Journal of Mechanical Science and Technology 25 (1) (2011) 183~192 www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-010-1115-8
Optimal operation strategy development for fuel cell hybrid vehicle† D. J. Xuan1, J. W. Kim2 and Y. B. Kim3,* 1
College of Mechanical Engineering, Wenzhou University, Wenzhou, China 2 Research Centre, Advanced Mechatronics Systems Co., Gwangju, Korea 3 Department of Mechanical Engineering, Chonnam National University, Gwangju, Korea (Manuscript Received October 14, 2009; Revised September 6, 2010; Accepted November 5, 2010) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract An overall simulation model for fuel cell hybrid vehicle (FCHV) power train in parallel configuration using MATLAB/Simulink programming is constructed in this study. The model runs on power control strategy by using logic-threshold approach, achieved by the hybrid control unit (HCU) and fuel cell stack number. Using accelerator and decelerator pedal positions deduced from the driving schedule as the primary input, the simulation implements power flow and distribution under different vehicle operating modes. The HCU control strategy also incorporates regenerative braking and recharge for battery capacity recovery. Using the D-optimality method for experiment points selection and sequential quadratic programming (SQP) algorithm for obtaining the optimal operational parameters, three control threshold variables of HCU and optimal stack cell number are selected for hydrogen fuel economy under certain driving cycles. The proposed method provides optimized configurations of the FCHV model and the fuel cell stack, which has the capability in satisfying drive power request while satisfying vehicle driving schedule and battery state of charge (SOC) recovery with lower fuel consumption. Keywords: FCHV; HCU; Modeling; Logic threshold; D-optimality; SQP algorithm ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction Concerns about stricter emission standards and shortage in global fuel supplies encourage researchers and automotive manufacturers to create new fuel-efficient vehicle technologies. The fuel cell hybrid vehicle (FCHV) uses one of the most viable technologies, showing significant potential in satisfying both fuel economy and emission standards demand within acceptable customer constraints [1]. Moreover, the FCHV overcomes some of the obstacles in pure electric vehicles and offers potential for improved vehicle performance [2]. Specifically, the FCHV has two advantages: (1) it offers great potential for fuel savings by load-leveling the fuel cell stack, and (2) it uses a smaller battery pack compared with the pure electric vehicle. Model-based systematic development processes are commonly adopted for traditional internal combustion enginepowered vehicles but are rarely explored to their full potential in the development of the FCHV [3, 4]. Recently, a fuel cell hybrid electrical vehicle (FCHEV) simulation model has been developed for evaluating potentials of hybridization [5]. Until †
This paper was recommended for publication in revised form by Associate Editor Kyoung Doug Min * Corresponding author. Tel.: +82 62 530 1677, Fax.: +82 62 530 1689 E-mail address:
[email protected] © KSME & Springer 2011
now, there are fuel cell system options in the simulation model ADVISOR [6], which can simulate FCHVs with ease. However, few papers have published on details of FCHV power train models, and systematic development processes have not been commonly mentioned in control design for FCHV power train. The major feature of this study is a simulation model-based control strategy design for the FCHV power train. The paper is organized as follows: In Chapter 2, the subsystems of FCHV are constructed based on vehicle dynamics mathematical model; then experiential data and Matlab/Simulink blocks and the overall FCHV system model are obtained. Chapter 3 discusses how the hybrid control unit (HCU) is designed for the implementation of the power control strategy based on the logic threshold approach. In Chapter 4, the control strategy is validated by simulation experiment based on the new European driving schedule cycle (NEDC), simultaneously using the D-optimality method and sequential quadratic programming (SQP) algorithm for control threshold variables optimal option in order to minimize hydrogen consumption. Simulation analysis and evaluation under optimal variables configuration are carried out in Chapter 5. Finally, the conclusion is presented in Chapter 6.
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Table 1. Subsystems of FCHV. Subsystem
Description Hydrogen fuel cell block with maximum power Fuel cell stack 15kW. Nickel-Metal-Hydride (NiMH) battery block with Battery pack nominal voltage 200V and rated capacity 6.5Ah. One-way DC/DC for fuel cell and two-way DC/DC for battery which adapt the lower voltage of fuel DC/DC Converter cell or battery to the DC bus which feeds the motor at rated voltage of 500V. AC machine with its inverter and vector control Motor/Controller drive block with 35 kW as the rated power. Including transmission and longitudinal vehicle Vehicle dynamics dynamics model. For deducing the AP from the speed cycle of drivDriver model ing schedule. For control strategy and power management imHCU plements.
Fig. 2. Polarization curve of the fuel cell stack. 100 *(1-u(1)/Q)
2 SOC
SOC(%)
SOC calculate No load voltage calculate
Integrator
E0-K *(Q/(Q-u(1)))+ A*exp (-B*u(1))
Ah
1/3600
i +
s
E
-
+
Internal resistance
-
Battery current
1 s
+Ubatt 1
-Ubatt 2
Fig. 3. Battery pack model.
Fig. 1. Fuel cell stack model.
2. Modeling of FCHV An FCHV power train model is constructed mainly based on SimulinkTM (registered trademark of the MathWorks, Inc.) blocks in Matlab/Simulink [7]. Each subsystem is modeled separately, and then according to the power transfer implemented by control strategy, the overall simulation model is obtained. Table 1 outlines the FCHV subsystems configuration. 2.1 Fuel cell stack modeling The fuel cell stack model shown in Fig. 1 represents a particular fuel cell with parameters such as pressures, temperature, element compositions, flow rates of fuel, and air variations. These variations affect the open circuit voltage Eoc and Tafel slope Afc. The Eoc and Afc are modified as follows: EOC = N ( En − A fc ln(i0 ))
(1)
A fc = RT / zα
(2)
where gas constant R = 8.3145 J/ (mol K); Faraday constant F = 96485 C/mol; Nset is the number of cells; z is the number of moving electrons; En is the Nernst voltage (V), which is the thermodynamics voltage of the cells and dependent on temperature levels and partial pressures of reactants inside the
stack; and i0 is the exchange current (A), which is the current resulting from the continual backward and forward flow of electrons from and to the electrolyte at no load. The exchange current is also dependent on the temperatures and partial pressures of reactants inside the stack. Moreover, α is the charge transfer coefficient, which depends on the type of electrodes and catalysts used, T is operation temperature, and +Ufc, -Ufc are two fuel cell electrical terminals. Many research papers and literature have been concerned with the dynamics modeling of fuel cell stacks [8-12]. Among the parameters, the Nernst voltage and the exchange current density can be determined using the rates of utilization of hydrogen and oxygen based on electric chemical principles [12]. Some assumptions are made for simplicity of the hydrogen fuel cell stack model, which include the following: the gases are ideal; the stack is fed with hydrogen and air; the stack is equipped with a cooling system, which maintains the temperature at the cathode and anode exits, are stable and equal to the stack temperature; the stack is equipped with a water management system that can maintain the humidity inside the cell at an appropriate level at any load; and the output voltage is closed to the open circuit voltage. The polarization curve of the fuel cell operating at fixed nominal gases conversion rate is shown in Fig. 2. 2.2 Battery modeling The major issue in battery modeling is dynamic representations of the battery capacity and state of charge (SOC). Battery capacity is an indication of the capability of the battery for sustained discharge of battery current. It is usually defined in terms of Ampere hour (Ah) capacity, which is considered as time integration of the battery current [13]. Using the bat-
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D. J. Xuan et al. / Journal of Mechanical Science and Technology 25 (1) (2011) 183~192 Nominal Current Discharge Characteristic at 0.2C (1.3A)
Voltage
250
Discharge curve Nominal area Exponential area
200
150 0
1 2 3 4 5 6 7 Time (hours) E0 = 214.023, R = 0.69076, K = 3.125, A = 24, B = 2.3077
Voltage
250
200
Fig. 5. Motor/controller model.
150 0
10
20
30
40 50 60 Time (Minutes)
70
80
90 Driveline Environment
Fig. 4. Characteristic curve of the battery.
Vx tire inertia 1
Env
Omega Terminator 1
Fz Fx
Fcn gear ratio
tery block in MATLAB/Simulink, a generic model parameterized to represent one type of nickel-metal hydride (NiMH) rechargeable batteries is modeled with the following assumptions: the internal resistance is constant during the charge and the discharge cycles and does not vary with the amplitude of the current; the parameters of the model are deduced from discharge characteristics and are the same for charging; the capacity of the battery does not change with the amplitude of current; the temperature does not affect the model behavior; and the self-discharge of the battery is not represented and the battery has no memory effect. The battery model is shown in Fig. 3. In Fig. 3, E represents no load voltage (V), E0 is constant voltage (V), K is the polarization voltage (V), Q stands for battery capacity (Ah), A is exponential voltage (V), B is an exponential capacity (Ah)-1, and +Ubatt and -Ubatt represent two battery electrical terminals. The characteristic curve of battery is shown in Fig. 4. In this model, the SOC for a fully charged battery is 100% and for an empty battery, 0%. The SOC is calculated as : ⎛ ⎞ ⎜ Q • 1.05 ⎟ SOC = 100 ⎜1 − ⎟. idt ⎟ ⎜ ⎝ ⎠
∫
-K m /s to km/h
F
1 Drive Shaft
2.3 Motor modeling A three-phase permanent magnet AC synchronous machine (PMSM) with its inverter and vector control drive AC6 block of SimulinkTM is used, as illustrated in Fig. 5. The electrical and mechanical parts of the PMSM are each represented by a second-order state-space model [14]. The PMSM operation mode is dictated by the sign of the mechanical torque, which is positive for ‘motor mode’ and negative for ‘generator mode’. 2.4 Vehicle dynamics The vehicle dynamics model shown in Fig. 6 includes the transmission and longitudinal vehicle dynamics model. The transmission transmits power from the motor drive shaft to the
B F1
B
Variable Ratio Gear
Differential Transmision inertia tire inertia 2
Fzf
Fxr
Fzr
beta
Longitudinal Vehicle Dynamics
Vx
1 Car Speed
Fxf
Vx F2
r
0 road angle
Omega Terminator 2
Fz Fx Tire 2
Fig. 6. Vehicle dynamics model.
tires by using a variable ratio gear, and the differential gear of transmission splits the input torque into two equal torques. The longitudinal vehicle dynamics block is used to represent the vehicle dynamics and motion influence on the overall system, including a two-axle vehicle with four equally sized wheels, moving forward or backward along its longitudinal axis. Its main function parameters and constants are summarized in Table 2. The vehicle dynamics mathematical equations are listed below. The vehicle dynamics and motion [15]: m
(3)
Tire 1
-1/30 *u(1)+5
dVx = Fxf + Fxr + Fd − mg • sin β . dt
(4)
Aerodynamic drag: 1 Fd = − Cd ρ AVx2 • sgn(Vx ) . 2
(5)
Tire dynamics and motion [16]: Iw
dΩ = τ drive − re ( Fxf + Fxr ) . dt
(6)
Concerning about wheel slip: Ω=
(1 − k )Vx . re
(7)
2.5 Driver model The driver model, as shown in Fig. 7, deduces the system
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Table 2. Vehicle dynamics parameters and constants. AP
Parameter and constant value m=700
Driver model
Meaning and Unit
AP Motor torque ref (Nm)
Motor torque _ref
Motor speed
Vehicle mass (kg)
Vx Fxf, Fxr Fd
Gravitational acceleration (m/s2)
g=-9.81 β
FuelCell
Motor enable
+FC
FC enable
+
A=2.0
Effective frontal vehicle cross-sectional area (m2)
Drive torque
Edrivebrake
Drive Shaft Car Speed
Electric Motor
Vehicle Dynamics Batt enable
Batt enable
+
Edrivebrake + Batt
+ Batt
-
- Batt
Battery
Mass density of air (kg/m3)
Ubus
Ubus
- Batt
ρ=1.2
Imot
+Ubus
FC_DC/DC Converter
FuelCell Stack
Batt
Aerodynamic drag coefficient (N•s2/kg•m)
Motor Enable
-Ubus
-
- FC
-FC
FC enable Imot
Hybrid Control Unit
Cd=0.2
Motor speed
+ FC
Batt
Incline angle (rad)
Batt_DC/DC Converter
Fig. 9. FCHV power train simulation model.
2
Iw=0.5
Wheel-tire assembly inertia (kg•m )
Ω
Wheel angular velocity (rad/s)
τdrive
1 AP
Effective rolling radius of wheel (m)
Vsx
Wheel slip coefficient Horizontal distance from CG (center of gravity) to front and to rear axle (m) CG height from ground
103 0.5
FC enable
AP
3 Car Speed
Wheel slip velocity (m/s)
k = −Vsx / Vx
4 Batt
-K-
f(u) Sign
Fd_air
Tire rolling radius
-K-
acceleration
3 FC enable 4 Batt enable
Batt Power_ref Motor torque _ref Motor speed
1 Motor torque _ref
FuelCell Prequest
Tvehicle
du /dt
2 Motor enable
System Operation Logic
5 FuelCell
Tvehicle
K-
Fx
Aerodynamic drag
Batt power_ref
Batt
rad/s
km/h to m /s
Batt enable
Car Speed
2 Motor speed NEDC
Motor Enable
Request Power
Torque applied by the axle to the wheel (N•m)
re=0.3
Driving schedule
FC enable
Car Speed
Longitudinal vehicle velocity (m/s) Longitudinal forces on the vehicle at the front and rear wheel ground contact points respectively (N) Aerodynamic drag force (N)
Torque ref
FuelCell
AP
m*a
Vehicle mass
f(u)
Twheel
Moter Reference Torque Calculation
Tdrive
2
Tire dynamics f(u) -K-
Vwheel_Omega
Wheel velocity considering slip
-1/30*u(1)+5
1 Accelerator/decelerator pedal position
gear_ratio_1
Fig. 10. Structure of the HCU.
Variable ratio gear1
Vmot
gear_ratio
-K-
rad /s to rpm
Variable ratio gear
The AP from the NEDC shown in Fig. 8 is obtained by the driver model.
Tmot
Motor Character map
zero avoider
2.6 FCHV power train model
Fig. 7. Driving schedule and driver model.
With each subsystem connected, the FCHV overall power train model is obtained in Fig. 9. The power delivered from the fuel cell is transmitted to the motor through a one-way DC/DC, and then the electric motor output torque is joined to the drive shaft connected by the transmission and vehicle dynamics. The battery and its two-way DC/DC are passively connected into the DC bus in parallel, and the difference between the current drawn from the motor inverter and the current outflow from the fuel cell DC/DC will be compensated by the passive battery [17].
0.6
AP
0.4 0.2 0
-0.2
0
200
400
600 Time (s)
800
1000
1200
3. Control strategy development
Fig. 8. AP in NEDC from the driver model.
input AP from driving schedule according to longitudinal vehicle dynamics, aerodynamics, and tire dynamics. In the driver model, the AP is defined as AP =
Tdrive Tavailable
.
(8)
In this study, the control strategy has to assure that the power delivered by the electric motor meets the power demand at any time [18]. The control strategy where the fuel cell is used as primary source and the battery is used as buffer and assistant energy source has already shown performance better than the reverse situation [19].
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1 Request Power
request power
> P_threshold
NOT NOT
AND
Start
double
== 0
Memory
1 4 Batt power _ref
Gain 1 3 Car Speed
> V _threshold
3 Batt enable
>0
AND
-K -
AND
Cruise
double
>= SOC_low
1 Motor Enable
1_Start
2 Gain 2
Interval Test 1 4 Batt
FCBatt
double
2 FC enable
Switch
(75 1 0 1) > AP _threshold
2 AP
Multiport Switch
(75 1 1 1) 2_FCBatt
3 (0
Gain 3
0
1
1)
3_Cruise 0
double
FCpower
0
== 0
1)
Gain 5 (0
== 0
1
5_FCpower
5
AND
double
Pause
0
0
0)
6_Pause
6 Gain 6
Fig. 11. Module of the system control logic.
3.1 Design of HCU Based on the logic threshold approach [20], the power control is based on the AP derived from driving schedules, which has the value between -1 and 1, with negative values simulating the braking. The APthreshold, is set for starting the fuel cell stack or the battery pack with reference to the SOC, power request, and vehicle speed. In addition, a recharge option for sustaining the battery SOC and regenerative braking for the recovery of the vehicle energy are also incorporated in the control strategy [21]. The implementation subsystem for the control strategy of the HCU is shown in Fig. 10, where its main modules are the system operation logic and the motor reference torque calculation. HCU determines the enable/disable signals and torque reference values for the fuel cell, battery, and electric motor. According to the control logic, these control signals are calculated using the input AP and the measured vehicle speed, motor speed, and SOC. 3.2 System operation logic The FCHV operates in different modes depending on the control strategy. Usually, six possible operating modes and power flows between each subsystem exist according to the particular conditions, as identified by the module of the system operation logic (Fig. 11). 1) Start mode: Vehicle is propelled by the motor and powered only fed by the battery. This mode continues until the car speed reaches Vthreshold, and the request drive power arrives at Pthreshold, which can be set equal to or smaller than the fuel cell nominal power. 2) Accel_FCBat mode: Accelerate mode powered by both of the fuel cell and the battery. When the request power becomes greater than Pthreshold, then the fuel cell mainly supplies its nominal power and the remainder is supplied by the battery. 3) Cruise mode: The request power corresponds to or is lower than the available fuel cell power, or the fuel cell acts as the only power source.
Preq
-K-
motor speed (rpm)
Treq
rad /s to rpm
Request torque
Motor Character map
4 AP
3 FuelCell
400
up
Tmax
FC power
u
y1
Tfc
|u| 2 Motor speed
1 Batt Power _ref
2 Prequest
Treq
Max available torque
Abs zero avoider
Add
-1
1 Motor torque _ref
lo
Saturation Dynamic
Tbatt
Fig. 12. Module of the motor reference torque calculation.
4) RE_Brake mode: This is a regenerative braking mode. When the request power is negative, corresponding to the vehicle deceleration (AP < 0), the electric motor is operated in the generating mode to recover braking kinetic energy for recharging the battery. In this case, the fuel cell is closed; the range of the regenerative braking torque would be from zero to the maximum torque of the motor under the given motor speed. However, this regenerative braking mode is enabled when the value of SOC is below than SOCup, to avoid battery overcharging. 5) Power_FC mode: When the battery SOC is below than SOClow, the battery is disabled and the vehicle is only propelled by the fuel cell. 6) Pause mode: During the driving cycle, when the vehicle speed is equal to 0, and the request power is also equal to 0 which corresponds to AP = 0, then the fuel cell, the battery, and the motor is disabled until AP > 0. Operating modes with their conditions and power balance implemented by the module of the system operation logic is given in Table 3. Among them, the Pthreshold is considered one of the control variables decided by the relative size between battery and fuel cell, and it is a main factor for FCHVs control optimization [22, 23].
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Table 3. Operating modes with their conditions.
Start
>0
Request power SOClow
Battery current Idischarge
Accel_FCBat
>APthreshold
> Pthreshold
No care
>SOClow
Idischarge
1
1
1
Pfc+Pbat=Pmot
Cruise
0~APthreshold
No care
> Vthreshold
> SOClow
0
0
1
1
Pfc=Pmot Pbat=Pmot
Operating mode
AP
Vehicle speed