Battery Hybrid Vehicular Power System

IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China

Control Algorithm of Fuel Cell/Battery Hybrid Vehicular Power System Xiangjun Li, Member, IEEE, Liangfei Xu, Jianfeng Hua, Jianqiu Li, Minggao Ouyang State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, China Email: [email protected] Abstract—In this paper, a control strategy for a vehicular power system combined with a proton exchange membrane fuel cell and a battery energy system (BES) has been presented. The control, witch takes into account the slow dynamic of fuel cell and the state of charge (SOC) of BES, is investigated based on the proposed fuzzy logic control (FLC) for the vehicular power system. Fuel cell output power was determined according to the driving load requirement and the SOC, using fuzzy dynamic decision-making and fuzzy self-organizing concepts. Analysis of simulation results is discussed by Matlab/Simulink software to verify the effectiveness of the proposed control strategy. The control scheme can be used to improve the operational efficiency of hybrid power system. Keywords—PEM fuel cell, energy storage system, renewable energy, fuzzy logic controller and dynamic modeling

NOMENCLATURE Fuel cell system (FCS) B,C constants to simulate the activation over voltage in the PEMFC system Vcell dc output voltage of FC system Nernst instantaneous voltage Ecell ηact activation over voltage ηohmi ohmic over voltage E0 standard no load voltage F Faraday’s constant IFC FC system current qreqH2 amount of hydrogen flow to meet load change N0 number of series fuel cells in stack Rgas universal gas constant Rint FC internal resistance T absolute temperature U utilization rate Battery system E open circuit voltage of battery Ri internal resistance CP peukert capacity CR total charge removed from the battery DOC depth of discharge SOC state of charge n number of batteries SOCmin minimum SOC of BES SOCmax maximum SOC of BES SOCrefmin minimum reference SOC of BES SOCrefmax maximum reference SOC of BES

C 2008 IEEE. 978-1-4244-1849-7/08/$25.00○

Vehicle system Fg gravitational force Froll rolling resistance force FAD aerodynamic drag force Facc acceleration force m total mass of vehicle g gravitational acceleration constant KR rolling resistance coefficient ηtr transmission efficiency of vehicle ρa air density KD aerodynamic drag coefficient frontal area of vehicle AF ωwh wheel angular velocity rwh wheel radius θ angle of gradient KM rotational inertia coefficient v vehicle velocity Rdr drive ratio Rde deceleration ratio Power control strategy Pfc power of fuel cell system power of battery system Pbat Pload demand of vehicular power system Pminfc minimum power output of fuel cell system Pmaxfc maximum power output of fuel cell system Pfc_fuzzy fuel cell power fuzzy value S Small M Medium B Big L Low H High I.

T

INTRODUCTION

HE various kinds of hybrid electric vehicles have been researched and developed on account of energy crisis and environmental issues. A fuel cell (FC)-powered hybrid vehicle is considered in this paper. Fuel cells offer high power density and low-to-zero emissions. Among the various FC types available, the proton exchange membrane (PEM) FC is the most promising for power systems to be used in automobile, residential, industrial, and other applications. The FC power converter system, for example, consists of a DC/DC converter to boost the stack voltage to a higher level, and a DC/AC inverter to drive the motor. Several variations of power converter architecture have been proposed in the literature ([1-5]),


each entailing advantages and disadvantages. In view of the fact that fuel cells alone might not be sufficient to satisfy the load demands in vehicular applications, in recent years, several control strategies for hybrid systems incorporating fuel cells and energy storage devices, such as super capacitors or/and batteries, have been presented. Meanwhile, intelligent control theory, for instance fuzzy logic and genetic algorithm, has been introduced to the control process [6-9]. In this paper, a fuzzy logic based power control strategy for a hybrid FC vehicular system is proposed. The paper is organized as follows. Section II presents the structure of fuel cell powered vehicular power system. The model of the fuel cell system is described in section III to properly represent the slow dynamics of fuel cell associated with the gas flows and the fuel processor operation. Then, the dynamic modeling of battery and vehicle is presented. Section IV describes a fuzzy logic based power control strategy. Simulation results and analysis are discussed in Section V. Section VI is the conclusions. II.

STRUCTURE OF FUEL CELL POWERED VEHICULAR POWER SYSTEM

The power system configuration is illustrated in Figure 1. The FC system consists of two stacks in parallel. It is connected to a DC link via a boost DC/DC converter, the efficiency of which is assumed to be 90%. Directly connected to the DC link is a battery to supply the transient energy demand and peak loads required during acceleration and deceleration. Under transient conditions, and because the FC current dynamics were intentionally reduced, the battery supplies all other load variations. An electrical traction machine is fed by the DC bus via the DC/AC inverter.

III.

A. Dynamic modeling of a PEM fuel cell system A PEM fuel cell model is realized in Matlab/Simulink as described in [1-2, 4]. Assuming constant temperature and oxygen concentration, the output voltage for fuel cell is presented as follows[1-2].

V fcs = E fcs + η act + η ohmic

(1)

η act = − B ln(C IFC )

(2)

Where

(3) ηohmic = −RintI FC The Nerst’s instantaneous voltage may be expressed as [10] ⎡ ⎡ p H PO R gas T 2 log ⎢ 2 E cell = N 0 ⎢E 0 + 2 F p ⎢ ⎢⎣ H 2O ⎣

⎤⎤ ⎥⎥ ⎥⎦ ⎥ ⎦

(4)

The amount of hydrogen available from the hydrogen tank is given by N I (5) q Hrq2 = 0 FC 2 FU The Matlab/Simulink based FC system model and the parameters of the PEM fuel cell system model are shown in Figure 2 and Table I, respectively. TABLE I. PEM FUEL CELL SYSTEM MODEL PARAMETERS Sign

Value

Sign

Value

B

0.04777 [A-1]

τO2

C

0.0136 [V]

KO2

6.74 [s] 2.1*10-5 [kmol/(s atm)]

F

96484600[C/kmol]

τH2O

18.418 [s]

E0

0.95 [V]

KH2O

7.716*10-6 [kmol/(s atm)]

N0

350

τH2

3.37

Nfc_p

2

KH2

4.22*10-3 [kmol/(s atm)]

Rgas

8314.47 [J/ kmol K]

U

0.8

9.0688*10 [kmol/(sA)]

rH_O

1.168

0.177 [Ω]

T

343 [K]

Kr Figure1. Structure of vehicular power system

PERFORMANCE AND MODELING OF THE SYSTEM

R

int

-7

Figure 2. Dynamic model of fuel cell system


B. Dynamic modeling of battery energy system A lead acid battery system is modeled in reference to the ADVISOR (ADVANCED VEHICLE SIMULATOR) [11]. The battery system consists of thirty 85Ah sub-battery. In general we know that ibat and Vbat may be expressed as Eqs. (6) and (7) when the power consumption of battery is P W. Meanwhile, the relationship between the battery internal resistance (Ri) and the battery depth of discharge (DOD) is fitted with the test data. The details are available in [12].

where

(7)

E = 6 × (0.22 × (1 − DOD) + 1.954)n

(8)

R i = f (DOD

(9)

DOD= CR/ CP

Value

Sign

Value

m

12965 [kg]

AF

7.5 [m2]

g

9.81 [m/s2]

rwh

0.502 [m]

KR

0.018

Rdr

3.002, 1.862

KD

0.7

Rde

6.83

ρa

1.2258

KM

1.1

(6)

Vbat = E − Ri Ibat

)n

Sign

0.6 0.5

(10)

FCS efficiency

I bat

E − E 2 − 4 Ri P = 2 Ri

TABLE II ASSUMED PARAMETERS FOR THE VEHICLE

0.4 0.3 0.2 0.1 0

Therefore, the SOC of battery energy system can be estimated as follows.

SOC = 1 − DOD

( Fg + Froll + FAD + Facc )v

ηtr

(12)

where

Fg = mg sinθ

(13)

Froll = mg KR

(14)

F AD =

ρa 2

AF K D v 2

Facc = mK M

ν = ω wh rwh

dv dt

5

10 15 20 25 30 35 40 45 50 Fuel cell net power(kW)

(11)

C. Vehicle dynamic model The load force of the vehicle consists of gravitational force, rolling resistance, aerodynamic drag force, and acceleration force. Hereby, the total electric power required for vehicle acceleration can be written as

Pload =

0

Figure 3. Net fuel cell system efficiency

The net fuel cell system efficiency for considered PEM fuel cell is shown in Figure 3. To operate the fuel cell system efficiently, the low efficiency operating rations should be avoided as shown in the figure. Therefore, the levels of Pminfc and Pmaxfc for each stack are chosen to 4kW and 40kW, respectively. The power balance of system can be expressed as

Pfc + Pbat = Pload + Ploss

(18)

subject to

Pfcmin ≤ Pfc ≤ Pfcmax

(19)

(15)

The fuel cell power output Pfc is calculated based on the SOC of battery and power demand Pload as follows.

(16)

⎡ ⎛ SOCref − SOC ⎞⎤ ⎟⎥ Pfc = Pfc _ fuzzy ⎢1 + α ⎜⎜ max min 2 ⎟⎠⎦ ⎝ SOC − SOC ⎣

(17)

The practical speed of the vehicle has been calculated through the above-mentioned Eqs.(12)-(17). Moreover, pedal positions model is used to simulate the driver intent to drive the vehicle at desired speed. Pedal positions are changed according to the desired and practical velocities using PID regulator. The assumed parameters of the vehicle are shown in Table II. IV. FLC BASED POWER CONTROL STRATEGY A FC stack can be controlled using either of the following principles: 1) Operation at the maximum power point; 2) Operation at maximum efficiency; 3) Operation at an optimal fuel utilization point. In this paper, the operation of fuel cell at optimal efficient region is selected.

(

where

)

Pfc _ fuzzy = f (SOC, Pload ) ⎧⎪ 1 ⎪⎩ 10

α =⎨

SOCre f

min ⎧ SOC ref ⎪⎪ max = ⎨ SOC ref ⎪ ⎪⎩ SOC

min i f SOC < SOC ref max if SOC > SOC ref

(20) (21) (22)

min if SOC < SOC ref max if SOC > SOC ref

(23)

otherwise

As shown in Eqs. (20) and (21), fuzzy logic is utilized in the power control strategy. Pfc_fuzzy is determined using fuzzy theory based on the SOC and Pload. A fuzzy rule table for Pfc_fuzzy is Table III.


TABLE III FUZZY RULE TABLE FOR PFC_FUZZY Pload

SOC

S

M

B

L

S

M

B

M

S

M

B

H

S

S

M

S

1

shown in Figure 7. Load profile according to the UDDS driving cycle is shown in Figure 8. The maximum load power is 50 kW. The SOCmax and SOCmin shwon in Eq.(20) were assumed to be 0.85 and 0.45, respectively. The simulation results are presented as follows.

B

M

0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SOC of battery energy system S

1

Figure 5. Vehicular power system modeled by Matlab/Simulink

B

M

0.5 0 0 10 20 30 40 50 60 70 80 90 Demand of vehicular power system (kW) S

1

M

B

20

40

0.5 0 0

60

80

Figure 6. Vehicle dynamic model

100

Fuel cell power fuzzy value (kW)

The fuzzy membership functions of the SOC, Pload and Pfc_fuzzy, are shown in Figure 4. To maintain the SOC of the battery within the expected region, a fuzzy selforganizing concept based on the parameters α and SOCref is expressed in Eq. (20). The SOCrefmin and the SOCrefmax are set to 0.6 and 0.7, respectively. V.

SIMULATION AND DISCUSSION

To evaluate the proposed control method, a cyclical driving simulation was conducted using the MATLAB/Simulink software. A forward simulation model is set up based on specified driving test cycle. The vehicular power system and vehicle dynamics modeled by Matlab/Simulink are shown in Figure 5 and Figure 6, respectively. The SOC target value can be changed for different applications, and in the simulation, 0.7 was selected. Vehicle speed profile of UDDS driving cycle was used, as

Speed (mph)

Figure 4. Fuzzy membership function

60 50 40 30 20 10 0 0

200

400

600

800

1000

1200

Time (s)

Figure 7. Vehicle speed profile of UDDS driving cycle

1400

0.8

60 50 40 30 20 10 0

0.7 SOC

Load power (kW)


0.6 0.5 0.4

0

200

400

600 800 T ime (s)

1000 1200 1400

SOCinit=0.5 SOCinit=0.6 SOCinit=0.7

SOCinit=0.55 SOCinit=0.65 SOCinit=0.75

400

1000

0.3 0

200

FC output power (kW)

Figure 8. Load profile according to UDDS driving cycle

1400

25 20 15 10 5 0 200

400

600

800

1000 1200 1400

T ime (s) Figure 9. Power output of FSC for initial SOC of 0.7 40 Battery power (kW)

1200

Figure 12. Change of SOC according to different initial SOC

30

0

30 20 10 0 -10 0

200

400

600

800

1000

1200

1400

-20

Figures 9 and 10 show the power profile of FCS and that of BES respectively when the initial SOC of BES is 70%. They show that fuel cell power output is increased largely to meet heavy driving load requirement. Meanwhile the battery discharges or charges rapidly to react to the fast load changes and to supply the supplementary power, because the output power change of the FC stack is intentionally restricted to a slow dynamic response in order to extend the lifetime of the FC system. Moreover, the FC power is used dynamically to charge the battery, thus maintaining the SOC target value when the load power is lower or zero. In Figure 11, it is evident that, using the proposed control algorithm, the SOC of the battery can be maintained around 70%. Figure 12 shows the change of SOC considering different initial SOC of battery energy system during UDDS driving cycle simulation. As shown in Figure 12, the SOC of battery is also attempted to maintain the target SOC of 0.7. VI.

Time (s)

-30

0.73 0.72 0.71 0.7 0.69 0.68 0

200

400

600 800 Time (Sec)

1000

1200

Figure 11. SOC profile for initial SOC of 0.7

CONCLUSIONS

In this paper, a new power control strategy, which secures the power balance and maintains the SOC in fuel cell hybrid vehicular power system, is proposed based on fuzzy control theory. The simulation results demonstrate that the proposed method is able to operate fuel cell system within the specified high efficiency region and manage the system power flows to maintain SOC of battery around target value during the driving loads.

Figure 10. Power profile of BES for initial SOC of 0.7

SOC

600 800 T ime (s)

ACKNOWLEDGMENT

1400

This work is supported by the National Energy-efficient and New Energy Vehicle Program-Research and Development of Fuel Cell City Bus Power System Technology Platform, which belongs to the eleventh five year “863” program-the hi-tech research and development program of China.

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