Optimization of Control Strategy for Plug-in Hybrid Electric Vehicle Based on Differential Evolution Algorithm Lipeng Zhang *, **, Cheng Lin * and Xiang Niu * * School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing, China

Abstract—In order to improve fuel economy, reduce emission and maintain battery life, the simulation model and control strategy for plug-in hybrid electric vehicle were established by means of PSAT and MATLAB/SIMULINK. Based on differential evolution algorithm, the control parameters were global optimized. The simulation result shows that the optimized control parameters can obviously improve the vehicle economy. It not only proves the necessary of carrying out control parameters optimization, but also reflects the excellent ability of differential evolution algorithm to realize the global optimization. Keywords- Plug-in hybrid electric vehicle; Control strategy; Differential evolution algorithm; Parameters optimization

I.

INTRODUCTION

As a new kind of electric vehicle, plug-in hybrid electric vehicle has gradually become the trend of hybrid electric vehicle. The battery of plug-in hybrid electric vehicle can be charged with on-board power supply, and the rechargeable battery can ensure a certain continued mileage with pure motor driving. Plug-in hybrid electric vehicle can play a more important role of fuel saving, emission reduction and environmental protection than hybrid electric vehicle. Due to the running mainly depend on pure electric mode, plug-in hybrid electric vehicle need low maintenance cost and have greater potential to promote. Control strategy is the guarantee to realize the purpose of energy saving and environmental protection, and is the core research content for plug-in hybrid electric vehicles. In this paper, consulting the parameters of BFC6110HEV bus, the control strategy of plug-in hybrid electric vehicles was proposed, and the control parameters were optimized based on the differential evolution algorithm. II.

DIFFERENTIAL EVOLUTION ALGORITHM

A. Background of Differential Evolution Algorithm Differential evolution algorithm was proposed by Rainer Storn and Kenneth Price in 1995[1]. It is a new heuristic approach mainly having three advantages: finding the true global minimum regardless of the initial parameter values, fast convergence, and using few control parameters. Differential evolution algorithm is a population based algorithm like

** School of Automobile and Transportation Engineering, Liaocheng University, Liaocheng, China

genetic algorithms using similar operators, crossover, mutation and selection. The main difference in constructing better solutions is that, genetic algorithms rely on crossover, while differential evolution algorithm relies on mutation operation. In differential evolution algorithm, all solutions have the same chance of being selected as parents without consideration of their fitness value. The best one of new solutions and its parent win the competition providing significant advantage of converging performance over genetic algorithms [2]. Differential evolution algorithm is a stochastic optimization method minimizing an objective function that can model the problem's objectives while incorporating constraints. As an efficient method for optimizing real-valued multi-modal objective functions, differential evolution algorithm has been applied to several engineering problems in different areas [3, 4]. B.

Principle of Differential Evolution Algorithm Assuming that the function for optimization is minn f ( x) , x∈R

the main steps of differential evolution algorithm are given [5]: 1) Initialization˖The differential evolution algorithm has a few control parameters: number of population N , crossover rate Pc , crossover constant F ∈ (0,1) , evolution algebra t = 0 variables’ lower bound lb and variables’ upper bound ub . The initial population randomly generated is JJG X (0) = { X 1 (0), X 2 (0),", X N (0)} .

Xi (t) = (x1( ) (0), x2( ) (0),", xn( ) (0)), i = 1, 2,", N . 2) Individual evaluation ˖ The target JJG value f ( X i (t )) of each individual X i (t ) in population X (t ) at time t should be Where,

i

i

i

calculated. 3) Evaluation ˖ For each target vector X i (t ) , an integer jrand ∈{1,2,", n} and three separate integers r1 , r2 , r3 ∈ {1, 2,| " , N } are randomly chosen and must be different from each other. A new individual vector X i′(t ) = [ xi′1 (t ), xi′2 (t )," , X in′ (t )] is generated, where xij′ (t ) must meet the conditions: if rand [0,1] < Pc or j = jrand , xij′ (t ) = xr1 j ( t ) + F ⋅ xr 2 j ( t ) − xr 3 j ( t ) ,

(

)

Sponsored by “The National High Technology Research and Development Program of China” (2006AA11A192)

978-1-4244-2487-0/09/$25.00 ©2009 IEEE Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on June 08,2010 at 14:44:58 UTC from IEEE Xplore. Restrictions apply.

else

xij′ (t ) = xij (t ) .

4) Selection ˖ The parent vectors are mixed with the mutated vector to produce a trial vector °­ X i′ ( t ) , if f ( X i′ ( t )) ≤ f ( X i ( t ) ) X (t + 1) = ® °¯ X i ( t ) , otherwise

G

5) Termination of the test˖If population X (t + 1) meets the termination criteria, take the individual vector with G minimum target in the population X (t + 1) as optimal solution and output it, otherwise back to 2). III.

MODEL OF PLUG-IN HYBRID POWER SYSTEM

Series hybrid electric vehicle is particularly suited to the complex driving cycle in city, such as operation in low-speed, frequent acceleration and deceleration, often parking. So this driving form was chose as the system structure of plug-in hybrid electric vehicles and figure 1 is the system structure.

Figure 2. Input and output of simulation model

The formula for motor output torque

Tm is

Tm = L × TM_max

Where, L is a control order for motor torque and L ∈ [0,1] , T M _m ax is available maximum torque at motor current speed.

C. Battery Model Lithium-ion battery is one kind of electrochemical batteries, which physical model is shown in figure 3.

Figure 3. Physical model for electrochemical

According to electrochemical batteries general equivalent circuit model, the equation of battery terminal voltage is

Ua = E − Ia R , Figure 1. System structure of plug-in hybrid electric vehicle

With the help of facing-forward simulation software PSAT, the models of plug-in hybrid electric vehicle were established. Due to integrating the complex dynamic models, facing-forward simulation can be used for the detailed design and simulation of dynamic performance, and getting more accurate calculation of the vehicle performance. Forward simulation is particularly suitable for hardware development and control strategy simulation [6].

A. Engine Model The relationship between power Pe and torque Te is Pe = Te ne 9550 The fuel consumption rate be can be calculated from the equation

be = 1000Qt P Where, ne is engine rotation speed, Qt is fuel consumption, P is instantaneous power.

R = Re 1 + Re

Where U a is terminal voltage, E is electromotive force, I a is current for charge or discharge, R is battery electric resistance, Re1 is Electrolyte resistance, Re is Electrode resistance. The capacity of battery is connect with temperature, load current and charge-discharge time. The available capacity is calculated as follows:

Qu ( I a , t ,τ ) = Q ( I a ,τ ) − ³0 I a ( t )dt t

Where, Qu ( I a , t ,τ ) is available capacity; Q ( I a ,τ ) is total capacity of batteries, which is a function of temperature and charging-discharging current; ³0 I a ( t )dt is electricity consumption, which is a function of current and time. t

D. Pilot Model In fact, the pilot model is a speed controller. The input and output

of pilot model is shown in figure 4. A PID controller is used in

B.

Motor Model The input and output of simulation model for motor and its controller are shown in figure 2. U is bus batteries voltage, I m is motor controller terminal current; Tm is motor output

torque and ωm is speed.

Figure 4. Input and output of pilot model

Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on June 08,2010 at 14:44:58 UTC from IEEE Xplore. Restrictions apply.

the model, which will transfer the difference value Δu between the entered expectation speed ud and the actual speed ua into accelerate pedal Instruction β acc or brake pedal instruction βbrk . The main variables of pilot model are the weight of driver and the PID parameters to descript different driving styles.

peak power of the motor is 150kW. The efficiency of the motor is shown in figure 7.

E. Vehicel Load Model When vehicle is running, there is a balance between the driving force and the resistance force [6], the balance equation is:

Ft =

vstep

ηT

(mg sinα + mgf cosα +

CD A 21.15

u + mδ 2

du dt

)

Where, Ft is driving force, m is vehicle quality, f is rolling resistance coefficient, g is gravity acceleration, α is slope angle, C D is air resistance coefficient, A is frontal area, u is vehicle speed, δ is coefficient of the revolving mass changes to linear mass.

Figure 6. Universal characteristic curve of engine

F. Accessories Model To keep running, vehicles need many kinds of annex to provide a variety of auxiliary functions. There are some energy consumption annexes, include DC-DC, air pump, oil pump, and so on. On the basis of reactive measured power consumption, the models of annexes may adopt constant power models. G. Driving Cycle Model According to the real vehicle test data and using the modeling approach of driving cycle, a bus driving cycle in Beijing was build. As shown in figure 5, the front 429s is congestion driving cycle, the last 826s is smooth driving cycle. Figure 7. Motor efficiency

Li-ion batteries are selected as the energy source. The capacity of a single battery is 90Ah, after 2 single batteries were connected in series, 104 batteries were connected in parallel, and the total capacity is 180Ah. IV. Figure 5. Bus driving cycle in Beijing

H. Select components BFC6110HEV bus was chose as the example for study, which quality m is 12980kg, rolling resistance coefficient f is 0.012, frontal area A is 8.9m2, and air resistance coefficient C D is 0.7. Besides these, the wheel rolling radius of this bus is 0.58m; the average power consumption of accessories is 3kW. In Beijing, gravity acceleration g is 9.8m/s2. A 120kW diesel engine and a rated power 100kW AC motor was installed in the bus, the efficiency and external characteristic curve of the engine is shown in figure 6. The

CONTROL STRATEGY OF PLUG-IN HEV BUS

In order to achieve the optimal efficiency of plug-in hybrid electric vehicle, the thermostat control strategy and the power following control strategy were combined. It can make full use of the high efficient zone of engine and battery, reach the highest overall efficiency. The control strategy of plug-in hybrid electric vehicle can be descripting as follows: if the battery SOC is higher than the target value, the battery doesn’t need to charge; otherwise, the battery need to charge. When the battery SOC is higher than the maximum value, APU system will initiative shutdown, it can not be start until the SOC reach the minimum value; when the battery SOC is lower than the minimum value, APU will initiative start immediately and will not initiative closure until the battery SOC reach the maximum value.

Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on June 08,2010 at 14:44:58 UTC from IEEE Xplore. Restrictions apply.

To realize this control strategy, the battery SOC needs to be adjusted according to the equation:

­ 0 ° P =® SOCt − SOC °PC.max SOC − SOC min ¯ t * B

SOC ∈[ SOCt , SOCmax ]

0.8 yuan/kWh. Table 1 is the economic comparison of different goals of SOCt, and figure 8 is the simulation result. TABLE I.

SOC ∈[ SOCmin , SOCt ]

COMPARISON OF ECONOMY IN DIFFERENT SOC

30%

Value 40%

50%

26.41 8.18

20.24 9.61

15.57 10.68

61.21

63.28

64.78

Object of Investigation

PB* is output power, which comes from the control strategy of battery SOC; PC .max is the battery maximum

Where,

recharge power, in order to avoid battery charge current too large, let PC .max is 30kW.

SOC Electricity(kWh) Diesel (L) Cost(yuan)

To keep the battery work at best state, the battery aim SOC initial set is 50%. In order to meet the adjust strategy of SOC and the demand of power-driven, the command of power output from the APU is

PAPU* = ( PΣ* − PB* ) . *

Where, PΣ is the demand driven power value given by the motor. This value is generated by the pilot model, and divided by the efficiency of driving axles, gearbox and electrical components. To avoid APU frequent switch, the constraint condition of APU output power is

min {PAPU } ≤ PAPU* ≤ max { PAPU } .

Figure 8. Simulation result in different SOC

What can be found from the research is that, in adjustment the control strategy of SOC, the choice of maximum value and minimum value of SOC ought to moderate, to ensure there is a full-span between the two values. But the value can not be too large or too small, lest the battery be overcharged or over discharged. For meeting the requirements described above, the limited value of maximum SOC is 70%, the minimum SOC is 30%. SOCt is a control parameter, which can be free chose between 30% and 70%. If the SOC objective value is too small, the engine must spend more time to work in low efficient areas. In addition, the smaller bus voltage will drop the efficiency of motor. In other hand, if the SOC objective value is too big, the battery need engine to add more energy, resulting in more fuel consumption. As a result, the optimal target value of SOCt needs to be study by simulation. In the simulation, the choose value of SOCt is 30%, 40% and 50%. The built models of plug-in hybrid electric vehicle and bus driving cycle in Beijing are also used. The objective function is

F ( x, y ) = x ⋅ f x + y ⋅ f y . Where, x is fuel consumption, y is power consumption, is the prices of oil and

fx

f y is the prices of electricity.

According to the survey in Beijing in February 2008, the price of 0# diesel is 4.9 yuan/L and the price of electricity is

From the simulation results can be seen, the lower the SOC target value, the better the economy. Because the price of electricity is cheaper than that of oil, the cost of using electricity is lower than using oil. Making full and efficient use of the reserved power in battery, relatively little use fuel, is the important way to improve the economy for plug-in hybrid electric vehicle, what in line with the original intention of the development of plug-in hybrid electric vehicle. V.

OPTIMIZATION OF CONTROL STRATEGY

A. Optimization Problem To alleviate the city's pollution, require bus to keep pure electric mode in the region of city center, the engine can not be opened in these regions. In pure electric driving, the battery SOC should not be too low; otherwise the battery will be damaged. In order to meet the constraints and achieve the best economy, when starting the engine and which kind manners the engine adopts to supplement the SOC is an issue need to be study. To find the optimal solution of the problem, the following parameters need to be optimized, including the goal value of SOC after engine starting, the maximum recharge power add to the battery, the minimum threshold for engine to start, the minimum output power after engine starting. There is not only an objective function, but also a number of parameters and constraints to be optimized. It is a multidimensional problem of global optimization. For effectively solving this complex problem, differential evolution algorithm was used.

Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on June 08,2010 at 14:44:58 UTC from IEEE Xplore. Restrictions apply.

B. Parameter Selection In this optimization, population size is 6, crossover rate is 0.3, and crossover constant is 0.5. The initial population is randomly selected. Set the minimum evolution algebra is Tmin , when evolution algebra reach Tmin , no individual is updated in the last generation of evolution Tend , the optimization should be terminated. In this paper, Tmin is 20, Tend is 5.

C. Control Strategy after Optimization Figure 9 is the optimizing result and the function value of optimal solution in each generation is shown. The total evolution time is 27. In the 19th generation, the optimal solution was found. From the 22ed generation, no individual was update; after the 27th generation, the evolution was end. Figure 10. SOC changing process with different control parameters

VI.

Figure 9. Evolutionary process

The optimized control parameters are these: the goal SOC of starting engine is 62.08%; the battery maximum recharge power is 22.39kW; the minimum threshold of starting engine is 32.03%; the minimum output power of engine is 7.37kW. The best objective function value F ( x, y ) min is 39.04 yuan, but with the initial control strategy, the objective function value F ( x, y ) min is 40.33yuan, the achieved economy improvement is 3.2%. Through the control parameters optimization we can see, it is quite obvious for the optimized parameters to improve the vehicle economy. It also proves the necessity to optimize the control parameters. Besides convergence to the global optimum, the population is ever lingering around two local optimal solutions. The two solutions are: the SOC goal value after starting the engine, 46.13% and 69.62%, the battery maximum recharge power, 29.88kW and 21.73kW; the minimum engine starting threshold, 31.37% and 31.99%; the minimum output power of engine, 7.88kW and 7.62kW. Take SOC target value as primary research object, the comparison of SOC changing process with the two groups control parameters is shown in figure 10. From the figure we can see, to appropriate enhance the SOC objective value and reduce the charge power will be beneficial to the whole vehicle economy. At the same time, we should also note that through the evolution of population, the local optimal solution was jumped out. It prove that differential evolution algorithm have enough capability in the searching for overall optimal solutions.

CONCLUSION

By using simulation software PSAT and MATLAB/ SIMULINK, and consulting the parameters of BFC6110HEV, an overall vehicle simulation model of plug-in hybrid electric vehicle was built. According to the structure of series hybrid electric vehicle and bus driving cycle in Beijing, the control strategy for plug-in hybrid electric vehicle was proposed, and the correctness and effectiveness of the control strategy were proved by the simulation results. In order to have a better performance to conservator energy and protect environment, differential evolution algorithm was used to optimize the control parameters. With this algorithm, the optimal control parameters have been achieved, the performance of plug-in hybrid electric vehicle was significantly improved. It finds a precise and efficient way for the optimization of continuous control parameters. The differential evolution algorithm seems to be a promising approach for engineering optimization problems. VII. REFERENCE [1]

[2]

[3] [4]

[5]

[6] [7]

Storn R and Price K. Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces [J]. Journal of Global Optimization, 1997, 114 : 341-359 Karaboga D and Okdem S. A simple and global optimization algorithm for engineering problems: differential evolution algorithm[J]. Turk J Elec Engin, 2004, 12, (1): 53 - 60 Rainer Storn. Designing nonstandard filters with differential evolution[J]. IEEE Signal Processing Magazine, 2005, 22 (1):103 - 106 Sandra Paterlinia and Thiemo Krinkb. Differential evolution and particle swarm optimizations in partitional clustering[J]. Computational Statistics & Data Analysis, 2006,50(5):1220 -1247 YU Tiemin and YAN Dongshu. Differential evolution algorithm for multi-objective optimization[J]. Journal of Changchun University, 2006, 16 (2): 77- 80 Zhang Xiang, Zhao Han, Qian Li jun, Zhang Bingli. Forward Simulation Approach in the PSAT[J]. Computer Simulation, 2005,22(5): 219 - 222 Yu Zhisheng. Automobile Theory [M]. Beijing: China Machine Press, 2003: 6 - 21

Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on June 08,2010 at 14:44:58 UTC from IEEE Xplore. Restrictions apply.