Post on 25-Apr-2023
Converting Conventional Cars in Mild Hybrid Solar Vehicles G.Rizzo*, M.Sorrentino*, C.Speltino**, I.Arsie*, G.Fiengo**, F.Vasca**
*Dept. of Mechanical Engineering, University of Salerno, 84084 Fisciano (SA), Italy
(Tel:+39 089 964069, e-mail: iarsie grizzo msorrentino @unisa.it)
**Dept. of Engineering, University of Sannio, Piazza Roma 21, 82100 Benevento, Italy
(Tel: +39 0824 305508, e-mail: gifiengo vasca cspeltin @unisannio.it)
Abstract: Hybrid electric vehicles (HEV) represent a good and feasible solution to reduce fuel
consumption and related emissions. Furthermore, there is an increasing interest toward the integration of
HEV’s with photovoltaic (PV) panels, in order to enhance their benefits. But, despite the recent
commercial success of HEVs, their market share is still insufficient to produce a significant impact on
global energy consumption. Moreover, due to the present crisis, a substantial substitution of conventional
vehicles with HEVs is unlikely, at least in short time. Consequently, a realistic strategy could consist in
developing solutions able to achieve part of the benefits of hybrid and solar vehicles on conventional
vehicles. A method for the mild solar hybridization of conventional vehicles is presented in this paper,
based on use of in-wheel motors on rear wheels, of a PV panels, of an additional battery and of control
system not interfering with the original ECU. A preliminary assessment of the benefits obtainable in
terms of fuel consumption as a function of the degree of mild hybridization is performed by simulation
analysis.
Keywords: Solar Energy, Solar Cell, Electric Vehicles, Hybrid Vehicles, Automotive Control
1. INTRODUCTION
Transportation has a marked impact on acoustic and
atmospheric pollution in urban areas, on fossil fuels depletion
and on greenhouse effect. Hybrid Electric Vehicles have
emerged as one of the most effective and feasible alternatives
to engine-driven vehicles, allowing significant reductions in
fuel consumption and emissions (Sciarretta and Guzzella,
2007).
Further substantial benefits can be achieved by Hybrid Solar
Vehicles, obtained by the integration of HEV’s with
photovoltaic panels, particularly for urban driving (Letendre
et al., 2003; Rizzo, 2010; Arsie et al., 2010; Rizzo et al.,
2010). The adoption of tracking solar roofs to maximize solar
contribution during parking phases is also under study
(Coraggio et al., 2010, I).
Fig. 1. Solar PV production and cost
In parallel, due to the pressing need for a renewable and
carbon-free energy (REN21, 2009), the diffusion of the
Photovoltaic has been growing exponentially in recent years
while their price is significantly decreasing (Fig. 1), and their
efficiency improving. The industrial interest toward
application of photovoltaic to cars is evidenced by the recent
launch of a new model of a HEV equipped with PV panels by
a major automotive company.
But, despite the recent commercial success of HEVs, their
market share is still insufficient to produce a significant
impact on energy consumption on a global basis. Moreover,
considering the current economic crisis, it is unlikely that, in
next few years, PV assisted EV’s and HEV’s will substitute
for a substantial number of conventional vehicles, since
relevant investments on production plants would be needed.
This fact could of course impair the global impact of these
innovations on fuel consumption and CO2 emissions, at least
in a short term scenario. Therefore, one may wonder if there
is any possibility to upgrade conventional vehicles to PV
assisted hybrid.
A such proposal has been recently formulated and patented at
the University of Salerno (www.hysolarkit.com). A research
project aiming at the development of a kit for mild-solar-
hybridization of conventional cars, proposed by University of
Salerno and University of Sannio, has been recently financed
by the Italian ministry of university and research.
In the following, the structure of the mild-hybrid vehicle are
presented and the main issues related to vehicle control
discussed. Then, the details of the models used for simulation
analysis are presented. Finally, the results of some
preliminary assessment of the benefits achievable with this
proposal are presented and discussed.
2. VEHICLE STRUCTURE
The vehicle structure is based on the conversion of a
conventional vehicle, where the front wheels are propelled by
an Internal Combustion Engine (ICE) controlled by an
Engine Control Unit (ECU). The ECU, as a rule, is equipped
by an On Board Diagnostics (OBD) gate that enables the
access to significant engine/vehicle operation data, such as
pedal position, vehicle and engine speed, manifold pressure,
thermal state, and environmental conditions. The mild
parallel hybrid structure is realized by substituting/integrating
Preprints of the 18th IFAC World CongressMilano (Italy) August 28 - September 2, 2011
Copyright by theInternational Federation of Automatic Control (IFAC)
9715
the rear wheels with in-wheel motors and by including an
additional battery pack and photovoltaic panels on the roof.
The upgraded vehicle can operate in i) pure electric mode -
when the ICE is switched off or disconnected by the front
wheels - or in hybrid mode - when the ICE drives the front
wheels while the rear wheels operate in traction mode or in
generation mode, corresponding to positive or negative
torque, respectively. The battery can be recharged by both in-
wheels motors, when operating in generation mode, and
photovoltaic panels. Optionally, the battery could be
recharged also by the grid, in Plug-In mode. A Vehicle
Management Unit (VMU) receives the data from the OBD
gate and the battery (for SOC estimation) to drive the in-
wheel motors, by properly acting on the electric node EN. A
display on the dashboard may advice the driver about the
actual system operation mode. Fig. 2 depicts a scheme of the
upgraded vehicle structure.
Fig. 2. Scheme of a system to upgrade a conventional car to Mild Hybrid
Solar Vehicle.
2.1. In-Wheel Motors.
One of the key aspects of this proposal concerns the
possibility of replacing the rear wheels with in-wheel motors.
This topic is very actual and of increasing industrial interest
(Fig. 3), being strongly related to the diffusion of electric
vehicles. In this sense, it is considered as a ‘disruptive
technology’ (Murata, 2010). Their use would also allow to
integrate advanced techniques for vehicle control (Braghin
and Sabbioni, 2010; Xiong at al., 2010) and to expand the
applicable range of vehicle control (Murata, 2010). Anyway,
the installation of a motor inside the wheel is made difficult
by the standpoint of space constraints. Moreover,
deterioration of ride comfort due to increase in unsprung
mass occurs. The complexity of these problems tends to
increase with motor power. Therefore, a parametric analysis
of the influence of in-wheel motor power on the expected
benefits of the hybridization strategy will be performed in the
following.
Fig. 3. Activities of OEM’s in the in-wheel motor technology (Gombert, 2007).
2.2. Control Strategies Issues
The powerflow control in the HEV is particularly challenging
because of the hybrid structure of the driveline and the
conflicting performance objectives: driver power demand,
fuel economy, SOC regulation, drivability. A flexible, model-
based, decoupling control strategy for power split in mild
hybridized vehicles would be suitable. In such case, the
control strategy should be composed of three main tasks: (1)
steady-state power management based upon consumption
minimization; (2) dynamic regulation of battery SOC, also
considering the energy contribution from PV panels during
driving and parking; (3) dynamic power split for energy
efficiency and drivability. Decoupling should be obtained in
the sense that control of battery SOC and drivability neither
does not affect the power demand nor does not influence each
other in the nominal operating conditions.
Regard to the operating modes achievable for the hybridized
vehicle, it should be noticed that in some vehicles pure
electric mode operation, with engine switched off, could not
be compatible with normal operation of steering and braking
systems. On the contrary, hybrid mode operation (with both
engine and electric motors working) should be always
possible, compatibly with driving behaviour, driveability and
safety issues. The following analysis is therefore referred to
the operation in hybrid mode only.
In that case, the energy management and control in the
proposed hybridization system would differ from classical
HEV by two main reasons.
The former is related to the addition of solar panels. In fact,
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. On the other hand, in case
of solar hybrid vehicle, as in Plug-In vehicles too, the battery
can be 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 (Arsie et al., 2006). Moreover, advanced
strategies could be necessary for the optimal management of
vehicle and battery, even adopting on-board weather forecast
to estimate the amount of solar recharge in next parking
phase (Coraggio et al., 2010, II).
The second reason is due to the fact that it would be
advisable to develop a kit which does not require any
modifications to the original ECU: in fact, the VMU would
drive the electric motors deriving its data from OBD port
(Fig. 2), and not interfering with the operation of the original
ECU. Of course, the need to design a control system
coexisting with the original ECU poses some specific
constraints in terms of driving requirements and driveability,
which result in different control strategies vs. those
implementable on a full hybrid vehicle. For instance, when
the driver steps on the accelerator in the hybridized vehicle,
so demanding higher vehicle power, an increase in the engine
power will necessarily result; on the contrary, in a ‘native’
HEV, where the splitting between thermal and electric engine
is managed by the control system, the increase in vehicle
power could be achieved even by reducing the engine power
and, in parallel, by increasing the electric motor power.
Similarly, in the hybridized vehicle a reduction in engine
Preprints of the 18th IFAC World CongressMilano (Italy) August 28 - September 2, 2011
9716
power will be always achieved when the driver releases gas
pedal.
Therefore, the achievement of a given level of power splitting
between thermal and electric motor can be obtained by
inducing the driver to modulate the pedal position until the
desired vehicle power would be reached. In other words, the
driver will act as the vehicle is running downhill. On the
contrary, the hybridized vehicle can operate in recharging
mode when the in-wheel motors absorb part of the power
generated by the engine: in this case the driver will act on the
pedal as the vehicle would run uphill. A detailed study of
driver behaviour is therefore needed to develop
implementable strategies for this kind of vehicle.
2.3. Vehicle Model
Vehicle simulation, whose results are presented in the next
Section, was performed by means of a longitudinal vehicle
model developed under the following hypotheses: i) the drag
force is considered acting on vehicle centre of gravity; ii)
vehicle inertia accounts for both vehicle mass (MHSV) and
rotational inertia of ICE, EM/EG and wheels, though the term
Meff; iii) the effects of elasticity in the mechanical
transmission are neglected. The resulting longitudinal model
relates requested power at wheels Pw to the road load, as
follows:
vdt
dvM
vACCvgMP
eff
xrHSVw
35.0sincos (1)
where and v are the road grade and vehicle speed,
respectively. In case of non negative Pw values, the
mechanical power is supplied by the ICE (PICE) and/or the in-
wheel motors (PEM), depending on the control variable PS
(Power Split) defined as:
0 w
w
EM PifP
PPS (2)
The control variable PS may range between negative values,
in case ICE provides an extra power to be recovered into the
battery, to unit (i.e. pure electric vehicle). In all cases the
requested power is given as the algebraic sum of ICE and in-
wheel motors power:
Pw=PICE+PEM (3)
In case of vehicle braking or deceleration (Pw<0), the
regenerative braking mode is active and the power is
recovered into to the battery, according to battery power
limitations and to in-wheel motors performance and
efficiency. These latter are computed from static maps
provided by the manufacturer as function of torque and
speed. Depending on in-wheel motors operation mode (motor
or generator) the electric power (PB) requested or supplied to
the battery is given by the following relationships:
0 w
tr
EMB Pif
PP
(4)
0 wEMwB PifPP (5)
2.4. Battery Model
A lithium-ion battery is composed of three principal parts:
two porous electrodes, namely cathode (positive) and anode
(negative) and an electrolyte solution that acts as separator
between the electrodes as shown in Fig. 4. During a discharge
process, the lithium active particles flow through the
electrolyte solution until they arrive at the positive electrode
The electrons produced in the negative electrode reaction
cannot flow inside the electrolyte, that acts as insulator, and
flow through an external circuit, producing the current. The
inverse reactions occur during the battery charge.
Due to their porous nature, the electrodes are represented as
small spheres of active material along the electrode, with the
chemical reactions occurring at the sphere surface Wang et
al. (1998a). The resulting Partial Differential Equations
(PDE) describe the battery system with four quantities, i.e.
solid and electrolyte concentrations (cs, ce) and solid and
electrolyte potentials (s, e) as function of the reaction
current density jLi
describing the current distribution along
the cell lenght x Gu and Wang (2000); Smith and Wang
(2006). The input variable of the model is the current I while
the output is the voltage at the metal collectors V.
Liex
effDex
eff jckkx
ln
(6)
Lisx
eff jx
(7)
Li
exeffDx
ee jF
tcD
t
c 01
(8)
ssrs cDt
c
(9)
where the current density is defined as:
(10)
The cell potential is computed as:
IA
RxLxV
fss )()( 0
(11)
where Rf is the film resistance on the electrodes surface and
A is the collectors surface. More details on the model and its
parameters can be found in Smith and Wang (2006),
Domenico et al. (2008a), and Wang et al. (1998b).
Fig. 4. Schematic macroscopic (x-direction) cell model with coupled
microscopic (r-direction) solid diffusion model. The electrodes are filled with the electrolyte solution.
Preprints of the 18th IFAC World CongressMilano (Italy) August 28 - September 2, 2011
9717
Reduced order model
The model obtained with the PDEs equations is useless for
real time applications or to derive a control systems because
of its extreme complexity. A more useful reduced order
model, derived in Di Domenico et al. (2008b), can be
achieved by neglecting the solid concentration distribution
along the electrode and considering the material diffusion
inside a representative solid material particle for each
electrode. In accordance with considering a mean solid
concentration, the spatial dependence of the Butler-Volmer
current can be ignored and a constant value jLi
is considered
which satisfies the spatial integral (for the anode or the
cathode)
(12)
where δn is the anode thickness. This averaging procedure is
equivalent to considering a representative solid material
particle somewhere along the anode and the cathode Di
Domenico et al. (2008b). The partial differential equation
(12), describes the solid phase concentration along the radius
of active particle, but the macroscopic model requires only
the concentration at the electrolyte interface. By using the
finite difference method for the spatial variable r, it is
possible to express the spherical PDE into a set of ordinary
differential equations (ODE), dividing the sphere radius in
Mr - 1 slices, each of size r = Rs/(Mr-1) and rewriting
boundary conditions Schiesser (1991). The new system
presents Mr-1 states cs = (cs1, cs2, …csMr-1 )T, representing
radially distributed concentrations at finite element node
points 1,…, Mr-1. Two sets of ODEs, one for the anode and
one for the cathode are then obtained in the classical form
(13)
where A, B and D are function of cell physical and chemical
properties. The positive and negative electrode dynamical
systems differ at the constant values and at the input sign. It
is convenient to define the normalized concentration, also
known as stoichiometry, x = cse,x/cse,max,x, with x = p, n for
the positive and negative electrode. The battery voltage (11),
using (13) and using the average values at the anode and the
cathode, can be rewritten as a collection of submodels
(14)
The results as well as more details can be found in Di
Domenico et al. (2008a) and Di Domenico et al. (2008b) and
are not reported here for brevity.
Finally, the battery voltage (14) can be rewritten as a function
of current demand and normalized solid concentration
(15)
where Kr is a term that takes into account both internal and
collector film resistances.
3. SCENARIO ANALYSIS
In order to assess the benefits associated to mild
hybridization of conventional cars, a simulation based
scenario analysis was carried out. Table 1 describes the basic
features and hypotheses of three selected scenarios. Case 1 is
nothing but the reference one, in that it provides the
conventional vehicle fuel economy. In Case 2 the benefits
achievable by only enabling regenerative braking trough in-
wheel motors are estimated. Finally in Case 3 a PV roof is
added to the mild hybrid powertrain, thus enabling the
achievement of further benefits in terms of fuel consumption.
The main difference between Case 2 and Case 3 energy
management policy lays in the final state of charge to be
reached at the end of the driving cycle, which in the current
scenario analysis is the standard NEDC driving path. Charge
sustaining strategy is adopted in Case 2, whereas in Case 3
the final SOC must differ from the initial one by the amount
of energy supplied by the PV roof during the parking phase
(Arsie et al. 2007). Particularly, it was assumed that driving
time is 1.5 hour/day, while parking phase lasts for 8.5 hours
on average during daytime (recharging with solar power),
while for the remaining parking time it is assumed that the
vehicle is not recharged. Considering the average daily solar
power that impacts on Southern Italy, the 300 Watts PV roof
assumed in Case 3 provides up to 1 kWh a day. It is worth
mentioning here that PV roof weight was assumed
approximately equal to 50 kg.
In both Cases 2 and 3 the hybrid components are managed as
follows:
0,,min max, tPtPtPtP wwIWMcIWMwb (16)
min
minmax,
&0,0
&0,,min
SOCtSOCtPtP
SOCtSOCtPtPt
tPtPStP
wb
wwIWM
cIWM
w
b
(17)
where P is power [kW], η [/] is efficiency and the footers w,
IWM, b and c stand for, respectively: wheel, in-wheel motor,
battery and converter. In this preliminary numerical activity,
the value of the power splitting PS was constantly set to 0.5.
It is also worth mentioning here that when Pw(t)>=0 the
remaining power demand is always met by the ICE. The
parameter SOCmin in (17) has been set as function of the
following variables: in-wheel motors power, size of battery
pack and presence of the PV roof (i.e. different final SOC,
i.e. SOCf, to be reached at the end of the driving path).
Regarding battery size, in the scenario analysis it was
imposed that the number of series connected lithium cells
always equals 50 (i.e. battery voltage is 185 Volts), whereas
the number of parallel connected cells varies in order to
match the nominal in-wheel power.
Table 1. Description of analyzed mild hybridization scenarios.
Case Regenerative braking PV roof
1 NO NO
2 YES NO
3 YES YES
The impact of additional weight due to Mild Hybridization is
also considered, in order to estimate their effects on fuel
consumption. In next developments, a study of additional
costs will be also included, in order to perform an optimal
design of the system considering both technical and
economic aspects and to assess the practical feasibility of the
proposed hybridization technique.
4. RESULTS
In this section the main outcomes of the scenario analyses
described in the previous section are presented and discussed.
Particularly, Case 2 and 3 were simulated varying the
Preprints of the 18th IFAC World CongressMilano (Italy) August 28 - September 2, 2011
9718
nominal in-wheel power (Pn,IWM), in the range [1, 12] kW (the
nominal power of each wheel is therefore the half of such
value). Table 2 lists the main specifications of the simulated
vehicle.
Table 2. Conventional car specifications.
Nominal ICE power [kW] 46
Fuel gasoline
Coefficient of drag (Cd) 0.35
Frontal area [m2] 2.24
Rolling radius [m] 0.294
Rolling resistance coefficient [/] 0.01
Base vehicle mass [kg] 1000
Next figures illustrate the impact of in-wheel motor and
battery size on fuel economy with and without PV roof. Fig.
5 shows that energy benefits due to mild hybridization
always increase in Case 2, reaching an asymptotic behavior
beyond about Pn,IWM = 7 kW. On the other hand Case 3
exhibits a maximum fuel economy between 6 and 8 kW,
beyond which fuel savings with respect to the reference case
decrease, mainly due to the weight increase, as shown in Fig.
6, and to variations in average in-wheel motor efficiency.
Furthermore, the comparison of Case 2 and Case 3 highlights
the importance of coupling in-wheel motors to the PV roof to
significantly enhance the energy saving effect achievable via
mild hybridization. The aforementioned optimal Case 3 value
corresponds with fuel savings as high as 15 % as compared to
the conventional car.
Fig. 6 shows the variation of weight increase due to mild
hybridization in Case 3. The curve is not perfectly linear
because battery size was modified varying in discrete way the
number of parallel connected cells. Therefore, the same
battery size was adopted for near Pn,IWM values (e.g. Pn,IWM =
5 and Pn,IWM = 6 in Fig. 6). The simultaneous analysis of
figures 5 and 6 suggests once again the opportunity of
selecting a reasonable maximum power for in-wheel motors.
Higher power not only may not further increase energy
savings, but also leads to unnecessary weight and inertia
increase of the hybridized vehicle.
Finally, Fig. 7 shows the variation of the target SOCf to be
reached at the end of the driving cycle in Case 3. As
expected, higher Pn,IWM results in larger battery size and,
therefore, in higher SOCf and smaller SOC variation with
respect to the initial value (i.e. SOC0=0.7).
Finally, it should be noticed that the presented analysis has
not yet exploited all the potentialities of this system. For
instance, in case that the vehicle requires low torque,
corresponding to low engine efficiency (i.e. point A in Fig.
8), it could be convenient to operate the engine at higher
torque, for instance corresponding to the maximum efficiency
at the given engine speed (i.e. point B), and recovering the
excess power by operating the electric motors in generating
mode, as it happens in full hybrid vehicles. Of course, the
convenience should be assessed considering the conversion
efficiencies involved, also taking into account the maximum
torque that in-wheel motor can deliver at the given speed.
Preliminary tests have confirmed that fuel consumption can
be improved with respect to the presented results by adopting
such strategy. Anyway, some issues related to the
implementability of this solution within the hybridization
strategy should be investigated.
More in general, this preliminary analysis should be
integrated by a more systematic study on the optimal
management strategy for the hybridization system. A not
causal reference solution, to be adopted as a benchmark for
on-board implementable strategies, is in course of study by
Dynamic Programming (DP) approach (Sundström and
Guzzella, 2009).
5. CONCLUSIONS
The availability of a system to upgrade conventional vehicles
to mild-solar-hybrid could have a relevant impact on fuel
consumption and CO2 emissions due to transportation, since
it may potentially be applied to most of the today fleet, and
without requiring expensive reconversion of production lines
for cars. A discussion on the main features of a such system,
on the open problems and on main control issues has been
presented. A preliminary study by simulation analysis has
confirmed that the proposed mild-solar-hybrid conversion
can give significant benefits in terms of fuel consumption,
even adopting in-wheel motors with limited power.
Further work is in progress to: i) develop optimal control
strategies that are suitable for online implementation (i.e. real
world application), ii) to address both safety and functionality
issues associated to car retrofitting, mainly due to the need of
addressing the interaction among driver action on
acceleration and brake pedal and the additional VMU; iii)
finally, develop a prototype of the whole mild-solar-
hybridization system.
Fig. 5. Variation of fuel economy as function of degree of mild
hybridization.
Fig. 6. Weight increase due mild solar hybridization.
Fig. 7. Final SOC to be reached in Case 3 as function of degree of mild
hybridization.
1 2 3 4 5 6 7 8 9 10 11 1218
19
20
21
22
23
24
25
Pn,IWM
[kW]
[km
/l]
Fuel economy [km/l] vs. nominal in-wheel power
Case 1
Case 2
Case 3
1 2 3 4 5 6 7 8 9 10 11 120
25
50
75
100
125
150
Pn,IWM
[kW]
[kg
]
Weight increase [kg] due to mild hybridization - Case 3
solar kit
in-wheel motors
PV
battery
1 2 3 4 5 6 7 8 9 10 11 120.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Pn,IWM
[kW]
Final SOC [/] vs. nominal in-wheel power - Case 3
SOC0
SOCf
Preprints of the 18th IFAC World CongressMilano (Italy) August 28 - September 2, 2011
9719
Fig. 8. Engine efficiency map and possible operating points in recharging
mode.
6. REFERENCES Arsie, I., Rizzo, G., Sorrentino, M. (2007). Optimal Design and Dynamic Simulation of
a Hybrid Solar Vehicle. SAE 2006 Transactions – Journal of Engines, Vol. 115-3,
pp. 805-811.
Arsie, I., Rizzo, G., Sorrentino, M. (2010). Effects of engine thermal transients on the
energy management of series hybrid solar vehicles. Control Engineering Practice,
doi: 10.1016/j.conengprac.2010.01.015.
Braghin F., Sabbioni E. (2010), Development of a control strategy for improving
vehicle safety in a hybrid vehicle with four independently driven in-wheel
motors, 10th International Symposium on Advanced Vehicle Control AVEC10,
August 22-26, 2010, Loughborough, UK.
Coraggio G., Pisanti C., Rizzo G., Senatore A. (2010, I), Model Based Control of a
Moving Solar Roof for a Solar Vehicle, In: 10th International Symposium on
Advanced Vehicle Control AVEC10, August 22-26, 2010, Loughborough, UK.
Coraggio G., Pisanti C., Rizzo G., Sorrentino M. (2010, II), Assessment of benefits
obtainable in a Hybrid Solar Vehicle using look-ahead capabilities for incoming
solar energy, In: 10th International Symposium on Advanced Vehicle Control
AVEC10, August 22-26 2010, Loughborough, UK.
Di Domenico, D., Fiengo, G., and Stefanopoulou, A. (2008a). Lithium-ion battery state
of charge estimation with a Kalman filter based on a electrochemical model.
Proceedings of 2008 IEEE Conference on Control Applications.
Di Domenico, D., Stefanopoulou, A., and Fiengo, G. (2008b). Reduced order lithium-
ion battery electrochemical model and extended Kalman filter state of charge
estimation. ASME Journal of Dynamic Systems, Measurement and Control -
Special Issue on Physical System Modeling.
Gombert B., (2007), http://www.munichnetwork.com/
fileadmin/user_upload/konferenzen/mobilitaetsforum-
2/071128MUN_Gombert_Bernd.pdf
Gu, W. and Wang, C. (2000). Thermal and electrochemical coupled modeling of a
lithium-ion cell. Proceedings of the ECS, 99, 748-762.
Letendre, S., Perez, R., Herig, C. (2003). Vehicle Integrated PV: A Clean and Secure
Fuel for Hybrid Electric Vehicles. Proc. of the American Solar Energy Society
Solar 2003 Conference, June 21-23, 2003, Austin,TX.
Lu Xiong, Zhuoping Yu and Yufeng Meng, (2010), Vehicle Dynamic Control for a 4
In-Wheel-Motored EV based on Identification of Tire Cornering Stiffness, 10th
International Symposium on Advanced Vehicle Control AVEC10, August 22-26,
2010, Loughborough, UK.
Murata S., (2010), Innovation by In-Wheel-Motor Drive Unit, Keynote lecture, 10th
International Symposium on Advanced Vehicle Control AVEC10, August 22-26,
2010, Loughborough, UK.
REN21, Renewables - Global Status Report - 2009 Update,
http://www.ren21.net/pdf/RE_GSR_2009_update.pdf
Rizzo, G. (2010). Automotive Applications of Solar Energy. 6th IFAC Symposium
"Advances in Automotive Control", AAC10, July 11-14, 2010, Munich
(Germany).
Rizzo, G., Sorrentino, M., Arsie, I. (2010). Rule-Based Optimization of Intermittent
ICE Scheduling on a Hybrid Solar Vehicle. SAE International Journal of Engines,
Vol. 2, No. 2, pp. 521-529.
Schiesser, W. (1991). The Numerical Method of Lines: Integration of Partial
Differential Equations. Elsevier Science & Technology.
Sciarretta, A., Guzzella, L. (2007). Control of Hybrid Electric Vehicles. IEEE Control
Systems Magazine, Vol. 27, No. 2, pp. 60-70.
Smith, K. and Wang, C. (2006). Solid-state diffusion limitations on pulse operation of a
lithium-ion cell for hybrid electric vehicles. Journal of Power Sources, 161, 628-
639.
Sundström O. and Guzzella L. (2009), A Generic Dynamic Programming Matlab
Function, 18th IEEE International Conference on Control Applications, Part of
2009 IEEE Multi-conference on Systems and Control, Saint Petersburg, Russia,
July 8-10, 2009
Wang, C., Gu, W., and Liaw, B. (1998a). Micromacroscopic coupled modeling of
batteries and fuel cells. part i: Model development. J. Electrochem. Soc., 145,
3407-3417.
Wang, C., Gu, W., and Liaw, B. (1998b). Micromacroscopic coupled modeling of
batteries and fuel cells. part ii: application to ni-cd and ni-mh cells. J.
Electrochem. Soc., 145, 3418-3427.
7. NOMENCLATURE Symbol Name Unit
Road Grade Deg
e electrolyte potential V
s solid potential V
ce electrolyte concentration mol cm-3
Cr Rolling resistance coefficient
cs solid concentration mol cm-3
cse solid concentration at electrolyte
interface
mol cm-3
Cx Drag coefficient /
I battery current A
ie electrolyte current density A cm-2
is solid current density A cm-2
jLi Butler-Volmer current density A cm-3
MHSV Vehicle Mass kg
P Power kW
PS Power Split index /
SOC State of Charge /
Un anode open circuit voltage V
Up cathode open circuit voltage V
v Vehicle Speed m/s
θn normalized solid concentration at anode -
θp normalized solid concentration at
cathode
-
Pedices
B Battery
EM Electric Motor
ICE Internal Combustion Engine
IWM In-Wheel Motor
W Wheels
Acronyms
HEV Hybrid Electric Vehicle
HSV Hybrid Solar Vehicle
PV Photovoltaic
8. ACKNOWLEDGEMENTS
This research has been financed by the Italian Ministry of
University and Research, within the PRIN Projects
(http://www.dimec.unisa.it/PRIN/PRIN_2008.htm).
0.10.150.15
0.15
0.2
0.20.2
0.2
0.25
0.250.25
0.2
5
0.25
0.3
0.3
0.3
0.3
0.3
1
0.31
0.31
0.31
0.32
0.32
0.32
0.32
0.33
0.3
3
A
B
Engine efficiency map
Engine speed [rpm]
Engin
e t
orq
ue [
Nm
]
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
10
20
30
40
50
60
70
80
90
Preprints of the 18th IFAC World CongressMilano (Italy) August 28 - September 2, 2011
9720