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. INTRODUCTIONThe 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 vehicles power

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 asoutputs. 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. DUALSOURCE ELECTRIC VEHICLE POWERTRAINThe 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

Particle Swarm Optimization for energy management fuzzy controller design in

dual-source electric vehicleZhang Chenghui1, Shi Qingsheng1, Cui Naxin1, Li Wuhua2

1.School of Control Science and Engineering, Shandong University, China Email: zchui@sdu.edu.cn

2. College of Electrical Engineering, Zhejiang University, China Email: woohualee@yahoo.com.cn

14051-4244-0655-2/07/$20.002007 IEEE

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:

vPPPPPPP t4m3i2c1scbat )( KKKKK (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 , 1K , 2K , 3K , 4K 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 ENERGYMANAGEMENT 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 performancethrough 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:

LEECR

7101.1 u (2)

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

storage system should be analyzed.

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:

crd1 FFFF (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:

2dd 5.0 AvCF U (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:

rr MgCF (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:

Dsinr MgF (6) 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:

3600/)sin5.0( r2

dload vMgMgCAvCP DU (7) Then PESS can be calculated as following:

3600/)sin5.0(1

1

r2

d

loadESS

vMgMgCAvC

PP

DUK

K

(8)

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

Figure 1.Configuration of the dual-source EV powertrain

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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: )()()( ESSbatbat tPtKtP (9)

)()()( ESSscsc tPtKtP (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,

maxbatbatminbat )( SOCtSOCSOC dd (11)

maxscscminsc )( SOCtSOCSOC dd (12) In this paper, the battery SOC is set to vary in [0.5, 0.8], and

supercapacitor SOC in [0.3, 0.8].

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 scbat],0[

tKtKECRTt

s.t. )(1)( loadESS tPtP K , ],0[ Tt

1)()( scbat tKtK

batmin bat batmax( )SOC SOC t SOCd d

maxscscminsc )( SOCtSOCSOC dd

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.

A. Principle of Particle Swarm Optimization Algorithm Particle Swarm Optimization algorithm, originally proposed

by Kennedy and Eberhart, is an evolutionary computation

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),, 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

))()((()))()((())()1(

,best2

,best1

iXigrandCiXiprandCiwViV

ll

llll

(14)

where )(iVl is the velocity along the direction l at time step i; wis the inertial weight; C1 and C2 are the cognitive and the social rate, respectively; )(,best ip l is the best position along the l-direction found by the agent during its own wandering up to i-th; )(,best ig l is the best position along the direction 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 )(,best ip l and )(,best ig l . The former term determines how much the agent is influenced by the memory of its own best (referred as the cognitive rate) and the value of C1encourages 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

tiViXiX lll ' )()()1( (15) where, )(iX l 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.

SOCbat

SOCsc Rule-base

Preq

Figure 2. Simplified block diagram of energy management fuzzy controller

Kbat

Def

uzzi

ficat

ion Inference

mechanism

Fuzz

ifica

tion

Inpu

ts sc

alin

g

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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 Pbatand 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.

TABLE I INITIAL RULES WHEN SOCSC=LE

SOCbatKbatLE ME GE

NB ME ML LE NM ME ML LENS ML LE LE ZE LE LE LE PS MB GE GE PM MB GE GE

Preq

PB MB GE GE

TABLE II INITIAL RULES WHEN SOCSC=ME

SOCbatKbat LE ME GE NB ME ML LE NM MB ML LENS MB LE LE ZE LE LE LE PS ML ME MB PM LE ME GE

Preq

PB ML MB GE

TABLE III INITIAL RULES WHEN SOCSC=GE

SOCbatKbat LE ME GE NB GE MB ME NM GE ML LENS GE LE LE ZE LE LE LE PS LE LE LE PM LE ML ME

Preq

PB 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.

Figure 3. Membership functions

0.6

LE ME GE

(SO

Cba

t)

SOCbat0.2 0.9

1

0.6

0

Preq-3 -2 -1 10 2 3

1

0.5

NB NM ZE PM PB

(P r

eq)

NS PS

h104

0

LE ME GE

(SO

Csc

)

SOCsc0.2 0.6 0.9

1

0.5

0

Kbat

(K b

at)

0.2 0.4 0.6 0.8 1

1

0

LE ML ME GEMB

0.5

Figure 4. Parameters to be optimized in MFz10

1

0.5

NB NM ZE PM PBNS PS

z1+z2 z1+z2+z3-z1-z1-z2-z1-z2-z30

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1 2 7 8 9 10 68 69 70 z1 z2 z7 3 3 2 1 3 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:

t

5.0)(1)(5.0)()(

)(xfloorxxfloorxfloorxxfloor

xRound

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.

V. SIMULATION RESULTSTo 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

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, batterys 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.

TABLE VECR 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 usingPSO-fuzzy controller have a better fuel economy performance than that of conventional fuzzy controller.

ACKNOWLEDGMENTThis 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

Glider mass (kg) 592 Rolling resistance Coefficient 0.012 Vehicle parameter

Frontal area(m2) 2.03 Aerodynamic drag coefficient 0.19 Type IM Peak power (kW) 60

Motor parameter Rated power(kW) 20 Rated speed (rpm) 3600

Type Saft Li-ion Module number 30 Battery parameter

Rated capacity of Single cell (Ah) 6 Gravity of single cell (kg) 0.7 Type MaxwellPC2500 Number of cells 120 Supercapacitor

parameter Rated output voltage (V) 2.5 Current range (A) (-225, 225)

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

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Proc.IEEE, vol. 90, pp. 247275, 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.

0 100 200 300 400 500 600 7000.77

0.775

0.78

0.785

0.79

0.795

0.8

0.805B

atte

ry S

OC

Figure 6. Diagram of battery SOC trend

PSO-fuzzyfuzzy

time (s)

0 100 200 300 400 500 600 7000.350.40.450.5

0.55

0.60.650.7

0.750.8

supe

rcap

acito

r SO

C

time (s)

PSO-fuzzyfuzzy

Figure 7. Diagram of supercapacitor SOC trend

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