2010, 12th International Conference on Optimization of Electrical and Electronic Equipment, OPTIM 2010
Particle Swarm Optimization for Optimal
Powertrain Component Sizing and Design of Fuel
Cell Hybrid Electric Vehicle
Omar Hegazy, Student Member, IEEE, and Joeri Van Mierlo
Department of Electrical Engineering and Energy Technology (ETEC), Vrije Universiteit Brussel
Omar.Hegazy@vub.ac.be
RP
ESR
Emax
Nscs
Nscp
Vscmax
Vscmin
SOCsc
SOCsc0
VSC-Bus
C2
Abstract -- In this paper, an optimal design to minimize the cost,
mass and volume of the fuel cell (FC) and supercapacitor (SC) in
a fuel cell hybrid electric vehicle is presented. Because of the
hybrid powertrain, component sizing significantly affects vehicle
performance, cost and fuel economy. Hence, during sizing,
various design and control constraints should also be satisfied
simultaneously.
In this research, there are two optimization techniques have
tested to achieve optimal design of the powertrain. These are
Genetic Algorithm (GA) and Particle Swarm Optimization
(PSO).
The proposed schemes have been simulated by
MATLAB/ SIMULINK. Simulation results have demonstrated
that the optimal sizing of the powertrain components has been
improved when the PSO is applied, which means highperformance operation for FCHEV.
Optimization and Control strategy
PSO
Particle swarm optimization
GA
Genetic Algorithm
PFC
Power of fuel cell
PReq
The required electric power demand
KFC
Ratio of PFC to PReq
PSC
Power of SuperCapacitor
LUT
Look-Up Table
PFC-Effmax Power of fuel cell at maximum efficiency
PFCmax
Maximum Power of fuel cell
PFCmin
Minimum Power of fuel cell
SOCmin Minimum SOC of SC
SOCmax Maximum SOC of SC
Index Terms—Fuel cell Hybrid Electric Vehicle (FCHEV),
Powertrain Modeling, Intelligent Optimization, Power
Management System
NOMENCLATURE
Fuel Cell System (FCS)
B, C
Constants to simulate the activation over
voltage in the PEMFC system
Vfc-Bus
Dc output voltage of FC system
E
Nernst instantaneous voltage
ηact
Activation over voltage
ηohmi
Ohmic over voltage
E0
Standard no load voltage
F
Faraday’s constant
IFC
FC system current
q
Amount of hydrogen flow to meet load change
Nfcs
Number of series fuel cells in stack
Nfcp
Number of parallel stacks
Rgas
Universal gas constant
Rint
FC internal resistance
T
Absolute temperature (K)
U
Utilization rate
C1
Cost per cell
I. INTRODUCTION
F
UEL CELL (FC) technologies are expected to become a
viable solution for vehicular applications because they
use alternative fuel converters and are environment friendly.
Although there are various FC technologies available for use
in vehicular systems, the proton exchange membrane FC
(PEMFC) has been found to be a prime candidate, since
PEMFC has higher power density and lower operating
temperatures when compared to the other types of FC
systems [1], [2]. A stand-alone FC system integrated into an
automotive powertrain is not always sufficient to satisfy the
load demands of a vehicle. Although FC systems exhibit
good power capability during steady-state operation, the
response of fuel cells during transient and instantaneous peak
power demands is relatively poor. Thus, the FC system can be
hybridized with an ultracapacitor (UC) bank to meet the total
power demand of a hybrid electric vehicle (HEV). In recent
req
H2
SuperCapacitor (SC)
C
Capacitance [F]
Ceq
Equivalent capacitance [F]
978-1-4244-7020-4/10/$26.00 '2010 IEEE
Parallel resistance [Ω]
Equivalent series internal resistance [Ω]
Maximum amount of energy [W.s]
Number of series capacitors
Number of parallel strings
Maximum voltage of SC
Minimum voltage of SC
State of charge of SC
Initial State of charge of SC
Dc output voltage of SC
Cost per cell
1
601
years, many research works in the power distribution strategy
of hybrid vehicles and sizing have been done. Some control
algorithms for global optimization, based on a priori
knowledge of a scheduled driving cycle, have been proposed
to achieve fairly fuel economy with minimum cost [3, 4, 5].
In [6], the optimal design and sizing of fuel cell and
supercapacitor in FCHEV were obtained by using trial and
error method. In [7], a control method was proposed for
energy control of supercapacitor/fuel cell hybrid power
source.
II. SYSTEM DESCRIPTION
The hybrid power train consists of two power sources: the
FC system (main source) and the SC bank (Energy Storage
System). These components are connected to the dc-link via
the Buck DC/DC converter (ηB=0.95) and Buck/Boost
converter (ηB/B=0.95), respectively. The desired value of the
DC-Bus voltage is chosen to be 400 V with variations of ±
10% are permissible. The power supplied by the power train
has to be obtaining from the power demand predicted by the
dynamics of the vehicle. The efficiency of each component in
the hybrid power train is taken into account. A detailed model
of the power train is built in MATLAB /SIMULINK. Figure
1 illustrates block diagrams of the hybrid power train.
In this paper, for a given driving cycle, the size and the
cost of fuel cell and supercapacitor are minimized by
identifying the best number of units of each, respectively.
Hence, a novel approach, PSO, is applied to evaluate the
optimal number of units of fuel cell and supercapacitor. By
analyzing and comparing the results, it is shown that PSO is
more efficient than GA to minimize the objective function.
(a)
(b)
Fig.1 Block Diagram of Fuel Cell/SuperCapacitor Hybrid Electric Vehicle
(a) One DC/DC Converter
(b) Two DC/DC Converters
2
602
A. Modeling of the vehicle power demand
The load force of the vehicle consists of gravitational
force, rolling resistance, aerodynamic drag force, and
acceleration force. Hereby, the load power required for
vehicle acceleration can be written as [2, 3]:
(F + F
+F
+F
) *V
g
roll
AD
acc
P
=
(1)
load
η
GB
Where:
F
g
F
F
= M . g . sin( α )
roll
AD
(2)
= M . g . f . cos( α )
r
= 0 .5 ρ
a
dV
F
= M .
acc
dt
V = ω . r
w w
.C
D
.A
F
.V
(a)
(3)
2
(4)
(5)
(6)
The total electric power required from sources can be
expressed as:
P
=
req
η
P
load
.η
.η
m
Inv
Conv
(7)
Fig.2 Vehicle speed and Total Electric Power demand
(a) NEDC Driving Cycle.
(b) FTP75 Driving Cycle.
The assumed parameters of the vehicle are given in Table I.
In this paper, the analysis of FCHEV is performed with two
standard driving cycles:
B. Dynamic Modeling of a PEMFC
1) the Federal Test Procedure (FTP75) Urban;
2) the New European Driving Cycle (NEDC)
The model of the PEMFC system predicts the output
voltage and the partial pressures of hydrogen and oxygen in
the FC stack for a certain electric current. The voltage signal
is fed to a control voltage source in the simulation
environment. The FC system consists of a FC stack with Nfcs
cells in a series and Nfcp in parallel configuration. The output
voltage of the stack can be calculated as follows [2, 8,9]:
V FC − BUS = E + η act + η ohmic
(8)
These driving cycles are represented by vehicle speeds
versus operating time. Figure 2 shows the vehicle speed and
the total electric power demand from sources. Suppose that
the efficiencies of the motor (ηm), inverter (ηInv), and DC/DC
converter (ηConv= ηB= η B/B) are 0.90, 0.94 and 0.95,
respectively.
TABLE I
ASSUMED PARAMETERS FOR THE VEHICLE [6]
M
Vehicle mass (kg)
1450
fr
Rolling Resistance Coefficient
0.013
CD
Aerodynamic Drag Coefficient (CD)
0.29
Af
Front Area (m2)
2.13
rω
Radius of the wheel (m)
0.28
ρa
Air density (kg/m3)
1.202
η act = − B ln (C . I FC
)
(9)
η ohmic = − R int I FC
(10)
The Nerst’s instantaneous voltage may be expressed as [10]

 pH 2
po 2  
RT
E = N fcs  E 0 +
log 
  (11)
2F
PH 2 O


 
The amount of hydrogen available from the hydrogen tank is
given by
q Hreq =
2
N
fcs
.N
fcp
2 FU
. I FC
(12)
The MATLAB/SIMULINK-based FC system is modeled in
this paper using the aforementioned equations. Table II shows
the specifications of PEM fuel cell system.
3
603
TABLE II
PEM FUEL CELL SYSTEM MODEL PARAMETERS [4, 6]
Activation Voltage constant (B)
0.04777(A-1)
Activation Voltage constant (C)
0.0136 [V]
Faraday’s constant (F)
96484600[C/kmol]
FC internal resistance (Rint)
0.177 (Ώ)
No load voltage (E0)
1V
Nominal voltage (V)
0.81
Nominal power per cell (w)
3.4
FC absolute temperature (T)
343 [K]
Fig.3 SuperCapacitor equivalent circuit [2]
Utilization factor (U)
0.85
Universal gas constant (R)
TABLE III
SUPERCAPACITOR SPECIFICATIONS [6, 8]
8314.47 [J/ kmol K]
Weight (M1) (g)
16.28
Capacitance (F)
2500
Volume (V1) (L)
0.0142
Internal Resistance (Rs)
65mΏ
Cost (C1) ($)
The parallel Resistance
(for Leakage Current) (Rp)
1.23
C. Modeling of a Supercapacitor
The natural structure of SC is appropriate to meet the
transient and instantaneous peak power demands. The
simulated super-capacitor is a Maxwell PC2500 whose
characteristics are reported in Table III [6]. The reason for
considering a supercapacitor in the vehicle setup is its high
specific power rate and its ability to accept a full recharge in a
very short time, which leads to an improvement in the vehicle
efficiency and energy economy. Figure 3 illustrates a simple
electrical equivalent circuit of a supercapacitor unit [2-3]. The
output voltage of the supercapacitor can be expressed as
follows:
Vsc _ cell = icell Rs +ν c
νc = −
1
C
i c = i cell
SOCsc
∫
= (
ν
c
R
p
V
V cup ( t = 0 ) = (
cell
C
Rated current (A)
625
Cost (C2) ($)
Initial State Of Charge (SOCSC0)
725
0.6
20
80%
III. OPTIMIZATION PROBLEM FORMULATION
This section describes the formulation of optimization
problem and their constraints.
A. The Objective Function
(14)
) 2 * 100
The first goal of optimization problem is to minimize the
cost of the fuel cell (FC) and supercapacitor (SC) in the fuel
cell hybrid vehicle. It is assumed that, the cost of the fuel cell
and supercapacitor is a function of the number of units of
each, respectively [6]. The layout of the fuel-cell stack and
that of the supercapacitor bank are shown in Fig. 4(a) and (b),
respectively. As shown in Fig.4, fuel-cell and supercapacitor
units are connected in series to form branches. The objective
function chosen for the study, F(x), is given as follows [6]:
(16)
_ max
SOCsc 0
)V max
100
2.5
Volume (V2) (L)
(15)
ν
Max_ Cell Voltage [Vmaxcell](V)
Weight (M2) (g)
(13)
ic (t ) dt + V cup ( t = 0 )
+
1kΏ -3kΏ
cell
(17)
The MATLAB/SIMULINK-based SC is modeled using
the aforementioned equations.
F ( x ) = C 1 . Nfcs . Nfcp + C 2 . Nscs . Nscp
4
604
(18)
P FC min ≤ Pfc ( t ) ≤ P FC max
(21)
4. Constraints of State Of Charge
The level of SOCmin and SOCmax are chosen to 25% and 90%,
respectively.
SOC min ≤ SOCsc ( t ) ≤ SOC max
(22)
IV. INTELLIGENT OPTIMIZATION [IO]
A. Genetic Algorithm (GA)
(a)
(b)
Fig.4. (a) Layout of the FC; (b) Layout of the SC
Genetic algorithms (GA) are stochastic global search
techniques, which mimic the process of natural biological
evaluation (Survival of fitness). They have been shown to be
an effective strategy to solve complex engineering
optimization problems characterized by non-linear,
multimodal, non-convex objective functions. The structure of
a GA is composed by an iterative procedure through the
following five main steps [10, 11]:
1. Creating an initial population P0,
2. Evaluation of the performance of each individual Pi of the
population, by means of a fitness function,
3. Selection of individuals and reproduction of a new
population,
4. Application of genetic operators: crossover and mutation,
5. Iteration of steps 2–4 until a termination criterion is
fulfilled
B. Constraints
1. Constraints of Nfcs and Nscs
It is considered that the desired value of the DC-link
voltage (VSC-Bus, and VFC-Bus) is chosen to be 270 V with
variations of ± 10% are permissible. These constraints are
presented in Table IV.
2. Constraints of Nscp
The supercapacitor is supposed to cover the power
fluctuation above the average power. The magnitude of
energy above Pav is calculated by:
t2
E = ∫ ( Pinst − Pav ) dt
t1
(19)
The GA search was performed in MATLAB environment.
To apply GA to the optimization of FCHEV, a fitness
function is required in order to evaluate the status of each
solution. This function can be formulated as follows:
Hence, the size of supercapacitor is calculated according to
the maximum value of the energy is found among various
intervals (t1, t2). Therefore, the equivalent of capacitance of
the SC is written as follows:
Ceq =
C * Nscp
2 . E max
≥
Nscs
(Vsc max 2 − Vsc min 2 )
Minimize F(x) (Nscp, Nfcp)
(20)
B. Particle Swarm Optimization [PSO]
Particle Swarm Optimization (PSO) is an evolutionary
computation technique (a search method based on a nature
system). PSO is a population based stochastic optimization
technique developed by Kennedy and Eberhart. PSO method
is a member of the wide category of Swarm Intelligence
methods (SI). It can be used to solve a wide range of
optimization problems. Most of the problems that can be
solved using Genetic Algorithms could be solved by PSO.
For example, neural network training and nonlinear
optimization problems with continuous variables can be
easily achieved by PSO. It can be easily expanded to treat
problems with discrete variables [12]. PSO shares many
similarities with evolutionary computation techniques such as
Genetic Algorithms (GA). The system is initialized with a
population of random solutions and searches for optima by
3. Constraints of power and Acceleration
The initial-acceleration performance for the vehicle is
defined as accelerating the vehicle from standstill to 60 mi/h
in 10 s. The level of PFCmin and PFCmax are chosen to 1kW and
50 kW, respectively. This range is satisfied to power demand
during acceleration and gradeability at maximum speed. The
power balance of the system is shown in (19).
TABLE IV
CONSTRANITS OF Nfcs & Nscs
Reference
DC-Link Voltage
Variation [V]
Nmin
Nmax = Nselected
FC
243 < Vdc < 297
243
297
SC
243 < Vdc < 297
97
119
5
605
updating generations. However, unlike GA, PSO has no
evolution operators such as crossover and mutation [13].
PSO can be represented by the concept of velocity and
position. The Velocity of each agent can be modified by the
following equations: (23 & 25):
v
k +1
k
X2
Agent
X3
k
= w v i + c 1 r1 * ( pbest 1 − s i ) +
(23)
k
X1
c 2 r2 * ( gbest − s i )
Where:
νk
ν i k+1
Xn
: Current velocity of agent i at iteration.
: Modified velocity of agent i
r1 , r2 : random number distributed [0,1],
Ski
: current position of agent i.
pbest
: p best of agent
gbest
: g best of the group.
ω
: weight function for velocity of agent i,
Fig.6. Searching concept with agents in a solution space by
PSO
In this research, PSO is applied to evaluate the optimal
number of units of each source that minimize the cost of the
fuel cell (FC) and supercapacitor (SC). In addition, PSO is
applied to determine the best degree of hybridization between
sources to minimize the energy consumption in (24). The
problems can be formulated as follows:
c1, c2 : positive constants; [c1+ c2< 4].
The following weighting function is usually utilized in (23).
ω = ω max −
ω max − ω min
iter max
* iter
(24)
Minimize F(x) (Nscp, Nfcp)
Where:
ωmax : Initial weight,
ϖ min : Final weight,
V. CONTROL STRATEGY BASED ON
EFFICIENCY MAP
itermax : Maximum iteration number,
iter : Current iteration number.
Using the above equation, a certain velocity can be
calculated that gradually gets close to (pbests) and (gbest).
The current position (searching point in the solution space)
can be modified by the following equation:
ski+1
This control strategy is applied to improve the hydrogen
consumption. A simulation is performed for each driving
cycle in such a way that the FCS works alternately in two
operating points, namely “On” and “Off”, according to the
actual SOSsc (k): (i) when SOSsc (k) < SOSsc0, the FCS is
operated at its point of maximum efficiency (the “On” point)
and, (ii) when SOSsc (k) > SOSsc0, the FCS is turned off (the
“Off” point). Figure 7 illustrates the efficiency map of FC.
Figure 8 shows a scheme with the FC operation to perform
the analysis previously described.
= ski + vki+1
(25)
Figure 4 shows the concept of modifying the searching
point by PSO. Figure 6 shows the searching concept with
agents in the solution space. Each agent changes its current
position using the integration of vector vk+1as shown in fig. 5.
Y
Sk+1
VK+1
Vgbest
VK
SK
VPbest
X
Fig.7 The efficiency map of Fuel Cell
Fig.5. Concept of modification of a searching point by PSO
6
606
TABLE V I
GA ALGORITHM PARAMETERS
Parameters
Value
Population size
40
Number of Generations
200
Crossover Probability
0.85
Mutation Probability
0.1
Figure 9 provides an example of the optimization
algorithm output. PSO is applied to minimize the total cost of
Fuel cell and supercapacitor during the FTP75 driving cycle.
Figure 10 illustrates the comparison between design methods.
Fig. 8 Scheme of Control Strategy Based on Efficiency Map
VI. SIMULATION STUDY
To verify that the optimal design based on intelligent
optimization of the FCHEV can provide the required vehicle
performance and the power of the powertrain corresponding
to a standard driving cycles such as FTP75 and NEDC are
simulated and presented. Simulation results are obtained
using MATLAB/SIMULINK and SimPowerSystems by
implementing the detailed mathematical and electrical models
of the system described earlier in section II.
In this section, there are three methods have been
designed to achieve the optimal sizing.
These are
conventional method, trial and error, as was mentioned in [6],
GA, and PSO. In addition, to minimize the fuel consumption
of the FCHEV, the control strategy based on max-efficiency
map described earlier in section V. The parameters used of
PSO are shown in Table V. The parameters used of GA are
shown in Table VI.
Fig.9 Best value of total cost for FTP75
TABLE V
PSO ALGORITHM PARAMETERS
Parameters
Population size
Max. iter
c1
c2
Max. weight
Min. weight
r1
r2
Lbnd [ Nscp Nfcp]
Upbnd [ Nscp Nfcp]
Lbnd [Kfc]
Upbnd [kfc]
Value
20
100
0.5
0.5
1.2
0.1
[ 0,1]
[ 0,1]
[1 2]
[10 60]
0
1
(a)
(b)
7
607
Fig.12 Power of fuel cell during the FTP75 driving cycle
(c)
Fig.13 DC-Bus voltage variation during the FTP75
In Fig.14, it is shown the comparative of the hydrogen
consumption between the control strategy and pure fuel cell
during the FTP75 and NEDC driving cycles. The results
show the control strategy based on efficiency map achieving
hydrogen improvement up to 9.22% during the NEDC
driving cycle and 13.29% during the FTP75 with respect to
the pure fuel.
(d)
Fig.10 Results of optimal design for FCHEV
(a) Optimal numbers of cells of FC and SC
(b) Driving cycles Comparison based optimal total cost
(c) Driving cycles Comparison based optimal total mass
(d) Driving cycles Comparison based optimal total volume
The power of the fuel cell and the supercapacitor during
the FTP75 driving cycle are shown in Fig.11 and Fig.12.
Figure 13 demonstrates the DC-Bus voltage variation during
the FTP75 driving cycle.
Fig. 14 Comparative of between the hydrogen consumption
between Pure FC and control strategy based on efficiency
map
Fig.11 Power of fuel cell during the FTP75 driving cycle
8
608
VII.CONCLUSION
This paper deals with the applicability of the intelligent
optimization to optimize both the vehicle design in order to
minimize the total cost, volume and the mass of the fuel cell
and supercapacitor components, and to minimize the fuel
consumption of fuel cell during different driving cycles based
on control strategy. As is clear from results, it is possible to
significantly improve the hydrogen consumption in FCHV
compared with the pure FC case without SC: 9.22% on
NEDC and 13.29% on FTP75. In addition, the reduction of
total cost of the fuel cell and supercapacitor components is
around 13.40% on NEDC and 12.21% on FTP75.
By analyzing and comparing the results, it is shown that
PSO is more efficient than GA to achieve the optimal
performance for FCHEV.
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