
of Mechanical Engineering – University of Salerno).
M.Back, M. Simons, F. Kirschaum, V. Krebs (2002).
Predictive Control of Drivetrains, IFAC 15th
Triennial World Congress, Barcelona, Spain.
P.Bauer, Zs. Preitl, T. Peter, P. Gaspar, Z. Szabo, J.
Bokor (2006). Control oriented modelling of a
series hybrid solar vehicle, Workshop on Hybrid
Solar Vehicles, November 6, 2006, University of
Salerno, Italy.
17
A. Bemporad, M. Morari, N.L. Ricker (2006). Model
Predictive Control Toolbox for Use with Matlab,
Users’ guide, Version 2, The Mathworks Inc.
E.F. Camacho, C. Bordons (1999). Model Predictive
Control, Springer Verlag London Ltd.
G.Gutmann (1999). Hybrid electric vehicles and
electrochemical storage systems – a technology
push – pull couple, Journal of Power Sources, Vol.
84, pp. 275-279.
M.W.T. Koot, J.T.B.A. Kessels, A.G. de Jager,
W.P.M.H. Heemels, P.P.J. van den Bosch, M.
Steinbuch (2005). Energy Management Strategies
for Vehicular Electric Power Systems, IEEE Trans.
on Vehicular Technology, 54(3), 771-782,.
B. Kulcsar, J. Bokor (2006). Measured Disturbance
Estimation for Model Predictive Controller,
Mediterranean Journal of Measurement and
Control, Vol 2., No 3, July 2006.
S.E. Lyshevski (2000). Energy conversion and optimal
energy management in diesel-electric drivetrains of
hybrid-electric vehicles, Energy Conversion &
Management, Vol. 41, pp. 13-24,.
J.M. Maciejowski (2002). Predictive Control with
Constraints, Pearson Education Ltd.
G.Maggetto, J. van Mierlo (2001). Electric vehicles,
hybrid electric vehicles and fuel cell electric
vehicles: state of the art and perspectives, Ann.
Chim. Sci. Mat, Vol. 26(4), pp. 9-26.
C. Musardo, G. Rizzoni, Y.Guezennec, B. Staccia
(2005). A - ECMS: An Adaptive Algorithm for
Hybrid Electric Vehicle Energy Management,
European Journal of Control, 11 (4-5), pp. 509-524.
S. Piller, M. Perrin, A. Jossen (2001). Methods for
state-of-charge determination and their applications,
Journal of Power Sources, Vol. 96, pp. 113-120.
18
CONTROL ORIENTED MODELLING OF A SERIES HYBRID SOLAR VEHICLE
P. Bauer*, Zs. Preitl*, T. Péter*,P. Gáspár**,Z. Szabó**, J. Bokor**
* Budapest University of Technology and Economics, Dept. Of Transport Automation,
H-1111 Budapest, Bertalan L.u. 2., Hungary
Email: [email protected], [email protected], [email protected]
** Computer and Automation Research Institute,
H-1518 Budapest, Kende u. 13-17, Hungary
Abstract: Nowadays more and more importance is dedicated to research in the field of
alternative vehicles. An option to conventional vehicles, having usually as energy source
a fuel tank with gasoline, consists in the so called hybrid electric vehicles (HEVs) which
have multiple main energy sources. These energy sources are the conventional fuel tank
and a battery, delivering both chemical and electrical energy. This can be completed with
a photovoltaic (PV) panel resulting in a hybrid solar vehicle (HSV). HEVs and HSVs can
be seen as a transition from conventional vehicles to fully electric ones. The paper
presents a study on modelling a series HSV. The model can be used for the development
of optimal control strategies which minimize the vehicle’s fuel consumption. After
modelling all of the components of the HSV, two simulation structures were built in
MATLAB Simulink. The first for basic simulations without control, the second for
controller design for example with MPC Toolbox. The basic model is mainly a backward
calculation scheme and provides reference solutions which can be compared with the
controlled system behaviour. The control oriented model is a forward calculation scheme
with given states, inputs and outputs. Linear models can be generated from it, were all
states are controllable and observable.
Keywords: hybrid solar vehicles (HSVs), component models, backward and forward
calculations
1. INTRODUCTION
It can also be used for control action design with
dynamical programming.
The paper presents a study on modelling a series HSV.
Series HSVs are optimal solutions for urban traffic
applications where the vehicle starts and stops
frequently during a drive cycle. So regenerative braking
can be often used, which substantially improves the fuel
economy of the vehicle. However, a series structure
applies fully electric driving, where instantaneous
large tractive forces provide good acceleration for the
vehicle. The overall structure of series architecture is
presented in figure 1.
The vehicle model can be used for the development of
optimal control strategies which minimize the vehicle’s
fuel consumption. Finally, two types of models were
generated.
The first model, which is meant for basic calculations,
provides reference data about the vehicle without
controller. In this model, one can consider that
regenerative braking only charges the battery, other
control actions were not applied. The simulation
scheme is mainly a backward calculation which
determines the inputs from the required system outputs.
Figure 1. Series hybrid architecture
The second model that can be used for controller
design, uses forward calculation scheme with given
states, inputs and outputs. Controllers can be designed
using this scheme, for example using the MPC Toolbox
of Matlab.
In the second section the specifications of all
components of the series hybrid driveline are given.
19
The third section deals with MATLAB Simulink model
construction and basic vehicle simulations. So reference
data was generated about the HSV. Finally the
conclusions end this paper.
2. COMPONENT MODELLING IN A SERIES
HYBRID ARCHITECTURE
The architecture of a series hybrid vehicle can be seen
in figure 1. First, the basic dynamics of the vehicle have
to be considered, using different drive cycles. This way
the extreme values of required drive power, torque and
angular velocity can be calculated.
After these calculations, the proper driveline elements
can be chosen which fit the requirements. These
elements are the following:
The main part is the electric motor (EM) which drives
the wheels or works as a generator during regenerative
braking. The electrical energy for the EM is delivered
by the electric generator (EG), the photovoltaic (PV)
panel and battery. The electric generator is in rigid
connection with the internal combustion engine (ICE).
These two components have to be considered as an
integral part of the vehicle, so power range, working
points and efficiencies must be fitted. The internal
combustion engine can be a diesel or a gasoline engine.
The EM considered in such applications is usually a
brushless DC motor which can be used both in motor
and generator modes.
PV panels can be used mainly during parking of the
vehicle, but on open area, they are useful supplements
for the electric power sources (EG and Battery) in
driving too.
The vehicle management unit (VMU) is used for
control and coordination of the components. When
designing the control strategies, one must consider the
properties of all the components and the goals of the
control application. Usually the main goals are
minimum fuel consumption during a trip and battery
charge sustaining.
In the following subsections the modelling of each is
component is presented in detail.
2.1 VEHICLE USED FOR HSV DEVELOPMENT
As a base vehicle, we selected the Porter glass van (see
figure 2) used at the University of Salerno. Few
technical data about the vehicle can be found in (Porter
2005-2006), but it is not enough even for basic
dynamical calculations. So, one has to search for data
about a similar van. This was the Subaru Libero mini
van (Subaru 2006). Using the data about both vehicles,
the parameters of the vehicle model are following:
o
o
o
o
o
o
o
o
o
m=1400kg vehicle mass
Ad=2.724 m2 frontal area
Cd=0.6 air drag coefficient
Cr=0.015 rolling resistance coefficient
ρ=1.225 kg/m3 air density
wr=0.3m wheel radius
fr=4 final drive ratio
Battery voltage: 84V 6 x 14V cells
Battery capacity: 180Ah
Figure 2. Porter glass van (Porter 2005-2006, MicroVett SPA)
For component selection, one has to calculate the
power, torque and angular velocity requirements for the
EM. This can be achieved using different drive cycles
and the well known basic dynamical relations in the
motion of vehicle. These relations are as follows:
f
ω (t ) = r v(t )
wr
M d (t ) =
wr
Fd (t )
fr
Fd (t ) = m ⋅ v& +
(1)
1 2
ρ v (t ) ⋅ Ad ⋅ Cd + m ⋅ g ⋅ Cr
2
Where ω is the angular velocity and Md is the torque
required from the EM. The velocity v(t) is given in the
specified drive cycles (for example figure 14, 15) and
the acceleration ( v&(t ) ) can be simply calculated from
it. So the required values for a given vehicle and drive
cycle can be estimated. The considered drive cycles are:
ECE_15, NEDC (New European Driving Cycle), FUDS
(Federal Urban Driving Schedule), FHDS (Federal
Highway Driving Schedule). The calculated maximal
power, torque and angular velocity requirements are
summarized in table 1.
Drive cycle Pmax [W] Mdmax [Nm] ωmax [rad/s]
ECE_15
15120
118.2
185.2
NEDC
57089
234.52
444.45
FUDS
10334
179.25
209.7
FHDS
35075
162.3
357.375
Table 1. Power, torque and angular velocity
requirements
As it can be observed, the EM must be able to deliver at
least 57089W maximum power. So, the choice of an
EM with 58 kW maximum mechanical power is
suitable for this vehicle. Of course the ICE and EG
must be fitted for this EM. This aspect will be discussed
later in subsections dealing with ICE and EG.
20
2.2 ELECTRIC MOTOR (EM)
Usually an attractive alternative for electric vehicles
and HEV driving systems are Brushless DC machines
(BLDC-m) (Crowder, 1998), (Ehsani et al, 2001). They
can function both in motor and generator regimes. As a
remark to the BLDCs, it can be mentioned that the
BLDC is in fact the combination of a permanently
excited synchronous motor and a frequency inverter,
where the inverter „replaces” the converter of a
classical DC motor (Rizzoni, 1993), (Filippa et al,
2004). From here results also the name Brushless DC
motor. BLDCs with inverter are mainly used in high
performance electric drives with variable speed, where
these values largely outrun the nominal rotation
velocity.
The BLDC-m is with “rare earth” magnetic materials
(Samarium-Cobalt (Sm-Co) or other materials), which
combine high flux-density with very large coercive
force. The BLDC-m has its own electro-mechanical
characteristics, it can not be used without a dedicated
power supply unit and control system, consisting in: the
power electronics unit: DC-AC or DC-AC - AC-DC
(inverter), the command and the control unit (digital
control unit), the BLDC-m servo-unit (Bay et al., 1996).
A suitable solution consists in using DC-AC (AC-DC –
for regenerative braking) inverter supply which ensures
the torque control with injected current (PWM
modulated control).
The four-quadrant operation mode for the BLDCmachine with control block is presented below in figure
3, based on (Tsai, 2002).
ω=
1
1,1
[U − Rm
M]
Ke
Kt
Where M is the torque, I is current, U is voltage, Kt, Ke,
are the electromechanical and the electromagnetic
constants of the machine (their values are numerically
close).
•
Steady-state
speed-torque
curves
M = f (ω;U − parameter) ; they are obtained by
inversing relation:
Kt
M=
[U − K eω ]
(3)
1.1Rm
The characteristic steady-state curves for this latter case
are presented in figure 4 (in normalised values). The
diagram is presented in normalized values of the torque
and speed, for the first quadrant according to figure 3.
nn is the nominal resolution, in Pel=Pmax =constant
regime.
Figure 4. Torque-speed characteristics in normalized
values
Brushless DC motor drive and brake characteristics
200
150
100
Torque (Nm)
50
0
-50
-100
-150
-200
Figure 3. Operation modes for a BLDC-m
In the paper the aspects regarding BLDC-m modelling
refer to a qualitative modelling (machine plus power
electronics structure) (Tsai, 2002), details regarding the
pure machine are not presented. The qualitative
modelling is achieved through the presentation of static
characteristics, with two possibilities:
•
Steady-state torque-speed curves,
ω = f ( M ;U − parameter) . The characteristics are
based on relation:
and
M = Kt (I − I0 )
I 0 ≈ 0.1 ⋅ I n =>
1
1.1
(2)
M =
M
M = 0.9 K t I => I =
0.9 ⋅ K t
Kt
0
500
1000
1500
2000
2500
Speed (rpm)
3000
3500
4000
4500
Figure 5. Speed-torque characteristics for quadrants I
and II.
For the given numerical data (nn=2300 rpm nominal
RPM, Pn=58kW nominal mechanical power, Un=84V
armature voltage, η = 0.8 efficiency factor) the speedtorque characteristics are given in figure 5, for different
values of the armature voltage. It must be mentioned
that the axes is figure 4 and figure 5 are inverted to the
axes of figure 3. The maximum torque is obtained at
the nominal armature voltage. The characteristics are
presented for quadrants I and II, according to figure 5.
Also the power balance between the electrical and
mechanical powers is taken into consideration,
21
according to which Pel=Pm/η. The Simulink model of
the BLDC-m is based on the above presented values.
2.3 PHOTOVOLTAIC (PV) PANEL
The PV panel is independent from the other
components. It can be chosen so that it has maximum
efficiency and a maintenance free robust structure.
These requirements are all fulfilled with a crystalline,
silicon on glass (CSG) 100 solar module manufactured
by CSG Solar AG. Characteristics for the module are
provided by the manufacturer in (CSG 2005) (see figure
6). In (Ocran et al., 2005) one can find detailed
calculation formulas about PV panels, but lack of
detailed data makes not possible to perform calculations
with these formulas. So, finally exponential functions
were fitted on the characteristics considering their
exponential like shape (see figure 6). The form of the
fitted function is as follows:
U −U max
⎛
I 0 = K ⎜⎜ 1 − e TU
⎜
⎝
⎞
⎟
⎟
⎟
⎠
variable. The U value at maximum power point ( U opt )
is different for different insolation values, but a second
degree polynomial describes it accurately.
The final model for optimal PV panel power is as
follows:
PPV =
U opt (λ )−U max (λ )
⎛
⎜
TU ( λ )
U opt (λ ) ⋅ K (λ ) ⋅ ⎜1 − e
⎜
⎝
(1 + K P (T − 25))
⎞
⎟
⎟⋅
⎟
⎠
(5)
Equation (5) describes correctly the PV panel power at
different insolation values, in maximum efficiency
point with temperature correction (T is the actual cell
temperature).
2.4 BATTERY MODEL
(4)
For battery modelling both simple and complicated
solutions can be found in the literature.
Where I 0 is the output current, U is the output voltage,
U max is the maximum possible output voltage, K and
TU are parameters to be calculated.
One should select the proper battery considering the
modelling purposes. We have selected a relatively
complex one, which models the battery as a real voltage
generator considering the change in open circuit voltage
when battery state of charge (SOC) changes. The sketch
of this model is presented in figure 7.
Figure 7. Battery model as real voltage generator
Figure 6. PV panel characteristics from (CSG 2005)
Calculations were performed for every insolation value
(λ = 200÷1000 W/m2), so K and TU are insolation
dependent. U max is also insolation dependent, so
finally one can get the model fitting curves on K, TU
and U max using insolation as independent variable. For
U max and TU third order polynomials were used while
K could be approximated with a single linear function.
Another important aspect is the consideration of
temperature effects in the model. This can be done
using the temperature coefficient of power K P (CSG
2005). With this, the PV panel output power should be
corrected. In (Ocran et al., 2005) a maximum power
point tracker controller for PV modules is derived, so
one can assume that the PV module is operated always
in the maximum efficiency region. This results in a
working line considering insolation as independent
The governing equations of this battery model are as
follows:
U oc = U OC min + (U OC max − U OC min ) ⋅ SOC
Ib = −
U OC − U OC 2 − 4 ⋅ ( Rint + Rt ) ⋅ Pb
(6)
2 ⋅ ( Rint + Rt )
I
dSOC
Q&
=
= b
dt
Qmax Qmax
In this type of formulation positive Pb (battery power)
means battery discharge, while negative Pb means
battery charge.
In (Koot et al., 2005) the efficiency of battery is also
dealt with, which is modelled with the following
expression:
Pb =
1 − 1 − 6 ⋅ 10 −5 ⋅ Pbn
(7)
3 ⋅ 10 −5
22
Here Pbn means nominal battery power. The overall
structure of the battery model, is presented in figure 8.
Figure 8. Battery simulation structure
The resultant battery model reflects all the important
characteristics of a battery. The open circuit voltage
decreases, when SOC decreases, the battery current
calculation in (6) is asymmetric, which means that
higher SOC rate can occur in discharging than in
charging. Nominal power ( Pbn ) losses occur even in
charging or discharging mode.
2.5 ELECTRIC GENERATOR AND INTERNAL
COBUSTION ENGINE MODEL
The electric generator and internal combustion engine
(ICE) must be fitted to the electric motor and to each
other. The selected electric motor with 58 kW
maximum output mechanical power, needs maximum
72.5 kW input electrical power. This must be provided
by the electric generator if battery discharge is not
possible and the weather is cloudy (no insolation on PV
panel). So, one has to select an electric generator that
satisfies these requirements.
Figure 10. ICE fuel map
In the fuel map, the fuel rate values are plotted against
ICE torque and angular velocity values. Every
combination of torque and angular velocity means a
possible output power value for the motor. However,
fuel rate is given at every point, from which input
power can be calculated using the lower heat value of
gasoline.
The quotient of output and input power is the ICE
efficiency. This way the efficiency map can be plotted
against torque and angular velocity values (see figure
11.). Of course, in points with zero input and output
power efficiency can not be calculated so one can
simply assume it to be zero.
Of course, the EG and ICE have to be fitted to each
other using the maximum efficiency region for both of
them. This way the EG can be described by a single
characteristic curve, between input mechanical and
output electrical power as in figure 9.
Figure 11. ICE efficiency map
Figure 9. Electrical generator characteristic curve
The description of ICE is possible in a similar way
considering the maximum efficiency working line. The
fuel map of the proper ICE (which can satisfy the EG
input power needs) is depicted in figure 10.
The determination of optimal working line is possible
using a characteristic value mixed from output power
and efficiency:
opt = M ⋅ ω ⋅ η
(8)
The goal is to find the trajectory which contains the
maximum power points from zero, to maximum
possible output power, with maximum efficiency. For
this purpose the map of opt values can be used (see
figure 12.)
23
battery SOC has to increase because of regenerative
braking and the lack of battery discharge. The initial
SOC value is 0.7 according to the literature (Musardo et
al., 2005, Koot et al, 2005).
Figure 12. Optimum variable map for ICE with optimal
working line
The optimal working line can be found with a gradient
method, starting from the point (M = 0, ω = 0).
Further, the next paragraph deals with MATLAB
Simulink model construction using the component
models.
Figure 14. New European Driving Cycle with time [s]
on horizontal and velocity [km/h] on vertical axis
3 MATLAB SIMULINK MODEL CONSTRUCTION
Model construction has multiple goals. The first goal is
to create a model for simulation without controller,
which gives an insight into the original characteristics
of HSV. The second goal is model construction for
controller design.
Of course, the resultant model will be strongly
nonlinear, so the linearization of model is required or
nonlinear control techniques must be used.
The model for initial vehicle simulations (backward
calculations) can be seen in figure 13.
Figure 15. Federal Urban Driving Schedule with time
[s] on horizontal and velocity [km/h] on vertical axis
Simulations were performed for different insolation
values. The resulting total fuel consumption data can be
used as a reference for controller design, from which
lower total consumptions have to be obtained. The
results are summarized in table 2.
2
1
λ [kW/m ]
SOC
0.7192
total fuel [g] 913.7265
NEDC
2
λ [kW/m ]
SOC
total fuel [g]
FUDS
1
0.7125
499.696
0.8
0.7189
916.015
0.6
0.4
0.7186
0.7183
918.1686 920.4583
0.2
0.7181
922.613
0
0.7178
924.768
0.8
0.6
0.4
0.2
0
0.7122
0.7119
0.7116
0.7113
0.711
502.8127 505.7325 509.5911 513.0373 515.9575
Table 2. Results from initial vehicle simulations
Figure 13. Structure for basic HSV simulations
In this model, one has to apply only a very simple
control decision, which covers battery charging with
regenerative braking.
Tests were performed for the NEDC (figure 14) and
FUDS (figure 15) driving cycles, since these are the
basic cycles used in urban traffic simulations.
During calculations, the total fuel consumption and
final battery SOC were registered. Of course, the
As it can be seen in table 2, the total fuel consumptions
increase, while the final SOC values decrease at lower
insolation values. The total fuel and SOC trajectories
for both drive cycles at maximum insolation are in
figures 16-19.
As a conclusion from these figures, one can state that
FUDS does not contain sudden high changes in
parameters, while the final part of NEDC contains
strong changes. This results in strong changes in total
fuel and SOC. The cause of this is the extra urban part
of NEDC with a maximum speed of 120 km/h.
24
slightly different model should be constructed for other
control design methods.
For MPC control framework a forward calculation
scheme is needed which can also be constructed from
the component models.
The selected model states, (control) inputs and outputs
are:

State variables: - x1: ICE power state,
- x2: SOC,
- x3: EM power state;

Inputs: - u1: ICE power,
- u2: Battery nominal power;
Figure 16. Total fuel consumption trajectory, NEDC

Controlled outputs: - o1: Drive power,
- o2: SOC,
- o3: Fuel rate;

Measured disturbance input: - dm: PV panel
power.
The model can be linearized with MATLAB linmod or
linmod2 functions. We have tested the resultant linear
models and they were all controllable and observable so
controller design for the HSV van is possible.
4. CONCLUSIONS
Figure 17. Total fuel consumption trajectory, FUDS
In this paper the control oriented modelling of
components of a hybrid solar vehicle (HSV) and the
overall vehicle structure was discussed.
Components are mainly modelled with their
characteristics (EM, EG, ICE), with calculation
formulas (vehicle dynamics and battery) or with
formulas derived from the characteristics (PV panel).
After component modelling the construction of two
different simulation structures in MATLAB Simulink
was performed.
The first model is for basic simulations and dynamic
programming controller design, so it uses mainly
backward calculation schemes. Only regenerative
breaking is considered in it.
Figure 18. SOC trajectory NEDC
The second model uses forward calculation which is
proper for controller design in MPC framework. In this
model the states, inputs and outputs are exactly defined.
Simulations were performed only for the first model,
generating reference total fuel consumption values for
controller design. Of course, one has to get lower total
fuel consumption from the controlled system. Results
are summarized in table 2 for NEDC and FUDS drive
cycles at several insolation values.
ACKNOWLEDGEMENTS
Figure 19. SOC trajectory FUDS
This initial model can be a basis for optimal control
input calculation with dynamic programming, while a
The authors gratefully acknowledge the contribution of
Hungarian National Science foundation (OTKA N:
K060767). This work was partially supported by the
Hungarian National Office for Research and
Technology through the project "Advanced Vehicles
and Vehicle Control Knowledge Center" (no: OMFB 01418/2004).
25
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26
SIMULATION PROGRAM AND CONTROLLER DEVELOPMENT FOR A 4WD
PARALLEL HEV
Ali Boyalıa, Murat Demircia, Tankut Acarmanb, Levent Güvença,*
Burak Kırayc, Murat Yıldırımc
a
Istanbul Technical University, Department of Mechanical Engineering,
Automotive Control and MechatronicsResearch Center and MEKAR Laboratories
İnönü Cad. No:87 Gümüşsuyu, Taksim, TR-34437 İstanbul, Turkey
b
Galatasaray University, Faculty of Engineering and Technology, Computer Eng. Dept.,
Çırağan Cad. No:36, TR-34357 Ortaköy, İstanbul, Turkey
c
Ford Otosan, İzmit Gölcük Yolu 14. Km, TR-41680 Gölcük, Kocaeli, Turkey
Abstract: In this paper, we present a simulation model and a rule based controller design
for a 4WD parallel HEV. A light commercial vehicle, equipped with inherited internal
combustion engine, assembled with a battery pack, electrical actuator and its power
converter is simulated by using the validated test results. A rule based controller and logic
design is optimized to reduce fuel consumption and undesired emission with the assistance
of the electrical actuator. Regenerative braking is shown to be capable of gaining back a
certain percentage of the tire kinetic energy. The performance of the designed controller
and logic switching between the two actuators are validated by experimental results.
Copyright © 2006 IFAC
Keywords: Control, modelling, design, rule-based systems, energy management systems
1. INTRODUCTION
Mass production of Hybrid Electric Vehicles (HEV)
is becoming a global strategy for car manufacturers
due to the prominent role of HEV in bringing down
fossil fuel consumption and emissions. Hybrid
vehicles are a temporary solution on the way to the
zero emission road vehicle. Toyota is planning to
produce all its vehicles with hybrid technology by
2012 (see Anonymous-a), and the sales volume of
hybrid electric vehicles in the U.S. is expected to
increase by 268 percent between the years 2005 and
2012 (see Anonymous-b).
The effectiveness of fuel consumption depends not
only on vehicle design but also on the control
strategy used. Several HEV control strategies have
been proposed in the open literature. The underlying
*
methodology in HEV control is to find the optimum
power split ratio between the two power sources. The
simplest and easiest to adapt control method is the
rule based control algorithm (see for ex. Boyalı, et al,
2006). In this algorithm, the vehicle states are
detected and the control commands are generated
based on rules corresponding to the particular state.
Rules are constructed based on engineering intuition
and rigorous analyses of fuel consumption and
emission maps belonging to the internal combustion
engine (ICE), rather than analytical computation of
optimum operating points based on minimization of a
cost function. In some HEV applications,
deterministic optimal control is applied, (see Lin, et
al., 2003). For a given speed profile, the global
optimum operation paths of vehicle components may
be calculated using the dynamic programming
method. However, in real-time driving conditions,
Corresponding author, Prof.Dr. Levent Güvenç
E-mail addresses : [email protected]
URL
: http://mekar.itu.edu.tr
27
the speed profile is not known a priori and a global
minimum can not be determined. The remedy is to
find sub-optimal solutions approaching the global
optimum. One of these suboptimal methods is to
compute equivalent fuel consumption and to evaluate
power split ratio instantaneously to minimize a
chosen cost function (Sciarretta, et al., 2004;
Paganelli, et al., 2001a; Paganelli, et al., 2001b;
Johnson, et al., 2000). Another approach is to apply
stochastic optimal control methods in the short time
intervals while predicting the speed profile of the
controlled HEV (Jeon, et al., 2001).
This paper discusses the modeling and control of a
four wheel drive hybrid electric vehicle and
experimental test results. An explanation of the
simulation model structure is given in section II. In
sections III, the control algorithm involving vehicle
states, transition states and switching logic between
two actuators are explained. In Section IV, the
hardware setup integrated into the experimental
vehicle for performing the proposed control
algorithm on a real-time basis is presented.
Simulation results are demonstrated in section V.
Experimental results are given in section VI. The
paper ends with conclusions.
This model consists mainly of six blocks. These
blocks are the longitudinal vehicle model, nonlinear
tire model, internal combustion engine model,
electric motor (EM) model, driver model and
supervisory controller.
The net longitudinal force acting on the vehicle is
used to compute vehicle acceleration by subtracting
the resistance forces such as aerodynamic, rolling
resistance and the resistance induced by road slope,
from the traction forces that are available from the
tire blocks. The Pajecka 2002 tire equations are used
for modeling the tire. Although the tire model is
capable of computing all tire forces and moments,
only longitudinal forces are utilized in this model.
The lateral forces and moments can be used for
further studies such as hybrid vehicle lateral stability
analysis due to the fact that the established model is
modular in structure.
The engine is modeled using engine maps that give
the output engine torque for the two inputs of engine
speed and accelerator pedal position. Transient
regimes of the engine are thus not treated. Negative
engine torque is computed to introduce function of
cylinder head temperature and instantaneous engine
speed.
2. VEHICLE MODEL
In this study, a four wheel drive Ford Transit
commercial
van
is
modeled
using
the
Matlab/Simulink toolbox. Since rear and front wheel
drive vans were commercially available, the
experimental vehicle was formed by combining these
two drive axles in one vehicle. The result was a four
wheel drive (4WD) hybrid electric vehicle. The front
drive is powered by the internal combustion engine
and the rear drive is powered by the electric motor. A
first prototype HEV of this construction was
explained in our previous work in Boyalı, et al, 2006.
This paper concentrates on a second prototype
vehicle based on this 4WD concept, referred to as the
experimental vehicle hereafter.
Modeling of this experimental vehicle is presented
first. The equations of dynamics for the considered
model may be found in Boyalı, et al, 2006. The
Simulink implementation of the model is shown in
Fig. 1.
Fig. 1. Simulink vehicle model
Transmission components are assumed to be rigid
bodies, only equivalent inertias and transmission
ratios are used to model the driveline. Even though
the efficiency of transmission components varies
with respect to transmission speed, gear ratio and the
torque, constant efficiency values are used for
computational simplicity.
For a given speed profile, the driver model accepts
the desired speed and actual speed as its two inputs.
Anti-windup Proportional-Integral (PI) controllers
are used to model the driver and to command the ICE
and EM. Two feedback options are available. Speed
feedback is not suitable for controlling the 4WD
vehicle since the rear and front axle dynamics require
different torques due to the different component
properties. Thus, torque feedback is used to follow
the desired speed profile. Once the desired speed
starts to increase, the controller sends the throttle
signal to the engine. Additionally, the driver model
generates clutch and brake signals. To imitate the
real clutch-engine relation for the EM only state, and
to improve driving feeling while shifting gears with
respect to conventional ICE vans, a potentiometer
that generates a linear signal between “0” and “1” is
used in the experimental vehicle.
Look-up tables including data of braking torque
versus brake pedal position are used for modeling the
brakes. In order not to change braking characteristics
of the vehicle, a force gap is allocated for
regenerative braking. Along this gap, only
regenerative braking is allowed. In designing
regenerative braking, the regulations on braking are
also taken into account. After a certain amount of
applied pedal force, conventional friction brakes are
28
activated and the regenerative braking torque is
decreased gradually as illustrated in Fig. 2.
A simple equivalent circuit is used as the battery
model. The open circuit voltage and internal
resistance depending on state of charge and current
flow direction are used to build the necessary
equations. For simplification of the overall electric
traction system modeling, a permanent magnet direct
current motor model is used (see Boyalı, et al, 2006).
•
•
•
Pure ICE excitation (ICE mode)
Charging or EM assist (Hybrid mode)
Braking mode (regenerative and conventional
friction braking)
To decide which state will be active, some transition
rules are used. If the vehicle speed is below a small
value such as 5 km/h, the vehicle is assumed to be in
standstill position. Other state transitions are
determined according to the logic rules given in
Table I. To avoid limit cycle oscillations, hysteresis
is added to the transitions.
Fig. 2. Regenerative braking characteristics
3. RULES AND FINE TUNING
The main aim of introducing rule based control is to
operate the ICE at high loads which correspond to its
efficient regions. For this reason, the electric motor
(EM) only mode operates under a predetermined
driver power request and also when direct EM
assistance is desired by the driver during gas pedal
kick-down. The required power to drive the vehicle
is computed for a given drive cycle. In real-time
driving conditions, driver power or torque request at
the wheels is computed by evaluating the accelerator
pedal position and brake pedal force reading.
Measured values are used in the ICE torque and
brake maps and corresponding positive or negative
Fig. 3. Vehicle states
Traction torque is supplied by the EM in the pure
EM mode where the ICE follows the wheel speed.
Since the manual clutch can not be commanded
automatically, the engine compression brake
becomes active as shown in Fig. 4. This is an
inherited disadvantage of the experimental vehicle
towards HEV real-time operation as the EM should
meet both the driver request and engine compression
brake during the EM only mode. This drawback is
Table 1. Transition Logic
Standstill
Vehicle
Speed
<5 km/h
State of
Charge
--
Requested
Power.
--
Pure EM
--
> SOClow
< 6 kW
--
Pure ICE
Pure ICE
EM Assist
----
< SOClow
> SOClow
> SOClow
< 6 kW
> 7 kW
--
EM Generator
--
< SOClow
--
Regen. Braking
--
< SOChigh
--
-> Requested. Torque
< Requested. Torque
<Req. Torque +Charge
Torque
--
Conv. Braking
--
>= SOChigh
--
Conv. Braking
--
< SOChigh
--
desired torques are calculated.
There are five main vehicle states in the control
algorithm which are, see (Fig. 3).
•
•
Standstill vehicle position (Standstill mode)
Pure EM excitation (EM mode)
Max. ICE Torque
Max. EM Torque
--
-< Requested.
Torque
----
Brake Pedal
Force
------
< Charge. Torque
--
--
< 80
--
--
--
--
--
> 90
compensated since the engine cuts off fuel while
braking.
Another difficulty is to keep drivability of the hybrid
electric vehicle at the same level as the conventional
vehicle in the presence of a manual clutch. This can
29
be compensated by using appropriate transition
functions between pure ICE and pure EM states and
by using the clutch potentiometer to sense clutch
position.
Fig. 4. Engine torque map
The transition function is a function of the torque
supplied by the power source at the wheels and time.
If the transition conditions are realized between ICE
and EM, the vehicle enters into the transition states
(Fig 5.).
torque, the driver does not feel an abrupt transition.
The change is smooth and is not noticed by the
driver. To avoid unwanted oscillations such as shunt
and shuffle during the transitions, the demanded
torque, engine torque and EM torque at the wheels
are computed as accurately as possible. This is
obviously an open loop control approach which uses
available offline data. If an accurate engine map, i.e.,
torque output versus ICE speed, is available, an
inverse map can be used to distribute required torque
between the EM and the ICE. Another easier
approach is to calibrate the accelerator pedal position
in such a way that the EM generates the same
amount of torque as the ICE for the same pedal
position (Boyalı, et al, 2006).
The current transmission stick shift position also has
to be estimated in real time in order to compute the
torque demand at the wheels. Vehicle speed and
wheel angular speeds are available on the CAN bus.
The ratio of these two speeds gives the transmission
gear ratio and thus the stick shift position. There are
upper and lower variations for each gear ratio as
plotted in Fig. 7. The gear position estimation is
carried out using a Stateflow diagram in Simulink.
Fig. 7. Gear ratio variations
4. HARDWARE SETUP
Fig. 5. Transition states
During the transition states, the instantaneous
required torque at the wheels is supplied by both
power sources. For instance the EM power starts to
decrease linearly as the ICE power increases linearly
to keep on supplying the required power (Fig. 6.).
Fig. 6. EM and ICE torques in transition states
Since the total torque always equals the demanded
A dSpace MicroAutoBox (MABX) complemented
with a RapidPro system is used as the main
electronic control unit to carry out the HEV control
algorithm. The MABX and Rapidpro system
installed in the Ford Transit van is shown in Fig. 8.
Fig. 8. HEV controller hardware connections in the
experimental vehicle
30
All signals required by the HEV controller are
gathered via the MABX and the RapidPro signal
conditioning units. Vehicle and battery states are
monitored via reading the CAN bus. The other
signals are analog signals. The general signal
connection diagram is shown in Fig. 9.
brake) allow smooth operation of the EM via its
driver. The HEV control unit sends the commands to
the controller as acceleration or brake requests. The
EM driver applies these requests according to the
motor operating region or generator operating region
maps.
The HEV control strategy is modeled in
Matlab/Simulink. Automatic code generation and
downloading into MABX is achieved by the Matlab
Real Time Workshop and dSpace Real Time
Interface tools as illustrated in Fig. 10.
Fig. 11. EM electrical and mechanical connections
(Boyalı, et al, 2006).
5. SIMULATION RESULTS WITH POWERORIENTED CONTROL RULES
The EUDC drive cycle is used in simulation to
compute fuel consumption and emitted emission
quantities. The results are listed in Table II for a
vehicle mass of 3000 kg. Emission values given in
Table II are the engine-out emissions. SOC is short
for state of charge of the batteries
Table 2. Fuel Consumption and Emissions
Fig. 9. General signal connection diagram
Fig. 10. Rapid HEV control algorithm prototyping
process diagram
Following the electrical and mechanical flows
plotted in Fig. 11, the EM driver enables the
conversion of DC voltage to AC voltage. The electric
power is supplied by a battery pack which is
connected to the motor driver through a circuit
breaker as a safety switch. The available EM driver
control signals (enable, direction, acceleration,
Conven.
Hybrid
Improv.
Fuel Consp.
Litre/100 km
11
9.3
% 15.5
Δ SOC %
--
0
--
NOx -- gr/km
0.77
0.55
% 28
CO2 -- gr/km
2.76
2.26
% 18
CO-- gr/km
5
4.75
%5
Acceleration tests are also performed. For this
reason, a gear shift algorithm pertaining to this
vehicle is necessary. To determine the gear up shift
points, the torque versus engine speed curves at the
wheels were drawn for each gear (Fig. 12). The
intersections of the curves are the gear shift points
that maximize the area and thus acceleration
performance under these curves. If this is repeated
for each accelerator position with a specified
increment, the gear shift graph in Fig. 13 is obtained.
In hybrid acceleration tests, the EM operates in the
assist mode according to the rule based control
algorithm. As the pedal opening exceeds 70% of its
full travel range, the EM starts to give assist torque
linearly.
Acceleration simulation results are given Table III
and Figures 14-15.
31
Fig 15. Simulated engine speed and gear position
history
Fig 12. Engine torque versus vehicle speed
6. EXPERIMENTAL RESULTS AND MODEL
VERIFICATION
Accelerator, brake, clutch pedal and gear positions
were recorded during an experimental acceleration
test and were used as inputs to the simulation model
in a subsequent simulation study.
The experimental and simulation results are
displayed in Figures 16 and 17. The simulated and
real test results, with their close matching, show the
effectiveness of the proposed simulation modelling
approach. The HEV control algorithm states entered
in the acceleration test are shown in Fig. 18.
Fig. 13. Optimal gear shift curves for acceleration
performance
Table III. Conventional and Hybrid Vehicle Acceleration
Performances
8-32,3 km/h
8-56,4 km/h
0-100 km/h
80-120 km/h
Conventional [s]
2.086
5.6
22.37
18,76
Hybrid [s]
2.08
5.6
17.13
12.34
Fig 14. Simulated Hybrid and Conventional Vehicle
acceleration performances
Fig
16. Conventional vehicle acceleration
comparison of simulated and experimental
responses
Fig 17. Hybrid vehicle acceleration comparison of
simulated and experimental responses
32
Fig 18. Vehicle speed and states during test drive
During driving tests, the state of charge of the
vehicle was also recorded and is shown in Fig. 19. In
the charge state, the torque request of the driver is
evaluated and a charge torque is calculated within
component constraints. Since the ICE meets both the
driver torque demand and the charge torque in the
charge mode, the driver does not feel a significant
change with respect to the conventional vehicle.
Fig. 20 Ford Transit Van and battery packs
ACKNOWLEDGEMENT
The authors acknowledge the support of Ford Otosan
R&D Department and the European Union
Framework Programme 6 project INCO-16426.
REFERENCES
Fig 19. SOC change in Charge state
7. CONCLUSIONS
Two vehicles were successively converted into
hybrid electric vehicles and instrumented with a
battery, an electric motor and sensors. The second
experimental vehicle is shown in Fig. 20. A
simulation model and its use in designing a rule
based control algorithm were presented. Simulation
and experimental results were compared to
demonstrate the validity of the results achieved.
Future work will concentrate on the use of local and
global optimization methods.
Anonymous-a, http://www.automotivedigest.com.
Anonymous-b, http://www.jdpower.com.
Boyalı A., Demirci M., Acarman T., Güvenç L., Kiray B., Özatay
E. (2006), Modeling and Control of a Four Wheel Drive
Parallel Hybrid Electric Vehicle, Proceedings of the IEEE
Conference on Control Applications, Munich, Germany,
November (to appear).
Lin C. C., Peng H., Grizzle J.W., and Kang J.M. (2003), Power
Management Strategy for a Parallel Hybrid Electric Truck,
IEEE Transaction on Control Systems Technology, Vol. 11,
No. 6. pp 849-839,
Sciarretta A., Back M., and Guzzella L., Optimal Control of
Parallel Hybrid Electric Vehicles (2004), IEEE Transactions
on Control Systems Technology, Vol. 12, No:3. pp. 352-363.
Paganelli G., Ercole G., Brahma A., Guezennec Y., Rizzoni G.
(2001), General Supervisory Control Policy for the Energy
Optimization of Charge-Sustaining Hybrid Electric Vehicles,
JSAE Review, Vol. 22, pp. 511–518
Paganelli G., Delprat S., Guerra T.M., Rimaux J., Santin J.J.,
(2001), Equivalent Consumption Minimization Strategy for
Parallel Hybrid Powertrains, Proceedings of Vehicular
Transportation Systems Conference, Atlantic City, NJ, USA.
Johnson V. H., Wipke K.B., and Rausen D.J. (2001), HEV Control
Strategy for Real-Time Optimization of Fuel Economy and
Emissions, SAE 2000-01-1543.
S. Jeon, K.B. Kim, S.T. Jo, and J.M. Lee (2001), Driving
Simulation of a Parallel Hybrid Electric Vehicle Using
Receding Horizon Control, Industrial Electronics, 2001.
Proceedings. ISIE 2001. IEEE International Symposium on,
Vol. 2, pp. 1180-1185,
33
34
A MODEL FOR A HYBRID SOLAR VEHICLE PROTOTYPE
Ivan Arsie, Raffaele Di Martino, Gianfranco Rizzo, Marco Sorrentino
Department of Mechanical Engineering, University of Salerno, 84084 Fisciano (SA), Italy
Abstract: The paper deals with a dynamic model for the simulation of a solar hybrid
prototype, developed in the framework of the Leonardo Program I05/B/P/PP-154181.
The model is based on a longitudinal vehicle dynamic model and allows evaluating the
effects of solar panels area and position, vehicle dimensions and propulsion system
components on vehicle performance, weight, fuel savings, autonomy and costs.
Simulation results show that significant fuel savings vs. conventional vehicle powered by
internal combustion engine can be achieved for intermittent use in urban area and that
economic feasibility could be achieved in the next future, considering the expected trends
in costs and prices. Furthermore the hybrid series architecture allows increasing
significantly vehicle autonomy vs. pure electrical vehicle.
Keywords: modeling, simulation analysis, hybrid solar vehicles, photovoltaic energy,
control.
1.
INTRODUCTION
In the last years, increasing attention has been spent
towards the applications of solar energy to cars.
Various solar car prototypes have been built and
tested, mainly for racing and demonstrative purposes
[1].
Despite a significant technological effort and some
spectacular outcomes, several limitations, such as low
power density, unpredictable availability of solar
source and energetic drawbacks, cause pure solar cars
to be still far from practical feasibility. On the other
hand, the concept of a hybrid electric car assisted by
solar panels appears more realistic [3][4][5][6][7]. In
fact, due to relevant research efforts [8], in the last
decades Hybrid Electric Vehicles (HEV) have
evolved to industrial maturity. These vehicles now
represent a realistic solution to important issues, such
as the reduction of gaseous pollution in urban drive as
well as the energy saving requirements. Moreover,
there is a large number of drivers utilizing daily their
car, for short trips and with limited power demand.
Some recent studies, conducted by the UK
government, report that about 71 % of UK users reach
their office by car, and 46 % of them have trips
shorter than 20 minutes, mostly with only one
passenger (i.e. the driver) [9]. The above
considerations open promising perspectives on the
integration of solar panels with “pure”-electric hybrid
vehicles (i.e. “tri-hybrid” cars), with particular
interest in the opportunity of storing energy even
during parking phases.
In spite of their potential interest, solar hybrid cars
have received relatively little attention in literature
[7]. An innovative prototype has been developed at
Western Washington University [5][6] in the 90s,
adopting
advanced solutions for materials,
aerodynamic drag reduction and PV power
maximization with peak power tracking. Other
studies and prototypes on solar hybrid vehicles have
been presented by Japanese researchers [3][4] and at
the Queensland University [10].
Although these works demonstrate the general
feasibility of such an idea, detailed presentation of
results and performance, along with a systematic
approach to solar hybrid vehicle design, seem still
missing in literature. Therefore, appropriate
methodologies are required to address both the rapid
changes in the technological scenario and the
increasing availability of innovative, more efficient
components and solutions. A specific difficulty in
35
developing a Hybrid Solar Vehicle (HSV) model
relates to the many mutual interactions between
energy flows, power-train balance of plant and sizing,
vehicle dimension, performance, weight and costs,
whose connections are much more critical than in
either conventional or hybrid electric vehicles.
The current study focuses on the extension of the
analysis methodologies presented in [11][12][18] to a
hybrid solar vehicle prototype, now under
development at DIMEC – University of Salerno. This
activity is being conducted in the framework of the
UE funded Leonardo project I05/B/P/PP-154181
“Energy
Conversion
Systems
and
Their
Environmental Impact” [17]. The on going research is
also extended to the study of real time control of solar
panels (MPPT techniques and their implementation)
and to the development of converters specifically
suited for automotive applications [19].
2.
THE SOLAR HYBRID VEHICLE MODEL
Different architectures can be applied to HEVs:
series, parallel, and parallel-series. The two latter
structures have been utilized for two of the more
widely available hybrid cars in the market: Toyota
Prius (parallel-series) and Honda Civic (parallel).
Instead, for solar hybrid vehicles the series structure
seems preferable [7], due to its simplicity, as in some
recent prototypes of HSV [10]. With this approach,
the Photovoltaic Panels (PV) assist the Electric
Generator EG, powered by the Internal Combustion
Engine (ICE), in recharging the Battery pack (B) in
both parking mode and driving conditions, through
the Electric Node (EN). The Electric Motor (EM) can
either provide the mechanical power for the
propulsion or restore part of the braking power during
regenerative braking (Figure 1). In this structure, the
thermal engine can work mostly at constant power
(Pav), corresponding to its optimal efficiency, while
the electric motor EM can reach a peak power PEM:
PEM = θ ⋅ Pav
(1)
PV
EG
EN
ICE
B
EM
rain etc.) and available for propulsion, a solar
calculator developed at the US National Renewable
Energy Lab has been used [12]. Four different US
locations were considered, ranging from 21° to 61° of
latitude, based on 1961-1990 time series. The
calculator provides the net solar energy for different
panel positions: with 1 or 2 axis tracking mechanism
or for fixed panels, at various tilt and azimuth angles.
The most obvious solution for solar cars is the
location of panels on roof and bonnet, at almost
horizontal position. Nevertheless, two additional
options can be accounted for: (i) horizontal panels (on
roof and bonnet) with one tracking axis, in order to
maximize the energy captured during parking mode;
(ii) panels located also on car sides and rear at almost
vertical positions. The maximum panel area can be
estimated as function of car dimensions and shape, by
means of a simple geometrical model. An analysis of
the effect of panel position at different latitudes has
been presented recently by the authors [11].
The energy from PV panels can be obtained summing
up the contribution from parking (p) and driving (d)
periods. While in the former case it is reasonable to
assume that the PV array has an unobstructed view of
the sky, this hypothesis could fail in most driving
conditions. Therefore, the energy captured during
driving can be reduced by a factor β<1. In order to
estimate the fraction of daily solar energy captured
during driving hours (hd), it is assumed that the daily
solar energy is distributed over hsun hours. A factor
α<1 is then introduced to account for further
degradation due to charge and discharge processes in
the battery for energy taken during parking. The net
solar energy available for propulsion, stored during
both parking and driving modes, can therefore be
expressed as:
E s , p = η p APV esun
hsun − hd
α
hsun
(2)
E s , d = η p APV esun
hd
β
hsun
(3)
Where esun is the average daily energy captured by
solar panels in horizontal position. Hereinafter, esun is
assumed equal to 4.3 kWh/day, which corresponds
roughly to the year average at a latitude of 30°. The
energy required to drive the vehicle during the day Ed
(kWh) can be computed as function of the average
positive power Pav (kW) and the driving hours hd:
Ed = ∫ P(t ) dt = hd ⋅ Pav
(4)
hd
Figure 1 - Scheme of the series hybrid solar
vehicle.
2.1 Solar energy for vehicle propulsion
In order to estimate the net solar energy captured by
PV panels in real conditions (i.e. considering clouds,
The instantaneous power (P(t)) is estimated for
assigned vehicle data and driving cycle, integrating a
longitudinal vehicle model based on a dynamic
vehicle simulator developed by the authors [15]. The
model allows estimating the drive torque and power
requested by the vehicle to accomplish the imposed
driving cycle, depending on transmission ratio and
36
efficiency, aerodynamic losses (CX, cross section)
and weight.
Thus, the required driving energy Ed depends on
vehicle weight and aerodynamic parameters, which in
turn depend on the sizing of the propulsion system
components and on vehicle dimensions, related to
solar panel area.
Battery, electric motor and generator have been
simulated by the ADVISOR model [16].
2.2 Vehicle weight
The parametric weight model of the HSV can be
obtained adding the weight of the specific
components (PV panels, battery pack, ICE,
Generator, Electric Motor, Inverter) to the weight of
the Conventional Vehicle (CV) equipped with ICE
(WCV) and by subtracting the contribution of the
components not present in the HSV (i.e. ICE,
gearbox, clutch).
Thus, the body (i.e. Wbody,HSV) and whole (WHSV) mass
of the HSV can be expressed as:
Wbody , HSV = WCV − PICE , CV ⋅ (wICE + wgear ) (5)
W HSV = Wbody , HSV +
+ PEG ⋅
w ICE
η EG
+ PEG ⋅ w EG + PEM w EM
Considering the lay-out described in Figure 1, the
required nominal battery power is:
(7)
Therefore the number of battery modules is evaluated
as:
NB =
PEM − PEG
PB ,u
(8)
where PB,u is the nominal power of a single battery
module. The power of the electric machine (PEM) is
computed imposing that the HSV Power to Weight
ratio (PtWHSV) equals the Power to Weight ratio of the
reference vehicle:
PtWHSV =
PICE ,CC
Wbody ,CC
PEM = PtWHSV ⋅ WHSV
(9)
(10)
2.3 Cost estimation
In order to assess the benefits provided by HSV with
respect to conventional vehicles, both the additional
costs, due to hybridization and solar panels, and
achievable fuel savings are to be estimated. The
additional cost CHSV can be expressed starting from
the estimated unit cost of each component:
cICE
η EG
+ PEG ⋅ cEG + APV cPV
(11)
+ Pmax cEM + C B N B − PICE ,CV ⋅ cICE
The last term accounts for cost reduction for Internal
Combustion Engine in HSV (where it is assumed PICE
= PEG/ηEG) with respect to conventional vehicle
(where PICE = PICE,CV). The daily saving with respect
to conventional vehicle can be computed starting
from fuel saving and fuel unit cost:
(
)
S = m f ,CC − m f ,HSV ⋅ c f
(12)
The pay-back, in terms of years necessary to restore
the additional costs with respect to the conventional
vehicle, can be therefore estimated as:
PB =
C HSV C HSV
=
nD S
300S
(13)
For further details about the meaning and the values
of some of the parameters introduced in eqs. 2
through 13, the reader is addressed to previous work
[11] [18].
3.
(6)
+ APV w PV + w B ,u ⋅ N B
PB = PEM − PEG
C HSV = PEG ⋅
ENGINE CONTROL FOR HSV
In most electric hybrid vehicles, a charge sustaining
strategy is adopted: at the end of a driving path, the
battery state of charge should remain unchanged.
With a solar hybrid vehicle, a different strategy
should be adopted as battery is charged during
parking hours as well. In this case, a different goal
can be pursued, namely restoring the initial state of
charge within the end of the day rather than after a
single driving path [12] [18]. For this end, the internal
combustion engine should be operated whenever
possible at maximum efficiency, corresponding to
power Popt. If the energy required to restore battery
charge is lower than the amount corresponding to a
continuous use at Popt throughout the driving time hd
(case B), an intermittent operation can be adopted
(cases A1-A2). In case that more energy is required,
the internal combustion engine is operated at constant
power between Popt and Pmax (case C). The different
operating modes can be described by the variable φ,
ranging from 0 to φmax = Pmax / Popt, as described in
Tab. I.
The optimal φ value is found by imposing that the
energy provided by ICE and PV panels during the
driving hours guarantees a charge sustaining strategy
over the whole day. This condition is expressed as:
∆SOCday (φ ) = ∫0 dSOC (φ )dt =
24 h
= ∆SOCd (φ ) + ∆SOC p = 0
(14)
Assuming that the driving schedule, of duration hd
hours, is composed of a sequence of ECE-EUDC
cycles, eq. (14) can be satisfied by iteratively solving,
over one cycle, the following nonlinear equation:
37
∆SOC ECE (φ ) =
− ∆SOC p
(15)
N cycles
Tab. I – Engine control strategies for HSV.
A1
φ <1
PICE = 0
0 < t < φ hd
A2
φ <1
PICE = Popt
φ hd < t < hd
B
φ =1
PICE = Popt
0 < t < hd
C
1 < φ < φmax
PICE = φPopt
0 < t < hd
exclusively supplied by the batteries (red line) that
experience a decrease of State of Charge (SOC), as
shown in Figure 5. This trend is inverted around 650 s
when the EG is switched on and powers both vehicle
and battery in order to meet the charge sustaining
strategy (see Figure 5). Of course, due to the
constraint introduced by eq. (15), the final SOC
differs from the initial value by a fraction of the
amount of energy provided by the PV panels during
parking hours.
where Ncycles is evaluated as function of each module
duration Tcycle (h):
N cycles =
hd
Tcycle
(16)
The results obtained in previous papers show that
relevant fuel savings, up to 45% for intermittent use
in urban driving, can be obtained by a proper
optimization of vehicle and powertrain components,
and that this kind of vehicle is not far from economic
feasibility, considering actual and expected trends in
oil price and vehicle components (solar panels,
batteries) [11][12][18].
4.
RESULTS
The simulation results presented in this section are
related to a prototype of solar hybrid vehicle with
series structures that is being developed at the
University of Salerno, within the EU supported
Leonardo Program I05/B/P/PP-154181 “Energy
Conversion Systems and Their Environmental
Impact” (www.dimec.unisa.it/leonardo).
The prototype is being developed starting from the
Electric Vehicle Piaggio-Micro-Vett Porter (shown in
Figure 2), whose main features concerning vehicle
and electric motor are summarized in Tab. II. With
the addition of solar panels and electric generator,
whose details also are given in Tab. II, the HSV is
obtained.
Figure 3 shows the driving cycle selected for the
simulation tests, which is derived from the European
Driving Cycle (ECE) and is representative of a
generic urban route.
The power contributions of electric generator (EG),
solar panels (PV) and battery (B) to drive the HSV
along the imposed route is shown in Figure 4, while
Figure 5 shows a comparison of SOC history between
HSV, pure Electric Vehicle (EV) and solar electric
vehicle (SEV), the latter been derived from the EV by
the addition of solar panels to the base vehicle.
Figure 4 evidences that since the variable φ is lower
than 1, according to the imposed control strategy
(Tab. I), the EG can be operated in an intermittent
way at constant load and speed, corresponding to its
highest efficiency (black line). Thus, in the former
part of the transient, the drive power (blue line) is
Figure 2 – The Micro-Vett Porter Electric Vehicle.
Tab. II – Electric Vehicle Technical Data.
Vehicle
(EV, SEV, HEV)
Length
Width
Height
Weight
Drive ratio
CX
Electric Motor
(EV, SEV, HSV)
Max speed
Continuous Power
Peak Power
Batteries
(EV, SEV, HSV)
Mass
Capacity
Photovoltaic Panels
(SEV, HSV)
Surface
Weight
Efficiency
Electric Generator
(HSV)
Max Power
Max Efficiency
Weight
Piaggio Micro-Vett Porter
3.370 m
1.395 m
1.870 m
1620 kg
1:4.875
0.4
BRUSA MV 200 – 84 V
52 Km/h
9 KW
15 KW
14 Modules Pb-Gel
226 Kg
130 Ah
Polycrystalline
1.44 m2
60 kg
0.13
Lombardini (500 cc engine,
3 phase induction machine)
15 kW
25 % @ 9 KW
100 kg
It is worth noting that the occurrence of an initial
discharging process, followed by a recharging one,
38
results in benefits for batteries losses since the lower
is the SOC, the more efficient is the recharging phase.
On the other hand, the SOC trajectories simulated for
EV and SEV (see Figure 5) both show a decreasing
trend. This is expected in EV because battery
recharge is performed by connection to the grid. For
the SEV the same recharging strategy must be
adopted since the amount of energy provided by the
PV panels mounted on the roof is relatively small.
simulation this is taken into account by shifting up the
initial SOC by a fraction of the energy stored during
parking hours (Figure 5). This leads to a final SOC
higher than the EV, which in turn results in increasing
vehicle autonomy by about 30 % (125 against 95 km
per battery cycle). Such a significant improvement
indicates the use of PV panels as range extender of
electric vehicles as a high potential application of
solar energy in the transportation field.
Reference vehicle speed [km/h]
2.4 Comparison with conventional vehicle equipped
with ICE
35
30
25
20
15
10
5
0
0
200
400
Time [s]
600
800
Figure 3 – Selected driving cycle.
HSV power KW
10
5
0
-5
-10
0
drive
gen
sun
batt
200
400
Time [s]
600
800
Figure 4 – Power contributions simulated for the
HSV over the selected driving cycle.
−
0.755
0.75
rpm [rev/min]
3500
3000
HSV
CV
2500
SOC [/]
0.76
The achievement of a charge sustaining strategy with
the HSV suggests the need for assessing fuel
economy improvements and economical aspects
related to the solar hybridization of conventional cars.
For this purpose, in this section a comparative
analysis is performed on the HSV presented before
and the ICE-powered Porter commercialized by
Piaggio (equipped with an S.I. engine 1.2 liters with a
max power of 48 KW; overall vehicle weight is 1550
kg).
Figure 6 shows a comparison of engine speeds in case
of hybrid and conventional vehicle, evidencing that in
the latter case (solid line), the engine always operates
in transient conditions and partial loads, with higher
values of specific fuel consumption and poor
efficiency, as evidenced in Figure 7. On the other
hand, as already shown in Figure 4, the hybrid vehicle
ICE generator works only in the latter part of the
transient, operating at constant speed (i.e. 3000 rpm)
corresponding to its maximum efficiency (i.e. 32%).
The different behaviour of engine operation results in
a significant improvement in fuel economy in case of
HSV, as indicated in Tab. III. For the selected driving
cycle, the amount of fuel needed by the hybrid
vehicle is 50 % less than that required by the ICEpowered vehicle.
∆SOC p
2000
N cycles
1500
1000
0.745
500
0.74
0.735
0.73
0.725
0
0
0
EV
SEV
HSV
200
400
Time [s]
600
800
Figure 5 – Battery state of charge trajectories for
the three simulated vehicles.
Nevertheless, battery recharge in SEV is postponed
with respect to EV due to the amount of energy
provided by PV during parking hours. In the SEV
200
400
Time [s]
600
800
Figure 6 – Comparison between HSV and CV
ICE’s rpm over the imposed driving cycle.
Tab. III also gives the pay-back in terms of years
necessary to restore the additional costs of the HSV
with respect to the conventional vehicle. With the
actual costs of fuel and PV the pay-back equals 7.7
years, whereas assuming to double the fuel price and
to reduce by 75 % the PV cost, the pay-back reduces
considerably, down to 2.4 years.
39
It is worth mentioning here that other strategies are
possible for HSV control, such as letting the ICE run
during parking mode too: in that case, the engine can
be used to restore battery charge by working always
at its maximum efficiency.
ICE efficiency [/]
0.35
0.3
HSV
CV
0.25
0.2
0.15
6.
0.1
0.05
0
0
The simulation performed along a urban driving cycle
has shown that the hybrid vehicle can accomplish a
charge sustaining strategy with intermittent use of
ICE-generator at maximum efficiency. Comparison
with conventional vehicle powered with ICE has
evidenced a significant improvement in terms of fuel
economy, close to 50 % in the selected driving cycle.
Furthermore, the pay-back to restore the additional
costs of hybrid components is 7.7 years with actual
costs of fuel and components while it decreases to 2.4
years assuming to double the fuel price and to reduce
the panels cost by 75%, in accordance with the actual
and expected trends in costs and prices.
200
400
Time [s]
600
800
Figure 7 – Comparison between CV and HSV
ICE’s Efficiency over the imposed driving cycle.
Tab. III – Energetic and economical aspects
associated with solar hybridization.
Fuel consumption
(g per cycle)
Weight (kg)
Pay-back
(years, with actual costs)
Pay-back
(years, considering future
cost trends)
Driving hours per day
Insolation (KWh/m2/day)
5.
HSV
CV
79
158
1780
1550
7.7
/
2.4
/
2
2
4.3017
CONCLUSION
A dynamic model for the simulation of a solar hybrid
prototype based on the electrical vehicle Piaggio
Micro-Vett Porter has been presented. The model
describes the energy flows between photovoltaic
panels, internal combustion engine (ICE), electric
generator, electric motor and batteries, considering
vehicle longitudinal dynamics and the effect of
control strategies. Vehicle weight is computed
starting from the electrical vehicle weight,
considering the effects of additional components
(ICE-generator, photovoltaic panels, etc.). The model
also predicts the additional costs with respect to
conventional vehicle and the pay-back.
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7.
cICE: ICE cost to power ratio (Eur/kW)
cEG: Electric generator cost to power ratio (Eur/kW)
cPV: PV specific cost (Eur/m2)
cEM: Electric motor cost to power ratio (Eur/kW)
cB: Single battery module cost (Eur)
cf: fuel unit cost (Eur/kg)
nD: number of days per year in the pay-back analysis
∆SOCday: state of charge variation over the whole day
∆SOCd: state of charge variation in driving phases
∆SOCp: state of charge variation in parking phases
CONTACT
Ivan Arsie ([email protected])
Raffaele Di Martino ([email protected])
Gianfranco Rizzo ([email protected])
Marco Sorrentino ([email protected])
Tel. +39 089 964080 – Fax +39 089 964037
Web www.dimec.unisa.it
8.
DEFINITIONS, ACRONYMS,
ABBREVIATIONS
Es,p: Solar energy stored during parking hours (kWh)
Es,d: Solar energy stored during driving hours (kWh)
ηp: PV efficiency
ΑPV: PV surface (m2)
wICE: ICE weight to power ratio (kg/kW)
wgear: Gearbox weight to power ratio (kg/kW)
wEM: Electric motor weight to power ratio (kg/kW)
wEG: Electric generator weight to power ratio (kg/kW)
wB,u: Single battery module weight (kg/kW)
wPV: PV specific weight (kg/m2)
PEG: Electric generator power for HSV
ηEG: Electric generator efficiency
41
42
A model of mismatched photovoltaic fields for simulating hybrid solar vehicles
G.Petrone*, G.Spagnuolo*, M.Vitelli°
*DIIIE, Università di Salerno
Via Ponte Don Melillo, Fisciano (SA), Italy
[email protected], [email protected]
°DII, Seconda Università di Napoli
Real Casa dell’Annunziata, Aversa (CE), Italy
[email protected]
Abstract – A numerical model of photovoltaic fields that allows
simulating both uniform and mismatched operating conditions
is introduced in this paper. It allows the simulation of a
photovoltaic generator whose subsections, e.g. cells, groups of
cells, panels or group of panels, work under different solar
irradiation values and/or different temperature. Furthermore,
different nominal characteristics, rated power, production
technology, shape and area can be accounted for any
subsections of the photovoltaic generator. The proposed model
is reliable and results into a non linear system of equations that
requires a moderate computational burdensome, both in terms
of memory use and processor speed. Numeric simulations
confirm the usefulness of the proposed approach in automotive
applications, especially in solar hybrid vehicles, in order to
design a proper electronic controller ensuring the extraction of
the maximum power from the photovoltaic generator.
I. INTRODUCTION
Renewable energy sources are gaining more and more
interest in recent years due to the exploitation of oilfields and
to political crises in some strategic areas of the world.
Among them, photovoltaic (PV) sources have found new
applications, e.g. solar hybrid vehicles. They work with
greatly varying solar irradiation levels due to the movement
and, especially if the solar cells are not placed only on the
roof, different subsections of the PV generator may receive
different sun irradiance levels.
In any case, it is mandatory to match the PV source with the
load/battery in order to draw the maximum power at the
current solar irradiance level. To this regard, a switching dcdc converter controlled by means of a Maximum Power
Point Tracking (MPPT) strategy is suitable to ensure the
source-load matching by properly changing the operating
voltage at the PV array terminals in function of the actual
weather conditions. Any efficient MPPT technique must be
able to detect the voltage value corresponding to the
maximum power that can be delivered by the PV source.
In literature, many MPPT strategies have been proposed, the
greatest part of them being derived by the basic Perturb and
Observe (P&O) and Incremental Conductance (IC)
approaches. Both P&O and IC strategies, if properly
designed, correctly work in presence of a uniform irradiance
of the PV array, since they are able, although by means of
different processes, to detect the unique peak of the power
vs. voltage characteristic of the PV array. Unfortunately, in
automotive applications, the PV field does not receive a
uniform irradiation and/or not all its parts (panels as well as
single cells) work at the same temperature, so that
mismatches among different parts of the array may arise.
Such a situation has been evidenced in literature and the
detrimental effect due to a panel of a PV array working under
an irradiation level or at a temperature, which is sensibly
different than that characterising the other panels has been
experimentally investigated.
Mismatching conditions are more likely to occur in
automotive applications than in stationary ones. For example,
parts of the array may be shaded by other parts of the vehicle
when the sun is at low angle and, moreover, unpredictable
shading takes place when the vehicle passes under the
shadows of buildings, trees, advertising panels. Even in
automotive applications characterized by a relatively small
duty cycle in the use of the vehicle, mismatching may play a
strong role on battery charging during the long parking time.
In such cases the shadows produced by objects surroundings
the car can give rise to a marked waste of available solar
energy.
To relieve the power drop caused by a mismatch, a bypass
diode is used in anti-parallel with each PV basic unit, e.g. a
panel. A blocking diode is placed in series with each totem
of PV basic units connected in series. This precaution
increases the plant cost, but avoids that a basic PV unit or a
series of them absorbs the current produced by others.
Whenever a mismatch occurs, both P&O and IC based
MPPT techniques have a high probability to fail the MPPT
goal. Indeed, the power vs. voltage characteristic of a PV
field under a uniform solar irradiation exhibits a unique
maximum point that is easily tracked by standard MPPT
techniques. Unfortunately, mismatches deeply affect the
shape of the PV characteristic, which may exhibit more than
one peak, with one absolute maximum point and one or more
relative points of maximum power. In this case, standard
MPPT techniques are likely deceived and consequently track
a point where dP/dv=0, but that is not the maximum power
point.
In order to design a MPPT strategy able to perform a
“global” tracking of the true PV array voltage associated to
the maximum power, without being trapped in local maxima,
it is of fundamental importance the realization of an accurate
numerical model of the PV field. It must be able to simulate
the PV basic units mismatching in a reliable and fast manner,
43
also accounting for the behaviour of real bypass and blocking
diodes.
In this paper a model with these characteristics is introduced:
features and drawbacks are illustrated by means of
simulations carried out in Matlab and PSIM environments.
The paper is organized as follows: Section II shows the
details of the proposed model and puts in evidence its
features. Section III shows the results of some application
examples and Section IV is devoted to conclusions and hints
for a future work.
II. THE MODEL
In fig.1 the usual circuit model of a photovoltaic (PV) panel
is shown.
Fig.1 Circuit model of a PV panel including the bypass diode Db.
Such a model recurs in literature very often (e.g. in []). It
includes the light induced current generator Iph and series
and shunt resistances Rs and Rh respectively; Db is the
bypass diode. We suppose, without loss of generality, that
one bypass diode is placed in antiparallel with the whole
panel.
The relation between the PV generator current I and voltage
V is evaluated by solving the following system of non linear
equations:
 VVd

I d = Isat ,d  e t ,d − 1




(1)
 − VV

I db = I sat ,db  e t ,db − 1




(2)
I = I db + I ph − I d − I h
(3)
Vd = V + R s ⋅ I s = V + R s ⋅ (I − I db )
(4)
Ih =
Vd V + R s ⋅ (I − I db )
=
Rh
Rh
(5)
bypass diode Db (2). In (1) Vt,d=ηd⋅VT,d and in (2)
Vt,db=ηdb⋅VT,db, Vt,d and Vt,db are expressed as the product of
the diode ideality factor and the thermal voltage. The latter,
as well as the two saturation currents Isat,d and Isat,db, depend
on temperature T only, whilst the light induced current Iph
depends on the irradiance level S and on the array
temperature T [1].
The system of equations (1)-(5) clearly shows that the PV
array current I is a nonlinear and implicit function of the PV
array voltage V, of the irradiance level S and of the
temperature T. Nevertheless, such a non linear system can be
symbolically solved in one of the symbolic calculation
environments, such as Matlab and Mathematica, actually
available. In this way, a non linear relationship between the
current I and the voltage V at the basic PV unit terminals can
be obtained. For space reasons such relationship is reported
in (6), at the end of the paper. It makes use of the LambertW
function of the term θ whose value depends on the terminal
voltage V and is reported in (7).
It is well known [3] that the LambertW function of the
variable θ, herein indicated as LambertW(θ), is a non linear
function of θ and it is the inverse function of:
f (θ) = θ ⋅ e θ
(8)
Note that the use of the LambertW function allows the
apparently explicit calculation of the array current as a non
linear function of the terminal voltage. The value of the
Lambert function, for an assigned value of the independent
variable θ, is efficiently provided in simulation environments
such as Matlab and Mathematica.
Expression (6), together with well known LambertW
function properties, allow to calculate the first derivative of
the panel’s current with respect to the terminal voltage, again
in apparently explicit form. In (9) it has been reported the
property expressing the derivative of the LambertW(θ)
function with respect to θ, and in (10) the expression of the
derivative of I with respect to V at the panel’s terminals is
given (see the end of the paper). In this way, the differential
conductance of the panel is explicitly expressed as function
of the panel’s voltage V only, by means of a non linear
function.
Thus, in this way, both the PV current and its derivative with
respect to the PV voltage have been expressed in closed form
as functions of the sole voltage.
This greatly helps in formalizing the non linear algebraic
system that describes a PV field composed by an arbitrary
number of panels ,which can be connected both in series and
in parallel.
In order to explain this concept, let us refer to a string of PV
panels connected in series. Fig.2 shows the string of N
series-connected panels and the blocking diode that avoids
current backflows.
It has been obtained by using Kirchhoff voltage and current
laws (3) and (4), linear characteristic equations for shunt and
series resistors (4) and (5), and non linear equations for the
diode D included in the model of the panel (1), and for the
44
to simplify the structure of the Jacobian matrix that, as it is
well known, needs to be inverted when using Newton
Raphson iterative methods. The Jacobian matrix structure is
reported in (12) which puts in evidence that it is sparse and
with a pattern which is characteristic of doubly bordered and
diagonal square matrices [2]. Moreover, the first row is
composed by (N+1) constants, while all the other rows
require the evaluation of dI1/dV1 and the calculation of just
another derivative. As a whole, the evaluation of the system
(11) requires N times the use of the equation (6) and one
time the (1); the calculation of the Jacobian matrix requires
N evaluations of (10) and one evaluation of (13).
Such features are useful both in terms of memory
requirements during the simulation and of computation time.
In Section III the features of the method are described by
means of a numeric example.
III. SIMULATION RESULTS
Fig.2 String of N PV panels connected in series and including the blocking
diode.
In order to model this series, it is possible to build up a
system of (N+1) equations in the same number of unknowns
{V1,V2,...,Vk,...,VN-1,VN,Vdiode}. It is enough to write one
Kirchhoff voltage law and N Kirchhoff current laws. The
topological constraints are formalized in (11) at the end of
the paper; they can be matched with the N equations of the
panels, expressed as in (6) in terms of Ik=Ik(Vk), k=1,2,...,N,
and with the characteristic equation of the blocking diode
expressed in the form (1), and taking into account the
dependency of such a characteristic equation from the
physical parameters of the real diode used. The non linear
system (11) includes N non linear equations and one linear
equation, the first one, in which the terminal voltage V, that
is assumed to be a known term, appears . Each non linear
equation includes only two of the (N+1) unknowns, and the
first one is always V1. This choice has been made to simplify
the expression of the Jacobian matrix needed to solve the non
linear system by means of, for example, the Newton Raphson
method.
Thanks to (10) it is possible to obtain each term of the
Jacobian matrix J as a function of the unknowns. Moreover,
the structure of the system has been properly chosen in order
Simulations have been conducted by considering Kyocera
KC120 PV panels, characterized by 36 series connected
cells, each one of area 0.0225 m2, Rs=0.006 Ω, Rh=104 Ω.
A string with two PV panels connected in series, and with
the blocking diode has been simulated. In this case the order
of the system is 3. The panels have been considered identical
in terms of manufacturing parameters and working
temperature (T=320K).
On the other hand, their irradiation level has been considered
very different, namely S=1000 W/m2 for the first panel and
S=100 W/m2 for the second one.
The whole simulation has been conducted in Matlab
environment; it required 45.3 s (on an Intel Centrino 2.0 GHz
platform) in order to calculate 100 linearly spaced points of
the power-voltage characteristic of the PV array. The
samples of the current in the series and of the voltage
distribution over the three devices have been also stored
during simulation. The curves are reported in figs.3 and 4.
They put in evidence the effect of the panel that receives the
lower irradiance level in terms of string current drop at high
voltage values.
It is worth noting that the curve of fig.3, obtained under
mismatching conditions of the PV string, exhibits two
maxima at two different voltage levels, with that one
occurring at about 44 V being characterised by a consistently
lower value of the power with respect to the other one placed
at about 18 V. This occurrence can compromise the energy
conversion operated by the switching converter connected at
the string terminals and responsible for the MPPT. This can
be understood by comparing plots of fig.3, representing the
mismatched string, with that one of fig.5, obtained by
imposing a unique irradiance level S=1000 W/m2 for both
the panels. If the MPPT controller acts so that the string
works at about 40 V under uniform irradiance, it ensures that
the maximum power – about 260 W – is converted. If a
sudden irradiance drop (from S=1000 W/m2 to S=100 W/m2)
occurs on one panel and the MPPT algorithm is not able to
perform a “global search” of the new maximum power point,
the relative maximum placed at about 40 V (see fig.3) is the
45
likely new operating point. This means that the MPPT
controller is not able to track the real maximum power point
and that about 90 W (the difference between the maximum
power of the best operating point at about 18 V and the
power of an operating point placed at about 44 V) are wasted
due to MPPT algorithm limit.
Such considerations have been verified by means of a PSIM
simulation of the PV field controlled by means of boost
switching converter that performs the MPPT function and
matches the PV field with a 48V battery (see fig.6). The
layout puts in evidence two dynamic link libraries that
implement the PV field (left) and the P&O based MPPT
controller (bottom). It has been simulated a sun irradiance
drop involving one of the two panels of the array: the steep
transition between the characteristic of fig.5 and that one of
fig.3 occurs at t=0.03s (see fig.7). The P&O controller tracks
the lower maximum because the voltage at which it occurs
(see fig.8) is close to the voltage corresponding to the unique
maximum of the characteristic depicted in fig.5. Fig.7 also
put in evidence the three-points behaviour at both steady
states: this characterizes the hill climbing of the two
maximum power points tracked at the two different
conditions. This result is confirmed by the boost converter
duty cycle variation shown in fig.9.
In conclusion, the model illustrated in this paper might be of
great help in developing an improved MPPT algorithm that is
robust with respect to this kind of conditions, since it allows
to test the MPPT performances with respect to different
shapes of the power-voltage characteristic of the PV
generator.
IV. CONCLUSIONS AND FUTURE WORK
In this paper a non linear model of mismatched photovoltaic
fields is introduced. It allows to simulate heterogeneous
arrays, with subsections (cells, groups of cells, panels or
groups of panels) characterized by different irradiation
levels, temperatures, semiconductor materials, areas,
operating parameters and so on. The model also allows to
take into account manufacturing tolerances and drifts
ascribable to aging effects.
Further work is in progress in order to use the simulator in
order to develop and test a maximum power point tracking
strategy able to ensure an efficient power conversion even if
the photovoltaic field works in mismatched conditions.
REFERENCES
[1]
S. Liu, R. A. Dougal: ”Dynamic multiphysics model
for solar array”, IEEE Trans. On Energy Conversion, Vol.
17, No. 2, June 2002, pp. 285-294.
[2]
William H. Press, Numerical Recipes in C, The Art
of Scientific Computing, Second Edition, Cambridge
University Press, 2002.
[3]
http://mathworld.wolfram.com/LambertWFunction.html
120
W
100
80
60
40
20
0
0
5
10 15 20 25 30 35 40 45 50
V
Fig 3. Power [W] vs. voltage [V] characteristic of the simulated mismatched
PV field.
A
7
6
5
4
3
2
1
0
-2 0 2 4 6 8 10 12 14 16 18 20 22 24 26
V
Fig.4 Current [A] vs. voltage [V] characteristic of the three devices in the
simulated string. Continuous line = blocking diode curve, dashed line =
curve of the panel with irradiation S=100 W/m2, dash-dotted line = curve of
the panel with irradiation S=1000 W/m2.
300
W
250
200
150
100
50
0
0
5
10 15 20 25 30 35 40 45 50
V
Fig 5. Power vs. voltage characteristic of the simulated matched PV field.
46
Figure 7. PV field output power.
Figure 9. Duty cycle during transient.
Figure 8. PV field voltage.
Figure 6. PSIM layout for the simulation of the MPPT controller.
[R ⋅ (I
I=
h
ph
+ Isat ,d ) − V
(R h + R s )
]+ I
 − VV

 t ,db − 1 − Vt ,d ⋅ LambertW(θ )
sat ,db ⋅ e

 Rs


(6)
47
θ=
(R h // R s ) ⋅ Isat ,d ⋅ e
(
)
 R h ⋅R s ⋅ Iph + Isat ,d + R h ⋅V 


Vt ,d ⋅( R h + R s )


(7)
Vt ,d
1
LambertW(θ )
d
=
LambertW(θ) =
LambertW ( θ )
[1 + LambertW(θ)]⋅ e
[1 + LambertW(θ)]⋅ θ
dθ
(9)
V
−
I
Rh
dI
1
V
=−
− sat ,db ⋅ e t ,db −
⋅ LambertW(θ)
(R h + R s ) Vt ,db
R s ⋅ (R h + R s )
dV
(10)
V1 + V2 + K + Vk + K + VN −1 + VN + Vdiode − V = 0

I1 (V1 ) − I 2 (V2 ) = 0


I1 (V1 ) − I 3 (V3 ) = 0

K

I1 (V1 ) − I k (Vk ) = 0


K


I1 (V1 ) − I N −1 (VN −1 ) = 0

I1 (V1 ) − I N (VN ) = 0


I1 (V1 ) − I diode (Vdiode ) = 0
(11)
 1
 ∂I1

 ∂V1
 ∂I1
 ∂V
 1
 M
 ∂I1
J =  ∂V1

 M
 ∂I1
 ∂V1
 ∂I
 1
 ∂V1
 ∂I1

 ∂V1
1
∂I 2
−
∂V2
1
−
...
1
...
1
1
∂I 3
∂V3
0
O
−
∂I k
∂Vk
O
0
−
∂I N −1
∂VN −1
−
∂I N
∂VN

















∂I diode 
−

∂Vdiode 
1
(12)
Vdiode
I
∂I diode
V
= − sat ,diode ⋅ e t ,diode
∂Vdiode
Vt ,diode
(13)
48
THE PROFITABLENESS OF HYBRID SOLAR VEHICLES (HSV)
Ion V. Ion, Ion C. Ionita, Daniela Negoita, Spiru Paraschiv
„Lower Danube” University of Galati – Romania
Thermodynamics and Heat Engines Department
Abstract. Being conscious that nowadays in the starting stage the competition between
classical car, powered by combustion engine and the HSV can live and develop only
with an additional financial support, the authors focused their attention on
mathematical expression of this support. They found the factors affecting the value of
this support and the conditions making HSV profitable. The analysis is based on the
compared cost to quality analysis, developed in the last 10 years.
Keywords: Compared cost-to-quality analysis
List of the used symbols
Latin letters:
(C )
CPICE -the total cost of a classical car, powered by
transport service, [€ / km HSV]
internal combustion engine, [€ / ICE car]
C
C
HSV
-the total
P
ICE
-the cost
S
cost of a HSV, [€ / HSV]
of the transport service in the case
ICE, [€/ km ICE]
C
HSV
S
-the cost of the transport service with HSV,
[€/ km HSV]
( CSICE ) -the investment cost of the ICE transport
I
service, [€ / km ICE]
(C )
ICE
S
C
-the consumption cost of the ICE transport
service, [€ / km ICE]
(C )
ICE
S
OM
-the operation-maintenance cost of the
ICE transport service, [€ / km ICE]
(C )
HSV
S
I
-the investment cost of the HSV transport
service, [€ / km HSV]
(C )
HSV
S
C
-the consumption cost of the HSV
transport service, [€ / km HSV]
HSV
S
OM
(C )
(C )
-the operation-maintenance cost of the HSV
ICE
P
I
-the investment cost of the ICE car, [€/car ICE]
ICE
P
C
-the consumption cost of the ICE car, [€/car
ICE]
(C )
ICE
P
OM
-the operation-maintenance cost of the ICE car,
[€/car ICE]
(C )
(C )
(C )
HSV
P
I
HSV
P
C
HSV
P
OM
-the investment cost of the HSV, [€/ HSV]
-the consumption cost of the HSV, [€ / HSV]
-the operation-maintenance cost of the HSV,
[€/ HSV]
HSV
sOM
-the operation-maintenance ratio of HSV car service,
(eq. 8);
ICE
sOM
-the operation-maintenance ratio of ICE car service,
(eq. 7)
f
ICE
-the unitary fuel consumption of ICE, [l/100km ICE]
-the unitary fuel cost, [€ / l fuel]
c ICE
f
49
k HSV
-the fuel reduction ratio of HSV, (eq. 10);
f
ICE
pOM
-the operation-maintenance ratio of ICE car
product, (eq. 11);
HSV
-the operation-maintenance ratio of HSV
pOM
product, (eq. 12);
100 km
S HSV
- the state unitary subsidy of HSV program,
[€/ 100 km]
Greek letters:
τ ICE -the
total life cycle of an ICE car, [km ICE /
As the compared cost- to- quality analysis needs, when
starting the evaluation it is necessary to choose an
adequate cost-to quality ratio. There are two possible
variants:
a. The production variant, where we have to calculate in
terms of Euro/car;
b. The service variant, accountable in terms of Euro/100
covered kilometers.
The authors considered the second variant option (b) to be
more appropriate because it expresses better the service
the car does, taking into consideration that the car is used
more or less during its life cycle span.
ICE car]
τ HSV -the total life cycle of a HSV, [km HSV / HSV
car]
Subscripts:
I-investment
C- consumption
P – product
S – service
OM - operation-maintenance
f – fuel
HSV – hybrid solar vehicle
Superscripts:
ICE – internal combustion engine
HSV – hybrid solar vehicle
1.
INTRODUCTION
The purpose of this paper is to analyze
mathematically the conditions when HSV could be
profitable. Starting on this way, we know that
presently the classical cars are cheaper than HSV.
This reality can be changed not so late in the future
because of some tendencies we see:
1) The classical cars pollution is increasing
permanently, due to raising number of vehicles, in
spite of their lowering individual pollution;
2) The solar cell panels are permanently perfectible
and their efficacy is continuously increasing while
their cost is lower and lower;
3) The unitary cost of organic fuel is presently
increasing exponentially. Being conscious that
nowadays in the starting stage the competition
between classical car, powered by combustion
engine and the HSV can live and develop only with
an additional financial support, the authors focused
their attention on mathematical expression of this
support. They found the factors affecting the value of
this support and the conditions making HSV
profitable.
The analysis is based on the compared cost-toquality analysis, developed in the last 10 years [6 –
18]. To obtain the expression of the necessary
subsidy, the authors considered two evident different
cases:
a) the case of a classical car, powered by
combustion engine (symbols with superscript ICE);
b) the case of a HSV powered both by combustion
engine and by photo-voltaic (PV) panels (symbols
with superscript HSV).
3.
THE QUALITY PARAMETERS OF THE
CONSIDERED CARS
For each car, classical or hybrid one, there are 31 different
quality parameters: QP 01–Accessibility; QP 02–
Adaptability; QP 03–Availability; QP 04–Cleanliness;
QP 05–Credibility; QP 06–Durability; QP 07–
Environmental Protection; QP 08–Fuel Consumption;
QP 09–Functional Engine Parameters; QP 10–
Inflammability; QP 11–Lighting Parameters; QP 12–Look;
QP 13–Maintainability; QP 14–Parking Capacity; QP 15–
Productivity; QP 16–Promptitude; QP 17–Protection;
QP 18-PV Panel Parameters; QP 19-Reliability; QP 20–
Safety; QP 21–Size; QP 22–Style; QP 23–Susceptibility;
QP 24–Pneumatic Tires Parameters; QP 25–Toxicity;
QP 26–Transportability; QP 27–Transport Capacity;
QP 28–Vulnerability; QP 29–Watching capacity;
QP 30–Weight; QP 31–Workings.
When considering the transport service made by these
cars, we have at least another 15 parameters: QS 01–
Accessibility; QS 02–Accuracy; QS 03–Comfort; QS 04–
Competence; QS 05–Confidence; QS 06–Credibility; QS
07–Efficacy; QS 08–Efficiency; QS 09–Feedback speed;
QS 10–Formalism; QS 11–Honesty; QS 12–Proficiency;
QS 13–Promptitude; QS 14–Punctuality; QS 15–Safety.
4.
THE COST EQUATION
The total cost of the purchased ICE car is:
(
C PICE = C PICE
) + (C ) + (C )
ICE
P
OM
ICE
P
C
I
[€/ICE car]
(1)
The total cost of the purchased HSV is:
CPHSV = ( CPHSV ) + ( CPHSV ) + ( CPHSV )
I
C
OM
[€/HSV car]
(2)
The total cost of the ICE car transport service is:
(
C SICE = C SICE
) + (C ) + (C )
ICE
S
C
I
ICE
S
OM
[€/km ICE]
(3)
The total cost of the HSV transport service is:
(
C SHSV = C SHSV
) + (C ) + (C )
I
HSV
S
C
HSV
S
OM
[€/km HSV] (4)
Taking into consideration that:
2.
CHOOSING THE NECESSARY COSTTO QUALITY RATIO
(C )
ICE
S
I
= C PICE / τ ICE [€/km ICE]
(5)
50
(C )
= C PHSV / τ HSV [€/km HSV]
HSV
S
I
km
(6)
S HSV
=0
(18)
(C )
ICE
= s OM
(C SICE ) I [€/km ICE]
In this case
(7)
(C )
HSV
= sOM
(C SHSV ) I [€/km HSV]
(8)
(C )
= f ICE c ICE
/ 100 [€/ km ICE]
f
ICE
S
OM
HSV
S
OM
ICE
S
C
HSV
HSV
(1 + sOM
)([ 1 + pOM
)(C pHSV )I + (C pHSV )c ]/ τ HSV =
ICE
ICE
)([ 1 + pOM
)(C pICE )I + (C pICE )c ]/ τ ICE +
= (1 + s OM
(9)
(C SHSV )C = k HSV
f ICE c ICE
/ 100 [€/ km HSV]
f
f
(10)
(C )
(11)
ICE
P
OM
(
)
C PHSV OM
ICE
= pOM
(C PICE ) I
=
HSV
pOM
(C PHSV
[€ / ICE car]
(
)
+ k HSV
−1 f
f
7.
ICE
c ICE
/ 100 [€ / km]
f
(19)
MATHEMATICAL MODELING, RESULTS
AND DISCUSSION
In the reference papers [1, 20] we found reasons to
) I [€ / HSV]
(12)
(
consider C pHSV = 1.3 C pICE ; C pHSV
)OM = (C pICE )OM ;
τ ICE = 0.8 τ HSV ; k HSV
= 0.6...0.8 ;
f
the expression of ICE transport cost becomes:
c ICE
= 1.77...3.54 €/l fuel.
f
ICE
ICE
data are argued below. From [20] we can read:
) [(1 + pOM
C SICE = (1 + s OM
) (C PICE ) I + (C PICE ) C ] / τ ICE These
+
“Hybrid vehicles do cost more than their gasoline-only
ICE ICE
+ f
c f / 100 [€/km ICE]
(13)
counterparts. On average, the price premium is $2,500 to
$3,000. Buyers, however, do have the benefit of a $2,000
while that of HSV transport cost is:
federal tax deduction for purchasing a hybrid as part of the
Internal Revenue Service's Clean Fuel Vehicle deduction.
HSV
HSV
HSV
HSV
The deduction, which was put into place as an incentive
CS
= 1 + s OM [(1 + p OM ) (C P ) I +
for consumers to consider this new technology, was
+ C PHSV C ] / τ HSV + k HSV
f ICE c ICE
/ 100
scheduled to decline gradually beginning in 2004 and
f
f
eventually be phased out. Congress has extended this
[€/km HSV]
(14)
credit, however, offering up to a $2,000 tax credit on
hybrids placed into service in 2004 and 2005. The credit
drops to $500 for 2006.
5. THE STATE SUBSIDY
Boughey received the $2,000 federal deduction as well as
a state deduction of $3,600, which was calculated based on
Knowing that presently the ICE transport is cheaper
his purchase of a hybrid as well as on the vehicle he
than that of HSV:
replaced — a 1991 Mercury Grand Marquis that was sold
for salvage.
ICE
HSV
[€ / km]
(15)
CS < CS
For comparison purposes, Laumann calculated first-year
insurance costs for all the versions of the 2004 Honda
to encourage the development of HSV research and
Civic four-door sedan including the Civic Hybrid. Costs
km
ranged from $835 to $849 for an average driver in the state
development it is necessary the subsidy S HSV
, so
of California with the Civic Hybrid falling near the middle
that:
at $844.
Like the other automakers, Toyota has also done a lot of
ICE
km
HSV
[€ / km]
(16)
C S + S HSV = C S
testing of its hybrid-specific components. Its battery packs
in particular have lasted for over 180,000 miles in testing.
From equations (13), (14) and (16) we can obtain the
"We've looked at all the things that put stress on batteries,
expression of the necessary subsidy:
such as the discharge/charge cycles and extreme
temperatures," says Dave Hermance, executive engineer
km
HSV
HSV
for environmental technology at Toyota.
S HSV
= 1 + sOM
1 + pOM
C pHSV I +
When it comes to regular maintenance, most hybrids do
ICE
ICE
+ C pHSV c / τ HSV − 1 + sOM
1 + pOM
C pICE I +
not require any maintenance on the hybrid-specific
components. One notable exception is an air filter on the
ICE
ICE
HSV
ICE ICE
+ C p c / τ + k f − 1 f c f / 100
Ford Escape Hybrid. "The air filter for the battery system
needs to be replaced every 40,000 miles," explained
[€/km]
(17)
Olson.
The gasoline engine in a hybrid requires the same
maintenance that it would if it were the only power source
6. THE PROFITABLENESS OF HSV
in the vehicle. That means oil changes every 5,000 to
10,000 miles depending on the vehicle and the driving
The relation (17) is essential when analyzing the
conditions.
profitableness of HSV. It allows us to see the
Another component that regularly needs to be replaced on
influence of the main factors, to find out how could
every vehicle is the brake pads, but with hybrids these last
km
we give up to subsidy S HSV , making the HSV
much longer thanks to regenerative braking. In
profitable. For this, we have to consider
(
(
)
)
(
(
(
)]
)]
)([
(
(
)(
)([
)
)
)(
)
51
regenerative braking, the electric motor becomes a
generator and captures the energy that would be lost
as heat through the brakes when the vehicle's brakes
are applied or when it is coasting. Once the energy is
captured, it is transformed into usable electricity,
which recharges the batteries and in turn increases
the number of miles than can be traveled per gallon
of gasoline. An added benefit is that the reduced heat
means less wear and tear on the brakes, which means
that they don't need to be replaced as often as
conventional brakes. "We've seen customers go
85,000 miles before they needed to replace their
brakes on their Prius vehicles," says Toyota's
Hermance.
One of the top reasons that people purchase a hybrid
vehicle is to get better fuel economy and they are
often disappointed that they don't experience the fuel
economy numbers listed on the window sticker in
their regular driving. "I just love my Honda Civic
Hybrid, but I have been a bit disappointed that the
gas mileage isn't better," says Ivey Doyal of Atlanta,
Ga.
To be sure, differences in projected fuel economy
versus real-world driving can mean serious
differences in your wallet over the long term.
Unfortunately, there is a discrepancy between the
EPA's fuel economy ratings, which are listed on the
window sticker when you buy a new car or truck,
and the real-world results that most drivers
experience, regardless of the type of vehicle they
drive. The EPA's ratings are the numbers
manufacturers are required by law to list in all the
promotional
materials
for
their
vehicles.
Unfortunately, the procedure the EPA uses to
calculate these numbers is outdated and isn't
indicative of the way most Americans drive today.
The EPA has made adjustments to its calculations to
try to compensate for this. Even with these
adjustments, however, the numbers still often differ
from the real world. "We've seen where the typical
driving style can be as much as 20-percent less than
the EPA fuel economy number," says Bienenfield.
While all vehicles are affected by this discrepancy,
hybrid vehicles have the appearance of being
affected even more so. "For example," explains
Bienenfield, "A vehicle that has a fuel economy
rating of 20 mpg may only get 18 mpg, while a
vehicle that is rated at 50 mpg may only get 45 mpg.
This seems like a bigger issue for the more fuelefficient vehicle, but in reality both vehicles are off
by 10 percent."
In the informal survey we did with Honda and
Toyota hybrid owners, fuel economy numbers
ranged from 33 to 49 mpg on average, which
reflected many driving styles and a wide range of
commutes. While these numbers are significantly
lower than the EPA ratings, all the owners we
interviewed were happy overall with the fuel
economy as it is still better than most gasoline-only
vehicles.
Perhaps what is most misleading about the fuel
economy ratings is that they don't show how widely
numbers can vary based on an individual's typical
driving route. "Short trips are the harshest on fuel
economy, so anyone who drives just a few miles in
his typical trip will see lower mpg numbers than
someone who drives, say, 15 miles to work," says
Bienenfield. Our unscientific poll showed these results as
well. Pittsburgh, Pa., resident Jen Bannan typically drives
just a few miles in each trip and, as a result, had the lowest
fuel economy of those we interviewed, averaging 33 mpg
in her 2002 Toyota Prius. "Is (the lower fuel economy)
disappointing? Sure, but I'm still filling up less than I did
in my old car and the Prius is the best car I've ever
owned," she said.
At the opposite end of the spectrum, Civic Hybrid driver
Boughey and Honda Insight owner Dana Dorrity of Tivoli,
N.Y., have commutes of 60 and 50 miles one way,
respectively, on roads with rolling hills. Both had the
highest fuel economy of those we spoke with, at 47 mpg
for Boughey and 49 mpg for Dorrity. Poughkeepsie, N.Y.,
resident Mary Koniz Arnold has no trouble averaging 50
mpg in her 2001 Toyota Prius (which she bought used in
April 2004) on longer trips, but she averages closer to 40
mpg during her one-way commute of 10 miles.
"To be fair," says Toyota's Hermance, "there is no way any
two tests will give the range of consumer exposure in
terms of driving conditions and temperatures. He
continued, "We are really measuring the wrong thing.
Since you don't get to choose how many miles you drive,
we should be measuring the gallons consumed."
Reading this large variety of documentary reasons, the
reader can understand better how difficult was the authors’
task to collect numerical data for their study.
Finally the authors made the following hypotheses:
HSV
ICE
sOM
= 0.07 ; sOM
= 0.05 ; C PICE = 10000 €;
HSV
ICE
pOM
= pOM
= 0.40 ; (C pHSV )I = 1.2 (C pICE )I ;
τ HSV = τ ICE = 75000 km ICE or HSV / ICE car or
HSV; (C pHSV )C = 1.2 (C pICE )C ; f ICE = 7 l / 100 km
(
ICE; C pICE
)
I
(
= 0.4 C pICE ; C pICE
)
C
= 0.4 C pICE
By using these data and the mathematical model
(
km
τ HSV
previously presented, the functions S HSV
km
S HSV
( c ICE
)
f
(fig. 2),
km
S HSV
( k HSV
)
f
)
(fig. 1),
(fig. 3), were
calculated.
From the fig. 1 we can see how the state unitary subsidy of
100 km
HSV S HSV
[€ / 100 km] is influenced by total life cycle
HSV
[km HSV/ HSV car]. The diagram was
of a HSV, τ
calculated with the values previously indicated and
inserted in diagram field. The compared cost-to-quality
analysis applied here shows us that:
100 km
1) The state unitary subsidy S HSV [€ / 100 km] is
lowering when the total life cycle of HSV τHSV [km HSV/
HSV car] is increasing. In other words, the more resistant
in time is HSV, the less is the necessary unitary state
subsidy. How much must be this total life cycle of HSV so
that the state subsidy to not be necessary? The calculus
results shows τ
HSV
= 830000 km for τ ICE = 75000 km and
τ HSV =101500
km when τ ICE = 93750 km. Of course,
these results are unacceptable, we must have in view other
practical solutions, like the fuel reduction ratio k HSV
f
increasing
value C
HSV
P
or to manufacture cheaper the HSV (the
).
52
2) The fig. 1 diagram shows also that the less is the
total life cycle of the ICE cars (the value τ
ICE
) the
155
, [€/100km]
The state unitary subsidy of HSV,
[€ / 100 km] is lower.
CPHSV =13000 €; CPICE = 10000 €;
HSV
ICE
HSV
ICE
sOM
= 0.07 ; sOM
= 0.05 ; pOM
= pOM
= 0.40 ;
150
100 km
S HSV
100 km
unitary state subsidy S HSV
(C )
HSV
p
145
(C )
ICE
p
I
140
f
ICE
I
= 4800 €; ( C pHSV ) = 4800 €;
(
= 4000 €; C
= 7 l / 100 km;
135
)
ICE
p
C
C
= 4000 €;
k HSV
= 0.8; c ICE
=1€/l
f
f
100 km
S HSV
= 0 for τ HSV =101.5 104 km
130
τ ICE =93750 km
τ ICE =75000 km
125
100 km
S HSV
= 0 for τ HSV =83 104 km
120
115
7.5
8
8.5
9
9.5
4
x 10
The total life cycle of a HSV,
τ HSV
[km HSV / HSV car]
100 km
[€/100km] versus the total life cycle of HSV
Fig. 1. The necessary subsidy S HSV
τ HSV
[km HSV / HSV car].
2
CPHSV =13000 €; CPICE = 10000 €;
, [€/100km]
HSV
ICE
HSV
ICE
sOM
= 0.07 ; sOM
= 0.05 ; pOM
= pOM
= 0.40 ;
S
100 km
HSV
1.5
(C )
(C )
HSV
p
I
ICE
p
C
f
ICE
= 4800 €; ( C pHSV ) = 4800 €; ( C pICE ) I = 4000 €;
C
=
HSV
4000 €; k f
=0.8
= 7 l / 100 km;
τ ICE = τ
HSV
=75000 km
1
=1 € / l
c ICE
f
0.5
=2 € / l
c ICE
f
0
0.5
0.55
0.6
0.65
0.7
0.75
0.8
HSV
The fuel reduction ratio of HSV, k f
100 km
[€/ 100 km] versus the fuel reduction ratio k HSV
of HSV.
f
53
Fig. 3 is showing intuitional conclusions:
100 km
1) The necessary subsidy S HSV
, [€/100 km] decreases
Fig. 2 gives some answers to the questions arisen
when examining the fig. 1.
1). The first conclusion at glance is that with the gas
ICE
price c f
when the unitary fuel cost c ICE
[€ / l fuel] increases.
f
= 1 € / l, if we can obtain k HSV
= 0.57,
f
100 km
, [€/100 km] must be
2) The necessary subsidy S HSV
the HSV manufacturing and sale does not need state
subsidy.
2). The second conclusion is that the state subsidy
100 km
increases when we use lesser the PV panels
S HSV
bigger when utilizing more solar energy ( k HSV
is
f
decreasing).
3) There are feasible situations when the necessary subsidy
100 km
, [€/100 km] can annul. The fig. 3 diagram shows
S HSV
(the value k HSV
is bigger).
f
3). The third conclusion is that when the gas price
c
ICE
f
increases, the state subsidy S
100 km
HSV
three such situations: k HSV
= 0.8 and c ICE
= 1,1 [€ / l
f
f
is lowering,
becoming even zero if the fuel reduction ratio of
= 0.7 and c ICE
= 1,4
fuel] ; k HSV
f
f
HSV, k HSV
= 0,787 and this price reaches to
f
k HSV
= 0.6 with c ICE
= 2,2 [€ / l fuel].
f
f
[€ / l fuel] and
=2 € / l.
c ICE
f
2
CPHSV =13000 €; CPICE = 10000 €;
, [€/100km]
HSV
ICE
HSV
ICE
sOM
= 0.07 ; sOM
= 0.05 ; pOM
= pOM
= 0.40 ;
(C )
HSV
p
1.5
(C )
ICE
p
I
100 km
S HSV
f
ICE
I
= 4800 €; ( C pHSV ) = 4800 €;
(
= 4000 €; C
= 7 l / 100 km;
C
)
ICE
p
C
τ ICE = τ
= 4000 €;
HSV
=75000 km
1
k HSV
= 0.6
f
0.5
k HSV
= 0.7
f
k HSV
= 0.8
f
0
1
1.5
2
2.5
The unitary fuel cost, c ICE
[€ / l fuel]
f
100 km
, [€/100 km] versus the unitary fuel cost c ICE
[€ / l fuel].
f
8. FINAL CONCLUSION
According to the done study there is a real feasible
solution to make HSV profitable in the next future.
This solution is characterized by the following
numerical parameters:
1. The total cost of HSV C
HSV
P
=13000 €;
2. The total cost of classical car, powered by internal
ICE
combustion engine, CP
= 10000 €;
4. The operation-maintenance ratio of ICE car
ICE
service (eq. 7), sOM
= 0.05 ;
5. The operation-maintenance ratio of ICE car product,
ICE
HSV
pOM
(eq. 11) and pOM -the operation-maintenance ratio
HSV
ICE
of HSV product, (eq. 12) pOM
= pOM
= 0.40 ;
(
HSV
6. The investment cost of the HSV, C p
)
I
= 4800 €;
3. The operation-maintenance ratio of HSV car service
HSV
= 0.07 ;
(eq. 8), sOM
(
HSV
7. The consumption cost of the HSV, C p
)
C
= 4800
€;
54
8.
The
(C )
ICE
p
I
9.
investment
of
the
ICE
car,
the
ICE
car,
= 4000 €;
The
(C )
cost
ICE
p
C
consumption
cost
of
= 4000 €;
10. The unitary fuel consumption of ICE, f
/ 100 km;
11. The total life cycle of an ICE car,
/ ICE car] and
τ
HSV
τ ICE
ICE
=7l
[km ICE
-the total life cycle of a HSV,
[km HSV / HSV car] τ ICE = τ
HSV
=75000 km.
Of course, this is only one of the possible solutions.
The done mathematical model presented here allows
the modeling according to concrete possibilities the
manufacturer has in order to achieve a better and
better HSV. Modeling so, using the compared costto-quality analysis as work procedure, the authors are
convinced that the best solution of a HSV is an ideal
[12, 16, 17, 18], untouchable as any ideal, but an aim
point for researchers.
REFERENCES
1. Arsie I., Di Domenico A., Marotta M., Pianese C.,
Rizzo G., Sorrentino M. (2005); A Parametric
Study of the Design Variables for a Hybrid
Electric Car with Solar Cells, Proc. of METIME
Conference, June 2-3, 2005, University of
Galati, RO.
2. Arsie I., Marotta M., Pianese C., Rizzo G.,
Sorrentino M. (2005); Optimal Design of a
Hybrid Electric Car with Solar Cells, 1st
AUTOCOM Workshop on Preventive and
Active Safety Systems for Road Vehicles,
Istanbul, Sept. 19-21, 2005.
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Optimization, John Willey & Sons, New York
4. Frangopoulos, A. C, Caralis, C. Y., A method for
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5. Juran, J. M., Godfrey, A. B., Juran's Quality
Handbook (5th Edition), McGraw-Hill, 1999.
6. Ionita, C. I., Termoeconomia, stiinta
interdisciplinara de minimizare a costurilor
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Minimizes the Product Cost by Means of
Exergy). Conferinta de Termotehnica, 1996, Iasi.
Termotehnica româneasca’96, vol. 1, pp. 35-39.
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the Power Plants. Heat Engines and
Environmental Protection, 25-28 May, 1997,
Proceedings, Tata, Hungary, pp. 233-239.
8. Ionita, C.I. ,About the Application of Extended Exergy
Analysis to the Optimization of Industrial Systems
Using Cost/Quality Ratio, ECOS 2000 Proceedings,
University of Twente, Nederland, pp. 187-198.
9. Ionita C.I., The Close Connection between Cost and
Quality of Energy Products, ECOS 2001, Istanbul,
Proceedings, vol. 2, pp. 813-820.
10. Ionita, C.I., The Cost-to-Quality Evaluation and
Optimization of the Heat Powered Systems, HPC’01
2nd International Heat Powered Cycles Conference,
CNAM Paris, France, Proceedings vol. II, pp. 255262.
11. Ionita, C.I., Popa. V. The Analysis of the HVAC
Systems Using Cost-to-Quality Criterion of
Optimization, 7th REHVA World Congress Clima
2000, Napoli 2001, Proceedings on CD.
12. Ionita C.I. (2003), Engineering and Economic
Optimization of Energy Production, International
Journal of Energy Research, Article Reference No.
811, Journals Production Dept., 26: 697-715 (DOI:
10.1002/er.811), John Wiley & Sons, Ltd, Chichester,
UK.
13. Ionita C.I., The Cost-to-Quality Ratio Based
Optimization of the Energy Production, Entropie nr.
232, 2001, pp. 10-19.
14. Ioniţă, C.I., Extending thermo-economic analysis by
cost to quality optimisation. Proceedings of ECOS
2002 July 3-5, 2002, Berlin, Germany, pp. 1434-1441.
15. Ionita C.I, Ion V.I. Cost-to-Quality Optimization of
Refrigeration, NATO Advanced Study Institute, June
23-July 5, 2002, Altin Yunus-Cesme, Izmir-Turkiye,
An International Meeting, Co-Directors: Prof S.
Kakac and Prof. H. Smyrnov, ASI No.978410.
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Sciences Academy of Romania, (2003), MOCM-9vol.2, pp.149-155, ISSN 1224-7480.
17. Ionita C.I., Thermal Systems Optimization and Cost-toQuality Analysis, International Journal of Heat and
Technology”, vol. 22 nr. 1, 2004 pp. 27-37.
18. Ionita C.I., Beyond thermo-economic analysis of
thermal systems: the compared cost-to-quality
analysis, 1st International Conference on Thermal
Engines and Environmental Engineering, METIME
2005, June 3-4, 2005, Galati, Romania.
19. http://www.toyota.co.jp/en
20. The Real Costs of Owning a Hybrid.
www.edmunds.com/advice/fueleconomy/articles/103708/a
rticle.html- 44k
21. http://www.hybrid-car.org/
55
56
TECHNICAL AND ECONOMICAL FEASIBILITY STUDY OF A SMALL HYBRID VEHICLE FOR
URBAN TRANSPORTATION
C. Boccaletti(*), G. Fabbri(*), F. M. Frattale Mascioli(§), E. Santini(*)
(*)
Department of Electrical Engineering, University of Rome “La Sapienza”
(§)
Department INFOCOM, University of Rome “La Sapienza”
Abstract: A technical and economical study has been carried out by the authors in order to
assess the feasibility of the hybridisation of a small vehicle for urban transportation. An
existing commercial vehicle powered by a 4kW internal combustion engine has been
taken as a reference. A possible layout of the new hybrid propulsion system has been
studied. Weights and volume occupancy have been examined. Initial and operating costs
have been estimated and compared with the present market costs of the original vehicle.
Performance calculations allowed to evaluate the vehicle behaviour in a standard mission
and management aspects have been discussed. Copyright © 2002 IFAC
Keywords: Hybrid Electric Vehicles, Urban transportation.
1. INTRODUCTION
In the last years the public perception of aspects
related to the quality of life in urban centres has
increased considerably, conditioning the individual
choices and the administration policies. As a
consequence, technical issues arising from the need
to reduce the polluting emissions of vehicles are
more and more important. According to the latest
available national (Italian) data, road transportation
is responsible for the higher percentage of NOx, CO
and
Non-Methanic-Volatile-Organic-Compounds
(NMVOC) emissions, as shown in Table 1. If the
contribution of these pollutants is splitted according
to the type of vehicles, one can see that passenger
cars are the main source of polluting emissions.
For this reason, the problem of air quality trusted in
the last years the demand for vehicles with a low
impact to the environment (C. Boccaletti, L.
Martellucci, 2001, K. Rajashekara et al., 2002, K.
Rajashekara, 2004). Moreover, urban areas with
restricted access are wider and wider, aiming to
reduce the air pollution. Since these areas are usually
those with the most intense traffic and the lowest
number of parking places, the vehicle size is also
important (F. Caricchi et al., 2003). In the following,
a technical and economical study to assess the
feasibility of the hybridisation of a small vehicle for
urban transportation is described.
2. THE ORIGINAL VEHICLE
The vehicle chosen for the hybridisation is a small
commercial vehicle suitable for city service (see
Fig. 1). This kind of vehicle is particularly conceived
to be used in the narrow streets of historical centres
and to make parking easier. The technical data and
size of the vehicle are listed in Tabs 2 and 4,
respectively. Two points of the characteristic curve
are reported in Tab. 3.
The engine and the other components of the existing
(traditional) propulsion system are located in the
front. Owing to the reduced size of the vehicle, the
various element are disposed in such a way that the
volume occupancy is optimised and the insertion of a
new bulk elements would be difficult. The bonnet or
the load deck (in the pickup version) are located in
the rear. A mean market price of the vehicle range of
8000 € can be taken as a reference.
57
Table 1 Contribution of road transportation to
polluting emissions in 2002 (%)
SOX
1.95
NOX
48.81
NMVOC
32.31
CO
65.27
CO2
27.85
Source: Elaboration from Apat (2006)
Fig. 1. The commercial vehicle chosen for the
hybridisation.
Table 2 Features of the commercial vehicle chosen
for the hybridisation
Engine
N° cylinders
Cyl. Volume
Cycle
Cooling Type
Max. Power
Max. Torque
Transmission
Gear Position
Traction
Electric Circuit
Voltage
Max. Speed
Max. Slope
Diesel
2
505 cm3
4 Strokes
liquid
4 kW @ 3600 rpm
14 Nm @ 2400 rpm
continuous variator with pulleys
and centrifugal masses
Inward / Backward / Idle
Front wheels with inverter
differential
12 V
45 Km/h
> 25%
Table 3 Performance data of the commercial vehicle
chosen for the hybridisation
rpm
2400
3600
Torque [Nm]
14
10.61
Power [W]
3500
4000
Table 4 Size and weight of the commercial vehicle
chosen for the hybridisation
3224 mm
Length
1487 mm
Heigth
Admissible Mass
Width
Mass
1378 mm
349 kg
675 kg
3. THE HYBRIDISATION
The expected benefits of the hybridisation are:
− Reduction of fuel consumption;
− Reduction of polluting emissions;
− Increased performance.
3.1 Parallel configuration
The first configuration of the hybrid system taken as
a reference is of the parallel type. In general, this
configuration is considered suitable for small
vehicles. The scheme of the propulsion system
includes a power-split drive train. According to the
complexity of such a device, together with other
considerations, the choice of a parallel configuration
could be not suitable to the series production in a
small enterprise with affordable costs and therefore
an acceptable commercial price. The configuration
has been studied for a specific use of the vehicle in
an urban environment, with limited flexibility. In
case of missions that are quite far from the city
standards, the availability could not be assured. In the
particular case of these vehicles, the Italian law
prescribes a maximum speed of 45 km/h, therefore
even the European standard for motorcycles (ECE47)
could not be taken as a reference, because it provides
a maximum speed of 50 km/h. However, nonconventional cycles have been proposed for the
analysis of the vehicle behaviour in an urban
environment, and among these one with a maximum
speed of 45 km/h (Avella, 2000) (see Fig. 2). This
cycle has been considered for our analyses.
Fig. 2. Urban cycle in heavy traffic conditions.
Chosing a Hybridisation Factor (HF) of 25%, the
1 pole, 60 Hz syncronous motor has a power of
1 kW. The electromagnetic torque is 3.18 Nm. The
storage system should have a capacity of at least
1.1 kWh. Lead-acid batteries (not too expensive, with
a quite long life), including supports and
connections, should weight about 30 kg, with a
volume of 10 litres. The voltage is 48 V. Lithium
batteries could be an alternative, with less weight and
volume occupancy. An inverter suitable for the
application has the features of Table 5. Considering
an efficiency of the charge/discharge cycle of 80%
and a battery charge efficiency of 90%, the electric
energy consumption is about 1.5 kWh per cycle (i. e.,
per day), corresponding to 0.26 € or 0.0052 €/km, if
50 km is the mean daily run. The battery cost is some
0.05 €/Wh. Therefore, 55 € are enough to ensure the
provided run in the first period of operation.
However, the capacity decreases of 0.04% per cycle,
so that after 365 cycles (one year), the daily run is
reduced. Usually, in this case the driver increases the
frequency of the charge cycles instead of changing
the batteries. In so doing, the battery aging becomes
faster and faster. In the most favourable case, with an
optimum management of charge/discharge cycles,
one can think to reach a battery life of 5 years, which
corresponds to 2000 kWh stored and 475 €.
Including the initial cost of the batteries, the cost per
58
year is 106 € and 0.0058 €/km. The above costs are
calculated with the electric propulsion as the only
one. Considering a 20% saving in hybrid mode,
thanks to the energy recovered during braking and
deceleration, the cost can be reduced to some
0.0046 €/km. For city service, the cost of fuel is
about 0.056 l/km, or 0.07 €/km. In hybrid mode, the
fuel consumption can be reduced of about 20%,
obtaining a cost of 0.05 €/km. Therefore, the total
operation cost of the hybrid vehicle can be calculated
in about 0.0546 €/Km. To redeem 2000 € (difference
with the price of a traditional vehicle), the vehicle
should run for 130000 km, corresponding to about 7
years at 50 km/day. During this period, one
substitution of the batteries has to be considered
(55 €). In conclusion, the complete amortization is
attained at the end of the vehicle life. Therefore, the
user should not benefit by significant economic
advantages. On the other hand, from the point of
view of the environmental impact a significant
reduction of polluting emissions can be obtained.
The above rough considerations, however, do not
take the possible additional production costs into
account, due to the choice of the power-split drive
train, needed for the coupling among the propulsion
and traction devices (L. Martellucci et al., 2001).
Moreover, the realisation of the drive and of the
relevant control system could require particular
technical skills, that are not always available in a
small enterprise. Although quite simplified, the
above results show that in this particular case the
parallel configuration does not have wide margins of
application, from both an industrial and customer’s
point of view.
Table 5 Inverter features
Voltage
Power range
Efficiency
Output voltage
12 Vdc or 24 Vdc ±15%
300 VA÷12 kVA with
intermittent service
71-77%
220 Vac
In order to increase the availability of the hybrid
vehicle also for missions quite far from the urban
cycle taken as a reference in the design phase, a
series configuration can be chosen. The latter
includes more components to be located into the
vehicle than the parallel solution, but the layout is
subject to less constraints. Moreover, the components
do not differ from commercial devices, whose
assemblage requires standard technical skills.
3.2 Series configuration
As said above, in this configuration there is no
mechanical coupling between the Internal
Combustion Engine (ICE) and the wheels, reducing
the constraints of the layout, and this is particularly
important for a small vehicle. However, there are
more components than in the parallel case, and more
space is needed for the batteries. The volume of the
engine bonnet in the original vehicle is not so large,
so that the electric motor, the inverter and the
batteries cannot be mounted in the same place. In
Fig. 3 a sketch of the proposed layout is shown. The
generator is positioned in the front engine bonnet, the
electric motor is connected to the rear wheel axis,
batteries and converters are in the rear coffin.
Fig. 3. Layout of the hybrid series propulsion system.
In order to choose the component size, the required
performance have to be considered. As above stated,
the vehicle has a maximum speed of 45 km/h. The
aerodynamic, mechanical and rolling resistances - the
latter including both the rolling friction and the tyre
deformation - contribute to the total resistance to the
vehicle motion. Such a resistance can be calculated
through
expressions
containing
empirical
coefficients. For our case, the rolling resistance is
assumed proportional to vehicle weight W. The
reference weight for the performance calculation is
assumed to be 500 kg. It follows
Ftyre = 8·g·W·10-3 = 8·9.81⋅0.5 = 39.24 N
(1)
The aerodynamic resistance can be calculated as
Faer=0.5·Cr·ρ·A·V2=0.5·0.3·1.2·2.0·12.52=56.25 N (2)
being Cr a drag coefficient, ρ the air density (kg/m3),
A the reference front section area (m2) and V the
maximum vehicle speed (m/s). Total resistance R is
95.49 N. The corresponding torque at the wheels is
T
= R·d = 95.49·0.252 = 24.06 Nm
(3)
being d the wheel radius (m). Therefore, the required
power is
P = T·ω = 24.06·7.88·2π = 1.19 kW
(4)
Since the chosen electric motor has a rated power of
4.2 kW, one can calculate the maximum slope the
vehicle can climb at the maximum speed. The
available additional power is 3.01 kW. It follows
Max Slope% = 3.01·3600/(500·9.81·45) = 4.9
(5)
One can also calculate at what speed the vehicle can
move up a slope of 10%, the standard value for
continuous running. In this case the rated power of
the electric motor allows to attain a speed of about
26 km/h. Up a slope of 20% the maximum speed is
about 15 km/h. The electric motor has a rated torque
of 40 Nm @ 1000 rpm and a maximum torque of
59
80 Nm. The weight is about 15 kg and the height and
axial length are about 25 cm and less than 30 cm,
respectively.
The battery pack consists of 5 lead gel batteries of
30 Ah, 12 V nominal. The total weight is 53 kg.
Height, length and width of a single battery are
15.5 cm, 19.5 cm and 13.3 cm, respectively. The noload voltage and the charge and discharge resistances
as a function of the State-Of-Charge (SOC) are given
in Table 6.
Table 6 Battery characteristics
SOC
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Rdis
0.0268
0.0163
0.0124
0.0107
0.01
0.01
0.01
0.0114
0.0114
0.011
V0
11.28
11.58
11.88
12.06
12.18
12.36
12.54
12.72
13.02
13.5
Rchg
0.0373
0.0259
0.0201
0.0173
0.0166
0.017
0.0196
0.0243
0.0348
0.1141
Based on the values of Table 6, a global battery
efficiency ηb = ηchgηdis has been estimated. A value
of 0.85 has been assumed. The generation efficiency
is defined as (S. Barsali et al., 2002)
η gl =
(Pd + Pb − Pb (1 − η b ) )η
Ps
(6)
gen
The goal is to obtain the value of the average power
to be delivered by the DC source as a function of
average drive power demand Pd. For each Pd, the
value of Ps corresponding to the maximum of ηgl can
be individuated. Thus, function Ps* = Ps*(Pd) can be
obtained.
The diesel generator has the characteristics of
Table 7. The efficiency can be evaluated through the
curves of power and specific fuel consumption given
by the manufacturer with reference to the ISO
3046/1-IFN standard (see Fig. 4). The maximum
efficiency corresponds to a power of about 4.1 kW.
Table 7 Engine characteristics
N° cylinders
Cyl. Volume
Max. Power
Max. Torque
When operating in ON-OFF mode, the DC source
logic is based on the battery SOC. The optimisation
procedure consists of calculating average drive
power demand Pd in a given time interval t,
estimating the battery SOC in t, defining the
operating state (ON or OFF) and finally calculating if the state is ON - reference power Ps* as the power
to be generated by the DC source corresponding to
the maximum generation efficiency.
1
315 cm3
5 kW @ 3600 rpm
15 Nm @ 2400 rpm
An efficiency of 0.9 has been assumed for the DC
(electric generator-inverter) generation system. The
values of Fig. 4 have been multiplied by this
efficiency, the procedure has been applied, and the
curve of Fig. 5 has been obtained. It shows the
average power to be delivered by the DC source vs.
Pd, in order to have the minimum fuel consumption
and to keep the battery SOC within the admissible “safety” - range. Beyond the minimum point, on the
right of the graph, the continuous operation (“load
following”) substitutes the ON-OFF mode and no
energy is stored in the battery pack.
4.5
4.45
4.4
4.35
Source power [kW]
0.32
Efficiency
0.31
0.3
4.3
4.25
4.2
4.15
4.1
0.29
4.05
4
1.5
0.28
2
2.5
3
Drive power [kW]
3.5
4
4.5
0.27
1.5
2
2.5
3
Power [kW]
3.5
4
4.5
Fig. 4. Engine efficiency vs. engine power.
Fig. 5. Optimal DC source operation curve.
The effects of the above control strategy on the
global efficiency (M. Pasquali, G. Pede, 2006) are
shown in Fig. 6.
In order to minimise the fuel consumption, a control
strategy has to be chosen. Once fixed a SOC
admissible range, the best operating point of the
generator as a function of the power required by the
drive is calculated minimising the fuel consumption
(S. Barsali et al., 2002).
60
0.29
0.285
optimised
load following
0.28
Global efficiency
0.275
0.27
0.265
0.26
0.255
Fig. 6. Main components and relevant power fluxes.
0.25
0.245
0.24
1.5
2
2.5
3
Drive power [kW]
3.5
4
4.5
Fig. 6. Global generation efficiency curves in case of
optimised control (blue) and load following
(green).
As above said, in the ON-OFF mode the generator
operates in optimum conditions and a part of the
produced energy is stored in the batteries. From
Fig. 5, one can see that the delivered power varies
only between about 4.05 and 4 kW in the ON-OFF
mode and within about 4 and 4.5 kW in the load
following mode. However, for urban use the power
demand of this kind of vehicle can hardly overcome
4 kW, unless additional power is required by
auxiliary devices (C. Boccaletti, L. Martellucci,
2001). Thus, the generator practically operates at a
fixed point, corresponding to the best efficiency. For
a given vehicle mission, like that of Fig. 2, power Pb
stored in the batteries can be calculated at every time
instant, as the difference between generated power Ps
and drive power demand Pd (see Fig. 6). An
efficiency of 0.85 can be assumed for the electric
drive. According to the battery SOC, the generator
should be switched on or off to keep the SOC within
the fixed range, say 0.4÷0.85. In this way it is
possible to calculate the energy produced by the
generator during a complete charging/discharging
cycle of the batteries, and the relevant noise and fuel
consumption. An evaluation of polluting emissions
could be performed by means of maps given by the
manufacturers, but an actual comparison with the
dynamical behaviour of the original propulsion
system is possible only on the basis of an
experimental on-road campaign (Avella, 2000).
However, a significant reduction of polluting
emission is expected, thanks to the limited operating
time of the engine, nearly in conditions of best
efficiency, covered distances being equal.
A software program has been set up to calculate the
number of standard urban missions (and then the
total covered distance) corresponding to a complete
charging/discharging cycle of the batteries within the
admissible range, and the relevant fuel consumption.
A maximum noise level of 78 db has been calculated
from manufacturer’s data, corresponding to the
engine operating conditions.
Starting from the established minimum SOC level
(0.4), the batteries are charged until the admissible
limit. At that point the generator is switched off, and
the drive power demand makes the stored energy
decrease, until the minimum SOC is attained again.
The charging/discharging cycle of the batteries is
completed in about 25 standard urban missions,
corresponding to a distance of 24.5 km. The fuel
consumption is about 160 g, and the total produced
energy is about 0.4 kWh. From the above
considerations, it comes out that such configuration
corresponds to a large flexibility and availability of
the hybrid vehicle, allowing its use also for missions
quite far from the urban cycle taken as a reference in
the calculations.
Finally, the cost of the main components of the new
propulsion system can be estimated between 1750
and 2250 €, according to the cost of the generator,
being the cost of the battery pack some 250 € and
that of the electric drive some 500 €.
4. CONCLUSIONS
An existing commercial vehicle powered by a 4kW
internal combustion engine has been taken as a
reference for a preliminary technical – economical
analysis of possible hybrid configurations. Weights,
volume occupancy and costs of a parallel and a series
layout have been estimated. A particular urban
mission, suitable for this kind of vehicles in both
configurations, has been individuated. Some aspects
of the vehicle management have been discussed with
particular reference to the series configuration, and
performance calculations allowed to evaluate the
characteristics of the propulsion system related to its
availability also for missions quite far from the
standard one. A significant reduction of polluting
emission is expected in both cases with respect to the
original (traditional) propulsion system. From both
an industrial and customer’s point of view, in the
particular case examined the series configuration
seems to have wider margins of application, although
a final answer could come only from more in-depth
economical analyses.
5. REFERENCES
F. Avella (2000)– “L’attivita’ sperimentale della
stazione sperimentale per i combustibili per la
61
valutazione delle emissioni generate dagli
autoveicoli” – Proc. of Seminario ANPA, Rome,
Italy (in Italian)
L. Martellucci, M. Santoro, C. Boccaletti (2001) - “A
Powertrain with Planetary Gear System:
Advantages and a Design Approach” – Proc. of
EVS 18 – The 18th International Electric
Vehicle Symposium, Berlin, Germany
C. Boccaletti, L. Martellucci (2001) – “Study of an
air conditioning system for a small hybrid
vehicle based on the absorption principle” –
SAE Paper 2001-01-3808, Proc. of Congresso
SAE Brasil 2001, São Paulo, Brazil
K. Rajashekara et al. (2002) - “Comparative study of
new on-board power generation technologies for
automotive applications,” in Proc. IEEE
Workshop Power Electronics in Transportation,
Auburn Hills, MI, pp. 3–10
S. Barsali, M. Pasquali, G. Pede (2002) - "Definition
of Energy Management Technique for Series
Hybrid Vehicles" - Proc. of EVS 19 – The 19th
International Electric Vehicle Symposium,
Pusan, Korea
F. Caricchi, L. Del Ferraro, F. Giulii Capponi, O.
Honorati, E. Santini (2003) – “Three-Wheeled
Electric Maxi-Scooter for Improved Driving
Performances in Large Urban Areas” - Proc. of
2003 IEEE International Electric Machines and
Drives Conference, IEMDC’03, Madison,
Wisconsin, USA
K. Rajashekara (2004) – “Hybrid and Fuel Cell
Systems for Transportation”, Meeting IV of
IEEE IASChapter, Hungary
M. Pasquali, G. Pede (2006) – “Ottimizzazione della
gestione energetica di un veicolo ibrido di tipo
serie” – Proc. of 17th Seminario Interattivo
ANAE, “Azionamenti Elettrici Evoluzione
Tecnologica e Problematiche Emergenti”,
Bressanone, Italy (in Italian)
62
PASSIVITY-BASED CONTROL OF HYBRID
SOURCES APPLIED TO A TRACTION
SYSTEM
Damien Paire ∗ , Mohamed Becherif ∗∗ ,
Abdellatif Miraoui ∗
∗
L2ES, UTBM, Belfort (cedex) 90010, FRANCE
SeT, UTBM, Belfort (cedex) 90010, FRANCE
[email protected]
Tel:+33 (0)3 84 58 33 96, Fax:+33 (0)3 84 58 34 13
∗∗
Abstract: Nowadays, energy management becomes an economic and technical
issue. To reduce systems consumption, the idea is to recover energy when it
is possible and to reuse it depending on the demand. To save energy, storage
components (supercapacitors here) are needed to absorb or supply power picks.
This article present an hybrid system suppling an electromotive force. In order
to supervise the power flows in the system, Passivity-Based Control is used and
different configurations are simulated.
Keywords: energy recovery, hybrid system, Passivity-Based Control, embedded
energy, supercapacitors
1. INTRODUCTION
In electric traction systems (like vehicles, elevators, . . . ), if the load is supplied using a single energy source, it has to answer to all solicitations of
the load. Thus, the source has to supply or absorb
the picks of power resulting from accelerations and
braking. So, the source has to provide energy and
power, this is strongly penalizing. In order to optimize the power transfer and to improve equipment
lifetime, supercapacitors (SC) and different kind
of DC sources can be hybridized. Then the SC
supply or absorb power picks and the DC source
provide the average power.
In this paper, a hybrid power source using DC
source (obtained from network or from batteries
alone or associated with photovoltaic panels) and
SC supplying a load is proposed. In a first step,
a dynamic modeling of the system is given. In
a second step, this system is written in a Port
Controlled Hamiltonian (PCH) form where im-
portant structural properties are exhibited. Then
a Passivity-Based Control (PBC) of the system is
presented proving the global stability of the equilibrium with the proposed control laws. Finally,
simulation results using Matlab are given.
2. HYBRID DC SOURCE SYSTEM
2.1 Structure of the hybrid source
As shown in Figure 1, the studied system comprises a DC link supplied by a DC source and a
no reversible DC-DC Boost converter which maintains the DC voltage VDC to its reference value
V DC and a SC storage device which is connected
to the DC link through a current reversible DCDC converter. The load consist of a resitor RL ,
a inductor LL and an electromotive force (emf)
E. This structure is used to model merely an
electrical machine.
63
iN LN
VN
iDC LDC
CS
TN
iSC LSC
VSC
VS
iL
CDC
VDC
1
[(1 − u1 )x2 − x4 ]
CS
1
ẋ2 =
[VN − (1 − u1 )x1 ]
LN
1
[x4 − x7 + (1 − u2 )x6 ]
ẋ3 =
CDC
1
ẋ4 =
[x1 − x3 ]
LDC
−1
ẋ5 =
x6
CSC
1
ẋ6 =
[x5 − (1 − u2 )x3 ]
LSC
1
[x3 − RL x7 − E]
ẋ7 =
LL
y = x3
ẋ1 =
E
LL
RL
T SC
CSC
TSC
Fig. 1. System electrical model
The function of the DC source is to supply the
mean power to the load, whereas the storage
device is used as a power source: it supplies and
absorbs peak loads required during acceleration
and braking. In order to manage energy exchanges
between the DC link and the storage device, three
operating modes are defined:
• Charge mode, in which the main source supplies energy to the storage device,
• Discharge mode, in which the storage device
and the main source supply energy to the
load,
• Recovery mode, in which the load supplies
energy to the storage device.
2.3 Equilibrium
After some simples calculations the equilibrium
vector is:
T
x̄ = x̄1 , x̄2 , x̄3 , x̄4 , x̄5 , x̄6 , x̄7
(3)
T
(Vd − E)Vd
Vd − E
Vd − E
= Vd ,
, Vd ,
, x̄5 , 0,
RL VN
RL
RL
Where Vd is the desired DC Bus voltage. An implicit purpose of the proposed structure (Figure 1)
is to recover energy to charge the SC. Hence, the
desired voltage x̄5 = VSC (t = 0) = 12V .
ū = ūN , ūSC
T
=
VN
x̄5
1−
, 1−
Vd
Vd
T
(4)
The natural energy function of the system is:
2.2 State space model of the system
The model of the hybrid system can be written
in a state space model by choosing the following
variables:
T
x = x1 , x2 , x3 , x4 , x5 , x6 , x7
T
= VS , iN , VDC , iDC , VSC , iSC , iL
H=
1 T
x Qx
2
(5)
where Q = diag{Cs ; LN ; CDC ; LDC ; CSC ; LSC ; LL } is a
diagonal matrix.
3. PROBLEM FORMULATION
The control vector is:
T T
u = u1 , u2
= uN , uSC
(2)
(1)
where uN and uSC ∈ [0, 1].
u = 1 means the associated transitor is closed and
u = 0 means the associated transitor is opened.
The 7th order overall state space model is then :
After system modeling, equilibrium points are
computed in order to ensure the desired behaviour
of the system. When steady state is reached, the
load has to be supplied only by the DC source. So
the controller has to maintain the DC bus voltage
to a constant value and the SC current has to be
cancelled.
During transient, the power delivered by the DC
source has to be the more constant as possible
(without a significant power peak), so the SC
deliver the transient power to the load. If the
load provide current, the SC recover its energy.
At equilibrium, the SC has to be charged and the
64
current has to be equal to zero.
In the next section, a controller will be found and
the system’s stability will be prouved.
4. PORT-CONTROLLED HAMILTONIAN
REPRESENTATION OF THE SYSTEM
PCH systems were introduced by [1] and has
since grown to become a large field of interest in
the research of electrical, mechanical and electromechanical systems. A recent and very interesting
approach to solve these problems is the IDA-PBC
method, which is a general way of stabilizing a
large class of physical systems, see [2, 4].
The desired closed loop energy function is:
Hd =
1 T
x̃ Qx̃
2
(6)
where x̃ = x − x̄ is the new state space defining
the error between the state x and its equilibrium
value x̄. So according to the state space model (2),
the following equations can be written:
1
x̃˙ 1 =
[(1 − u1 )(x̃2 + x̄2 ) − x̃4 − x̄4 ]
CS
1
[VN − (1 − u1 )(x̃1 + x̄1 )]
x̃˙ 2 =
LN
1
x̃˙ 3 =
[(x̃4 + x̄4 ) − (x̃7 + x̄7 )
CDC
+(1 − u2 )(x̃6 + x̄6 )]
1
[(x̃1 + x̄1 ) − (x̃3 + x̄3 )]
(7)
x̃˙ 4 =
LDC
−1
(x̃6 + x̄6 )
x̃˙ 5 =
CSC
1
x̃˙ 6 =
[(x̃5 + x̄5 ) − (1 − u2 )(x̃3 + x̄3 )]
LSC
1
x̃˙ 7 =
[(x̃3 + x̄3 ) − RL (x̃7 + x̄7 ) − E]
LL
The PCH form of studied system with the new
variable x̃ and in function of the gradient of the
desired energy (6) is:
x̃˙ = (J (u1 , u2 ) − R) .∇Hd + Ai (x̄, u)
where
J (u1 , u2 ) − R =
(8)
⎡
0
⎢
⎢ 1 − u1
⎢− C L
⎢ s N
⎢ 0
⎢
⎢
⎢ 1
⎢ Cs L
DC
⎢
⎢ 0
⎢
⎢
⎢ 0
⎢
⎣
0
1 − u1
Cs LN
0
0
0
0
0
0
Cs LDC
0
1
CDC LDC
−1
CDC LDC
0
0
−1
0
0
−
0
0
1 − u2
CDC LSC
1
CDC LL
0
0
⎤
0
0
0
0
0
0
0
1
CSC LSC
0
0
1 − u2
CDC LSC
0
−1
CSC LSC
0
0
⎥
⎥
⎥
⎥
−1
⎥
⎥
CDC LL ⎥
⎥
0
⎥
⎥
⎥
0
⎥
⎥
⎥
0
⎥
⎦
−R
0
L
L2
L
⎡
⎤
Cs x̃1
⎢ LN x̃2 ⎥
⎢
⎥
⎢CDC x̃3 ⎥
⎢
⎥
⎥
∇Hd = ⎢
⎢LDC x̃4 ⎥
⎢ CSC x̃5 ⎥
⎢
⎥
⎣ LSC x̃6 ⎦
LL x̃7
⎤
(1 − u1 )x̄2 − x̄4
⎥
⎢
⎥
⎢
Cs
⎥
⎢
⎢ VN − (1 − u1 )x̄1 ⎥
⎥
⎢
⎥
⎢
LN
⎥
⎢
⎥
⎢
⎢ x̄4 − x̄7 + (1 − u2 )x̄6 ⎥
⎥
⎢
⎥
⎢
CDC
⎥
⎢
⎥
⎢
x̄1 − x̄3
⎥
Ai (x̄, u) = ⎢
⎥
⎢
⎥
⎢
LDC
⎥
⎢
⎥
⎢
−x̄
6
⎥
⎢
⎥
⎢
CSC
⎥
⎢
⎥
⎢
⎢ x̄5 − (1 − u2 )x̄3 ⎥
⎥
⎢
⎥
⎢
LSC
⎥
⎢
⎣ x̄3 − RL x̄7 − E ⎦
⎡
LL
J (u1 , u2 ) = −J T (u1 , u2 ) is a skew symmetric
matrix defining the interconnection between the
state space and R = RT ≥ 0 is symmetric positive
semi definite matrix defining the damping of the
system.
Ai (x̄, u) evaluated at the equilibrium points (3)
gives:
65
⎤
(E − Vd )(VN − (1 − u1 )Vd )
⎥
⎢
⎥
⎢
RL VN Cs
⎥
⎢
⎥
⎢
VN − (1 − u1 )Vd
⎥
⎢
⎥
⎢
LN
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
0
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
Ai = ⎢
0
⎥
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
0
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
x̄5 − (1 − u2 )Vd
⎥
⎢
⎥
⎢
LSC
⎥
⎢
⎦
⎣
0
⎡
control laws (10). In this case, the load is considered as a receiver. To illustrate the controller
efficiency, the DC bus voltage reference, the electromotive force (emf) and the resistance are modified (see Figure 5 and Figure 6). The DC bus
voltage is initialized at 36V and the DC Bus
voltage reference is set at 42V at the beginning.
(9)
Figure 2 presents the system response to changes
in the DC Bus voltage reference (Vd ), emf (E)
and load current iL . The DC Bus voltage tracks
well the reference, i.e. very low overshoot and no
steady state error are observed.
d
The following control laws are proposed:
u1 = ū1
u2 = ū2 − rx̃6
V &V
DC
(V)
50
35
0
0
0
0
0
0
−1
CDC LDC
0
0
0
0
−
1 − u2
CDC LSC
1
CDC LL
Cs LDC
0
1
CDC LDC
0
0
0
0
0
0
0
0
0
1 − u2
CDC LSC
0
0
1
CSC LSC
0
−1
CSC LSC
rVd
−
L2
0
SC
0
⎤
0
⎥
⎥
⎥
⎥
−1
⎥
⎥
CDC LL ⎥
⎥
0
⎥
⎥
⎥
0
⎥
⎥
⎥
0
⎥
⎦
iL(A)
0
5
6
0
1
2
3
t(s)
4
5
6
Fig. 2. (a) DC Bus voltage and its reference. (b)
Load current.
Figure 3 shows the source voltage (VN ) and current (iN ). In our modeling, we assume that the
DC source is ideal, thus VN stay at constant value
regardless of the current iN . A smooth behavior
of the current is observed regarding the changes in
Vd , E and RL , because the SC supply the transient
power.
0
16
15.5
15
N
Cs LN
(11)
J (u1 , u2 ) − R =
−1
4
1
V (V)
0
3
t(s)
0.5
14.5
14
0
1
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
−RL
L2
8
L
6
R = R ≥ 0. The derivative of the desired
energy function (6) along the trajectory of (11)
is:
T
Ḣd = ∇HdT x̃˙ = −∇HdT R ∇Hd ≤ 0
5. SIMULATIONS
N
⎢
⎢− 1 − u1
⎢ Cs LN
⎢
⎢ 0
⎢
⎢ 1
⎢
⎢ Cs LDC
⎢
⎢ 0
⎢
⎢
⎢ 0
⎢
⎣
1 − u1
2
1.5
i (A)
0
1
2
Proof. The closed loop dynamic of the PCH system (8) with the laws (10) and (4) with the radially unbounded energy function (6) is:
⎡
0
2.5
Proposition 1. The origine of the closed loop PCH
system (8), with the control laws (10) and (4)
with the radially unbounded energy function (6),
is globally asymptotically stable.
where
40
(10)
where r is a design parameter (r ≥ 0).
x̃˙ = [J (u1 , u2 ) − R ] ∇Hd
45
4
2
0
(12)
5.1 Load works as a receiver
The following simulations present the system response and control obtained with the proposed
Fig. 3. (a) DC source voltage. (b) DC source
current.
Figure 4 shows the SC voltage and current responses. The SC supply power to the load in the
transient and in the steady state no power or
66
11
10
L
R (Ω)
energy is extracted since the current iSC is nul.
The positive sens of iSC means that the SC supply
the load and the negative one corresponds to the
recover of energy by the SC. At time t = 4s, the
SC absorb the current pick to respond quickly to
the fast DC reference change.
9
8
7
(V)
E(V)
SC
V
1
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
30
12
11.999
11.998
0
25
20
0
1
2
3
t(s)
4
5
6
6
Fig. 6. (a) Load resistance change. (b) Load emf
change.
2
0
i
SC
(A)
4
−2
−4
−6
0
1
2
3
t(s)
4
5
6
100
Load
80
DC source
Fig. 4. (a) SC voltage. (b) SC current.
60
40
Power (W)
Figure 5 and Figure 6 present the network Boost
controller, the SC bidirectional converter controller, the changes in the load resistance RL and
in emf. UN and USC are in the set [0, 1].
SC discharge
20
0
SC
−20
−40
0.65
U
N
SC charge
−60
0.6
0.55
0
1
2
3
t(s)
4
5
0
1
2
3
t(s)
4
5
6
6
Fig. 7. Power transfers
0.8
U
SC
0.75
0.7
0.65
0.6
0
1
2
3
t(s)
4
5
6
Fig. 5. (a) Source Boost control. (b) SC converter
control.
Figure 7 presents the power transfers in the system. Power pick are absorbed or supplied by
SC, thus a smooth power is provided by the DC
source. This can reduce significantly the harmonics on the line.
It can be seen from Figure 2 that the system with
the proposed controller is robust towards load
resistance changes and emf variations.
5.2 Load works as a generator
The following simulations present the system response when the load is considered as a generator.
So, the proposed control laws can be tested during
recovery mode (between t=1s and t=4), only the
electromotive force (emf) is modified for these
simulations. The DC bus voltage is initialized at
36V and the DC Bus voltage reference is set at
42V.
in the emf (E). The DC Bus voltage tracks well
the reference during the first second, then a small
overshoot and a steady state error are observed
when the load current becomes negative. This is a
7% error which is acceptable in most of the case,
an improvement will be presented in section 6 to
cancel this error.
Figure 9 shows the source voltage and current. VN
stay at constant value, as it is explained in the
last simulations (5.1). A smooth behavior of the
current is observed regarding the changes in E,
this is because the SC supply the transient power.
When the load provides energy, all goes to the
SC because the DC-DC source converter is not
reversible.
67
Figure 11 shows the emf changes and the control
signals of the converters.
45
0.8
40
UN
d
V &V
DC
(V)
50
0.7
35
0
1
2
3
t(s)
4
5
0.6
6
USC
2
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
0.7
1
L
1
0.8
3
i (A)
0
0.6
0
50
0
1
2
3
t(s)
4
5
6
E(V)
−1
40
30
20
Load current.
control. (c) Load emf change.
16
V (V)
15.5
N
15
14.5
14
0
1
2
3
t(s)
4
5
6
8
N
i (A)
6
Figure 12 presents the power transfers in the
system. As in Figure 7, power pick are absorbed or
supplied by SC, so a smooth power is provided by
the DC source. During the energy recovery, all the
power coming from the load goes to the SC and
the DC source provides a very low power (due to
the source converter model).
4
100
2
80
0
1
2
3
t(s)
4
5
Load
6
60
current.
All the current provided by the load is absorbed
by the SC during the recovery mode, as shown
Figure 10. The SC supply power to the load in
the transient like it was shown in section 5.1. The
SC voltage increase when the load works as a
generator.
12.015
40
Power (W)
0
DC source
20
0
−20
−40
SC
−60
0
1
2
3
t(s)
4
5
6
The system behaviour follows requirements developed in section 3.
12.005
V
SC
(V)
12.01
12
11.995
0
1
2
3
t(s)
4
5
6
6. IMPROVEMENT
5
0
i
SC
(A)
6.1 New control
−5
0
1
2
3
t(s)
4
5
6
In the last solution, only one measure (iSC ) was
done. In order to cancel the steady state error on
the DC bus voltage, a integrator can be added. DC
bus voltage (VDC ) has to be known so its measure
is necessary. The integrator action is added in the
control equation u2 (10) and allows to reduce the
68
16
15.5
V (V)
15
N
error between VDC and Vd . So the new control
laws are:
⎧
⎨ u1 = ū1
(13)
⎩ u2 = ū2 − rx̃6 − Ki x̃3
14.5
14
The stability proof is given in [8]. Since the
close loop system is stable, the addition of an
intergrator do not modify the stability. In the next
part, the results are presented.
0
1
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
8
N
i (A)
6
4
2
6.2 Simulations
0
in the emf (E). The steady state error is cancelled with this new control but there is still an
overshoot around 8V. The current value is very
similar to the one Figure 8, except during the
recovery mode. Its value is different because DC
bus voltage is maintained at 42V.
current.
12.02
VSC(V)
For the simulations, the same configuration as in
5.2 is chosen, new control (13) is applied.
12.01
12
11.99
0
1
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
5
6
5
SC
(A)
45
40
0
i
d
V &V
DC
(V)
50
35
0
1
2
3
t(s)
4
5
−5
6
3
L
i (A)
2
1
0
−1
100
0
1
2
3
t(s)
4
5
Load
80
6
60
As shown Figure 14, during the energy recovery,
the DC source current goes close to zero because
the DC-DC converter is not reversible. A small
overshoot of the current is observed when the DC
source start to provide energy to the system (at
t=0s and t=4s).
Figure 15, the SC still provide transients, but do
not go to zero during steady state. This is due to
the new term in the control equation 13. So when
the load absorbs energy, the DC source and the
SC provide it together.
The same thing can be underline on Figure 16,
the load power is the sum of SC and DC source
power during steady state.
Figure 17 shows the emf changes and the control
signals of the converters.
40
Power (W)
Load current.
DC source
20
0
−20
−40
SC
−60
0
1
2
3
t(s)
4
7. CONCLUSION
A modeling of hybrid sources system composed
of a DC energy source and SC power source is
presented. PCH structure of the overall system is
given exhibiting important physical properties in
terms of variable interconnection and damping of
the system. The problem of the DC Bus Voltage
69
U
N
0.8
0.7
0.6
0
1
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
0
1
2
3
t(s)
4
5
6
U
SC
0.8
0.7
0.6
E(V)
50
40
30
[6] M. Becherif, M.Y. Ayad and A. Miraoui,
“Modeling and Passivity-Based Control of Hybrid Sources: Fuel Cell and Supercapacitors”
41st IEEE-IAS, 2006
[7] M. Becherif, “Passivity-Based Control of Hybrid Sources: Fuel Cell and battery” 11th IFAC
Symposium on Control in Transportation systems, 2006
[8] R. Ortega and E. Garcia-Canseco, “Interconnection and Damping Assignment PassivityBased Control: A Survey”, European Journal
of Control, 2004
20
control. (c) Load emf change.
control is solved using simple linear controller
based on an IDA-PBC approach.
An important property has to be underline, only
iSC measure is needed for the first controller (10).
Global stability proof is given and encouraging
simulation results has been obtained. Many benefits can be expected from the proposed structure
such that supplying and absorbing the power picks
by using SC which also allow recovering energy. At
the same time, this can reduce significantly the
harmonics on the line.
Finally, two sensors (instead of one) are used to
cancelled the steady state error with an integrator
(13). Thus depending of the application requirements, a solution with one sensor can be chosen
or a second solution with two sensors.
REFERENCES
[1] A.J van der Schaft, B.M. Maschke, “On the
hamiltonian formulation of nonholonomic mechanical systems”, Reports on Mathematical
Physics, vol.34, no.2, pp.225-233, 1994.
[2] R. Ortega, A. Loria, P.J. Nicklasson, and
H. Sira-Ramirez, “Passivity-based control
of Euler-Lagrange systems,” in Communications and Control Engineering. Berlin,
Germany:Spring-Verlag, 1998.
[3] R. Ortega, A.J van der Schaft, B. Maschke
and G. Escobar, “Interconnection and damping assignment passivity-based control of portcontrolled hamiltonian systems,” Automatica
vol.38, pp.585-596, 2002.
[4] M. Becherif and E. Mendes, “Stability and
robustness Disturbed-Port Controlled Hamiltonian system with Dissipation,” 16th IFAC
World Congress, Prague ,2005,
[5] S.M. Halpin and S.R. Ashcraft, “Design considerations for single-phase uninterruptible
power supply using double-layer capacitors as
the energy storage element” IEEE-IAS, San
Diego, 1996, v4, pp 2396–2403
70
HYBRID ELECTRIC VEHICLES :
FROM OPTIMIZATION TOWARD REAL-TIME
CONTROL STRATEGIES
Gregory Rousseau ∗,∗∗ Delphine Sinoquet
Pierre Rouchon ∗∗
∗
∗
Institut français du pétrole, 1 et 4, avenue de Bois-Préau,
92852 Rueil-Malmaison Cedex - France
∗∗
Ecole des Mines de Paris
Abstract: Hybrid-electric vehicles appear to be one of the most promising technologies for reducing fuel consumption and pollutant emissions. The presented
work focuses on two types of architecture : a mild hybrid and a full hybrid where
the kinetic energy in the breaking phases is stored in a battery to be re-used
later via the electric motor. This additional traction power allows to downsize
the engine and still fulfill the power requirements. Moreover, the engine can be
turned off in idle phases for both architectures and for the parallel architecture,
it may be turned off whereas the electric motor furnishes all the traction power.
The optimal control problem of the energy management between the two power
sources is solved for given driving cycles by a classical dynamic programming
method and by an alternative method based on Pontryagin Minimum Principle.
The real time control laws to be implemented on the vehicle are derived from the
resulting optimal control strategies. These control laws are evaluated on another
driving cycle which was not given a priori.
Keywords: Hybrid vehicle, Optimal control, Dynamic programming, Pontryagin,
Control strategies
1. INTRODUCTION
Growing environmental concerns coupled with
concerns about global crude oil supplies stimulate research on new vehicle technologies. Hybridelectric vehicles appear to be one of the most
promising technologies for reducing fuel consumption and pollutant emissions (German, 2003) :
mainly thanks to the system stop’n go that allows
to turn off the engine in idle phases, to the recuperated braking energy to be stored in a battery
and re-used later via the electric motor and to the
possibility to downsize the engine.
The energy management of hybrid power trains
requires then some specific control laws : they rely
on the estimation of the battery state of charge
which provides the remaining level of energy, and
the variable efficiency of each element of the power
train has to be taken into account. Optimization
of energy management strategies on given driving
cycles is often used to derive sub-optimal control
laws to be implemented on the vehicle (see among
others (Sciarretta et al., 2004), (Scordia, 2004),
(Wu et al., 2002), (Delprat, 2002)).
IFP, in partnership with Gaz de France and the
Ademe, has combined its downsizing technology
with a natural gas engine in a small urban demonstrator vehicle (VEHGAN vehicle), equipped with
a starter alternator and supercapacitor manufactured by Valeo (Tilagone and Venturi, 2004).
71
80
0.19
0.2
0.18
0.23
0.22
0.21
70
0.2
00000.2
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.2124
21389
60
0.
5
0.2
24
0.26
50
40
30
20
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0.2
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205.
.2021213.489
0000..2. 0.27
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0.3 0.31
0.28
0.32
0.330.34
0.29 3
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0. 0.31
0.32
0.365 0.37 0.3
0.
0.3
0.330.34
0.38
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0.32
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0.3
1 20.44
0.4
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0.39
0.36 0.3
0. 00.43
0.4
0.3530.34
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4
0.3
0.4
5
0.42
4
0
4
0.41
.
0.43
0.3
9
5 0 3
0.44
0.36 0.37
0.38
0.40.3
0.42
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1
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0.40.39
0.4
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0
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3
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34
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18
0.
37
2
23
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24
0.
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0.
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0.2
Engine Torque (N.m)
90
8
0.02.29 0.3
In this paper, we present two different optimization algorithms and apply them to a simplified
model of the VEHGAN vehicle and to a parallel
architecture version of this vehicle: a classical Dynamic Programming algorithm ((Wu et al., 2002),
(Scordia, 2004), (Sciarretta et al., 2004)), and an
original algorithm based on Pontryagin Minimum
Principle that allows to handle constraints on the
state and control variables. Finally, we propose
two types of control strategies derived from the
optimization results on given driving cycles and
evaluate them as a real time strategy on a driving
cycle which was not given a priori.
1000
2000
4000
3000
Engine Speed (rpm)
5000
6000
Fig. 1. Fuel consumption map of natural gas
engine of VEHGAN vehicle
2. SYSTEM MODELLING AND OPTIMAL
CONTROL PROBLEM
2.1 Characteristics of the considered hybrid vehicle
Two different architectures are modelled:
• a mild hybrid architecture : the engine can
not be stopped when the requested torque is
provided only by the electric motor, except
for the stop’n go mode at the idle speed.
So, for a control that cancels the engine
torque and for positive torque request, the
fuel consumption does not vanish (Figure 1),
• a full parallel hybrid architecture : the engine
can be stopped to let the electric motor
power alone the vehicle. In that case, the fuel
consumption vanishes.
In both cases, the battery is regenerated in braking phases accordingly to the available minimum
electric torque at the considered engine speed.
In order to solve the optimal control problem of
energy management, we build a simplified model
which is composed of :
• a driving cycle to be followed (imposing vehicle speed and gear shifts),
• a vehicle model defining its mass, wheel inertia, resistance force,
• a manual gearbox with 5 gear ratios,
• a 660CC natural gas engine characterized by
a fuel consumption map displayed in Figure 1
and a maximum torque depending on the
engine speed (see (5)),
• a starter alternator (3kW for mild-hybrid,
6kW for full-hybrid) characterized by a maximum torque and a minimum torque for regenerative braking phases, both depending
on the engine speed (see (6)). Its efficiency is
assumed to be 1 in the presented examples,
• a battery characterized by a capacity of
0.4Ah for mild-hybrid architecture and 40Ah
for full-hybrid one. The variations of the battery state of charge are modelled by
ẋ(t) = −
ω(t)Tm (t)K ′
Ubatt ncapa
(1)
with ω(t), the electric motor and engine
speed (assumed to be equal), Ubatt , the battery voltage considered to be constant, K ′ ,
a scaling constant and ncapa , the nominal
capacity of the battery.
The driving cycle is converted in a (engine speed,
torque) trajectory either thanks to a backward
model based on the vehicle model, or thanks to a
forward model as in AMESim Drive library which
furnishes a more realistic trajectory taking into
account a simulated behavior of a driver as the
anticipation of the driving cycle.
2.2 Optimal Control Problem
The optimal control problem under study consists
in minimizing the fuel consumption of the vehicle
along a given driving vehicle cycle, taking into
account physical constraints from battery, engine
and electric motor. The control variable associated with this problem is called u(t). It represents
the distribution of the requested torque Trq , between the engine torque Te and the electric motor
torque Tm , written as

 Trq (t) = Te (t) + Tm (t)
Te (t) = u(t)Trq (t)
(2)

Tm (t) = (1 − u(t))Trq (t).
The state variable is the battery state of charge
x(t) and follows from (1)
ẋ(t) = −Kω(t)(1 − u(t))Trq (t) = f (u(t), t), (3)
where K =
K′
Ubatt ncapa .
The resulting optimization problem is then the
following :
72



ZT







min
J(u)
=
L(u(t),
t)dt
+
g(x(T
),
T
)

 u 

0

subject to : ẋ = f (u(t), t),




x
≤ x(t) ≤ xmax

 min
umin (t) ≤ u(t) ≤ umax (t)
x(0) = x0
3. DYNAMIC PROGRAMMING
OPTIMIZATION
(4)
with 0 and T , respectively the initial and the
final times of the given driving cycle, L(u(t), t),
the instantaneous fuel consumption, computed
from the map displayed in Figure 1, g(x(T ), T ),
the penalization term that constrains the final
state of charge to be close to the initial state of
charge in order to maintain a null electrical energy
balance (to avoid to discharge totally the battery
for minimizing the consumption).
The bound constraints on the state and on the
control in (4) are derived from the following constraints :
• the engine can only produce a positive
torque, and is limited to a maximum torque
which depends on engine speed ω(t), written
as 0 ≤ Te (t) ≤ Temax (ω(t)), and leads to
0 ≤ u(t)Trq (t) ≤ Temax (ω(t)),
(5)
• the electric motor torque is limited between
a maximum torque and a minimum torque
min
(ω(t)) ≤
during regenerating breaking, Tm
max
Tm (t) ≤ Tm (ω(t)), and leads to the control
constraints
The Dynamic Programming method (DP) is classically used to solve the problem (4) ((Wu et
al., 2002), (Scordia, 2004)) : it relies on the principle of optimality or Bellman principle. First, the
optimal control problem (4) is discretized in time

N
−1

X


 min J(u) :=
Lk (uk ) + g(xN )
uk ∈Uk
(8)
k=0



 subject to : xk+1 = fk (xk , uk ), x(0) = x0
xmin ≤ xk ≤ xmax
where Lk (uk ) is the cumulated fuel consumption
over the time interval [k, k + 1], xk is the state
of charge of the battery at time k, fk is the
function that modelizes the battery state of charge
evolution in the discrete form of (3) and g(xN ) =
β.(xN − x0 )2 is the penalization term for the
constraint on final state of charge (β is a constant
to be chosen 1 ), N being the final time of the
driving cycle.
From Bellman principle, the minimum cost Vk (xk )
at the time step k, 0 ≤ k ≤ N − 1, is expressed as
Vk (xk ) = min (Lk (uk ) + Vk+1 (fk (uk ))).
uk ∈Uk
(9)
At time N , the cost function is VN (xN ) = g(xN ).
This optimization problem is solved backward
from final time step to initial time step using a
max
min
(ω(t)),(6) discretization of function V in the control space
(ω(t)) ≤ (1 − u(t))Trq (t) ≤ Tm
Tm
and in the state space.
• the storage capacity implies a minimum and
a maximum state of charge of the battery
(which are fixed to 0% and 100% in our
3.1 DP Optimization algorithm
example)
xmin ≤ x(t) ≤ xmax .
(7)
In this optimal control problem, we make several
assumptions
A standard time step used in our examples is 1s,
and the step for state discretization is 0.5%. Two
algorithms may be used to solve the DP problem :
• a classical DP algorithm, called Ford algorithm in the following (Scordia, 2004), consists in exploring all the feasible controls (to
go from a point xik to an other point xjk+1 ),
finally taking the best trajectory (the trajectory which minimizes at each step k the sum
Lk (uk ) + Vk+1 (fk (uk ))). In such a method,
the state of charge trajectory remains on the
points of the defined grid in the state space
which may lead to inaccurate results.
• the chosen algorithm interpolates the function V (xk , k) in the state space, for each
time step k thanks to an upwind scheme
(Guilbaud, 2002) :
• the pollutant emissions are not taken into
account in the optimization process,
• the engine speed and the electric motor speed
are equal,
• in the mild hybrid case, recharging the battery is only possible for negative torques
(breaking request), we did not consider regeneration by an additional engine torque
beyond the driver request torque. Thus the
control u(t) remains between 0 and 1. In the
full hybrid case, u(t) can take values larger
than 1, allowing battery regeneration with
additional engine torque.
In the following, we will call U (t) in continuous
time (respectively Uk in discrete time) the feasible
domain for u(t) (respectively uk ) with respect to
the constraints (5) and (6).
1
In the following results, a value depending of battery
capacity has been implemented
73
Torque (Nm) and Speed (m/s)
Vehicle speed and requested torque
100
Requested torque (Nm)
Vehicle speed (m/s)
80
60
40
20
0
0
200
100
300
900
800
700
600
500
Time
State of charge trajectories
400
1000
100
State of charge (%)
80
60
40
20
0
−20
0
200
100
300
400
500
Time (s)
600
Upwind scheme with dX=2.5% − CPU Time 86s
Upwind scheme with dX=0.5% − CPU Time 354s
Ford algo with dX=2.5% − CPU Time 18s
Ford algo with dX=0.5% − CPU Time 197s
PMP algorithm − CPU Time 3s
1000
900
800
700
Fig. 2. Urban Artemis cycle (Top); Optimal state of charge trajectory of VEHGAN vehicle computed
with PMP & DP algorithm (Bottom).
Vk (xik ) = min [∆tLk (uk ) + Vk+1 (xik+1 )
uk ∈Uk
+fk (uk )
i−1
Vk+1 (xik+1 ) − Vk+1 (xk+1
)
∆t], (10)
∆x
where ∆x and ∆t are respectively the state
and the time discretization step size. We refer
to (Guilbaud, 2002) for some theoretical results on the convergence of this method and
error estimations. Therefore, it is possible
to use a (state) continuous constrained optimization algorithm to solve each problem (9)
which should furnish more accurate results
than Ford algorithm. Nevertheless, this algorithm is generally more expensive in terms of
computing time.
These two optimization algorithms are only used
when Trq > 0 : when the requested torque is
negative, the optimal control uk is completely
known, as the battery is regenerated as much as
possible, the control uk being constrained by the
minimal electric motor torque from (6) and by
maximum SOC from (7).
Optimization results obtained with DP method
are displayed on Figure 2.
4. PONTRYAGIN MINIMUM PRINCIPLE
OPTIMIZATION
In this section, we propose an alternative method
to solve the optimal control problem (4). It relies
on the Pontryagin Minimum Principle (PMP)
and unlike the DP method does not require any
discretization scheme.
4.1 Pontryagin Minimum Principle
First we consider the optimization problem (4)
and introduce the Hamiltonian function, without
considering state and control constraints
H(u(t), x(t), p(t)) = L(u(t), t) + p(t)ẋ(t).
(11)
p(t) is called the co-state of our system. We
assume here that L is a smooth convex function
of u.
The Pontryagin Minimum Principle states the
following conditions for the unconstrained optimal
control problem :
∂H
= −ṗ
∂x
and
∂H
= 0.
∂u
(12)
We refer to (Pontryagin et al., 1974) and (Bryson
and Ho, 1975) for further details about Pontryagin
Principle.
4.2 Application
The fuel consumption L(u(t), t) to be minimized
in (4), is defined by a discrete map L(ω, Te ), mod-
74
elled by a 2-order polynomial, which is represented
as
2
X
L(ω, Te ) =
Kij ω i Tej ,
which allows to model a large variety of engine
maps (Rousseau et al., 2006).
4.2.1. Mild-Hybrid case In the mild-hybrid vehicle case, the fuel consumption can not be cancelled. We do not consider the stop and start, as
well as the possibility to power the vehicle only
with the electric motor.
From (12) and (3) we obtain
ṗ = 0 ⇒ p = constant = p0 .
(14)
Without any constraint on the state and on the
control, the problem of minimizing H can be easily
solved. The minimum fuel consumption is then
reached for u∗ so as
∂f
∂L
∂H
= 0.
+p
=
∂u
∂u
∂u
(15)
The optimal control u∗ can be calculated easily by
solving the equation (15), which depends linearly
on u (thanks to (3) and (13)) . u∗ finally depends
on p(t), Trq (t) and ω(t)
u∗ (t) = − i=0
2
Ki1 ω(t)i + p0 .K.ω(t)
2
X
.
(16)
Ki2 ω(t)i .Trq (t)
i=0
The expression of p0 is obtained by replacing
u∗ (t) by its expression in the state equation (3),
and by integrating this equation in time, between
Tinit and τ , Tinit and τ being respectively the
considered initial and final times.
4.2.2. Full-Hybrid case
With the full-hybrid
case, we have to consider the possibility to power
the vehicle only with the electric motor. The
previous expression of Hamiltonian becomes unadapted, as the fuel consumption can be completely cancelled. The fuel consumption function
is then discontinuous
0
if u(t) = 0
Lf h (ω(t), T e(t)) =
(17)
L(ω(t), T e(t)) if u(t) 6= 0.
The Hamiltonian, in the only electric motor case
(u(t) = 0), is then written
Hm (x(t), p(t)) = p(t)ẋ(t).
u∗ = argmin[H(u(t), x(t), p(t)), Hm (x(t), p(t))].(19)
(13)
i,j=0
2
X
The optimal control u∗ must then be written as
(18)
4.2.3. Handling constraints on control and state
variables
The previous section presents the
computation of the optimal control of the continuous problem in a restricted case where no
constraint is introduced. While control constraints
are generally easily taken into account, handling
the state constraints in the continuous optimal
control problem is cumbersome: several singular
cases can be found in (Bryson and Ho, 1975).
In our application, we are not able to find an
analytic solution of the optimal control problem
with control constraints : indeed, these constraints
depends on time and depends on p0 which depends
on final SOC (cf. previous section). By an iterative
method (called algo1 in the following), we can
compute the value of p0 in order to reach the
desired SOC at final time with the control, expression (16), projected on its bound constraints.
(Hartl et al., 1995), (Pontryagin et al., 1974),
(Evans, 2000), (Bryson and Ho, 1975), (Guilbaud,
2002) have studied the general problem (4) with
the state constraints. In our application, we can
show that p(t) presents discontinuities at the
time steps where the state inequality constraints
are saturated. These time steps are not a priori
known : this prevents us to solve explicitly the
continuous optimal control problem with these
state constraints.
4.2.4. PMP Optimization algorithm Considering the difficulties described in previous section,
we propose a heuristic iterative method that allows to find a sub-optimal trajectory from the
constrained continuous optimal control problem
(4). The proposed algorithm consists in an initialization step and 3 steps :
(0) algo1 is applied on the driving cycle [0, T ]
(see Figure 3 Step 0). The obtained optimal
trajectory violates the state constraints, the
farthest SOC (ie the ”most violated point”)
from the bounds being for instance at point
(x(tv ) = −37%, tv = 818s). The initial time
is called ti , here set to 0.
(1) The SOC at tv is projected on the nearest
bound of the feasible state domain (for instance, SOC is fixed to xmin = 0 at point
tv ).
(2) algo1 is applied again on [ti , tv ] (see Figure 3
Step 2). If the obtained trajectory still violates the state constraints on [ti , tv ], steps 1
and 2 are applied again on the farthest SOC
from the bounds (defining a new point tv ).
This procedure is repeated until the trajectory remains on the feasible domain. Then
75
Step 0
80
60
kinetic energy, we assume that it is possible to
recharge the battery by using the engine at better
OP, with an ideal efficiency of 1.
Step 3
100
80
40
SOC
SOC
60
20
40
0
20
−20
−40
0
200
400
600
Time
Step 1 & 2
800
1000
1200
100
0
0
800
600
Time
Final trajectory
1000
1200
800
1000
1200
200
400
200
400
100
80
80
60
40
SOC
SOC
60
20
40
0
20
−20
−40
0
200
400
600
Time
800
1000
1200
0
0
600
Time
Fig. 3. The proposed algorithm based on Pontryagin Minimum Principle.
the last point tv becomes the new initial time
ti in step 3.
(3) algo1 is applied on [ti , T ] (see Figure 3 Step
3). If the obtained optimal trajectory still
violates the state constraints, steps 1 and 2
are repeated. This sequence is repeated until
we reach the final step T at the desired final
SOC, without violating the state constraints
(Figure 3 bottom right).
4.3 Some optimization results
4.3.1. Mild Hybrid case We can compare the
two optimization algorithms (DP and PMP) on
the Urban Artemis driving cycle (André, 2004),
in the mild Hybrid case, on Figure 2. The curves
are very similar; we can notice that smaller is the
state step size, nearer to the PMP curve are the
DP curves.
Figure 4 presents the operating points (OP) of the
engine obtained with PMP algorithm.
In this vehicle configuration, the state constraints
are active 5 times, giving 6 different values of the
Lagrange multiplier p(t). We display the six curves
∂H
(p) = 0, which give optimal en(green lines) ∂T
e
gine torque, function of engine speed. The engine
OP are thus moved toward the green optimal
curves when it is possible: the OP located below
the curves remain unchanged (no battery regeneration being possible for positive torque requests
for mild hybrid) whereas the OP located above are
moved toward the curves by decreasing the engine
torque as much as possible (saturating electric
motor torque constraints).
4.3.2. Full Hybrid case Figure 5 gives optimized
operating points for the engine and the electric
motor (PMP algorithm is used). In addition to
As for mild-hybrid case, the optimal trajectory
(continuous green line) gives the optimal operating points of the engine by finding the solution of
∂H
∂Te = 0. Thus, many of low torque OP are moved
to the optimal trajectory, recharging the battery
by imposing a negative electric motor torque. As
the full-hybrid configuration allows to turn off
the engine for non-zero vehicle speed (pure electric mode), most of OP associated with engine
speed below 3000 rpm and requested torque below
20Nm, lead to turn off the engine (points where
engine torque is zero) : turning off the engine
is more efficient than the optimal engine torque
∂H
= 0).
(green curve : ∂T
e
5. REAL-TIME CONTROL
From optimization results on Urban Artemis cycle, we derive suboptimal control laws that will
be tested on an other cycle. In this section, the
FTP72 cycle has been chosen, for its realism of
urban driving.
Two different control laws will be tested : the first
one, based on Optimization results from Pontryagin principle, consists of varying the value of p
regarding to the state of charge, to control u(t),
then the electric motor. The reference Lagrange
multiplier value p is the mean of optimal values of
p, obtained on Artemis Urban cycle with off-line
optimization using PMP algorithm.
The second one uses a map of electric motor
torque created by the optimization results on
Urban Artemis cycle. The electric motor torque
from the map is then weighted by the state of
charge of the battery : reduced if the SOC is
low, increased if the SOC is high. The obtained
results are displayed in Table 1. For the mild hybrid configuration, the suboptimal laws give fuel
consumptions which are close to the optimal one.
Table 1. Fuel Consumption
Consump.
(l/100km)
Th.
veh.
Optimal
control
Mild-H.
3.32
3.22
Mild-H with
Stop’n go.
Full-H.
p-control
based
3.23
Elec. mot.
torq. map
3.23
(-3,01%)
(-2,71%)
(-2,71%)
2.86
(-13,62%)
2.70
(-18.67%)
2.87
(-13,49%)
2.83
(-14,76%)
2.88
(-13,33%)
2.86
(-13,85%)
For the full hybrid architecture, the two control
laws give degraded results compared to optimal
results. Many reasons can explain these differences. First, even if Urban Artemis cycle and
FTP72 cycle are both realistic of an urban driving, operating points are very different. While
76
110
Engine operating points
Electric motor operating points
Requested operating points
Optimal operating point lines
100
90
80
Request Torque
70
60
50
40
30
20
10
0
1000
1500
2000
3000
2500
Engine Speed
3500
4000
4500
Fig. 4. Operating points of engine in Mild-Hybrid mode obtained by PMP algorithm for the urban
Artemis Driving Cycle.
100
Optimal operating point line
Engine operating points
Electric motor operating points
Requested operating points
80
Requested Torque
60
40
20
0
−20
1000
1500
2000
2500
Engine speed
3000
3500
4000
4500
Fig. 5. Operating points of engine in Full-hybrid mode obtained by PMP algorithm for the urban Artemis
Driving Cycle.
77
requested operating points of Artemis cycle are almost uniformly located in the whole engine speed
and torque space, all requested operating points of
FTP72 are below ω = 3200 rpm, with a majority
below ω = 2000 rpm. The consequence is a unadapted electric motor map for the second control
law. Concerning the first control law, the optimal
p (obtained with PMP algorithm on FTP72) is
quite different from the optimal p obtained for
Artemis cycle, leading to degraded results.
Nevertheless, the consumption gain remains high :
−14.76%.
These results illustrate that several driving cycles
are needed to develop efficient suboptimal control
laws based on p-control or electric motor map.
The vehicle speed (related to engine speed by gear
ratios) could also be taken into account to improve
fuel consumption gains.
6. CONCLUSIONS
In this study, we have presented two methods
for optimal control optimization. The heuristic
method based on Pontryagin Minimum Principle,
well known in the free state constraint case, has
been applied successfully to our state constrained
problem, with very similar results to Dynamic
Programming methods and a computation time
divided by 100. Nevertheless, there is currently no
theoretical proof to confirm the presented validation results. Moreover, there are some limitations
to this approach, mainly the assumptions on the
fuel consumption map, modelled by a smooth convex function of control u (2-order polynomial) ;
this limitation could lead to a bad approximation
of the real fuel consumption for some particular
engines.
Other degrees of freedom, as the gear-shifting
sequence should also be taken into account in
the optimization problem to improve the fuel consumption gain. Reduction of pollutant emissions
will also be studied by considering a second state
based on exhaust temperature.
From optimization results are derived two types of
suboptimal feedback laws based on state of charge
measurements. These laws give encouraging results even if it needs to be improved in the full
hybrid case.
REFERENCES
André, M. (2004). The artemis european driving cycles for measuring car pollutant emissions. Science of The Total Environment 334335, 73–84.
Bryson, E. and Y.C. Ho (1975). Applied Optimal
Control. Hemisphere Pub. Corp.
Delprat, S. (2002). Evaluation de stratégies de
commande pour véhicules hybrides parallèles.
PhD thesis. Université de Valenciennes et du
Hainaut-Cambresis.
Evans, Lawrence C. (2000). An Introduction To
Mathematical Optimal Control Theory. University of California Berkeley.
German, J.M. (2003). Hybrid powered vehicles.
Society of Automotive Engineers (SAE).
Guilbaud, T. (2002). Méthodes numériques pour
la commande optimale. PhD thesis. Université de Paris VI.
Hartl, Richard F., Suresh P. Sethi and Raymond G. Vickson (1995). A survey of the
maximum principles for optimal control problems with state constraints. SIAM Review.
Pontryagin, L.S., V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko (1974). Théorie
mathématique des processus optimaux. Editions Mir moscou.
Rousseau, G., D. Sinoquet and P. Rouchon (2006).
Constrained optimization of energy management for a mild-hybrid vehicle. E-COSM Rencontres Scientifiques de l’IFP.
Sciarretta, Antonio, Lino Guzzella and Michael
Back (2004). A real-time optimal control
strategy for parallel hybrid vehicles with onboard estimation of the control parameters.
Proceedings of IFAC Symposium on Advances
in Automotive Control AAC04 pp. 502–507.
Scordia, J. (2004). Approche systématique de
l’optimisation du dimensionnement et de
l’élaboration de lois de gestion d’énergie de
véhicules hybrides. PhD thesis. Université
Henri Poincaré - Nancy 1.
Tilagone, R. and S. Venturi (2004). Development
of natural gas demonstrator based on an urban vehicle with a down-sized turbocharged
engine. Oil and Gas Science and Technology
59(6), 581–591.
Wu, B., C-C. Lin, Z. Filipi, H. Peng and
D. Assanis (2002). Optimization of power
management strategies for a hydraulic hybrid medium truck. Proceeding of the 2002
Advanced Vehicle Control Conference, Hiroshima, Japan.
ACKNOWLEDGMENTS
We would like to thank Gilles Corde, Philippe
Moulin and Antonio Sciarretta for helpful discussions and advice at various stages of the elaboration of this work. We acknowledge Quang Huy
Tran for his advice on numerical methods.
78
PERFORMANCE TESTING OF HYBRID VEHICLES IN BARI DOWNTOWN
L. Mangialardi, L. Soria, N. Caccavo, G. Carbone
Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Bari (IT)
Abstract: The analysis of homologation rules ECE 91/441 and further modifications has
moved the authors of this paper to investigate how a driving cycle taking place in the
realistic traffic conditions of a town could lead to different results in terms of fuel
consumption, when compared to the ones obtained by cars manufacturers in respect of the
standard cycles proposed by the European Standards. By this, two driving cycles have
been considered and experimented in the city of Bari, Italy, one following a urban route,
the other taking place on a suburban track. The experiments have been carried out
utilizing two different Hybrid Electric Vehicles provided by two leading and competing
car Manufacturers. The analysis of those experiments has shown which architecture can
be more suitable for final users, and how far the homologation standards are from reality.
Also the theoretical amount of kinetic energy that could be recovered thanks to this class
of passenger cars has been investigated.
Keywords: HEV, series/parallel hybrid vehicles, ECE 91/441 cycle, regenerative energy,
fuel consumption.
1. ARCHITECTURE OF HYBRID ELECTRIC
VEHICLES
The complete panorama of HEV classes is showed in
fig.1 (see Cerami, 2005, Genta, 2000).
The indication “Hybrid Vehicle” sometimes is not
enough to precisely identify the architecture of the
vehicle under consideration, as behind the same
name many differences are hidden especially
depending on the ‘mission’ of the vehicle. That is
why it is necessary to analyze this various
typologies.
1.1 HEV Components and classification
Before describing the Hybrid Electric Vehicles
(which will be referred to as HEV) classes, it is
necessary to briefly summarize the components that
typically can be found on board of any of these
vehicles.
On all HEV one can always find an internal
combustion engine (ICE), an electric machine (also
called motor), a battery pack, a power converter and
a transmission, that mechanically links engines to
wheels.
The way by which these components match,
generates a different classification of HEV:
-
Series Hybrid;
Parallel Hybrid;
Series –Parallel Hybrid;
Complex Hybrid.
Fig. 1. Classification scheme of HEVs
To completely develop the potentiality of HEV it is
necessary to design carefully what is called the
Power Management, that is the control strategy
which determines the management and use of power
sources. Usually this control strategy is operated by a
control unit which can coordinate the hybrid system
to satisfy certain aims such as fuel saving, polluting
emissions reduction and performances optimization
(see Amelia, 2005; Szumanowski, 2000).
79
Although the Power Management depends on
the vehicle architecture, we can identify some
common characteristics:
1.
2.
3.
4.
the electric machine can work as an
electromechanical converter in order to
assure the power flow from batteries to
wheels and vice-versa;
batteries can be recharged during
decelerations and/or braking (Regenerative
Braking);
it is possible to move the vehicle only by
the electric machine, in order to obtain a
complete Zero Emissions Vehicle (but not
for all the hybrid vehicles);
in case of vehicle stop or in other
circumstances, when the driver does not
require power, the thermal engine can be
switched off (Idle Stop Mode), with a
consequent fuel saving and a temporary
interruption of emissions (see Westbrook,
2001).
1.2 The hybrid vehicles utilized for the tests
The HEVs considered for the investigation have been
two cars competing on the European market: the
Toyota Prius and the Honda Civic IMA (Integrated
Motor Assist) (see fig. 2). These two vehicles have a
different architecture (Prius is a series/parallel
hybrid, Civic IMA is a parallel one) but they are
comparable in terms of weight (see Toyota Prius,
Caratteristiche Nuovo Modello, 2003, and Honda,
Gamma Civic’04, 2003).
Fig. 2. The two utilized cars: Toyota Prius (left) and
Honda Civic IMA
As a consequence of the different architecture the
power management is of course different in the two
cases: in the parallel architecture of Honda the motor
only gives an “assist” (overboost effect) when the
driver asks for more torque, whereas in the Toyota
case the motor can work also in synergy with the
combustion engine. In fact on the Toyota Hybrid
System the motor can, under certain conditions,
move the car on its own, creating in this way, a Zero
Emissions
Vehicle
(ZEV).
Moreover
the
transmission of the Honda Civic is a classic
mechanical five gears gearbox, while on the Toyota,
torque is transferred to wheels thanks to an epicyclic
gear which is automatically controlled.
2. TESTS
Before getting in production, each car is subjected to
a series of tests aiming to measuring the fuel
consumption and polluting emissions by using
standard procedures as to make the results
comparable.
2.1 ECE Directives
Measurements take place in closed chambers under
controlled atmosphere, where the vehicle is placed on
a “rolling-test bench” which is able to vary the
resistance force and therefore simulate the rolling
resistance of tyres and the aerodynamic drag. The
test is carried out by a driver who continuously
follows the velocity cycle and the gear shift sequence
(shown on a screen) as requested by the European
Standards. The tests are completed with the analysis
of the exhaust gases operated by an instrumentation
downstream the car exhaust pipe. It is interesting to
point out that among the European Countries it exists
a sort of standardization for what concerns the
collection of polluting emissions and the analysis of
the fuel consumption data. But, not the same happens
in the case of the sequences of accelerations, speeds
and gear shifting that has to be followed during the
tests. Nowadays, several standard cycles exist (five
are the most important) which reproduce the average
use of passenger cars in Europe, United States and
Japan. In Europe, at the end of the ‘60s, the
environment and energy saving aspects have lead to
the birth of the international commissions, whose
goal was the monitoring of real traffic conditions in
different urban textures. These commissions
generated a series of judging criteria which gave life
to the European Directive ECE R15-04 which has
been utilized till to a few years ago. The ECE R15-04
cycle was made of an ideal track of 1013 meters to
be repeated four times at the following conditions: (i)
average speed of 18.7 km/h, (ii) maximum speed of
50 km/h and (iii) duration time of engine idling mode
equal to 31% or total running time. Later –in 1993–
in order to take into account also higher vehicle
speeds, the European Ministry Council approved a
new homologation cycle, the ECE 91/441, that
modified the previous one by adding a new piece of
track at higher speed for a total length of 11 km. The
average and maximum speeds in this case became
respectively of 32.5 and 120 km/h. At the same time
more severe restrictions were put on polluting
emission limits, this was the Directive Euro 1.
Directives Euro 2, 3 until 4 follow substantially the
same methodology but imposing more and more
severe restrictions.
2.2 Merits and lacks of the ECE standards
From the given information it is clear that the
homologation directive 91/441 and its further
modifications offers some important advantages:
• fixing the test parameters, they allow a
direct
comparability
among
the
performances of different vehicles operating
in similar conditions;
80
•
the cycle is of great utility in the statistical
study of vehicles reliability in long periods,
offering conditions that are easily
reproducible in industrial environments.
Unfortunately, to this positive notes some evident
limitations are opposed:
o the cycle does not reproduce the real
driving style of an average driver,
especially in metropolitan areas where the
traffic conditions are more severe and the
vehicle is subjected to a higher frequency
of “stop-&-go”;
o the ECE cycle does not follow any realistic
urban topography, it is just an ideal track,
not related at all to the actual traffic
conditions, fuel consumption and polluting
emissions which can be encountered in day
life;
o recorded data on fuel consumption result
fake: in particular they show fuel
consumptions to be better than realistic
values, providing to the user, in this way,
not completely reliable indications;
o the measured emissions – directly
depending on the amount of burnt fuel –
may be altered and, by consequence,
polluting emission values can be higher
than the ones obtained respecting the
European standards.
Because of the aforementioned limitations and due to
the fact that actual standards, having been developed
on the basis of studies of more than forty years ago,
do not provide such realistic consumption values as
to support the final user with reliable information, an
analysis of fuel consumptions in realistic traffic
conditions is needed. The European Community
scientific society does agree with these outlines as
witnessed by the creation of the Artemis cycle – in
many ways similar to the ones realized in this work –
proposed by some research institutes leaded by the
TNO (NL) as a valid alternative to the actual norms
(see TNO Report, 2003).
The traffic conditions under consideration are those
that can be encountered in the city of Bari. The
topography of the city shows an average sidewalk
length shorter than the typical middle European
town (which may be better represented by the ECE
cycle because of their smaller number of stop-&-go),
and closer to that of the southern Europe towns.
2.3 Track choice
In order to have a complete scenario of a driver real
ride, the test was split in two tracks:
1.
2.
urban cycle
suburban cycle.
As a starting point it was chosen the Dipartimento di
Ingegneria Meccanica e Gestionale (DIMeG),
located in Japigia district in the southern part of the
city. The Urban cycle (also referred to as the slow
test) has been conceived with speeds always lower
than 50 km/h (law limit). From the DIMeG the two
vehicles moved towards the downtown, where
offices and shops are located, drawing a closed ring
track; tests were performed during daytimes, from
8.30 – 9.30 a.m. to 1.00 – 1.30 p.m., when the traffic
conditions are critical. The total length of this track is
of 9 km and 300 meters.
The Suburban cycle (the so called fast test) is,
instead, a route passing close to the city centre
(without entering in it), and later moving (still 50
km/h speed limit) towards the external ring of the
city. Entering the ring the driver keeps an higher
constant speed (90 km/h) which leads him to leave
the ring at the Bari’s southern extreme exit, thus
entering the Japigia district. The length of this track
is of 12 km and 300 meters.
For each car one slow test and one fast were carried
out each day. One day the order was first the slow
test and then the fast one, the day after the inverse
order was followed.
The two tests were characterized by the following
data:
Urban test:
• maximum allowed speed: 50 km/h
• predicted average speed: 18km/h
• predicted maximum number of stops: 42,
split in:
a. stops and priorities: 15
b. traffic lights:
27
• average distance between two stops: 220 m
(approx.)
Suburban test:
• maximum allowed speed:
o 50 km/h inside city walls
o 90 km/h on the ring
• predicted average speeds:
o 18 km/h inside city walls
o 85 km/h on the ring
o 30 km/h globally
• predicted maximum number of stops: 24,
split in:
a. stops and priorities: 6
b. traffic lights:
18
• average distance between two stops:
a. 512 m (approx.) including ring
route,
b. 355 m (approx.) excluding ring
route (that is 3780 m)
Preventive stop number calculations have been made
considering the worst conditions, so considering a
complete vehicle standstill at stops and priorities and
the unfortunate event of always red lamp at traffic
lights.
2.4 Measurement and observation modes
Measurements and checkouts were of two kinds:
a) “on board”
b) “on ground”.
The “on board” ones consisted of data acquisition
using a laptop linked to a GPS with an external
antenna. This allowed the real time recording of the
actual followed routes, thus enabling the calculation
81
The fuel tank level check was performed using a
graduated flexible stick. Air conditioning was kept
off in order to avoid the introduction of a disturb
variable in the final consumption data. Starting
position was previously fixed choosing a flat
horizontal zone close to the DIMeG laboratories:
positions of tyres were marked on the ground. Fuel
was refilled using an hand pump which allowed an
accurate control of the amount of liquid provided, an
auxiliary tank of 5 liters was used to this end. A
precision balance
was
used
for
weight
measurements. The auxiliary tank was weighted
before and after each refill together with the hand
pump in order to take into account any possible
residual quantity of fuel.
Concerning the fuel, it was always bought from the
same company, Total Italia Spa. The same company
provided official documents declaring specific
weight of gasoline and its origin. Every day the data
concerning the meteorological conditions were
acquired at the DIMeG (humidity, temperature,
pressure, etc.). Before every test tyre pressure was
checked and possibly set using a digital manometer
and an air compressor.
3. RESULTS
A total number of 35 tests were performed using the
two mentioned vehicles; for each test the kinematic
data were collected by the GPS and fuel consumption
data –as said before– by the direct measurement.
3.1 Meteorological conditions
After collecting temperature, relative humidity,
atmospheric pressure and precipitation data, an
attempt was made to find a direct link between
weather conditions and tests duration, as one can
think that a raining event can push more users to
engage the road net. However, measurements showed
that the duration time increased specially during
intense raining but less or even did not increase
during weak phenomena. In fact, there were days
when in spite of a dry weather, particularly long
duration times were recorded. The comparison
between the weather situation and test duration
showed a significant correlation only in suburban
tests case; in urban tests there was no apparent direct
connection. Theoretically this phenomenon can be
explained by observing that the ring traffic is affected
by less variables than the city traffic. The workers or
commuters that have to cover long and middle range
distances will indeed use their cars anyway, either in
case of rain or in case of sun; on the contrary, city
centre traffic is subjected to factors that may be not
only related to meteorological phenomena.
3.2 IMA time
Being a parallel hybrid vehicle, the Honda Civic
internal combustion engine is continuously running
during the ride (except during standstills in “idle stop
mode”). In this case the main data, which were
collected, concerned the motor inserting time, i.e. the
periods of time during which the electric machine
was providing torque (“Assist mode”). The obtained
values are shown in figure 3.
HONDA CIVIC IMA
IMA Assist Time
100
90
80
[% on total time]
of the partial and total times, effective distances,
instantaneous and average speeds, positive and
negative accelerations, standstill and constant speed
running times. On the Prius, moreover, there was
also the presence of a real time acquisition system
provided by the Manufacturer itself. This, under
constant control of an on board systems operator,
allowed even to collect running times of each driving
unit (ICE and motors), revolution speeds and torque
provided by the motors, ICE revolution speeds and
vehicle speed (this data was later compared with the
one provided by the GPS).
On the Civic IMA the presence of only a
speedometer made more difficult the work of the
operator who had to collect gear shifting and stint
times by the use of an electronic chronometer for
every single test. Duty of the driver was, beyond
driving, the indication of shifting instants and gear
ratio used. Gear shifting had to take place by first
bringing the revolution speed of the combustion
engine to the value of 2200 rpm and then up-shifting
except for the fifth (last) gear, that was engaged until
the ring’s speed limit is reached.
On ground measurements and checkouts were made
in the labs. They consisted of vehicle setups before
tests, and additional data acquisitions. In detail the
following checkouts were performed:
- fuel tank full;
- accumulators charged;
- on board systems switched on and correctly
running;
- air conditioning system switched off;
- car on starting position;
- auxiliary fuel tank weighted;
- refuelling pump weighted;
- (only for Prius) e/v (electric) mode on;
- chronometer present and reset;
- laptop charged and ready;
- GPS antenna positioned and linked;
- (only for Prius) real time acquisition data
system reset and connected;
- (for some sample tests) video-camera
positioned and ready;
- mileage counter reset;
- tyre pressure checked and set.
70
URBAN TEST: IMA Time
60
SUBURBAN TEST: IMA Time
50
40
30
20
10
0
Fig. 3. IMA assist time. Columns show the motor
inserting time in percentage on total tests
duration
82
One can note that the driving style significantly
influences the motor insertion: in fact, the motor
gives its contribute depending on the torque demand
from the driver: the more intense and longer the
power demand is, the more the insertion lasts. Since
we adopted a soft driving style, the electric assist was
– in terms of time – rather low.
Driving in suburban cycle, of course, required higher
power because of the higher average velocities. This
of course turned out in longer motor insertion times.
3.3 ICE insertion periods
Prius data more carefully analyzed were concerned
with the internal combustion engine running. The
different architecture of the car (series/parallel), in
fact, allowed only a minimum driver’s autonomy in
the choice of which driving unit to use. So, having
given priority to the use of the motor, it came out that
the endothermic engine running time was, in the
series/parallel architecture of the Prius, much less
than in the parallel one of Honda (fig. 4).
Differences in insertion times can be explained
considering that during each experiment, the use of
the electric propulsion was always preferred.
TOYOTA PRIUS
Endothermic Engine Running Times
100
90
[% on total test time]
80
70
URBAN TEST: ICE Running Time
centre. The stop-&-go time were carefully analyzed
together with the duration time in which the vehicles
travelled at constant speed. This allowed to carry out
a comparison with the standard European cycles.
Concerning stops, the average values were:
• 50 stops per each urban test (9310 m),
equivalent to one stop every 185 metres
approx.
• 28 stops per each suburban test (12300 m),
equivalent to one stop every 440 metres
approx. .
Table 1 shows the percentages on total time during
which the vehicles had no acceleration, that is in
cases of standstills or constant speed motion. Data
are put in comparison with the ones from the
European Directive: one can note that only in the
case of vehicle moving at constant speed in suburban
tests, experimental data are relatively close to the
ones of the European standards. In all the other cases,
the obtained values differ remarkably from reality,
thus supporting the conclusion that real city traffic
possesses features which deeply differs from the
model provided by Community directives.
Table 1. Comparison European Norm/Tests in Bari
Percentages on
total time
NEDC Norm
Urban
Tests
Suburban Tests
33
41
30
36
26
38
Standstill
Constant
Speed motion
SUBURBAN TEST: ICE Running
Time
60
50
3.5 Speed
40
30
20
10
0
Fig. 4. ICE running time shown as a percentage on
total test duration
Now, the electric propulsion is subordinated to the
battery state of charge and the avoiding of 50 km/h
speeding (that is also the road code limit). The
Toyota Power Management, indeed, was such to
insert the ICE when this speed value was exceeded.
In this way the ICE was running only in few
occasions as during the (rare) requests of torque
surplus, and when the low batteries state of charge
was reached. This led to a lower time percentage use
of the internal combustion engine with respect to the
total ride time. On the contrary, in the suburban cycle
– on the ring – where higher average and maximum
speeds, over 50 km/h are imposed, the fully electric
propulsion mode was disengaged and the IC engine
remains substantially always switched on.
3.4 “Stop-&-Go”
As it clearly appears, the coverage time of a test is
heavily influenced by times and durations of stops.
Of course one expects that a urban test has a greater
number of stops and re-starts (“stop-&-go”) than a
comparable length suburban one.
Tests in Bari confirmed this expectation showing an
high number of stop-&-go especially in the city
The GPS system allowed the monitoring of the
position and velocity of vehicles with relatively good
precision.
Table 2 presents the average speeds recorded during
the execution of tests for both the cars.
Figures 5 and 6 show for comparison an example of
speed trends for a vehicle in suburban test and the
ECE cycle.
Table 2. Tests average speeds
Urban Tests
[km/h]
Suburban Tests
[km/h]
Toyota Prius
Honda Civic IMA
13.15
13.85
29.39
27.57
3.6 Acceleration
As previously mentioned, during the execution of the
tests great care was given to avoiding sudden
accelerations. This was accomplished by using a soft
driving style, in order to save as much fuel as
possible.
It is important to underline that during normal
driving, it is not always possible to adopt such a
similar driving style. Thus, the measured
consumption data should be considered as close to
the best obtainable values, that represent an inferior
limit.
After collecting acceleration data, they were
processed and divided in positive and negative
83
Central Stint Speeds
Urban Tests - Positive Accelerations
40
35
d.s. = standard deviation
25
20
15
[d.s. 0.26]
10
120
5
100
0
Speed [km/h]
[d.s. 5.0]
30
time [%]
accelerations and subdivided in classes of 0.5 m/s2.
Positive accelerations were put in comparison with
the New European Driving Cycle (NEDC) norm,
negative ones were used to calculate the theoretical
amount of energy that can be regenerated by the
electric machines.
0 - 0.5
0.5 - 1.0
80
[d.s. 0.17]
[d.s.
1.0 - 1.5
1.5 - 2.0
[d.s. 0.11]
2.0 - 2.5
[d.s. 0.08]
2.5 - 3.0
2
Acceleration Classes [m/s ]
60
Fig. 8. Amount of percentage time of acceleration
classes for slow test typology
40
20
0
450
550
650
750
850
950
1050
Suburban Tests - Positive Accelerations
Time [sec]
40
Fig. 5. Example of speed trends during a suburban
test
[d.s. 2.2]
35
d.s. = standard deviation
Time [%]
30
25
20
15
10
[d.s. 0.6]
5
0
[d.s. 0.3]
0 - 0.5
0.5 - 1.0
1.0 - 1.5
[d.s. 0.3]
[d.s. 0.2]
1.5 - 2.0
2.0 - 2.5
[d.s. 0.03]
2.5 - 3.0
2
Acceleration Classes [m/s ]
Fig. 9. Amount of percentage time of acceleration
classes for slow test typology
Fig. 6. ECE Cycle: composition of UDC, Urban
Driving Cycle plus EUDC, Extra Urban Driving
Cycle
Concerning the positive accelerations, the
comparison with the European Directive showed a
substantial difference in the distribution of time
percentages: the Norm, in fact, dedicates most of the
time to acceleration classes between 0.5 and 1.0
m/s2, whereas during realistic tests the major amount
of time during which the acceleration was kept into a
certain class fell in the range between 0 and 0.5 m/s2
(see figure 7). Moreover the Norm does not contain
positive accelerations larger than 1.5 m/s2, whereas
in realistic situations they do exist accelerations
beyond this limit. Of course the weight of these is
not prevailing (see figures 8 and 9), but one has to
remember that for intense accelerations and high
RPM number, the endothermic engine goes through
decreasing
efficiency
conditions,
and,
by
consequence, faces a worsening of fuel consumption.
Comparison on positive accelerations
45
0-0.5
40
35
Time [%]
30
Positive Accelerations
Suburban Test
0.5-1
25
Positive Accelerations
ECE Directive
20
15
10
5
1-1.5
1.5-2
2-2.5
0
2.5-3
2
Acceleration classes [m/sec ]
Fig. 7. Comparison between positive accelerations
imposed by the ECE directive and real values
obtained during the suburban test
3.7 Regenerative energy
An HEV is as more useful as its electric mode
autonomy increases (see Advanced Hybrid Vehicle
Powertrains 2005, 2005). Unfortunately one simple
charge of the batteries is not able to provide a good
autonomy, that is why modern HEVs use a
regenerative process consisting of a partial recovery
of the vehicle’s kinetic energy during decelerations.
This is achieved thanks to the electric machine that is
able to work both as a motor and as a generator.
During braking and/or slowing down, the power
management system switches off both the driving
units and the let the wheels to drag in rotation the
electric machine making it work as a generator, thus
recharging the accumulators.
This operation cannot take place in every conditions,
as long lasting or too intense decelerations could
create such thermal and vibrational stresses (see
Componenti e Sistemi per Veicoli a Trazione
Elettrica, Parte Seconda, 1991) as to damage the
whole system. Moreover, the braking effect of the
generator alone is not enough to stop the vehicle in
emergency conditions.
Data collected were studied by dividing decelerations
in classes of 0.25 m/s2, then it was investigated the
amount of energy that could have been regenerated
per unit of mass, in case the whole vehicle’s kinetic
energy contributed to the regeneration and in case
where a couple of hypothesized threshold limits were
reducing the kinetic regenerable energy. Of course
deceleration values excessive for the hybrid system
survival were excluded from the calculation: in
particular classes with module more than 2.0 m/s2
were
ignored.
Calculations
also
excluded
84
[J/Kg]
Regenerative Energy - Urban Tests
1000
900
800
700
600
500
400
300
200
100
0
Negative
accelerations up
to -1.50 m/sec2
Negative
accelerations up to
-1.0 m/sec2
Negative
accelerations up
to -2.0 m/sec2
d.s.: 80
d.s.: 80
d.s.: 80
d.s.: 53
d.s.: 51
d.s.: 62
d.s.: 81
d.s.: 50
0 ÷ -0.25 -0.25 ÷ -0.50-0.50 ÷ -0.75-0.75 ÷ -1.0 -1.0 ÷ -1.25-1.25 ÷ -1.50-1.50 ÷ -1.75-1.75 ÷ -2.0
Deceleration classes
[m/sec2]
TOYOTA PRIUS - Consumption
10
9
8
7
[L/100km]
decelerations under a speed threshold of 20 km/h, as
generally the response time and the amounts of
recoverable energy until this value is negligible. In
order to take into account energy losses, a reasonable
value of the efficiency of conversion of about 0.850.90 has to be considered: of course this is an
approximate value as neither Toyota or Honda
provided the actual values. Figures 10 and 11 report
the theoretical amounts of regenerative energy
ordered by deceleration classes, expressed in J/kg;
please note that in each diagram the two vertical
lines identify the threshold limits which guarantee
the aforementioned system integrity. In fact, as the
real physical limits due to the electric machines was
not known, we assumed two different thresholds
related to two different level of acceptable
deceleration intensities.
6
4
3
2
1
0
[J/kg]
Negative
accelerations up
to -2.0 m/sec2
Deviation
%
Comb.ed
cycle
declared
[l/100km]
Suburban
cycle
measured
(average)
[l/100km]
Deviation
%
5.69
+32.3
5.69
+42
Toyota Prius
5.0
6.03
6.0
8.17
+20.6
4.3
Honda Civic IMA
d.s.: 80
d.s.: 100
d.s.: 40
+36
4.9
d.s.: 65
d.s.:
118
d.s.: 70
4. CONCLUSIONS
0 ÷ -0.25 -0.25 ÷ -0.50-0.50 ÷ -0.75-0.75 ÷ -1.0 -1.0 ÷ -1.25-1.25 ÷ -1.50-1.50 ÷ -1.75-1.75 ÷ -2.0
Fig. 11. Regenerative energy, fast test
3.8 Consumption
HONDA CIVIC IMA
Consumption
10
9
Combined/Suburban
Cycle
Urban Cycle
8
dev.std: 0.92
7
dev.std: 0.62
[L/100km]
Urban
cycle
measured
(average)
[l/100km]
d.s.: 120
d.s.: 35
Deceleration classes
2
[m/sec ]
6
5
4
3
2
0
Declared**
Consumption Suburban Cycle
Measured
The experiments showed that the measured fuel
consumptions of the two vehicles are not the same as
declared by the Manufacturers during the
homologation. This, of course shows that
homologations obtained using the actual standards
give not realistic values. The following figures 12
and 13 show the summary of measured fuel
consumptions for both the two hybrid cars, and
compare the urban and the suburban test data with
the ones declared by the car Manufacturers.
In both cases, one can note the measured data are
always larger than the declared ones as also shown in
table 3.
[l/100km]
1
Declared**
Consumption - Urban
Cycle
Fig. 13. Toyota Prius: comparison measure/declared
consumption
Regenerative Energy - Suburban Tests
Negative
accelerations up
to -1.50 m/sec2
Measured
Consumption - Urban
Cycle
**: by Directive 80/1268/EEC reprised by Directive
1999/100/EC
Urban
cycle
declared
Negative
accelerations up to
-1.0 m/sec2
dev.std: 0.94
Table 3. Toyota, Honda: deviation percentages
between declared and measured consumption values
Fig. 10. Regenerative energy, slow test
1000
900
800
700
600
500
400
300
200
100
0
dev.std: 0.89
5
Measured
Consumption - Urban
Cycle
Omologation
Consumption* Urban Cycle
Measured
Omologation
Consumption* Combined Cycle
*: Omologation 1999/100/EC
Fig. 12. Honda Civic IMA:
measured/declared consumption
comparison
This work concerned the study and experimental
analysis of two consumption cycles, urban and
suburban, conceived to verify the correspondence of
the ECE 91/441 cycle and its further modifications,
to the real traffic conditions of a vehicle moving in a
metropolitan town as the city of Bari is.
The experimental analysis, moreover, interested two
motorcars belonging to a rapid development and
diffusion category, the hybrid vehicles, which are
driven by the combination of two engines: one is the
IC engine and one an electric machine.
The analysis put in evidence that the vehicle
performances differ as a consequence of the different
architectures adopted on the two cars.
Between the two considered architectures, the Toyota
series/parallel one appears to be the more promising
from the fuel consumption point of view. In the
Honda’s parallel system, instead, the advantages of
the electric motorization are available only when the
driver requires high values of torque and power; so
when a soft driving style is used, the electric motor is
often disengaged.
85
Regeneration represents a further frontier of
development for HEVs: at the state of the art,
regenerative braking, together with other technical
devices, provides an energetic recovery estimated
around 30% on global consumption by the
Manufacturers. Vibrations and working temperatures
of electric components limit this chance; so it clearly
appears that this energy increase passes through the
functional streamlining of electric machines and their
related components.
Then, the analysis took in consideration the
homologation cycle ECE in its most recent version
Euro 4. In comparison with it we utilized two
realistic cycles in the city of Bari. Results have
evidenced a significant distance between data
obtained by the Manufacturers respecting the
normative, and the ones recorded during the
experimentation. In fact, although during the
experimentation the same acceleration classes of the
norm were respected (assumed as a reference), it was
found out how the single weights differ. In
agreement on this main lines seems to be the whole
European scientific community. Both the hybrid
vehicles showed the validity of their projects and
allowed to underline a deviation in declared
consumption data that in the best event was of the
20% and reached a top of more than 40%, showing,
in this way, all the limitations of the actual European
homologation cycle.
Renewable Energy, Office of Transportation
Technologies. Annual Progress Report. USA.
Evaluation of the Environmental Impact of Modern
Cars on Petrol, Diesel, Automotive LPG and
CNG
(2003).
TNO
Report,
03.OR.VM.055.1/PHE.
Gabriel Martin G.. Innovations in Automotive
Transmission Engineering, SAE International
Publications, T - 109, 2004.
Genta Giancarlo. Meccanica dell’Autoveicolo
(2000). Levrotto & Bella, Torino.
Honda, Gamma Civic ’04 (2003). Cartella Stampa
Honda, Verona.
Szumanowski Antoni. Fundamentals of Hybrid
Vehicle Drives (2000). Warsaw-Radom 2000.
Toyota Prius,Caratteristiche Nuovo Modello (2003).
Serie NHW20, Toyota Motor Publication,
NCF256IT.
Westbrook Michael H.. The Electric and Hybrid
Electric Car (2001). SAE International
Publications.
Aknowledgments: the Authors would like to
thank Toyota Motor Italia and Honda Automobili
Italia for having provided the two motorcars and
the Automobile Club d’Italia – Bari that
sponsored the survey.
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86
HYBRID VEHICLES WITH ELECTRICAL MULTI ENERGY UNITS
M. Cacciato, A. Consoli, G. Scarcella, A. Testa
Department of Electrical, Electronics and System Engineering
Viale Andrea Doria, 6 - 95125
Catania, Italy
Abstract: In order to evaluate electrical and hybrid vehicles performance, mathematical
models of SCs, FCs, and PV modules have been implemented in Advanced Vehicle
Simulator. A deep analysis about the advantages of integrate standard batteries with new
storage devices, as super-capacitors, fuel-cells and photo-voltaic modules has been done.
For each electrical units described above, an accurate balance has been done. Moreover,
using a multi-criteria approach a cost-benefit analysis has been performed considering in
a period of ten years, in order to evaluate the economical advantages of using the
additional units.
Keywords: Super-capacitors, photo-voltaic modules, ADVISOR, cost-benefit analysis.
1. INTRODUCTION
In the last years, the global request of energy has
increased at high rate and the forecasts for the next
future guess a faster rate of growing in the energy
demand. As a consequence, many environmental
problems has been experienced related with the high
percentage of Carbon Oxide (CO), Nitrogen Oxides
(NOx), subtle dusts, etc., present in the atmosphere.
Such a problems are more relevant in urban areas
because of high density of population and,
consequently, of the use of polluting devices. In
particular, in the last years an enormous increasing of
the pollution has been experienced due to the rising
number of vehicles. On the other hand, conventional
energy sources, as petroleum, are expected to be
exhausted in some tens or, at most, few hundreds of
years. Considering such a scenario, it is essential to
develop ‘clear’ and highly efficient vehicles, such as
electrical ones, ‘pure’ or ‘hybrid, that allow to reach
high performance, similarly to those of internal
combustion engine, while using clean energies.
In order to increase the performance of electrical and
hybrid vehicles, enabling technologies are SuperCapacitors (SCs), Fuel Cells (FCs) and Photo Voltaic
(PV) modules, that can be integrated in hybrid and
electrical vehicles.
To evaluate the vehicles
performance, mathematical models of SCs, FCs, and
PV modules have been implemented in Advanced
Vehicle Simulator (ADVISOR), developed by the
National Renewable Energy Laboratory (NREL) of
the U.S. Department of Energy. The ADVISOR is a
very flexible tool, implemented in Matlab, that
enables fast and accurate performance analysis and
to calculate fuel savings of conventional and
advanced, light and heavy-duty vehicles, as well as
hybrid electric and fuel cell vehicles (A. Brooker et
al., 2002). Using such a tool, a deep analysis has
been done for two vehicles, a car and a bus.
Moreover, the cost of different solutions has been
considered to evaluate their impact on the vehicles
economy.
2. ADVISOR MODELS
In order to investigate the impact on FC vehicles
performance of new electrical units as SCs and PV
modules installed on board, the model of two
electrical vehicles, powered by a FC, has been used.
To this aim, new models of SCs and PV modules
have been developed in Matlab/Simulink and
implemented in such a way to be integrated in the
ADVISOR environment. The great flexibility of
such an approach, allows to easily evaluate many
vehicle configurations in different situations and to
easily compare the results (A. Emadi et al., 2004).
2.1 Car model.
As a reference car, an electrical Mercedes-Benz FCell, has been used. Such vehicle is the electrical
powered version of standard Class A car, equipped
with a fuel cell and a small battery pack to support
the fast power transient during the quick
accelerations. The main vehicle specifications are
reported in Tab. 1 (M. C Pera et al., 2002).
Tab. 1: Main parameters of F-Cell car.
Car
Length [m]
3,838
Width [m]
1,764
Height [m]
1,593
Curb weight [kg]
1509
87
PEM
Voltage [V]
700
250-450
Power [kW]
80
Pressure [bar]
350
# of mudules
66
Power [kW]
72
Module capacity [Ah]
40
Weight [kg]
274
Induction
Machine
65
Total weight [kg]
800
Technology
Voltage [V]
Fuel Cell
Technology
Power [kW]
Electrical
Motor
Battery
Efficiency
0.94
Maximum current [A]
384
Minimum voltage [V]
200
Weight [kg]
86
Technology
Ni-Mh
Voltage [V]
150-250
Power [kW]
15-20
# of mudules
25
Module capacity [Ah]
45
Total weight [kg]
156
Number of gears
1
Transmission Gear ratio
Weight [kg]
ZF / HP502C6
Producer/Mod.
6
Number of gears
Transmission
3,43 2,01 1,42
1,0 0,83 0,59
Gear ratio
305
Weight [kg]
2.3 PV roof.
It is considered the possibility to integrate a PV
generation system in the roofs of the car and bus.
For the car, it is considered to built a PV roof
suitably designed using single PV cells, while for the
bus standard PV modules have been considered. The
PV roofs parameters are reported in Tab.s 3 and 4, at
a radiance of 1000 W/m2 and 25 °C.
9.9
108
Tab. 3: Parameters of car PV roof.
Technology
Thin film
Voltage @ open circuit [V]
0,68
2.2 Bus model.
Current @ short circuit [A]
0,016
As a reference bus, the electrical Mercedes-Benz
Citaro, has been used. Such vehicle is electrical
powered and equipped with a fuel cell. The main
vehicle specifications are reported in Tab. 2.
Peak power [mW]
Tab. 2: Main parameters of Citaro bus.
Bus
Motor
Battery
8,5
Cell area [mm ]
45
Cell length [mm]
6,5
Cell weight [g]
0,23
Roof fill factor
0,79
Length [m]
11,95
Width [m]
2,55
# of cells in series for string
265
Height [m]
3,69
# of strings in parallel
162
Total weight [kg]
10
Curb weight [kg]
Fuel Cell
2
18.000
Max load [kg]
4900
Producer/Mod.
Ballard
Mark902
Technology
PEM
Voltage [V]
760
Current [A]
510
Power [kW]
280
Weight [kg]
238
Technology
Induction
Machine
Power [kW]
187
Tab. 4: Parameters of bus PV roof.
Single crystalline
Technology
Module length [m]
0,66
Module width [m]
1,48
2
Module area [m ]
0,98
Module weight [kg]
11,9
# of modules for string
8
# of strings
3
Total weight [kg]
2
286
Efficiency
0.95
Total area [m ]
23,52
Maximum current [A]
540
21,3
Minimum voltage [V]
400
Current @ short circuit [A]
8,1
Weight [kg]
91
Roof fill factor
Technology
Pb
Module peak power [W]
0,752
130
88
2.4 Super capacitors.
Nowadays, SCs are an emerging class of passive
devices, able to store relevant energy quantities while
working at high power levels. The SCs are derived
from standard electrolytic capacitors largely used in
power electronic applications which are able to
operate at high power, in addiction, SCs show a very
high capacitance value per volume, up to one
hundred time the electrolytic capacitors (Barker P. ,
2002).
In high efficiency vehicles, the regenerative braking
is highly desirable, but, the batteries can not be
recharged at the power level of braking, that can
reach the nominal power of the electrical machine.
Therefore, two technical solutions are possible, the
former consists in a partial recovery of the available
energy during the braking, because of the limited
power that can recharge the batteries. The latter,
using a energy buffer like SCs, allows the full
recovery of the breaking energy. The last solution,
although energetically efficient, is more expensive
because of the actual high price of SCs and the need
of an auxiliary power converter for controlling the
power flowing trough SCs. The characteristics of
SCs, as reported in Tab.5, well match the
requirements of automotive applications.
The
benefits obtainable using such components have been
evaluated.
performances are obtained as a combination of
standard cycles and stop periods.
The cycle used to test the F-Cell car is constituted by
two ECE speed profiles, a stop period and a standard
EUDC speed profile, as reported in fig. 1.
Fig. 1. Used test cycle used for F-Cell car.
The elevation is introduced as a parameter. The
cycle used to test the Citaro bus is constituted by two
groups of, respectively, seven and five ECE speed
profiles, split by a stop period, as reported in fig. 2.
Tab. 5: Parameters of single SC and SC bank.
2,4
SC weight [g]
15
ESRd [mΩ]
12,6
Energy density [Wh/kg]
6,1
Power density [W/kg]
3500
# of SCs in a bank
196
Nominal bank voltage[V]
450
Bank power [kW]
10
Total weight [kg]
2,86
Fig. 2. Used test cycle for Citaro Bus.
3. VEHICLES PERFORMANCE EVALUATION
3.1 F-Cell Car.
Considering the test cycle reported in fig. 1, the
following F-Cell car configurations have been
simulated:
• WES without energy storage systems
2.5 Test cycles.
The test cycles used to evaluate the vehicles
• CB with batteries
• UC with super capacitor banks only
• CBUC with batteries and super capacitor banks
Fig. 3. Matlab scheme of the vehicles with FC, batteries, PV and SC units.
89
• CBPb with lead-acid batteries
The first configuration (WES) consists in the F-Cell
car without any batteries, then, the energy recovery
during the braking operation is not allowed. The
second configuration (CB) uses standard batteries.
The third configuration (UC), only uses a SCs bank,
while the last configuration exploits both storage
systems, opportunely sized.
In Tab. 6, are reported the car weights in
correspondence of each configuration.
• CBNiMh with NiMh batteries
• UC with super capacitor banks only
• CBUCPb with lead-acid batteries and SC banks
• CBUCNiMh with NiMh batteries and SC banks
In Tab. 8, are reported the bus weights for each
configuration. In Tab. 9, are shown some of the
simulation result obtained for each configurations
and different SOCs of each storage system.
Tab. 6: Gross weight of F-Cell car for different
configurations [kg].
with PV
without PV
Car
roof [kg]
roof [kg]
Config.
1363
1373
WES
CB
1519
1529
UC
1375
1385
CBUC
1462
1472
Tab. 8: Gross weight of Citaro bus for different
configurations.
Bus
with PV
without PV
Config.
roof [kg]
roof [kg]
18.000
18.286
WES
In Tab. 7, are reported the simulation results for the
car. For taking into consideration the initial State Of
Charge (SOC) of the storage systems, one or two
letters (xx) are used, indicating the SOC of each
storage system as follows:
SOC low (≤ 0,6)
In red are stressed the results of the worse
performance, while in green the best ones. As can be
noted, the PV roof considerably reduces the fuel
consumption, while the car dynamic performance
slightly worsens because of the weight increasing.
CBNiMh
18.277
18.571
UC
18.020
18.306
CBUCPb
18.508
18.794
CBUCNiMh
18.285
18.571
For each electrical units described above, an accurate
balance has been done, taking into account the
energy saved or recovered by the units and power
losses due to each unit efficiency and the increment
of the vehicle weight. Such energy balance is
evaluated for the F-Cell car supposing a journal trip
of 2, 8 hours per day, corresponding to a route of 65
km, obtained combining some standard cycles. For
the Citaro bus, a daily duty of 16 hours,
corresponding to a route of 250,5 km has been
considered.
Similarly for F-Cell car, some configurations of
Citaro bus have been simulated considering two
battery technologies:
• WES without energy storage systems
Config.
19.086
4. COST-BENEFIT ANALYSIS
3.2 Citaro bus.
Car
18.800
It is noticeable that, using a PV roof, the fuel saving
is higher with respect to the cases of the car because
of the large extent of the bus roof.
• S SOC high (≥ 0,8)
• s
CBPb
without PV roof
with PV roof
Equivalent Acceleration
H2
[litres] Fuel [litres] 0-100 km/h
Max
speed
Equivalent Acceleration
H2
[litres] Fuel [litres] 0-100 km/h
Max
speed
WES
83,9
5,7
17,7
153,8
79,9
5,4
17,7
154,1
CB S
32,1
2,2
15,3
154,2
31,2
2,1
15,4
154,2
CB s
102,9
7,0
19,8
152,5
98,1
6,6
19,8
152,7
UC S
80,2
5,1
14,0
154,0
71,0
4,8
14,1
154,3
UC s
80,0
5,4
17,8
153,7
75,5
5,1
17,9
154,0
CBUC SS
57,9
3,9
14,8
154,7
53,2
3,6
14,9
154,7
CBUC Ss
60,2
4,1
15,7
154,7
55,2
3,7
15,7
154,7
CBUC sS
89,1
6,0
17,2
153.2
83,7
5,7
17,1
153,6
CBUC ss
91,2
6,2
19,0
153,0
86,2
5,8
19,0
153,3
90
Consumption
Acc. 0-50 km/h
[l/100 km]
[s]
SOC
Bus
Config.
WES
CBPb
CBNiMh
UC
CBUCPb
CBUCNiMh
Batt.
SC
without
PV roof
with PV
roof
without
PV roof
with PV
roof
//
//
1172,0
1119,9
14,7
14,7
81,9
81,9
0,62
//
1158,8
1109,7
15,4
15,4
82,0
82,0
0,75
//
1049,2
999,8
12,3
12,5
81,8
81,8
0,62
//
1136,7
903,6
15,1
14,4
82,0
81,9
0,75
//
1031,0
819,0
12,0
13,1
81,8
81,8
//
0,55
1112,3
861,8
14,7
13,9
81,9
81,9
//
0,75
1107,3
857,3
13,3
12,5
81,9
81,9
0,62
0,55
1128,8
1077,5
15,1
15,1
81,9
82,0
0,62
0,75
1125,2
1073,9
13,4
13,4
82,0
82,0
0,75
0,55
1066,4
1015,4
12,3
12,4
81,8
81,8
0,75
0,75
1063,6
1012,6
12,1
12,3
81,8
81,8
0,62
0,55
1117,7
1065,0
14,9
14,9
81,9
81,9
0,62
0,75
1113,9
1061,1
13,1
13,2
82,0
81,9
0,75
0,55
1050,1
997,8
12,1
12,3
81,8
81,8
0,75
0,75
1046,6
994,3
11,9
12,1
81,8
81,8
Moreover, taking into account the prices of the fuel
and units, with a multi-criteria approach a costbenefit analysis has been performed, to evaluate the
economical advantages of using the additional units
in a period of ten years (Chiodo E., 2005). The
adopted criteria are max speed, max acceleration,
units cost, fuel cost.
The algorithm has been implemented in Matlab as a
tool of the ADVISOR. In Tab. 10, are reported the
Car config.
WES
Max speed
[km/h]
without
with PV
PV
roof
roof
costs used in the cost analysis, the cost of the fuel
cell is considered as desired in the next future.
Tab. 10: Costs of electrical units.
Pb batteries
100 €/kWh
NiMh batteries
300 €/kWh
SC
80 €/kW
PV
5,4 € / Wp
Tab. 11: Results of the MC analysis for the F-Cell car.
Accel. 0-100 km/h Max speed Electrical units
Savings
[s]
[km/h]
costs [€]
[€]
17,3
155,0
0,00
0,00
Score
0,0874
WESFV
17,5
155,0
4.284,00
-1.019,00
0,0632
CBNiMh
14,6
154,0
5.883,00
-2.478,00
0,0233
CBNiMiPV
14,8
154,0
7.287,00
-3.392,00
0,0016
UC
15,4
155,0
4.880,00
-1.405,00
0,0501
UCPV
15,6
155,0
6.284,00
-2.319,00
0,0283
CBUCNiMh
14,1
154,8
5.476,00
-1.931,00
0,0353
CBUCNiMhPV
14,3
154,9
6.880,00
-2.775,00
0,0151
91
Bus config.
Tab. 12: Results of the MC analysis for the Citaro bus.
Accel. 0-100 km/h Max speed Electrical units
Savings
[s]
[km/h]
costs [€]
[€]
Score
WES
12,30
81,90
0,00
0,00
0,0586
WESPV
12,50
81,90
18.500,00
-1.700,00
0,0536
CBPb
10,90
81,70
21.000,00
-700,00
0,0525
CBPbPV
11,10
81,80
39.500,00
-10.800,00
0,0323
CBNiMh
10,60
81,70
9.500,00
26.900,00
0,1034
CBNiMhPV
10,80
81,70
28.000,00
23.800,00
0,0959
UC
11,20
81,80
6.400,00
31.050,00
0,1123
UCPV
11,40
81,90
24.900,00
31.100,00
0,1105
CBUCPb
10,70
81,80
15.525,00
18.075,00
0,0869
CBUCPbPV
10,80
81,80
34.025,00
15.325,00
0,0798
CBUCNiMh
10,50
81,80
8.000,00
25.600,00
0,1011
CBUCNiMhPV
10,70
81,80
26.500,00
33.350,00
0,1132
As it is reported in Tab.s 11 and 12, the cost-benefit
analysis shows that, for fuel cell car there are no
economical advantages in introducing additional
power units, while for the bus it is convenient to use
NiMh batteries instead of led-acid ones, SC banks
and PV roof.
5. CONCLUSIONS
In the last years, a relevant increasing of the
pollution has been experienced due to the rising
number of vehicles. It is essential to develop ‘clear’
and highly efficient vehicles, such as electrical ones,
that, at the same time, show performance close to
that of internal combustion engine.
New
technologies as fuel cells, super-capacitors and
photo-voltaic modules are now available to
increasing the performance of electrical and hybrid
vehicles. In this paper, energy and economical
evaluations of vehicles performance using those
components have been done. To this purpose,
mathematical models of SCs, FCs, and PV modules
have been implemented in Matlab and integrated in
the Advanced Vehicle Simulator, obtaining a very
flexible and accurate analysis tool. Using such a
simulator different solutions have been evaluated and
interesting results have been obtained and reported.
REFERENCES
Brooker, A.; Hendricks, T.; Markel, T.; Johnson, V.;
Kelly, K.; Kramer, B.; O'Keefe, M.; Sprik, S.;
Wipke, K. (2002). ADVISOR: A Systems
Analysis Tool for Advanced Vehicle Modeling
Journal of Power Sources, Volume 110, Issue 2
, 22 August 2002, Pages 255-266.
Emadi, A.; Ehsani, M.; Miller, J. M. (2004).
Vehicular Electric Power Systems, Marcel
Dekker Inc, New York.
Pera M. C., Hissel D., Kauffmann J. M. (2002) Fuel
cell systems for electrical vehicles, IEEE 55th
Vehicular Technology Conference (VTC), 6-9
May 2002, vol. 4 , pp. 2097 – 2102.
Barker P. (2002) Ultracapacitors for use in power
quality and distributed resource applications,
IEEE 2002 Power Engineering Society Summer
Meeting, 21-25 July 2002 pp. 316 – 320.
Chiodo E. (1991). Strumenti di supporto alle
decisioni per la tecnologia e l'ambiente: analisi
multicriteriale deterministica applicata al
progetto dei veicoli elettrici, Manutenzione Tecnica e Management.
92
IMPEDANCE MATCHING FOR PV GENERATOR
Angel Cid-Pastor1,3, Luis Martínez-Salamero2, Corinne Alonso1, Guy Schweitz3 and Ramon Leyva2
1
2
LAAS-CNRS, Laboratoire d’Analyse et des Architectures des Systèmes, Toulouse, France
ETSE Universitat Rovira i Virgili / Dept. Eng. Electrònica, Elèctrica i Automàtica, Tarragona, Spain
3
EDF R&D / LME Department, Moret sur Loing, France
Abstract.- A comparative analysis between a DC power
transformer and a DC power gyrator on equal bases of
operation is presented. Both approaches are used to solve
the problem of maximum power transference from a PV
panel to a DC load. An outdoor measurements system has
been implemented and comparative experiments have been
carried out during six hours. Results show that both
approaches are practically equivalent in terms of efficiency.
I. INTRODUCTION
Impedance matching in power electronics basically
means solving the problem of maximum power transfer
between a dc generator and a dc load. In particular, the
maximum power transfer from a photovoltaic panel to a
dc load is an important technological problem in many
practical cases dealing with the optimization of a PV
conversion chain.
Although there are many works devoted to the problem
of the maximum power point tracking (MPPT) in a PV
array, only few of them deal with the nature of the power
interface while most of them focus on different types of
tracking algorithms. The problem of finding the most
appropriate power interface is discussed next. The main
antecedents in the study of matching power interfaces can
be found in the works of Singer and Braunstein on the
coupling of a PV array and a dc load by means of a dc
transformer with variable transformer ratio [1]-[2].
In this paper, we will study the impedance matching for
the maximum power point tracking (MPPT) in
photovoltaic arrays using power gyrators. It will be
demonstrated that both G-gyrators with either controlled
input or output current can be used to solve the MPPT
problem with similar efficiency to that of conventional
solutions based on the DC-transformer approach.
We will first analyze the matching problem using the
notion of a dc transformer and subsequently we will
demonstrate that such problem can be solved by using a
power gyrator. We will compare, by means of an outdoor
test [3], the performances of both systems during 6 hours
of measurements.
The outline of the paper is as follows. Impedance
matching by means of DC transformer is presented in
Section II. In Section III, impedance matching by means
of DC power gyrator is analyzed. An outdoor test for
efficiency evaluation of both systems is presented in
Section IV. A concluding discussion is given in Section V.
II. IMPEDANCE MATCHING BY MEANS OF A DC POWER
TRANSFORMER
A. Static operating point of the PV array
A DC-to-DC switching converter can be modeled
according to Middlebrook’s paradigm as an ideal DC
transformer whose the transformer ratio n(D) is a function
of the duty cycle. The connection of the PV generator and
the load using a switching converter as interface is shown
in Fig.1 where both generator and load have been modeled
by a first quadrant v-i characteristic.
I1
+
V1
v
i
-
I2
VOLTAGE -TO -VOLTAGE
DC-TO-DC
SWITCHING
CONVERTER
+
V2
-
v
fo(i)
RL
+
VB
-
i
LOAD
PV
Fig. 1. Matching a PV generator to a DC load using a voltage-tovoltage DC-to-DC switching converter
The behavior of the converter in steady-state can be
described by means of the following equations
V2 = n( D)V1
(1)
1
I1
n( D )
which define a DC ideal transformer.
The DC load can be modeled by means of the following
function v = f( i )
I2 =
v = f o (i ) = VB + RLi
(2)
with VB > 0 and RL > 0.
which corresponds to the Thevenin equivalent of the
usual DC loads supplied by a PV generator. Namely,
storage batteries, permanent magnet DC motor, shunt DC
motor, electrolysis pool, etc.
From (1) and (2) the following function v1 = fin(i1) is
derived
v1 = f in (i1 ) =
V2
V
R I
V
RL
I1
= B + L 2 = B +
2
n( D ) n ( D ) n ( D ) n ( D ) n ( D )
(3)
If we consider that the load is a battery with a very
small equivalent series resistance (RL→0), expression (3)
becomes
93
v1 = f in (i1 ) ≈
VB
n( D )
(4)
Fig 2 shows the intersection of characteristics fo and fin
with the PV curve under different hypotheses. In this case,
the direct connection of the load to the panel would
correspond to an operating point (VB) where the output
current of the PV generator is zero. As a matter of fact, the
value of the voltage battery is greater than the open circuit
voltage of the PV generator. It can be deduced from (4)
that the characteristics fin will be placed below fo if n(D) >
1. Therefore, from (4) the intersection point A could be
placed at left side of M for a certain value of duty cycle
D1. On the other hand, the intersection point B
corresponds to a duty cycle D2 > D1 since n(D) is an
increasing monotonous function of the duty cycle D [4].
The objective of the converter is to achieve a finop
characteristic so that it intersects with PV curve at the
optimal operating point M.
v
VB
VOC
The election of converter structure will imply a
restriction in the values of n(D). Therefore, we obtain
values of n(D) < 1 with a buck converter, values of n(D)
> 1 with the boost converter and both of them with the
Cuk converter. However, the Cuk converter imposes a
sign inversion at the output port.
B. Operating point trajectory of the PV array
Now, we will analyze the influence of the duty cycle
variations in equation (4) in order to study the trajectories
that allow the displacement of the operating point along
the v-i characteristic curve of the PV array.
Therefore
dV1
V B dn( D)
=−
<0
dD
n 2 ( D) dD
since
(5)
d (n( D))
> 0 in any converter [4] and we
dD
assume n(D) > 0.
fo
A
On the other hand, we can write
f in(D1 )
M
∆V1 =
f inopt
B
f in(D2 )
i
I SC
Fig. 2. PV Array operating points ( n(D) >1, D2 > D1)
v
VOC
C
dV1
∆D
dD
(6)
Therefore, we can conclude that increasing the duty
cycle will produce a trajectory to the right along the v-i
curve ( ∆ V1 negative), while decreasing D will result in a
trajectory to the left along the v-i curve irrespective of the
step-up or step-down nature of the converter.
C. Experimental Verification
It has been recently demonstrated that an extremum
seeking algorithm was stable in the sense of Lyapunov
and that it could applied to the maximum power point
tracking of a PV generator by using a voltage to voltage
dc-to-dc switching converter in PWM operation [5]. The
circuit performing the MPPT control is illustrated in Fig.
4.
f in(D2 )
M
f inopt
B
f in(D1 )
iSA
vSA
Analog
Multiplier
Differentiator
Hysteretic
comparator
Flip-flop +
Inhibition
delay
Integrator
vC
Fig. 4. Realization of the MPPT controller
A
ISC
fo
i
Fig. 3. PV array operating points ( n(D) < 1, D2 < D1)
Similarly, figure 3 illustrates the case of an operating
point corresponding to a direct connection (point A) which
is located at the right of M. In this case, it is mandatory to
perform the matching with a n(D) < 1. Note that it can be
deduced from (4) that the characteristics fin will be placed
above fo if n(D) < 1. Therefore, from (4) the intersection
point C could be placed at left side of M for a certain
value of duty cycle D2. On the other hand, the intersection
point B corresponds to a duty cycle D2 < D1.
The PV panel is a solar array of monocrystalline cells
with an open circuit voltage of 22.1 V and a nominal
voltage value at the maximum power point of 18 V. Since
the load is a 24 V acid-lead battery, the dc-to-dc
conversion structure must be performed by a boost
structure. Fig.5 shows the practical implementation of a
boost dc-to-dc voltage transformer-based with MPPT
function. The boost parameters are given by L1 = 75 µH,
C1= 12 µF, C2 = 20 µF, V2= 24 V and a constant
switching frequency of 150 kHz.
94
III. IMPEDANCE MATCHING BY MEANS OF A DC POWER
GYRATOR
A. Static operating point of the PV array
If the voltage to voltage dc-to-dc switching converter of
Fig. 1 is substituted by a voltage to current dc-to-dc
switching converter, i.e., a G-power gyrator [6], the
steady-state equations at both input and output ports of the
converter will be given by
I1 = gV2
(7)
I 2 = gV1
Fig. 5. Practical implementation of a boost converter performing the
MPPT of a PV array
Next, it will be shown the experimental behavior of the
Is, Vs, Ps of the PV generator and also the duty cycle of the
boost converter with the extremum-seeking control
algorithm under different operating conditions. Fig. 6.a
shows the PV system response after the connection of an
additional panel in parallel with the PV generator. As it
can be expected, the current increases while the voltage
remains practically unchanged except in the transient-state
connection. Since the voltage operating point has not
changed, the maximum power point is almost
instantaneously reached. A similar situation is observed in
Fig. 6.b in which the panel previously added is removed.
vC
PS
VS
IS
where g is the gyrator conductance.
From (2) and (7), we conclude that the input
characteristics iin = fin (v1) will be expressed as
I 1 = f in (V1 ) = gV 2 = g (V B + R L I 2 ) = gV B + g 2 R LV1
(8)
Considering that the load is a battery with an equivalent
series resistance RL→0 the expression (8) becomes
I 1 = f i n ≈ gV B
Expression (9) shows that the input current will be
proportional to the battery voltage with a proportionality
factor g (the gyrator conductance).
Figs. 7 and 8 show the intersection of characteristics fo
and fin with the PV curve in similar situations as those
illustrated in figs. 2 and 3 respectively. Fig. 7 describes
the direct connection of the load and the PV array
resulting in an operating point located at the left of the
maximum power point. It can be derived from (9) that the
intersection point B can be placed at the right side of M by
an appropriate choice of conductance G (a value of the
gyrator conductance g). If we assume that the intersection
at point B corresponds to a certain value G1 of the gyrator
conductance, then intersection at A will correspond to a
value G2 < G1 as derived from (9).
v
VB
VOC
a)
(9)
f in(G2 )
A
f inopt fin(G1 )
fo
M
vC
B
VS
PS
IS
b)
Fig. 6. Response to a parallel connection and removal of an additional
panel (Time scale: 10 ms/div).
I SC
i
Fig. 7. PV array operating points. Impedance matching by means of a
G-gyrator (fo(i2) intersects at the left side of M)
Fig. 8, in turn, illustrates the case of a direct connection
at point C, which is located at the right side of point M. By
an appropriate selection of the gyrator conductance (G =
G2) the operating point can be placed at the left side of M
(point A). Increasing the conductance value to G1 (G1 >
95
G2) will establish the operating point at point B, which is
located at the right side of M.
v
f in(G2 )
VB
VOC
f inopt fin(G1 )
A
M
B
C
I SC
current source at the input port. Since the regulator
establishes the gyrator characteristics through the control
of current i1, we will call this class of circuits G-gyrators
with controlled input current [6]. Hence, we impose a
sliding mode surface S(x) = gV2 - i1, where V2 is a constant
voltage.
The analysis of the sliding-mode induced by
considering S(x) = gV2 - i1 results in a stable equilibrium
point for the boost converter, the characteristic equation
being of zero order.
The practical implementation of a boost-converterbased G-semigyrator with controlled input current is
shown in Fig. 10 for the set of parameters L1 = 75 µH,
C1= 12µF, C2 = 20 µF and V2 = 24 V.
fo
i
Fig. 8. PV array operating points. Impedance matching by means of a
G-gyrator. (fo(i2) intersects at the right side of M)
B. Operating point trajectory of the PV array
Now, we will study the influence of conductance g
variations in equation (9) in order to study the trajectories
or the operating point along the v-i curve. Hence,
dI 1
= VB > 0
dg
(10)
Therefore, we can conclude that increasing the gyrator
conductance will result in a trajectory towards the right
( ∆ I1 positive), while decreasing g will result in a
trajectory to the left along the v-i curve.
C. Experimental Verification
In [6, 7, 8], different types of power gyrators have been
synthesized and classified. Fig. 9 shows the block diagram
of a power gyrator of type G with MPPT function. In
order to compare in the same conditions the DC power
transformer of section II with the DC power gyrator we
have selected the same converter structure to implement a
power gyrator, i.e., the boost converter. The boost
converter has a pulsating output current, therefore
according to the definition of power gyrator gave in [7],
the use of a boost converter leads to a power semigyrator
implementation.
iSA = i1
+
G
vSA = v1 GYRATOR
PV
Array
Module
I1 = gV2
I2 = gV1
i2
+
v2
-
Battery
24 V
Fig. 10. Practical implementation of a boost-converter-based Gsemigyrator operating at variable switching frequency with MPPT
function
Note that variable vC depicted in Fig. 4 becomes the
gyrator conductance of the power gyrator (Fig. 10). The
variation of is with constant time-derivative is achieved by
imposing such behavior to the gyrator conductance G.
Next, It will be shown the experimental behavior of Is,
Vs, Ps of the PV generator and also de conductance g of
the power semigyrator with the extremum-seeking control
algorithm under different operating conditions. Fig. 11.a
shows the PV system response after the connection of an
additional panel in parallel with the PV generator. As it
can be expected, the current increases while the voltage
remains practically unchanged except in the transient-state
connection. Since the voltage operating point has not
changed, the maximum power point is almost
instantaneously reached. However, when a different
situation is observed in Fig. 11.b in which the panel
previously added is removed. Now, the imposed input
current is too large and the operating point of the PV
generator remains during 20 ms in the short-circuit point
delivering zero output power. The PV generator starts to
deliver power when the conductance of the gyrator (g)
diminishes until a value that implies a current i1 inside of
v-i characteristic.
g
iSA
vSA
MPPT
Control
Fig. 9. Block diagram of a MPPT of a PV array based on a power
gyrator of type G.
In this case, we would synthesize a G-gyrator intending
to transform a voltage source at the output port into a
96
g
VS
PS
IS
a)
Fig. 12. Measured efficiencies of the boost converter-based voltage
transformer with MPPT function
g
VS
PS
IS
b)
Fig. 11. Response to a parallel connection and removal of an additional
panel (Time scale: 10 ms/div).
IV. EFFICIENCY EVALUATION
The overall system efficiency of PV conversion
structure (ηTOTAL) is given by [9]
η TOTAL = η PV η MPPT η CONV
(11)
where ηPV is the ratio of the maximum available
electrical power of the panel for the entering solar
irradiance, ηMPPT is the ratio of the real available electrical
power of the panel for its maximum available electrical
power and ηCONV is the ratio of the power at the
conditioner output for the power at the conditioner input.
Our automatic measuring system provides the values of
ηMPPT and ηCONV along a complete day. Figs 12 and 13
shows this efficiencies values during an outdoor test of 6
hours. In this test we can compare the efficiencies
performances obtained by means of a DC-power
Transformer MPPT (Fig. 12) and by means of a DCpower gyrator (Fig. 13). The converter efficiency is better
for the case of DC transformer; and this could be in part
due to a higher consumption of the control circuitry and
also to the variable switching frequency of the power
gyrator. In fact, a variation in the switching frequency
could imply a reduction of the converter efficiency. On
the other hand the MPPT efficiency is bigger for the DC
power gyrator for low levels of input power.
Fig. 13. Measured efficiencies of the boost converter-based Gsemigyrator with MPPT function
Table I shows the energy balance and the averaged
efficiencies during the 6 hours test. The total efficiency
η T = η MPPT η CONV shows that we obtain slightly better
efficiencies with the matching circuit performed by the
DC transformer.
TABLE I. ENERGY BALANCE AND AVERAGED EFFICIENCIES
Transfor
mer
Gyrator
Available
Energy
Absorbed
Energy
90.2 Wh
88.1 Wh
88 Wh
86.5 Wh
Output
Energy
η MPPT
η CONV
ηT
81.3 Wh
97.7 %
92.2 %
90.1 %
77.6 Wh
98.3 %
89.7 %
88.2 %
V. CONCLUSIONS
In this work, we have compared the realization of
impedance matching circuits to track the maximum power
point of a PV array by means of two concepts: the DC
power transformer and the DC power gyrator.
A DC transformer-based boost converter has been
implemented to match a lead-acid battery of 24 V with a
PV array.
97
Also, it has been shown that power gyrators of type G
with controlled input current can be used as impedance
matching circuits to track the maximum power point of a
PV array. The selected gyrator structure is the boostconverter-based G-semigyrator with controlled input
current.
We have compared the dynamic and static
performances of both possibilities by means of
experimental verification. An outdoor test has been made
to compare the averaged efficiencies in real conditions.
The dc transformer-based boost converter has only an
averaged efficiency 3 % bigger that the DC gyrator-based
boost converter operating in sliding mode. It has to be
pointed out that the transformer structure has a better
dynamic performance when larges changes in the
irradiation appear. This is due to the fact that when “the
load is a battery” the input current varies almost
instantaneously for the transformer case, while it takes
some additional time in the case of the gyrator because the
changes in the input current follows the change of the
output voltage.
Similar studies are in progress for other converter
structures like buck converter and Cuk converter.
VI. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
S. Singer and A. Braunstein, “Maximum power transfer from a
nonlinear energy source to an arbitrary load” IEEE Proceedings,
Pt G, 1987 pp 1-7
A. Cid-Pastor, C. Alonso, B. Estibals, D. Lagrange and L.
Martinez-Salamero, “Automatic measurement system for testing
photovoltaic conversión chains”, 30th Annual Conference of IEEE
Industrial Electronics Society, Proceedings of IECON 2004,
Pusan, Korea, November 2004.
J. Calvente, “Control en modo deslizante aplicado a sistemas de
acondicionamiento de potencia de satellites”. Tesis doctoral,
UPC, 2001. http://www.tdx.cesca.es (in spanish)
R. Leyva, C. Alonso, I. Queinnec, A. Cid-Pastor, D. Lagrange and
L. Martínez-Salamero, “MPPT of photovoltaic systems using
extremum seeking control” IEEE Transactions on Aerospace and
Electronic Systems, Vol. 42, No. 1, Jan. 2006, pp 249-258
A. Cid-Pastor, L. Martínez-Salamero, C. Alonso, G. Schweitz, J.
Calvente and S. Singer, “Classification and synthesis of power
gyrators” IEE Proceedings Electric Power Applications (Accepted
for publication)
A. Cid-Pastor, “Energy Processing by means of Power Gyrators”
Ph.D Dissertation. Technical University of Catalonia (UPC),
Barcelona July 2005 (available at http://www.tdx.cesca.es)
A. Cid-Pastor, L. Martínez-Salamero, C. Alonso, B. Estibals, J.
Alzieu, G. Schweitz, and D. Shmilovitz , “ Analysis and design of
power gyrators in sliding-mode operation” IEE Proceedings
Electric Power Applications, Vol. 152, No. 4, July 2005.
M. Jantsch, M. Real et al., “Measurement of PV maximum power
point tracking performance”, 14th European Photovoltaic Solar
Energy Conf., Barcelona 30 June- 4 July, 1997.
S. Singer and A. Braunstein, “A General Model of Maximum
Power Point Trackers” Proceedings of MELECON’85. pp 147-151
98