Cheng Hui 2007

Particle Swarm Optimization for energy
management fuzzy controller design in
dual-source electric vehicle
Zhang Chenghui1, Shi Qingsheng1, Cui Naxin1, Li Wuhua2
1.School of Control Science and Engineering, Shandong University, China
Email: [email protected]
2. College of Electrical Engineering, Zhejiang University, China
Email: [email protected]
Abstract-How to distribute the power between battery bank
and supercapacitor modules to obtain good performance is a vital
problem in dual-source electric vehicles. Traditional fuzzy
controller design for energy management relies too much on the
expert experience, and is easy to get the sub-optimal performance.
In order to overcome this drawback, Particle Swarm
Optimization (PSO) is introduced for energy management fuzzy
controller design in dual-source propelled electric vehicles. In the
paper, based on the systemic analysis of the power in energy
storage system (ESS), the drag power the vehicle encounters and
the constraints the ESS should obey, the mathematic model of
energy management problem is established. Then, different
operation modes of dual-source ESS are presented and so is the
design of conventional fuzzy controller. Followingly, we show how
to use PSO method to better the fuzzy control. Finally, compared
to the traditional fuzzy control strategy, we carry on some
simulations in ADVISOR software. The results show the validity
of the proposed strategy.

I. INTRODUCTION
The increasing concerns on energy conservation and
environmental protection throughout the world result in the
revival of the electric vehicles (EVs) [1]. EVs have a number of
advantages including low exhaust emissions, low operation
noise and reasonably good energy efficiency. However, limited
life cycle of the battery and limited range of the vehicle after
each battery charge become the major obstacles for the
commercialization of EVs. The supercapacitor is an
electrochemical device that can supply a large burst of power,
but cannot store much energy [2]. By connecting the two
energy sources together in parallel configuration, the benefits
of both can be achieved as a complete energy source. A novel
electric vehicle using the dual-sources is proposed recently [3].
And the power distribution between the dual-sources becomes
a tough and promising issue.
Much research work has been done in recent years to design
proper control strategy for dual-source energy management. In
[4], a dynamic variable K is defined as the power taken from
the battery and the power taken from the supercapacitor is the
difference when K is subtracted from the vehicle’s power

1-4244-0655-2/07/$20.00©2007 IEEE

request. Also a lookup method is used to determine the
different K value at different supercapacitor State-of-Charge
(SOC). The strategy is smart and easy to implement, but the set
of K value is not flexible. In [5], a fuzzy control strategy is
proposed for energy management in multi-source electric
vehicle. The required power, NiMH SOC and super-capacitor
SOC are taken as inputs and the power distribution factor as
outputs. This strategy obtains better vehicle performance than
the lookup method or logic-threshold control method, but the
set of fuzzy rules and memberships are mainly dependent on
the expert experience, and is easy to get the local optimum
performance. In this paper, PSO is adopted to optimize the
fuzzy rules and membership in the fuzzy energy management
controller. PSO is a population-based algorithm [6]. It can
search automatically the optimal solutions in the vector space.
So, it is to improve the design of the fuzzy controller.
The rest of this paper is organized as follows: The
mathematic model of dual-source energy management is set in
section II. The operation modes of energy storage system are
analyzed in section III. In section IV, the design of energy
management fuzzy controller based PSO is given. The
simulation results are presented in Section V. Finally,
concluding remarks are given in Section VI.
II. DUAL–SOURCE ELECTRIC VEHICLE POWERTRAIN
The configuration of the dual-source electric vehicle
powertrain with the battery and supercapacitor as the
energy-storage device is shown in Fig.1. The powertrain
consists of battery module, supercapacitor bank, a dc/dc
converter, an inverter, an ac motor, and a transmission. The
battery module stack is paralleled with the supercapacitor bank
to make the dc link. The dc/dc converter regulates the dc-link
voltage. The inverter converts the regulated dc voltage to an ac
voltage to drive the ac motor. The transmission is a gearbox
that multiplies the motor torque via gear reduction.
In the dual-source EV powertrain, when the vehicle demands
high power, the battery and supercapacitor provide

1405

storage system should be analyzed.

Figure 1.Configuration of the dual-source EV powertrain

power to the shaft of the vehicle through the DC/DC converter,
the inverter, ac motor, and the transmission. In this case, one
can have:
K ( Pbat  Psc ) K1 Pc K 2 Pi K 3 Pm K 4 Pt Pv
(1)
where, Pbat, Psc, Pc, Pi, Pm, Pt and Pv are the power of the battery
module, power of the supercapacitor bank, power of the
DC/DC converter, power of the inverter, power of the ac motor,
power of the transmission and the vehicle power demand,
respectively. And K , K1 , K 2 , K 3 , K 4 are the efficiency from
energy storage system, converter, ac motor, transmission to
wheels, respectively.
On the other hand, when the vehicle demands low power, if
the SOC of the supercapacitor is higher than the lower safe set
point, the supercapacitor alone provides power to the shaft of
the vehicle through the DC/DC converter, the inverter, ac
motor, and the transmission and charges the supercapacitor
directly; otherwise, the battery modules alone provide the
power to drive the vehicle.
When the vehicle brakes, the ac motor converts the kinetic
energy of the vehicle into electricity and charges the battery
and supercapacitor through the inverter and the DC/DC
converter using the generated electricity.
III. THE MATHEMATIC MODEL OF DUAL-SOURCE ENERGY
MANAGEMENT IN ELECTRIC VEHICLE
According to the analysis in section II, we can see that the
goal of energy management is to attain the minimized energy
consumption under the requirement of the vehicle performance
through the proper assignment of the power of the battery and
supercapacitor.
Here, energy consumption rate is used as the performance
index to evaluate the economy of electric vehicle, which
denotes that the energy vehicle consumed in one hundred
kilometers cycle. It is usually obtained by the following
equation:

1.1 u 10 7 E
(2)
L
where, L is the drive distance in km, E is the consumed energy
during the drive cycle in J, and can be got by power integral in
time domain, 1.1u10-7 is the conversion factor.
In order to establish the mathematic model of dual-source
energy management, the power and constraints in energy

A. Different power in dual-source electric vehicles
As it is said in section II, during the run, energy storage
system (ESS) outputs energy to the electric motor through
power bus, and the motor passes energy to drive wheels to
overcome the road load, denoting as F1. According to the
theory of vehicle dynamics [7], this road load F1 consists of
three main componentsaerodynamic drag force Fd, rolling
resistance force Fr and climbing force Fc as given by:
F1 Fd  Fr  Fc
(3)
The aerodynamic drag force is due to the drag upon the
vehicle body when moving through air. Its composition is due
to three aerodynamic effectsthe skin friction drag due to the
air flow in the boundary layer, the induced drag due to the
downwash of the trailing vortices behind the vehicle, and the
normal pressure drag(proportional to the vehicle frontal area
and speed) around the vehicle. The skin friction drag and the
induced drag are usually small compared to the normal
pressure drag, and are generally neglected. Thus, the
aerodynamic force can be expressed as:

Fd 0.5UC d Av 2
(4)
where, Cd is the aerodynamic drag coefficient, U is the air
density in kg/m3, A is the frontal area in m2, v is the vehicle
velocity in km/h.
The rolling resistance force is due to the work of
deformation on the wheel and road surface. The deformation
on the wheel heavily dominates the rolling resistance while the
deformation on the road surface is generally insignificant. This
rolling resistance force is normally expressed as:
Fr MgC r
(5)
where M is the vehicle mass in kg, g is the gravitational
acceleration, Cr is the rolling resistance coefficient.
The climbing force is simply the climbing resistance or
downward force for a vehicle to climb up an incline. This force
is given by:
(6)
Fr Mg sin D
where, D is the angle of incline in radian or degree.
So, the road load power Pload can be computed by
multiplying (2) by the vehicle velocity. In that case:

Pload (0.5UC d Av 2  MgC r  Mg sin D )v / 3600
Then PESS can be calculated as following:
1
PESS
Pload

K

ECR

1

K

(7)

(8)

(0.5UC d Av 2  MgC r  Mg sin D )v / 3600

B. Constraints in ESS
On one hand, to ensure that the vehicle can effectively run,
ESS should provide enough energy for meeting the required
vehicle power Preq at any time, as shown in (8). Suppose the

1406

Psc (t ) K sc (t ) PESS (t )
(10)
where, the sum of Kbat(t) and Ksc(t) is 1. So, adjusting the Kbat(t)
and Ksc(t) consequently results in the change of Pbat and Psc.
On the other hand, as the battery and supercapacitor are
concerned, if their SOC is too high, the ability to recuperate
braking energy would decrease, and result in the desert of the
surplus energy. Conversely, if the SOC is too low, ESS may not
supply enough power to meet the vehicle requirement when
accelerating. In order to extend lifecycle of battery and
supercapacitor, their SOC should operate in proper range as
much as possible, that is,
(11)
SOC bat min d SOC bat (t ) d SOC bat max

technique inspired by social behavior of a flock of birds and
insect swarms [9][10]. In the PSO algorithm, each particle of
the swarm flies in an n-dimension space, and the position at a
certain instant is identified by the vector of the coordinates X
X(i)=(X1(i), X2(i), Ž, Xn(i))
(13)
Each component Xn(i) represents a parameter of the problem
that has to be optimized. At the beginning of the process, each
particle is randomly located at a position, and moves with a
random velocity, both in direction and magnitude. The particle
is free to fly inside the n-dimensional space defined by the user,
within the constraints of the n boundary conditions, which limit
the extent of the search space and, hence, the values of the
parameters during the optimization process.
At the generic time step i+1, the velocity is expressed by
Vl (i  1) wVl (i)  C1 ˜ rand () ˜ ( p best,l (i)  X l (i)) 
(14)
C 2 ˜ rand () ˜ ( g best ,l (i)  X l (i))

(12)
SOC sc min d SOC sc (t ) d SOC sc max
In this paper, the battery SOC is set to vary in [0.5, 0.8], and
supercapacitor SOC in [0.3, 0.8].

where Vl (i ) is the velocity along the direction l at time step i; w
is the inertial weight; C1 and C2 are the cognitive and the social
rate, respectively; p best ,l (i ) is the best position along the

C. Mathematic model of dual-source energy management
According to the above discussion, mathematic model of
dual-source energy management can be formulated as:
min ECR K bat (t ), K sc (t )

l-direction found by the agent during its own wandering up to
i-th; g best ,l (i ) is the best position along the direction

1

Pload (t ) , t  [0, T ]

K
K bat (t )  K sc (t ) 1

SOCbatmin d SOCbat (t ) d SOCbatmax
SOC sc min d SOC sc (t ) d SOC sc max
IV. FUZZY CONTROLLER DESIGN BASED PSO FOR ENERGY
MANAGEMENT

According to the analysis in section III, we can see that the
vital of energy management is to decide proper value for power
split factor Kbat(t) and Ksc(t). Considering that dual-source
energy management problem is virtually a nonlinear
optimization problem, the traditional optimization method is
unfit here. Fuzzy control is a practical alternative for a variety
of challenging control applications since it provides a
convenient method for constructing nonlinear controllers via
the use of heuristic information [8]. However, as pointed out in
section I, Fuzzy control has some inherent drawbacks, which
need to be improved. So, Particle Swarm Optimization
algorithm is introduced to optimize the fuzzy controller in this
paper. Before we start to design the energy management fuzzy
controller based PSO, the principle of PSO algorithm is
presented first.

how much the agent is influenced by the memory of its own
best (referred as the “cognitive rate”) and the value of C1
encourages the independent search for the best, regardless of
the experience of the swarm. On the other hand, the latter term
is related to the influence the swarm has on the particle (called
the “social rate”) and C2 controls the exploitation of the actual
best. The random generator introduces the proper chaotic
component of a real swarm. The position of each particle is
then simply updated according to
(15)
X l (i  1) X l (i )  Vl (i ) ˜ 't
where, X l (i ) is the current position of the agent along the
direction at the iteration i-th , and 't is the time step. The
boundary conditions implemented are those for reflecting walls,
which change the sign of the velocity of the particle whenever
it hits the designated border.

A. Principle of Particle Swarm Optimization Algorithm
Particle Swarm Optimization algorithm, originally proposed
by Kennedy and Eberhart, is an evolutionary computation

1407

Preq
SOCbat
SOCsc

Inference
mechanism
Rule-base

Defuzzification

s.t. PESS (t )

Fuzzification

t[ 0,T ]

discovered by the entire swarm; and rand() is a generator of
random numbers uniformly distributed between 0 and 1.
At each iteration step, the new velocity is the sum of the
actual velocity, scaled by the factor w which represents the
weight of the particle, and two terms that express the attraction
due to p best ,l (i ) and g best ,l (i ) . The former term determines

Inputs scaling

power assignment factor of battery and supercapacitor are
Kbat(t) and Ksc(t) respectively at time t, the power assignment of
the two can be expressed in the following form:
Pbat (t ) K bat (t ) PESS (t )
(9)

Figure 2. Simplified block diagram of energy
management fuzzy controller

Kbat

B. Energy management Fuzzy Controller Design based PSO
algorithm
Fig.2 presents a simplified block diagram of fuzzy controller
for energy management. The inputs of controller are Preq,
SOCbat and SOCsc. And the output is the power split factor of
battery Kbat. Once Kbat is given at time step t, the split power Pbat
and Psc can be easily determined.
The membership functions on the universes of discourses
and linguistic values for three inputs and single output are
shown in Fig.3.
The linguistic values “NB, NM, NS, ZE, PS, PM, PB, LE,
ML, ME, MB, GE” represent “negative big,” “negative
medium,” “negative small,” “zero,” “positive small,” “positive
medium,” “positive big,” “little,” “medium little,” “medium,”
“medium big,” “great”, respectively.
The rule-base can be treated as a queue of fuzzy sets of input
and output variables. A typical rule will take on the form:
“If Preq is NB, SOCbat is LE, and SOCsc is LE, Then Kbat is
ME.”
Because the number of inputs is more than two, it is hard to
list the rules in one table, so Table I, II and III work together to
show the premises and consequents of all the initial rules.
As far as the MF of Preq is concerned, it is symmetrical about
the center of the universe. The peak value has depicted in Fig.4.
From the diagram, we can see that, z1, z2, z3 are the parameters
that need to be optimized in MF of Preq. The set of optimized
parameters in MFs of SOCbat, SOCsc, Kbat is also similar to that
in Preq. Thus, the number of optimized parameters is 7.

µ(Preq)

1

NB

NM

NS

ZE

PM

PS

TABLE I
INITIAL RULES WHEN SOCSC=LE
Kbat
NB
NM
NS
ZE
PS
PM
PB

Preq

NB
NM
NS
ZE
PS
PM
PB

Preq

µ(SOCbat)
µ(SOCsc)

3
h104
GE

0

0.2

0.9

0.6
SOCbat

GE

ME

LE

0.5
0
0.2

1

LE

0.9

0.6
SOCsc
ML

ME

MB

GE

ME

ML

LE

MB

ML

MB
LE
ML
LE
ML

LE
LE
ME
ME
MB

Kbat

PB

0.6

1

µ(Kbat)

2

1

ME

LE

1

0
Preq

SOCbat
ME

LE
LE
LE
MB
GE
GE

TABLE III
INITIAL RULES WHEN SOCSC=GE

0
-1

LE
LE
LE
GE
GE
GE

LE

Kbat

Preq
-2

GE
LE

TABLE II
INITIAL RULES WHEN SOCSC=ME

0.5
-3

SOCbat
ME
ML
ML
LE
LE
GE
GE
GE

LE
ME
ME
ML
LE
MB
MB
MB

NB
NM
NS
ZE
PS
PM
PB

LE

SOCbat
ME

GE

GE

MB

ME

GE

ML

GE
LE
LE
LE
LE

LE
LE
LE
ML
ME

LE
LE
LE
LE
ME
MB

In the case that the queue of premises of rules is given, we
just need to optimize the corresponding consequents. From
Table I, II and III, we can see that the number of energy
management fuzzy rules is 63, which are described by 63
integers in [1, 5]. 1 to 5 denotes the five fuzzy sets of Kbat.
Position encoding of each particle is depicted in Fig.5. The
front 7 dimensions is the MF parameters to be optimized,
encoding in real number; and the rear 63 dimensions are the
consequents of rules, encoding in integers. The velocity of
particle has the same dimensions as the position, but it encodes
in real.
NB

GE

NM

NS

ZE

PS

-z1-z2

-z1

0

z1

PM

PB

1
0.5

0.5
0

0
0.2

0.4

0.6
Kbat

0.8

1

-z1-z2-z3

z1+z2 z1+z2+z3

Figure 4. Parameters to be optimized in MF

Figure 3. Membership functions

1408

1
z1

2
z2

…
…

7
z7

8
3

9
3

10
2

…
…

68
1

69
3

supercapacitor using different methods during the specific
cycle. From the Fig.6, we can see that, because the regenerative
energy is small, it is charged only to the supercapacitor. So, as
the main source, battery’s SOC decreases along with time. The
SOC trend using PSO-fuzzy method decreases slower than that
of conventional fuzzy method. It is shown in Fig.7 that,
supercapacitor discharges or charges frequently during the run,
and the SOC trend of supercapacitor using PSO-fuzzy method
varies more frequently than that of conventional fuzzy method.
To evaluate the validity of the proposed strategy more clearly,
the fuel economy in terms of ECR for the two strategies is
compared. From Table V, we can see that the vehicle adopting
conventional fuzzy controller has an ECR value of 13. 6kWh,
while the one using the PSO-fuzzy controller is 12.3 kWh, that
is, adopting the latter controller, the ECR value is improved by
9.8 percent.

70
4

Figure 5. Position encoding of each particle

Besides defining the position and velocity of particles, the
evaluate index, which is called fitness here, should also be
defined. As it is mentioned above, the goal of energy
management is minimizing the ECR with a satisfactory
performance. So, ECR is adopted as the fitness function during
the optimal process.
Due to the existence of w, C1 and C2, although encoding of
position or velocity in current iteration are integers, the next
position or velocity may be real number. Therefore, the new
real number position should take integer operation to avoid the
infeasible solutions. Round operator is used to implement the
operation. It is defined as follows:
x  floor ( x)  0.5
­ floor ( x)
Round ( x) ®
¯ floor ( x)  1 x  floor ( x) t 0.5
where, floor(x) denotes integer operation.
In summary, the process for fuzzy controller design based
PSO algorithm is as follows:
Step 1: Encode the MF parameters of inputs and outputs and
consequents of rules as Fig.5 presents.
Step 2: Initialize positions vector X and associated velocity V
of all particles in the population. The MFs and rules we set in
Table I, II and III are added to the population as experienced
particles. Others are produced randomly.
Step 3: Update the velocity of particles using (14), and the
position using (15). After update, take integer operation for
particles’ rule position using Round operator.
Step 4: Decode each particle, and output the results to the
controller. Based on dual-source electric vehicle, ECR in a
specified cycle is taken as fitness to update pbest and gbest.
Step 5: Repeat Step 3 and Step 4 until a stop criterion is
satisfied or a predefined number of iterations are completed.

TABLE V
ECR COMPARISION USING TWO CONTROLLERS
Controller type

ECR (kWh)

Conventional fuzzy controller

13.6

PSO-fuzzy controller

12.3

VI. CONCLUSION
In this paper, dual-source energy management modeling
and optimal control are discussed in detail. After the systematic
analysis of objective function and constraints in ESS, the
energy management model is established. From the model, we
get that how to distribute the power between battery bank and
supercapacitor modules to obtain good performance is the vital
to implement optimal control of energy management. Fuzzy
controller is the conventional method to handle this problem,
but it is easy to trap into sub-optimal performance. Thereby, the
swarm based method -Particle Swarm Optimization is used to
optimize the rules and memberships of the conventional fuzzy
controller. The simulation results show that the vehicle using
PSO-fuzzy controller have a better fuel economy performance
than that of conventional fuzzy controller.

V. SIMULATION RESULTS
To validate the performance of the energy management
fuzzy controller based on PSO, compared to conventional
fuzzy controller, simulations are taken on the typical drive
cycle JA1015 using ADVISOR software [9]. The hypothetical
small car is roughly based on a 1994 Saturn SL1 vehicle with
the main data listed in Table IV.
Fig.6 and Fig.7 show the SOC trends of battery and

ACKNOWLEDGMENT
This work was supported and funded by the National Natural
Science Foundation of China under Grant (50477042) and
Nature Science Foundation of Shandong Province (Z2004G04).

TABLE IV
MAIN PARAMETERS OF DUAL-SOURCE ELECTRIC VEHICLE
Vehicle parameter
Motor parameter

Glider mass (kg)

592

Rolling resistance Coefficient

0.012

Frontal area(m2)

2.03

Aerodynamic drag coefficient

0.19

Type

IM

Peak power (kW)

60

Rated power(kW)

20

Rated speed (rpm)

3600

Type

Saft Li-ion

Module number

30

Rated capacity of Single cell (Ah)

6

Gravity of single cell (kg)

0.7

Supercapacitor

Type

MaxwellPC2500

Number of cells

120

parameter

Rated output voltage (V)

2.5

Current range (A)

(-225, 225)

Battery parameter

1409

0.805
PSO-fuzzy
fuzzy

0.8
Battery SOC

0.795
0.79
0.785
0.78
0.775
0.77

0

300
400
500
600
time (s)
Figure 6. Diagram of battery SOC trend
100

200

supercapacitor SOC

0.8
0.75

700

PSO-fuzzy
fuzzy

0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35

0

100

200

300
400
500
600 700
time (s)
Figure 7. Diagram of supercapacitor SOC trend

The authors would like to thank the comments of the
anonymous reviewers that helped clarify the presentation.
REFERENCES
[1]

C. C. Chan, “The state of the art of electric and hybrid vehicles,”
Proc.IEEE, vol. 90, pp. 247–275, Feb. 2002.
[2] A. Burke, “Ultracapacitors: why, how, and where is the technology”,
Journal of Power Sources, 2000, pp. 37-50.
[3] J. X. Yan and D. Patterson, "Improvement of drive range, acceleration
and deceleration performances in an electric vehicle propulsion system",
in Proc. Power Electronics Specialists Conf, Madison, WI, 1999, pp.
638-643.
[4] A. C. Baisden and A. Emadi, “ADVISOR-Based Model of a Battery and
an Ultracapacitor Energy Source for Hybrid Electric Vehicles, ” IEEE
Transactions on vehicular technology, vol. 53, 2004, pp. 199-205.
[5] Q. M. Yu, Y. N. Wang and Y. Zhong, "Fuzzy Control Strategy and
Simulation of EV with Energy Hybridization", Chinese Journal of
Computer Simulation, vol. 21, issue. 9, 2004, pp. 144-147.
[6] J. Kennedy and R. Eberhart, "Particle Swarm Optimization", Proc. of
IEEE international Conference on Neural Networks, Perth, Australia,
1995, pp. A1942-1948.
[7] T. D. Chan and K. T. Chau, Modern Electric Vehicle Technology, Oxford
University Press, SBN 019-850416-0, 2001.
[8] M. P. Kevin and Y. Stephen, Fuzzy control, Addison Wesley Longman,
Menlo Park, CA, 1998.
[9] Y. H. Shi and R. C. Eberhart, "Parameter Selection in Particle Swarm
Optimization", The 7th Annual Conference on Evolutionary
Programming, San Diego, USA, 1998.
[10] R. C. Eberhart and Y. Shi, "Comparing Inertia Weights and Constriction
Factors in Particle Swarm Optimization", 2000 Congress on Evolutionary
Computing, 2000, vol. 1, pp. 84-88.
[11] National Renewable Energy Laboratory, "ADVISOR Documentation",
Golden, CO. http://www.ctts.nrel.gov/analysis.

1410