Research on Modeling and Simulation of Fuel Cell Bus Power System Based on Forward-Backward energy flow balance method

Abstract

The modeling and simulation research of fuel cell buses’ power system is an important part of accelerating the process of industrialization. This paper firstly analyzes the advantages and disadvantages of different topologies of power systems to determine the optimal configuration, then conducts the parameter matching study of the power system, derives and determines the main vehicle dynamics parameters and the total power demand of the power system, and further completes the parameter matching of the drive motor, gear ratio and power supply, as well as the design of the fuel cell stack. On the Matlab/Simulink platform, the forward-backward energy flow balance method is used to establish a fuel cell power system model divided into power calculation modules and power shunt modules. Finally, model simulation and comparative analysis was car-ried out. The simulation results of the power system model in this paper were compared with the data of the 2010 World Expo FCB real-vehicle test. The result shows that the simulation results of the dynamic system is in good agreement with the real vehicle data. The power system model conforms to the actual situation, has feasibility and high engineering value.

Introduction

The power generation process of a fuel cell is to directly convert the chemical energy in the fuel into electrical energy through an electrochemical reaction. The unit cell is composed of two positive and negative electrodes (fuel electrode, oxidizer electrode) and an electrolyte. Hydrogenation reaction occurs on both sides of the electrolyte membrane. Oxygen reduction reaction, and electrons work through an external circuit to generate electricity. As long as the fuel and oxidant (pure oxygen or air) are continuously input, the fuel cell will continuously generate electricity. As a result, the fuel cell has the characteristics of a battery and a heat engine, and has high energy conversion efficiency, no environmental pollutant emissions, low temperature quick start, low vibration and noise level. Therefore, fuel cell electric vehicles are strongly connected with pollution-free, high efficiency, low noise, and immidiate energy replenishing. The characteristics of this product have been recognized by major companies, prototype cars have been successfully produced. Due to development time and funding constraints, computer simulation analysis has become an important method of development research.^1–5

Liu developed a 30 kW hydrogen fuel cell and power battery parallel electric-electric hybrid power system which uses a current-adjustable boost DC/DC converter for designing the power distribution controller to realize the continuous and adjustable function of the output power of the hydrogen fuel cell. ⁶ Sami presented an ordinal optimization approach to determine good enough designs of the FCHEV power units for the purpose of reducing hydrogen fuel consumption, lowering operation and investment cost. ⁷ Wang developed three types of drivetrain configurations of fuel cell city buses which belong to energy hybrid and the power hybrid-type, implemented experiments to optimize the structure and improve the performance. ⁸ Chen constructed model of PEM fuel cell vehicle power system which integrates the advantages of both empirical model and theoretical model. ⁹ Ran proposed a system configuration of a fuel cell hybrid bus, and conducts modeling and simulation through CRUISE to verify the rationality of its power system. ¹⁰ Jia proposed a hybrid power system of Chinese fuel cell city bus, comprised a proton exchange membrane fuel cell and Ni/MH batteries to combine the high energy density of fuel cells with the high power density of batteries. ¹¹ G.Napoli developed and tested a hybrid powertrain (Fuel cell and Batteries). ¹² Liu carried out the design calculation and matching of driving motor, storage battery and fuel cell system of the fuel cell vehicle, conduct simulation experiments under the established road conditions of typical Chinese cities on ADVISOR. ¹³ Xiong presented an object oriented modeling language to unify the physical modeling method and establish the physical model of FCV powertrain and the critical components base upon Maplesim platform. ¹⁴ Liu, XU, Guo, F Sergi make some contributions to the modeling and simulation methods of different types of fuel cell vehicle power systems. ^{15 – 15} Nicu, Xu, Lai, C.A. Ramos-Paja also conduct research in para-metric design, mechanism and testing of fuel cell vehicle power system. ^{19 – 19} Farhani S shed the light on the modelling and the realization of a DC/DC isolated converter connected to a fuel cell for electric hybrid vehicle. ²³ El Manaa B presents a simple strategy for controlling an interleaved boost converter that is used to reduce the current fluctuations in proton exchange membrane fuel cells, with high impact on the fuel cell lifetime. ²⁴

In this paper, after completing analysis and selection of different power system topology structure as well as parameter matching, on Matlab/Simulink platform, forward-backward energy flow balance method is used to establish a fuel cell bus power system model. Simulation data of the power system model are compared with the data of the 2010 World Expo FCB real vehicle test, the result verifies the validity, feasibility and engineering use value of the power system model.

FCB architecture definition

The first, the structure of fuel cell bus power system should be discussed and determined by the comparison of different structure.

In this part, 3 plans are given by their topological structure. After the different structures are analyzed, the advantages and disadvantages of each structure are revealed and thus the proper structure can be decided.

Introduction to three kinds of topological structure

Three kinds of topological structure are listed, as shown in Figures 1 to 3. Structure #1 “single-FC, single-motor” is mainly consisted of single FCE, DC/DC converter and motor. The power system of this kind of topological structure has good dynamic and static characteristic, steady bus voltage and low demand for motor and driving system. Besides, battery can save the extra energy either generated by the FC or brakes, which will improve the energy utilization efficiency. Moreover, battery can also provide power when the FC breaks down, improving the reliability of the vehicle.

Figure 1.

Schematic of “single-FC, single-motor” FCB system.

Figure 2.

Schematic of “dual-FC, dual-motor” FCB system.

Figure 3.

Schematic of “single-FC, dual-motor” FCB system.

Structure #2 “dual-FC, dual-motor” includes double FCE, DC/DC converter and motor which is the improvement on Structure #1. In addition to the advantage of Structure #1, the powertrain of this kind of topological structure also has high redun-dancy and easy maintenance. The structure has been used in 2010 World Expo FCB successfully.

Structure #3 “single-FC, dual-motor”retains the structure of dual-motor, but it only uses single-FC compared with structure #2. The FC system of the powertrain of this kind of topological structure is simpler than that of structure #2, and then FCE power could be selected in wider range.

Selection of the power system structure

As shown in Table 1, “dual-FC and dual-motor” structure has the advantage of redundancy fault tolerant while has the disadvantage of complex system and high manufacturing cost. Compared with “single-FC, single-motor” structure, “single-FC, dual-motor” structure has the advantages of matured and secure technologies of motor for car or tour bus, redundancy fault tolerant and good power performance, because the Permanent Magnet Synchronous Motor for car or tour bus has been successfully used in FC cars and tour buses in Beijing Olympic Games and Shanghai Expo. Besides, because of Electric vehicle industrialization project in China, the motor for car or tour bus will be volume-produced in the near future, when cost of this kind of motor will be lower. Apart from that, the drive and control technologies of dual-motor structure have been successfully applied in 2010 World Expo FCB. Of course, the “single-FC, single-motor” structure has its advantages, too. With the advance in technology, tech-nologies of motor for city bus will be improved. At that time, ‘single-motor” structure will be better than “dual-motor” structure.

Table 1.

Comparison of n3 topologic structures of power system.

Structure	Advantage	Disadvantage
Dual-FC, dual-motor	Redundancy fault-tolerant; Low maintenance cost	Complex system; High manufacturing cost
Single-FC, single-motor	Simple system; Low manufacturing cost	Immature technologies of motor for city bus
Single-FC,dual-motor	Matured and secure technologies of motor for car; Redundancy Fault-tolerant; Good power performance;	Complex drive system

According to the comparison above, structure #3“single-FC, dual-Motor” structure is now the most suitable structure for the bus. The article adopts“single-FC, du-al-Motor” structure to modeling FCB power system.

Parameter match of FCB powertrain

Main vehicle dynamic parameters of 2010 world expo FCB

The vehicle parameters based on a typical fuel cell bus can be used to match the powertrain according to the Chinese typical bus cycle. The vehicle dynamic parameters are shown in Table 2.

Table 2.

Main vehicle dynamic parameters.

Parameter	Value	Parameter	Value
Vehicle length	12m	Half-load weight	15500kg
Vehicle width	2.5m	Tire radius	0.47m
Vehicle height	3.2m	Rolling resistance coefficient	0.012
Seats	38	Frontal area	7.89m2
Passenger Quantity	60	Drag coefficient	0.65
Base curb mass	13500kg	Transmission efficiency	86%
Full-load weight	17500kg	Main reduction ratio	6.2

Total power requirement of the power system

According to the analysis and calculation, the total power requirement of the powertrain is given in Table 3. In terms of the practical experience, the average efficiency of motor and its controller can be assumed to be 90% and then the motor input power is calculated as the following Table 3 shows.

Table 3.

Total power requirements of FCB system.

Driving cycle			Motor power(kW)		Accessory power (kW)		Total power requirement (kW)
			Driving power	Input power	Air conditioner	others	AC on	AC off
Power performance	Maximum speed	Cruising speed 70 km/h	68.1	75.7	15	9	99.7	84.7
		Instantaneous Speed 80 km/h	87.2	96.9			120.9	105.9
	acceleration	0–50 km/h, 23s	120	133.3			157.3	142.3
		0–50 km/h, 20s	136	151.1			175.1	160.1
	Grade ability	10 km/h, 18%	103.6	115.1			139.1	124.1
		15 km/h, 18%	155.6	172.9			196.9	181.9
Chinese typical bus cycle	Mean power		19.35	21.5			45.5	30.5
	Peak power		202.2	224.7			248.7	233.7
	Maximum motor power		176	195.6			219.6	204.6
Constant Velocity cycle	Constant Velocity (20 km/h)		12.4	13.8			36.4	21.4
	Constant Velocity (40 km/h)		28.6	31.8			55.8	40.8

Selection of driving motor

There are at least two principles for the selection of driving motor:

(a)Rated output power P_nom:

P_nom > power requirement of maximum speed (80 km/h, 87.2 kW) and P_nom > 87.2 kW

(b)Peak output power P_max:

P_max > power requirement of acceleration (136 kW) and grade climbing (155.6 kW)

P_max > most of driving power requirements in city cycle (170 kW, 99.85%)

Then P_max >max {136 kW, 155.6 kW, 170kW} should be met according to (a) and (b).

According to the principles above, the total rated power and peak power of the two motors are designed as 84 kW and 176 kW. Furthermore, the motor driving power should also meet the cycle requirement. The Table 3 shows that the driving motor can meet more than 99.85% of the power requirement in Chinese typical bus cycle. So the motor can meet the requirement. Main parameters of motor are shown in Table 4.

Table 4.

Main parameters of motor and motor controller.

Parameter	Value	Parameter	Value
Rated voltage	375 V(DC)	Peak torque	210N·m
Rated power	42kW	Rated torque	100N·m
Peak power	88kW	Maximal Efficiency	93%
Maximal rotation speed	11500rpm	Weight	81kg
Rated rotation speed	4000rpm	Motor type	Permanent-magnet synchronous motor

Selection of gear ratio

The main reduction ratio is i₀ = 6.2. The transmission system is designed based on the final drive gear ratio and the range of motor speed. Firstly, the dynamic coupling box for dual-motor structure should be designed. The reduction ratio is 3:1. Then the transmission gear ratio can be designed according to the maximum speed and the maximum grade ability. The first gear ratio is i_g1 = 2.588 and the second gear ratio is i_g2 = 1.31.

Power source match

According to the practice, The DC-DC average efficiency can be assumed 92% and 1%∼ 2% power margins is considered. Then the power the fuel cell needs to provide can be calculated.

According to the Table 5, the fuel cell's rated power can be chosen from 50 kW to 110 kW.

Table 5.

Fuel cell power.

	City cycle power	Cruising cycle power
Total power needed	45.5 kW	99.7 kW
Fuel cell power	50.5 kW	108.4 kW

Firstly the battery power is determined by the fuel cell rated power. The discharge safety should be also considered in the peak power demand conditions. Secondly, the bus voltage range (340V−420 V), battery continuous discharge capacity and other fac-tors should also be considered. So the lithium iron phosphate battery is chosen for the better charge and discharge capacity and higher energy density. The battery rated voltage is 384 V and the bus voltage can be assumed to be 400 V.

According to the fuel cell power level and the principle that the discharge current is less than 3C, some schemes are given as the Table 6 shows.

Table 6.

Battery's choice under different FC power level.

Peak power Requirement (kW)	Fuel Cell engine		Battery
	Rated power(kW)	Available Peak power(kW)	Maximum power(kW)	Minimum voltage(V)	Capacity (Ah)	Maximum current(A)
219.6	50	64	155.6	370	160	420.5/2.6C
	60	70	149.6		160	404.3/2.5C
	70	82	137.6		150	371.9/2.5C
	80	94	125.6		120	339.5/2.8C
	90	106	113.6		110	307/2.8C
	100	118	101.6		90	274.6/3.1C
	110	132	87.6		80	236.8/2.9C

Among them, the demand of system peak power is calculated based on the maxi-mum output power of the motor, which is 219.6 kW; FCE rated power is 75% of the maximum power as a estimation and FCE maximum output power is the actual max-imum output power considering the discharge safety (not to exceed the 95% of maxi-mum output power) and DC-DC efficiency (92%). According to the practical experi-ence, the battery minimum voltage can be assumed to be 370 V.

The rate of capacity of battery is based on specifications of battery suppliers. There are 30Ah, 40Ah, 55Ah power battery cell in the market. Therefore, 80Ah, 90Ah, 110Ah, 120Ah, 150Ah and 160Ah power battery can be got by parallel connection of same kind of battery cell.

Under ideal conditions, 40Ah lithium iron phosphate batteries can last 20 min of 3C discharging, the peak discharge current can get to 6C and sustain for 10 s. But considering the complexity of the vehicle environment, and battery's aging and decline, the battery peak discharge current should be kept less than 3C.

The technical features of 40Ah cell are shown as table 7:

Table 7.

Technical parameters of single battery.

Parameter	Value	Parameter	Value
Battery type	Lithium iron phosphate	Continuous discharge current	2C
Specification	40Ah	Peak discharge current	6C,10 s
Rated voltage	3.2 V	Continuous charge current	2C
Rated capacity	40 Ah	Peak discharge current	4C, 10 s
Internal resistance	< 2.5 mΩ	Mass	1.7 kg
Dimension	123*48.5*160 mm	Single voltage range	2.3–3.65 V

Design of fuel cell stack

According to the previous assured fuel cell power, the bus voltage range (340 ∼ 410 V) and existing fuel cell data, the main parameters of the stack can be preliminary designed, such as cell number, cell area and so on. In the Fuel Cell Stack of the article, the capacitance value of double layer capacitance is much smaller than 1F, at the same time, the activation and concentration polarizations is much less than 5 fold, the double layer effect diminished within milliseconds, so it is reasonable to exclude the double layer in this condition. Poor quality transmission will cause serious fuel cell performance loss,in the article, mass concentration loss of fuel cell is controlled to be less than the threshold so as not to affect the fuel cell performance. Of course, it is only a preliminary design for better simulation because we cannot take into account the factors such as cell uniformity. Therefore, the designed stack parameters are just the ideal values. 50kw FC stack characteristic is shown in Table 8 and Figure 4:

Table 8.

Fc stack characteristic parameters.

Parameter	Value	Parameter	Value
Current Density	1000 mA/cm2	Current	0∼320A
Rated power	60kW	Cell number	400
Peak power	80kW	Cell Area	320cm2
Voltage	264∼416V

Figure 4.

Fc stack characteristic curve.

Modeling of FCB power system

Modeling principle

As shown in Figure 5, the typical fuel cell bus powertrain system mainly consists of fuel cell engine, DC/DC Converter, battery, motor controller, vehicle controller, main gear reducer and so on. A DC/DC converter is installed between the fuel cell and the motor controller, and the terminal voltage of the fuel cell is matched with the voltage level of the system DC bus through the up-down voltage of the DC/DC converter. The motor controller is an integrated circuit that controls the motor to work in accordance with the set direction, speed, angle, and response time through active work. The motor controller converts the electric energy stored in the power battery into the electric energy required to drive the motor according to the instructions of the vehicle controller gear position, throttle, and brake, and controls the start-up braking, torque and speed of the motor. DC-DC power converters only perform up-down voltage functions without complex control circuits, while motor controllers usually have complex control circuits and control functions.This kind of powertrain has good dynamic and static characteristic: stable bus voltage, low demand for the motor and driving system; The battery can save the extra energy either generated by the FC or brake, improving energy utilization efficiency; moreover, battery can also provide power when the FC breaks down, improving the reliability of the vehicle.

Figure 5.

The structure of typical fuel cell bus power train system.

The basic idea of modeling: (1) Based on the principle of energy balance, we take power flow as the mainline, consider efficiency loss in each power flow link synthetically and construct sub model with efficiency figure; (2) The model mainly consists of power calculating section and power splitting section. the power flow between them is mainly backward and supplemented with forward; (3) Driver module is introduced into the power calculating section, in which forward-facing approach simulation is applied; the simulation method of power splitting section is mainly backward and supplemented with forward approach.

Based on the idea above, After comparing the advantages of both Forward-facing Approach and Backward-facing Approach simulation method,the FC power system model is built in Matlab/Simulink platform with forward-backward energy flow balance method, which is shown in Figure 6.

Figure 6.

Structure of the model.

As shown in Figure 6, the model mainly consists of power calculation module and power splitting module. Power calculating module includes the following sections: driving cycle, driver, motor & controller, hydraulic brake and vehicle and so on. The power splitting module includes the following sections: fuel cell engine, H2 supply, DC/DC converter, battery, accessory, energy management and so on. Moreover, post-process section is also included.

Driver module

Driver module includes the PID regulator, feedback brake force distribution unit and the gear shifting module, mainly used to regulate the output torque based on the speed tracking error, distribute feedback brake force and analog shifting behavior of the driver. In this module, according to the difference of target vehicle speed v* and actual speed v, drive torque T_d* and brake torque T_b*are calculated, and distribution of hydraulic brake force and regenerative brake force is done; moreover, it need to send out the Shift order to vehicle section according to shifting strategy.

Energy management system module

Energy Management System module includes power splitting module, SOC of power battery and regenerative braking module, mainly used to distribute power, to regulate SOC of power battery and to regulate the rate of repayment brake. It Calculates the total required power according to required driving power P_d* and required accessory power P_a*, distributes the power FC system and battery needs according to the energy distributing strategy.

Motor module

Motor module includes the speed - torque characteristic curve, as shown in Figure 7, the motor efficiency map and power calculation module. Speed - torque curve and the motor efficiency map, as shown in Figure 8, are achieved by looking-up the Table. It can be obtained from Figure 8 that when the motor speed is greater than 4000 r/min, the motor system efficiency is greater than 90%, and when the motor speed is greater than 2000 r/min, the motor system efficiency is greater than 80%. Power calculation module is used to calculate the electrical power requirements according to the motor required torque and motor speed. Motor module calculates the required power $P_d^{*}$ according to required driving torque $T_d^{*}$ and motor speed, sending the message to Energy Management System.

Figure 7.

Curve of motor torque with rotation speed.

Figure 8.

Curve of motor system efficiency with torque and rotation speed.

Vehicle module

Vehicle Module consists of the longitudinal dynamic model and the shifting module. Gear shifting module is used to perform the selection of the shift and the shift; longitudinal dynamics module is established based on the following formula:

$${\displaystyle \frac{T_{tq}\cdot i_g\cdot i_0\cdot {\eta }_T}{r}=Gf\cos \alpha +{\displaystyle \frac{C_D\cdot A}{21.15}{u}_a^2+G\sin \alpha +\delta m{\displaystyle \frac{d{u}_a}{dt}}}}$$

Fuel cell system module and battery module

Fuel Cell System module contains fuel-cell stack module and air compressor module, as shown in Figure 9. The fuel cell system works as follows: DC/DC converter convert the required power P_fr of fuel cell system according to its efficiency, and calculate the demand for the fuel cell engine power $P_s^{*}$ ; then check the FCE P-I Curve, find out the fuel cell current I* (the actual fuel cell current I), and input the current to the stack model to simulate the load current; at the same time, the demand current I* need to be converted to H₂ Flow Rate and Air Flow Rate, and after inquiring hydrogen storage, the hydrogen and air will be provided to the stack, to power the stack, in order to meet the power demand for vehicle to fuel cell. ²⁵

Figure 9.

Schematic of battery system module.

Battery module includes SOC calculation module and voltage calculation module, as shown in Figure 10. The principle of batter module is similar to fuel cell system module. As distributed power in Energy management system module is put into this module, battery current will be calculated. And then, through controlled current source, the current will be put into the battery module. Thus, the parameters of each single battery such as power, voltage and current will be got. Main parameters can be imported by an input interface.

Figure 10.

Schematic of battery system module.

DC-DC Convertor module contains efficiency plot and conducts power conversion,as shown in Figure 11.

Figure 11.

Curve of DC-DC efficiency with output power.

Auxiliary Equipments module outputs power requirements of air compressor for fuel cell stack, DCL and air conditioner, etc.

Simulation and comparative analysis

2010 World Expo FCB solution is a representative one provided by Tongji. The solution has been applied in the demonstration of fuel cell bus during the 2010 Shanghai World Expo. Real vehicle test data of the demonstration is used to verify the fuel cell bus power system model by comparison of simulation result and real vehicle test data.

Simulation of 50 kW solution

The energy management system includes three parts: power splitting, SOC management and regenerative braking. The power splitting strategy is dominant in this system Tables 9 to 14.

Table 9.

Simulation setting.

Parameter	Value	Parameter	Value	Parameter	Value
Vehicle mass	11700 kg	Half-load mass	15658 kg	Load	Half load
FC Engine mass	250 kg	Peak power	204.3 kW	Air Conditioner power	15 kW
Battery mass	816 kg	Mean power	20.06 kW	Other Accessory power	9 kW
H2 supply system	1000 kg	Driving cycle	Chinese City Cycle	Sample time	0.2s
32 people	1900 kg	Cycle distance	5.8 km	Brake Regeneration energy	10% to 20%

Table 10.

Key data of motor torque, drive power and speed.

Key data	value	Key data	value
Maximum drive power	176 kW	Proportion of Regeneration energy in total brake energy	8.77%
Maximum rotation speed	8290 r/min	Average efficiency of motor	89.5%
Maximum drive torque	326N·m

Table 11.

Key data of Bus, battery, FC and accessory power.

Key data	value	Key data	value
Maximum bus power	226 kW	Maximum FC Stack power	69 kW
Maximum discharge power of battery	168 kW	Maximum charge power of battery	−18 kW

Table 12.

Key data of Bus, battery and FC current.

Key data	value	Key data	value
Maximum bus current	607A	Maximum FC current	374A
Maximum discharge current of battery	425/2.7C (<2 s)	Maximum charge current of battery	−36

Table 13.

Key data of Bus, battery and FC voltage.

Key data	value	Key data	value
Minimum FC voltage	177V	Maximum battery voltage	407V
Minimum battery voltage	372V

Table 14.

Mileage and energy cost.

City cycle	H2 consumption	Variation of SOC	Energy consumption	H2 consumption	Efficiency of FCE	DC-DC Efficiency	Driving range
AC on	568g	−12.3%	2.9752 kWh/km	0.1727 kg/km	55.3%	93.7%	168 km
AC off	466g	−6.3%	2.0453 kWh/km	0.1184 kg/km	56.0%	92.8%	245 km

Building the power splitting strategy needs to meet the following three requirements: ²⁶

1. make FC work in the high efficient power range

2. SOC varies in the safe range which we set up

3. in the beginning, battery and FC work together in order to provide large power and protect FC from overloading

The power splitting strategy for 50 kW solution is shown in the Figure 12. This strategy is built by means of a series of sinusoidal functions. The curve changed slowly near the two points (20% and 60% of FC peak power). The efficiency of FC was high, working in range of 20%∼60%. The sinusoidal functions could meet the requirement.

Figure 12.

Fc power and total power.

FCB total power requirement in 50 kW solution is shown as Table 6. The FC stack characteristic is shown in Table 8 and Figure 4. The simulation results in the Chinese typical bus cycle are shown as following Figures 13 to 19.

Figure 13.

Vehicle speed. (a) Vehicle Speed Vehicle Speed is shown in Figure 13. (b) Motor Torque, Drive Power and Speed. (c) Bus, Battery, FC and Accessory Power. (d) Bus, Battery and FC Current. (e) Bus, Battery and FC Voltage. (f) Mileage and Energy Cost.

Figure 14.

Motor torque, drive power and speed.

Figure 15.

Bus, battery, FC and accessory power. Corresponding data from Figure 15 is shown as Table 11.

Figure 16.

Bus, battery and FC current. Corresponding data from Figure 16 is shown as Table 12.

Figure 17.

Bus, battery and FC voltage. Corresponding data from Figure 17 is shown as Table 13.

Figure 18.

Mileage and energy cost (AC ON).

Figure 19.

Mileage and energy cost (AC OFF). Corresponding data from Figure 18 and Figure 19 is shown as Table 14.

Demonstration of 2010 world expo FCB solution

The typical 2010 World Expo FCB Cycle data section was used in the demonstration. The actual motor input power, instead of model simulation result, was used as the input for power distribution section. Then the power, voltage, current of fuel-cell stack, battery and SOC signal of battery were compared with the test data after power dis-tribution.

Scheme and Major specifications of 2010 world expo FCB power system

Power system scheme: “FC + B” power hybrid dual-power driving system was shown in Figure 2. Vehicle parameters are shown as Table 2, fuel cell parameters are shown as Table 15, power battery parameters are shown as Table 16, and motor pa-rameters are shown as Table 17.

Table 15.

Main parameters of fuel cell engine.

parameter	value	parameter	value
Rated net output power	55 kW	Response time	13s
Output Voltage	280∼450V	Weight	250 kg
Hydrogen pressure	1.76∼3.2bar

Table 16.

Main parameters of power battery.

parameter	value	parameter	value
Rated voltage	384V	Continuous power	64 kW
Rated Capacity	80Ah	Peak power	192 kW
Continuous discharge current	160A	Weight	408 kg

Table 17.

Main parameters of motor and motor controller.

parameter	value	parameter	value
Motor type	Permanent-magnet synchronous	Rated rotation speed	4000 r/min
Rated voltage	375 V(DC)	Maximal rotation speed	11500 r/min
Rated power	42 kW	Peak torque	210N·m
Peak power	88 kW	Rated torque	100N·m
Weight	67 kg	Maximal Efficiency	93%

Test vehicle speed

Test vehicle speed is shown in Figure 20.

Figure 20.

2010 World expo FCB vehicle speed in expo cycle.

Comparative analysis of simulation result and real vehicle test data

Compare simulation result of FCB power system model in this article with real vehicle test data of 2010 World Expo FCB solution.

(a) Fuel Cell Stack power, voltage and current

In Figure 21, the power of fuel Cell₂ (the second fuel cell stack of 2010 World Expo FCB) is larger than real vehicle test data in some spots, which is the result of the changing energy management strategy in actual program.

Figure 21.

2010 World expo FCB fuel Cell₂ power of test and simulation.

Comparison of fuel cell voltage is shown as Figure 22, in which the minimal value of simulation is larger than Expo data because of the changing U-I characteristic of fuel cell stack.

Figure 22.

2010 World expo FCB fuel Cell₂ voltage of test and simulation.

The result of Figure 23 could be interpreted by making advantage of relation between P, U and I.

Figure 23.

2010 World expo FCB fuel Cell₂ current of test and simulation.

(b) Battery power, voltage, current and SOC

Comparison of battery power is shown as Figure 24, in which peak minus power is greater because of the delay of fuel cell power.

Figure 24.

2010 World expo FCB battery power of test and simulation.

Comparison of battery voltage is shown as Figure 25, in which simulation results do not accord with real vehicle test data sometimes. There are two reasons accounting for the phenomenon: (1) essential resistance of battery is actually changed with time, but the relation curve between them is not accessible. (2) due to the delay effect of filter, the simulation power of battery decreases faster than the actual one does, resulting in the fact that battery voltage rises faster than the actual data.

Figure 25.

2010 World expo FCB battery voltage of test and simulation.

From these figures above, although there are some local errors caused by real data sampling time interval and measuring error in data itself, it could be inferred that the simulation results of fuel-cell stack and battery fit the real vehicle test data well. Thus the fuel-cell power system model is in accordance with real situation and feasible Figures 26 and 27.

Figure 26.

2010 World expo FCB battery charge current of test and simulation.

Figure 27.

2010 World expo FCB battery SOC of test and simulation.

Conclusion

Using the forward-backward energy flow balance method on the Matlab/Simulink platform, the fuel cell bus power system model was established. Comparing the simulation results of the power system model with the 2010 World Expo FCB real vehicle test data, it is concluded that the simulation results of the power system are in good agreement with the real vehicle data, the power system model is in line with the actual situation and is feasible with high engineering use value.

Author biographies

Xinbo Chen received the PhD degree in mechanical engineering from Tohoku University, Japan, in 1995. From 1988 to 1995, he was an assistant professor with the School of Mechanical Engineering, Tongji University. From 1996 to 2002, he was an associate professor with the School of Mechanical Engineering, Tongji University. Since 2002, he has been a professor with the School of Automotive Studies, Tongji University. His research interests include electric vehicle electric drive system and power system. Email: austin_1@163.com.

Jian Zhong is a PhD student in Tongji University now. His research interests include electric vehicle electric power system and decision-making & path planning for autonomous vehicles Email: 17863964958@163.com.

Jingzhou Wei is a Postgraduatet in Tongji University now. His research interests include electric vehicle electric power system and Electric vehicle chassis technology.