Multi-mode control strategy for fuel cell electric vehicles regarding fuel economy and durability

Multi-mode control strategy for fuel cell electric vehicles regarding fuel economy and durability

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Multi-mode control strategy for fuel cell electric vehicles regarding fuel economy and durability Liangfei Xu a, Jianqiu Li a, Minggao Ouyang a,*, Jianfeng Hua a, Geng Yang b a

State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, PR China b National Laboratory for Information Science and Technology, Department of Automation, Beijing 100084, PR China

article info


Article history:

A proton electrolyte membrane (PEM) fuel cell system and a Li-ion battery (LIB) are two

Received 6 October 2013

power sources in a fuel cell electric vehicle (FCEV). The fuel cell system is composed of a

Received in revised form

fuel cell stack and subsystems for air/hydrogen supply and cooling water. The operation

27 November 2013

procedure of the fuel cell system can be generally separated into several processes, e.g.

Accepted 30 November 2013

starting up, normal/abnormal working and shutting down. In this paper, a multi-mode

Available online 25 December 2013

real-time control strategy for a FCEV is proposed. The strategy is established based on three typical processes (starting up, normal working, shutting down) of the fuel cell sys-


tem, taking the fuel economy and system durability into consideration. The strategy is

Proton electrolyte membrane fuel

applied into a platform vehicle for the 12th 5-year project of “the next generation tech-


nologies of fuel cell city buses”. Experiments of the “China city bus typical cycle” on a test

Electric vehicles

bench for the bus were carried out. Results show that, the fuel economy is 7.6 kg (100 km)1

Multi-mode strategy

in the battery charge-sustaining status. In a practical situation, a total driving mileage of

Energy management

more than 270 km can be achieved. Cycle testing also showed that, the degradation rate of

Fuel economy

the fuel cell was reduced to half of the original level. No performance degradation of the LIB


system was observed in the cycling test. Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.



In order to cope with issues of energy crisis and environmental pollution, vehicle electrification has been identified as an important way to achieve sustainable development for humans. Battery electric vehicles (BEVs), range-extended electric vehicles (REEVs), plug-in hybrid electric vehicles (PHEVs) and fuel cell electric vehicles (FCEVs) are common powertrain electrification approaches. Recently, noted disadvantages in working lifetime of the battery, combined with

range anxiety, make it hard for BEVs to be commercialized in the near future. The REEV or PHEV with internal combustion engine generating electric power when battery depletes can provide an extended range. However, the attendant use of fossil energy contributes to the energy crisis and environmental pollution. A proton electrolyte membrane (PEM) fuel cell system converts the chemical energy of hydrogen gas into electric power. Although most industrial hydrogen is produced from steam methane reforming (SMR) method with CO2 emission, this kind of centralized emission is much easier to be dealt

* Corresponding author. Tel.: þ86 10 62773437; fax: þ86 10 62785708. E-mail addresses: [email protected] (L. Xu), [email protected] (J. Li), [email protected] (M. Ouyang), [email protected] (J. Hua), [email protected] (G. Yang). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

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with than the distributed emission from traditional vehicles with internal combustion engines. The efficiency of SMR can reach 86%. The PEM fuel cell system is locally clean, efficient, and quiet, so it is favorable for transportation application. FCEV combined with a plug-in function of the battery pack can utilize clean hydrogen gas and cheap electric energy from the grid. Normally, in such a powertrain system, the fuel cell system works at a quasi-stable state near the high efficiency point, and the battery provides the dynamic power demand. Hydrogen consumption and durability of fuel cell system and battery are affected by the energy management strategy [1]. Generally, energy management strategies in the literature fall into several classes: rule-based strategies [2], off-line optimized strategies [3e5], online optimized strategies [6,7], and other control theory based strategies [8]. In a rule-based strategy, the power flow is controlled in accordance with several predesigned rules, which can be set up based on researcher experiences or some optimal results. An off-line optimized strategy is always designed for a global optimized problem, which aims at minimizing fuel consumption in a determined driving cycle. The non-causal nature of the off-line strategy limits its use in real-time controllers. In an online optimized strategy, a local cost function is defined and solved. It requires previous knowledge of the driving cycle. Therefore, it can be applied in practice. Recently, several papers addressing the energy management problem for fuel cell vehicles have appeared in the literature [9]. The powertrain architectures are similar. The fuel cell system serves as a low dynamic power source, and it is always combined with other power sources having quick response characteristics, e.g., battery packs [10e15], or supercapacitor systems [16e18], or both [19e22]. Rule-based control strategies are still favorable in real-time control situations [12,22,23]. Hwang et al. proposed a modebased strategy for a fuel cell/battery hybrid vehicle. Four operation modes are defined, and control rules for each mode are designed [12]. Fuzzy logic is a special rule-based strategy widely utilized in designing real-time control strategies [11,16,17,21]. Martinez et al. utilized a survey-based type-2 fuzzy logic system for a fuel cell hybrid system comprising a fuel cell system, a super-capacitor system, and a battery pack [16]. Li et al. compared hydrogen consumption with different powertrain configurations and control algorithms. Results show that by using a fuzzy logic controller (FLC), hydrogen consumption can be reduced by 5.9% in an Urban Dynamometer Driving Schedule (UDDS) driving cycle [21]. From a perspective of system dynamics, the energy management problem is an optimized problem in the low frequent domain. Different kinds of optimal control strategies can be utilized in this area [17,20,24e26]. Fadel et al. compared diverse strategies e a PID strategy, a fuzzy logic strategy, and an instantaneous strategy. Compared to a PID strategy, the fuzzy logic and instantaneous strategies can reduce hydrogen consumption by 4.4% and 7.4%, respectively [17]. Zheng et al. proposed a real-time optimized strategy based on Hamiltonian functions [24]. A novel equivalent hydrogen evaluation was introduced based on the study. Thounthong et al. studied energy management strategies based on modern control theories. Control algorithms for three voltage loops were designed for a fuel cell/battery/ultra-capacitor powertrain


system [20]. They also applied the flat system theory to the energy split problem of a fuel cell/solar cell/super-capacitor system for a building [25]. However, reducing energy consumption is not the only goal of fuel cell vehicles, durability, reliability, and vehicle dynamic performance should also be considered. Several papers paid attention to the multi-objective optimal problem. Yu et al. studied an active power-flow control strategy regarding energy cost and battery life. A real-time strategy was proposed based on the global optimized problem. The end value of the State of Charge (SoC) was kept at a relatively high level, so as to prolong the working lifetime [19]. Lin et al. researched an adaptive optimal control method for a fuel cell/supercapacitor powertrain. A constrained optimal control problem is defined first. It is converted to an unconstrained optimal problem using the penalty function method. Radial-basisfunction networks were utilized to solve the problem, and fuel consumption of the fuel cell, peak power, and instantaneous rate of change in power were limited in the simulation [18]. Kelouwani et al. studied a multi-criteria strategy targeted at minimizing hydrogen consumption as well as preserving battery life. High-power demand for the battery during stopand-go and the remaining energy in the battery were limited to a prescribed level. A 5% hydrogen saving was realized in the simulation [10]. From the recent literature review, we reached the following conclusions. 1) Control strategies based on optimal theories are still hot research topics in the energy management field for fuel cell electric vehicles. The multi-objective optimized problem is the most recent focus. Besides reducing hydrogen consumption, prolonging the working lifetime of the fuel cell and battery is taken into consideration. Consideration of durability is reflected by constraints in the optimized problem. Defining penalty coefficients in the optimized problem is the key issue. 2) Most papers are based on simulation in Matlab/Simulink. In some cases, small-scale experimental systems have been set up to verify control strategies. Bench or on-road testing results for control strategies in real fuel cell vehicles are strongly lacking. This paper studies a multi-mode real-time energy management strategy of a plug-in fuel cell electric vehicle for the multi-objective optimization problem. The major contributions found here are as follows. 1) A multi-critical constrained optimized problem regarding fuel economy and durability of fuel cell and battery is defined. And a multi-mode strategy is proposed to solve the problem. 2) Bench testing results for 20 cycles for a real fuel cell/battery powertrain of a plug-in city bus are shown. The rest of the paper is organized as follows. In Section 2, we introduce a theoretical model describing the multiphysical-based powertrain system. Section 3 describes the optimization problem in the FCEV regarding fuel economy and system durability at the meanwhile. Section 4 introduces


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multi-mode control strategy for the FCEV. In Section 5, we present the cycle testing results to show the effectiveness of the strategy. Finally, in Section 6 we provide conclusions.


battery hybrid city bus. Lithium-ion battery packs can be charged from the grid, so the bus is also called a plug-in fuel cell vehicle. The Li-ion battery serves as the primary power source, and the PEM fuel cell works as the secondary power source. A d.c. converter is installed to link together a fuel cell system, a Li-ion battery, and an a.c. inverter. The d.c. converter is a key component in the powertrain, because it regulates the output power of the fuel cell system. And it is regarded as the actuator of the energy management strategy [27e30]. The length of the city bus is 12 m, and the unloaded mass is about 13 tons. According to the requirements of public transportation, the maximal vehicle velocity is designed to be

Theoretical model for the powertrain

In order to overcome the technical bottlenecks and accelerate the commercialization of fuel cell vehicles in China, a platform vehicle of the 12th 5-year project named “the next generation technologies of fuel cell city buses” was built up. Fig. 1(a) illustrates the powertrain structure of the fuel cell/

(a) External ROM

Digital Signals

Ine rfa ce


Inner SRAM Inner Flash MPC561


Operation mode switch module

Drive circuit

Output signals

Primary control module

Analog Signals

Filt er


Signal processing, fault diagnosis and tolerant control module



On line monitoring

CAN receive/transmit

Online programming


(b) Fig. 1 e (a) Powertrain structure of the fuel cell/battery electric vehicle, (b) principle of the digital core.

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80 km h1, and acceleration from zero to 50 km h1 takes less than 25 s. The vehicle is equipped with a LIB of 63 kWh, and several high pressed hydrogen tanks (35 MPa) with a stored hydrogen mass of around 20 kg. Table 1 shows primary parameters of the fuel cell/battery electric vehicle. The fuel cell/battery electric vehicle is a typical complex mechatronics system with multi energy domains. The energy flow is controlled by the information flow, which is coordinated by a vehicle control unit (VCU), as shown in Fig. 1(a). A distributed networked control system is designed for the fuel cell city bus, and the VCU is the core of the networked system. Input signals to the VCU include: 1) analog signals such as position signals of the accelerating and brake pedals, 2) shift signals, 3) switch signals such as on/off command for the fuel cell system, and 4) other digital signals like hydrogen leakage warning signal. Output signals from the VCU are some drive signals for relays. Besides, the VCU communicates with other controllers through a Controller Area Network (CAN) bus. The VCU receives information from the fuel cell system (FCS), the d.c. converter controller (DCC), the LIB management system (BMS), and the electric motor controller (MCU). The received information includes voltage, current and temperature of each component, as well as some other status information for a specific component, e.g. SoC of the battery, rotational speed and torque of the electric motor. The VCU sends control commands to the FCS, the DCC and the MCU, including on/off commands for the fuel cell system and the d.c. converter, target power of the fuel cell system, target current of the d.c. converter and target torque of the electric motor. Fig. 1(b) illustrates the principle structure of the VCU. Interface/drive/communication circuits are designed for the peripheral signals. A microchip of MPC561 is chosen as the digital core. The controller software includes several parts, the hardware driver codes, the signal processing module, the fault diagnosis and tolerant control module, the operation mode switch module and the primary control module. The primary control module is the most important algorithm within the

VCU to coordinate the energy flow among all the components of the powertrain system, and it is also called the energy management strategy in some cases. The input electric power of the d.c. to a.c. inverter for the electric motor to drive the vehicle Pm is represented by Equation (1) when the vehicle drives. mgfuveh cos a þ 0:5CD Aru3veh þ dmuduveh =dt þ mguveh sin a ¼ Pm hT hmd

mgfu cos a þ 0:5CD Aru3 þ dmudu=dt þ mgu sin a ¼ Pm =ðhT hmb Þ þ Pfric

Vehicle weight (kg) Maximal velocity (km h1) Driving distance in urban cycle (km) Wheel radius (m) Front area (m2) Coefficient of air resistance Coefficient of rolling resistance Final drive ratio Rotating mass coefficient Rated power of the electric motor (kW) Rated net power of the fuel cell system (kW) Capacity of the LIB (A h) Stored hydrogen (kg) Hydrogen pressure (MPa) Bus voltage range (V) Bus rated voltage (V)

13,000 (unloaded)/ 18,000 (full load) 80 250 0.475 7.95 0.7 0.012 6.3 1.1 100 50 175 20 35 260e410 345


where hmb is brake efficiency of the electric motor, and Pfric is friction power during the braking process by the traditional brake system. Transmission efficiency hT can be regarded as a constant, and drive/brake efficiencies hmd/hmb of the electric motor are functions of rotational speed and mechanical torque and are slightly influenced by the input voltage in the normal working range. The power balance between the two power sources can be expressed as follows. Pm þ Paux ¼ Pfce hdc þ Pbat


where Paux is auxiliary power of the vehicle. It is consumed by several electric components, e.g. the electric steering system and the electric air conditioning system. The average auxiliary power of the vehicle is between 3 and 13 kW, depending on driving cycle and working conditions [31]. Pfce is net output power of the fuel cell system, Pbat is output power of the battery, and hdc is efficiency of d.c. converter. Efficiency of the d.c. converter is a function of output power, and it changes slightly, between 90 and 95%. Hydrogen consumption by the PEM fuel cell system can be calculated as follows. Zt2



where m is vehicle mass, g is acceleration due to gravity, f is rolling resistance coefficient, uveh is vehicle velocity, a is road angle which may be uphill (a > 0) or downhill (a < 0), CD is air drag coefficient, A is front area, r is air density, hT is transmission efficiency, and hmd is drive efficiency of the electric motor, d > 1 is the inertia mass coefficient. When the vehicle brakes, the vehicle longitudinal dynamics can be expressed as follows.

Table 1 e Parameters of the fuel cell city bus. Name (unit)


DmH2 ¼

  Pfce = hfce LHV dt



where DmH2 is accumulated hydrogen consumption (kg), LHV is low heat value of hydrogen (121 MJ kg1), and hfce is net efficiency of the fuel cell system. Parameters t1 and t2 stand for the starting and ending time for calculating the consumed hydrogen. Defined as the division of net output power by _ H2 Þ, net efficiency of the hydrogen energy hfce ¼ Pfce =ðLHV$m fuel cell system can be expressed as a function of fuel cell net power, which can be calculated using a cubic function hfce ¼ aP3fce þ bP2fce þ cPfce þ d. Net output power Pfce is the difference between fuel cell total output power and fuel cell auxiliary power. Pfce ¼ Pfc  Pfcaux


where Pfc is fuel cell output power and Pfcaux is fuel cell auxiliary power required by the blower and water pumps.


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Fig. 2(a) shows the relationship between the fuel cell net efficiency hfce and net output power Pfce, and the relationship between Pfcaux and Pfc, according to experimental data. The rated net power of the fuel cell system is 40 kW. It is composed of 620 cells, each cell with an effective area of 270 cm2. The average net efficiency of the fuel cell system reaches 57% when Pfce ˛ [10, 40] kW. The auxiliary power Pfcaux changes between 1 and 5.3 kW nonlinearly along with fuel cell power increasing from 2.2 to 57.6 kW. Ignoring the mass transfer resistance and the anodic over potential, the relationship between fuel cell voltage and current can be described as follows [32].   Vfc ¼ Vfc0  Rfc Ifc  b ln Ifc


where Vfc is the fuel cell voltage, Vfc0 is the open-circuit voltage, Rfc is the inner resistance, b is the Tafel slope. However, the relationship between Vfc/Ifc and Pfc can’t be formulated analytically basing on Equation (6). In the modeling, we set up the nonlinear relationships according to experimental data from the test bench, as shown in Fig. 2(b). Fig. 2(b) presents the relations between Vfc/Ifc and Pfc, as well as the VeI

curve for each cell. For the whole system, the output voltage changes between 420 V and 580 V, and the output current fluctuates between 138 A and 3 A, while the fuel cell power decreases from 57 kW to 3 kW. The voltage for one cell changes between 0.68 and 0.94 V, whereas current density decreases from 0.5 to 0.01 A cm2. Considering the slow dynamic processes in the fuel cell system, a first-order model for output power is formulated: Pfce ¼

Pfce;tg ss þ 1


where Pfce,tg is target net output power of the fuel cell system, and s is time constant of the fuel cell system (ws). The electric energy consumed by the battery pack is determined by the charging/discharging current Ibat, which can be calculated based on a Rint model [33] as the following equation: Ibat ¼


pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Vocv  4Rbat Pbat 2Rbat


where both of open-circuit voltage Vocv and battery resistance Rbat are functions of the SoC. 

Vocv ¼ f2 ðSoCÞ Rbat ¼ f3 ðSoCÞ


Battery SoC can be calculated as follows [33]. Ztk SoC ¼ SoC0  0

Ibat hcolm dt Qbat


where SoC0 is initial SoC, Qbat is battery capacity, hcolm is column efficiency, t ¼ 0 corresponds to the initial SoC, t ¼ tk corresponds to the current SoC. A manganese-based material is used in the Li-ion battery. The battery package is composed of 480 cells. Each cell features a capacity of 35 A h, a voltage range of 2.7e4.2 V, and a rated voltage of 3.6 V. The cells are connected in a 5P96S (5 parallel 96 serial) method. As a result, the battery package features a capacity of 175 A h, a voltage range of 260e400 V, and a rated voltage of 345.6 V. Fig. 3 presents the relationship between Vocv, Rbat, and SoC. The open-circuit voltage changes between 320 and 400 V. Charge and discharge resistances are similar. They reach 0.1 U when battery SoC is low, and they reduce to half when battery SoC is higher than 20%.

Fig. 2 e Characteristics of a 40 kW rated fuel cell system: (a) net efficiency vs. net output power, auxiliary power vs. fuel cell power, (b) voltage, current vs. power, cell voltage vs. current density.

Fig. 3 e Battery characteristics.

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Energy consumption by the Li-ion battery includes two parts: the charging/discharging power to the outside, and the power consumption on the inner resistance. In summary, it can be expressed as in Equation (11): Ztk Ebat ¼

Vocv Ibat dt


primary means of prolonging the working lifetime. In order to preserve working lifetime of the battery pack, the reduction of high charging/discharging current during acceleration or deceleration and the limitation of minimum State of Charge (SoC) to a prescribed level are considered. Taking hydrogen consumption and fuel cell/battery durability into consideration, an optimization problem can be defined as follows.


A positive value of Ebat stands for a discharging energy from the battery, and a negative value means a charging energy into the battery. If the open-circuit voltage changes slightly, this expression can be further simplified to Ebat ¼ Vocv Qbat DSoC=hcolm


The performance of the fuel cell system decays with working time. A degradation rate of 2e10 mV h1 is commonly accepted for most applications [34]. Degradation happens because of failures in the membrane, the electro-catalyst and catalyst layer, the gas diffusion layer, the bipolar plate, or the sealing gasket. The main causes of stack degradation are carbon corrosion and Pt dissolution. Carbon corrosion occurs during start-up processes because of high potential (>0.85 V). Cathode Pt dissolution happens in the idling process because of high potential, and in the load cycling process because of potential cycling [35,36]. Therefore, from a perspective of system dynamics, there is a nonlinear relationship between degradation rate 3fc (mV h1) and cycle information,   3fc ¼ kp P01 n1 þ P02 n2 þ P03 t1 þ P04 t2


where kp is the accelerating coefficient by reasons of air quality. The four parameters P01 , P02 , P03 and P04 are deteriorate rates resulted in by large load change cycling, start-stop cycling, idle condition and high-power load condition, separately. Other four practical load parameters n1, n2, t1 and t2 are load changing times, start-top times, idle time and high-power load time per hour [37]. On the other hand, not only does the fuel cell system decay in the fuel cell electric vehicle, but also does the LIB. Working temperature, operation voltage, and depth-ofdischarge (DoD) are the primary reasons for battery degradation. Similarly, there is a relationship between degradation rate of the battery capacitor 3bat (A) and other factors:   3bat ¼ f2 Tbat ; Vmax ; Vmin ; Idis_max ; Ichg_max ; DoD


where Tbat is working temperature of the battery, Vmax and Vmin are maximal and minimal operational voltages, and Idis_max and Ichg_max are the maximal discharge and charge current.

3. Optimization problem regarding fuel economy and system durability Manipulating a fuel cell/battery hybrid powertrain involves controlling the d.c. converters and splitting power between the two power sources. The response time of the d.c. converter is very quick, so in the energy management problem, steady/transient-state errors can be ignored. For the PEM fuel cell system, avoiding high voltage and reduction of frequent on/off operations, limitation of high-power demand during acceleration, and limitation of large loading rate are the


min J0 ¼

N1 X 

_ H2 ðuðkÞÞDT m



s.t. 8 Vlowerbat < Vbat ðkÞ < Vupperbat > > > > < Imaxchg < Ibat ðkÞ < Imaxdis Vlowerfc < Vfc ðkÞ < Vupperfc > > SoCðNÞ ¼ SoCtg > > : jDuðkÞj < DPfc


_ H2 is where u(k) ¼ Pfc(k) ˛ [0, Pfc,max] is the control variable, m hydrogen consumption rate (kg s1), DT is control cycle determined by the embedded controller, DPfc is allowed power change rate of the fuel cell system during operation, SoCtg is target end value of battery SoC, Du(k) is the power change rate of the fuel cell system. Variables Vupperbat and Vlowerbat are upper limit voltage and lower limit voltage of the battery, and Imaxdis and Imaxchg are maximal discharge and charge currents of the battery, respectively. Variables Vupperfc and Vlowerfc are upper limit voltage and lower limit voltage of the fuel cell, respectively. Equations (15) and (16) describe a standard optimization problem with constraints. According to optimal control theory, it can be converted to an unconstraint optimization problem by adding some penalty functions. The new cost function J for assessing the performance of the fuel cell electric vehicle can be written as follows. J¼

N1  X

 2  _ H2 ðuðkÞÞDT þ L1 ðkÞ þ L2 ðkÞ þ P1 DuðkÞ  DPfc m


 2 þ P2 SoCðNÞ  SoCtg


where P1 and P2 are positive weight coefficients, and L1(k) and L2(k) are penalty functions defined as follows: 8  2 2 > L1 ðkÞ ¼ R1 Vbat ðkÞ  Vupperbat þ R2 ðVbat ðkÞ  Vlowerbat Þ > >   > 2 2 > < þR3 ðIbat ðkÞ  Imaxdis Þ þ R4 Ibat ðkÞ  Imaxchg  2  2 L2 ðkÞ ¼ Q1 Vfc ðkÞ  Vupperfc þ Q2 Vfc ðkÞ  Vlowerfc > > > > > : DuðkÞ ¼ uðkÞ  uðk  1Þ; k  1 Duð0Þ ¼ 0


where Ri, i ¼ 1e4, Q1, Q2, are weight coefficients. The six weight coefficients are defined as follows: 8 R1 > 0 > > > > R1 ¼ 0 > > > > > R2 > 0 > > > R2 ¼ 0 > > > > R >0 > > < 3 R3 ¼ 0 R4 > 0 > > > > > R4 ¼ 0 > > > > Q >0 > > 1 > > Q1 ¼ 0 > > >Q > 0 > > : 2 Q2 ¼ 0

if if if if if if if if if if if if

Vbat > Vupperbat Vbat  Vupperbat Vbat  Vlowerbat Vbat > Vlowerbat Ibat > Imaxdis Ibat  Imaxdis Ibat  Imaxchg Ibat > Imaxchg Vfc > Vupperfc Vfc  Vupperfc Vfc  Vlowerfc Vfc > Vlowerfc



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The target of the optimization problem is to find the optimal control sequence {u(k)}, so that J is minimized. The optimization problem defined in Equations (17)e(19) takes the most important factors that influence durability of the fuel cell/battery hybrid system into consideration. The variable L1 reflects the impact of battery current/voltage/power on working lifetime, the second variable L2 reflects the impact of fuel cell voltage (especially high voltage) on its lifetime. Penalty coefficient P1 shows the influence of fuel cell load cycling on performance degradation, and P1 shows the end SoC value on battery lifetime. This optimized problem can be solved using several numerical methods, e.g. dynamic programming [38]. Lin et al. employed radial-basis-function (RBF) networks to construct an adaptive optimal control (AOC) algorithm [18] for a similar optimal problem. However, neither the method of dynamic programming nor the AOC algorithm is sufficiently simplified for real-time applications. In our study, we propose a multimode control algorithm basing on the operation processes of the fuel cell. The optimization of fuel economy and system durability is mainly considered in the normal working status. In the other cases because the time percentages can be ignored compared to that of the normal working status, only the system durability is considered.

Generally speaking, the operation procedure of the fuel cell system can be divided into four stages: starting up, normal working, abnormal working and shutting down. For the abnormal working status, and a fault diagnosis and tolerant control strategy is always specially designed [39]. Thus, the real-time multi-mode strategy presented in this paper takes the other three statuses into consideration. It includes five algorithm blocks: start-up process control, stop process control, optimal power allocation in normal operation, closed-loop control for the power, and voltage regulation, as shown in Fig. 4. Fig. 4 illustrates the relationship among these five blocks. The entire operation process can be divided into three abovementioned stages: starting up, shutting down, and normal operations. The target power of the fuel cell system Pfctg is calculated according to the driver commands and statuses of each component in the three operation modes. The power control algorithm is designed for setting fuel cell output power in the target value. It outputs the first target current of the d.c. converter Idctg1. The voltage regulation algorithm is designed for limiting the operating voltage within the upper and lower bounds. The outcome of the algorithm is the final target current of the d.c. converter Idctg2.


In the starting up process, the target of the control algorithm is to regulate the increasing trajectory of the water cooling temperature, which reflects the inner status of the fuel cell system. According to the Nernst equation [40], the output power of the fuel cell system is limited when the inner temperature is not high enough. On one hand, the output power of the fuel cell system should not exceed the limitation value determined by the temperature. On the other hand, there will not be enough energy to heat the fuel cell stack if the output power of the fuel cell system is too low. The dynamic heating process of the fuel cell system can be expressed as follows [41]:

4.1. Power control of the fuel cell system in starting up process

Real-time multi-mode strategy

According to the analysis in the former paragraphs, in order to prolong the working lifetime of the fuel cell and reduce hydrogen consumption, it is necessary to  make the fuel cell work in the high efficient range with steady status;  make the fuel cell not work in the high voltage range;  get an optimal transient control strategy for power changing. Similarly, in order to prolong the working lifetime of the battery, it is necessary to

Pfc kfc ¼ C

Electric motor status Battery status Fuel cell status

Starting up process control Shutting down process control Optimal power split in normal operation



Target power of the fuel cell Pfctg


where Pfc is fuel cell stack power, kfc (z1  hfc) is heat conversion efficiency of the fuel cell system, C is thermal capacity of the fuel cell, Q is radiating coefficient of the fuel cell, and Tfc is fuel cell temperature. T0 is the environmental temperature, and it is also the initial temperature of the fuel cell system. A feed forward and feedback control algorithm is designed to realize a linearly increasing fuel cell temperature, shown as in Fig. 5.

 make the fuel cell deliver the average output power of the powertrain, so that the battery can only provide a limited dynamic power;  control the end value of the battery SoC. The end value of the battery SoC corresponds to the DoD, which is a very important fact that affects the battery working lifetime.

Driver command

  dTfc þ Q Tfc  T0 dt

Target current of the d.c. converter

Target current of the d.c. converter

Voltage regulation

Power control Idctg1


Fig. 4 e Structure of the real-time multi-mode strategy.



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This optimization problem can be solved using a DP algorithm for a determined driving cycle. However, we have another choice, Pontryagin’s minimum principle (PMP) strategy [42,43]. This method is a necessary but not sufficient condition of DP strategy. It introduces a co-state variable and turns the overall optimization problem into an instantaneous optimized problem. According to PMP, optimal power Pfc at each time is derived according to the following equation:

The target is to control fuel cell temperature to increase it linearly to a certain level, Tfc_tg ¼ T0 þ kt. The outcome of the start process control algorithm is the target power Pfctg_st, which is composed of two parts, the feed forward part Pfctg_1 and the feed backward part Pfctg_2. The feed forward part meets the average power requirement for the powertrain, so the battery sustains it charge: Pfctg_1 ¼

Pm þ f ðSoC; Tbat Þ ðss þ 1Þhdc


Pfc ¼ arg min H

The feed backward part Pfctg_2 is formulated with a proportional integral (PI) algorithm:   Pfctg_2 ¼ kp T0 þ kt  Tfc þ kI


 T0 þ kt  Tfc dt

The variable H is the Hamiltonian function, which is defined as follows [42]: 8 Ibat _ H2  l hcolm


where t stands for working time, t ¼ 0 is switch-on time of the fuel cell system, and Kp and KI are the proportional and integral coefficients, respectively. The target output power in the start-up process Pfctg_st is the sum of the upper two parts, with constraints of maximal output ability determined by fuel cell temperature Pfcmax:     Pfctg_st ¼ min Pfctg_1 þ Pfctg_2 ; Pfcmax Tfc

Power control in normal operation


Optimal power allocation

lhbat Ibat kocv pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi l_ ¼  2 Qbat Vocv  4Pbat Rbat 0

min J ¼

N1 X

_ H2 ðuðkÞÞDT þ P2 SoCðNÞ  SoCtg m



Power constraints due to transient process

According to Section 4.2.1, optimal output power of the fuel cell system is allocated. It is not a constant but changes dynamically. There are several papers focusing on transient process control. Myers et al. suggested a slow-down fast-up (SF) method for transient process control. However, other


, Ibat hcolm SoC ¼  Qbat


Staring up process conrol

Pm Pfctg_1 +

SoC, Tbat


Pfctg_st Kp







Power control

Voltage regulation

+ ∫





where kocv is the linear coefficient for the open-circuit voltage and battery SoC. When an initial value of l is set, the co-state variable l can be calculated based on Equation (28). The determined space [0, Pfcmax] can be discretized, and the optimal power can be chosen according to Equations (26)e(28). By adjusting the initial value of the co-state variable l0, the end value of the battery SoC can be adjusted. A suitable value of l0 is required, if we want to get a long working time of the battery by keeping the DoD at a suitable level.




lh kocv B 1 C  1A ¼  bat @pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2Rbat Qbat 1  4ðPm  uÞRbat Vocv

After the fuel cell system is fully heated, the hybrid powertrain switches to normal work mode. In this mode, we need to split the power requirement between the fuel cell system and the battery so as to minimize the cost function described in Equation (17). In the real-time strategy, factors in Equation (17) are considered in several blocks, e.g. the “voltage regulation” block takes care of L1 and L2; the “transient process control” block considers power change rate. Therefore, the optimization problem described by Equations (17)e(19) can be simplified as 0


In the plug-in vehicle, the battery SoC normally changes in the range of [20%, 100%]. In this region, resistance can be regarded as a constant, and the open-circuit voltage can be regarded as changing linearly with SoC. Thus, the second part of Equation (27) can be simplified as follows:




Fuel cell system

Fig. 5 e Details of the starting up process control algorithm.



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studies show that if output power of the system decreases too fast, the membrane will be decomposed [44]. Therefore, both increasing and decreasing rates of the output power should be limited. When the optimized output power Pfc is larger than the current output power Pfc, then the target power of the fuel cell system Pfctg_nl in the normal process can be calculated as follows.   Pfctg_nl ðkÞ ¼ min Pfc ðk  1Þ þ DPfc_add ; Pfc ðkÞ


where DPfc_add > 0 is maximal rising rate of the fuel cell power. Otherwise, when the optimized output power Pfc is smaller than the current output power Pfc, the target power of the fuel cell system Pfctg_nl in the normal process can be calculated as follows:   Pfctg_nl ðkÞ ¼ max Pfc ðk  1Þ  DPfc_minu ; Pfc ðkÞ


where DPfc_minu > 0 is maximal decreasing rate of the fuel cell power.

the accumulated water in the anode channel is brought out by hydrogen. And then the fuel cell system can be switched off.


Closed-loop algorithm for output power regulation

According to Sections 4.1e4.3, the target power of the fuel cell system is calculated in a different working mode. By manipulating the output current of the d.c. converter, output power of the fuel cell system can be controlled. An open-loop algorithm is widely used in regulating the output power of the fuel cell system as follows: Idctg_open ¼ Pfctg hfcele hdc =Vdc


where Idctg_open is the target current of the d.c. converter in the open-loop algorithm, Vdc is the actual output voltage of the d.c. converter (equal to the voltage of the battery). Parameter hdc is the efficiency of the d.c. converter, and hfcele is the electric efficiency of the fuel cell stack, which is defined as follows: hfcele ¼ Pfce =Pfc


Stopping process control of the fuel cell

In the stopping process, the fuel cell system cannot be shut down directly. Fig. 6 illustrates a typical shut-down process, which is coordinated by the vehicle control unit (VCU) and the fuel cell control system (FCC). Normally, after receiving the “shut down” command from the VCU, the FCC will switch into the shut-down mode and send a message back to the VCU. The output power of the fuel cell system will be reduced slowly to a certain value. The transient process of the output power of the fuel cell system in this procedure should guarantee that no water flooding or drying occurs in the electrolyte membrane. Typically, a maximal decreasing power rate is calculated by the FCC to limit the output power. Pfctg_sp ðkÞ ¼ Pfc ðk  1Þ  DPfc_sp


where DPfc_sp > 0 is the maximal decreasing rate of the fuel cell power in the stopping process. After the power is reduced,


Assuming the output current of the d.c. converter can be accurately controlled, and the output voltage of the d.c. converter can be accurately measured, the fuel cell output power Pfc can be calculated as follows:   Pfc ¼ Idc Vdc = hdc hfcele


where Pfc and Pfce are the fuel cell system power and net output power. However, the two efficiencies hdc and hfcele can change in the operating process because of variations of system conditions, e.g., temperatures. Therefore, there is always a difference between the actual and the target value of the output power of the fuel cell system. This problem can be solved by using a closed-loop control algorithm. Fig. 7 presents the proposed closed control algorithm with a forward þ feed backwards structure. In Fig. 7, there are several variables. Parameter Kf is the forward coefficient, Kp and KI are the proportional and integral

Shut down command from the Driver Shutting down process control

VCU received CAN

VCU received

Pfctg_sp calculated by VCU

Voltage regulation

Power control


FCC switched into shutdown mode

Can the Yes system be shut down?

ΔPfc_sp calculated by FCC

Shut down

No Fuel cell system

Fig. 6 e Details of the shutting-down process control logic.

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coefficients in the feed backwards algorithm, respectively, Ksys is the system coefficient. The four coefficients can be written as follows: 8 > > > <

Kf ¼ hfcelehdc =Vdc  Ksys ¼ Vdc = hfcele hdc   > KP ¼ fP DPfc > > : KI ¼ fI DPfc


where DPfc ¼ Pfctg  Pfc is the power difference between the target and actual value of the fuel cell system. The target current of the d.c. converter in the closed-loop algorithm Idctg1 can be written as follows: Zt Idctg_1 ¼ Pfctg Kf þ KP DPfc þ KI

DPfc dt



The transfer function G(s) between the power difference and the target power can be expressed as follows:   GðsÞ ¼DPfc =Pfctg ¼ hfcele hdc  hfcele hdc s= h  i  KI Vdc þ KP Vdc þ hfcele hdc s


where s is the complex variable in the transfer function. The system illustrated in Fig. 7 is stable because the root of the transfer function in Equation (37) is less than zero. Thus, the stable power difference always equals to zero when the target power is a constant. Parameters of Kp and KI can be optimized according to the time constant and the stable difference in a linearly increasing process. Paper [45] describes formulas for choosing suitable parameters. By using this method, the output power of the fuel cell system can be controlled within a relative error of 2.5%.


Voltage regulation

As referred to in Ref. [35], the output voltage of the fuel cell system is critical to its working lifetime. Carbon corrosion occurs in an obvious way in the situation of high potential. It is therefore very necessary to control the working voltage of the fuel cell system under an upper limit Vfc_max. Meanwhile, a low voltage of the fuel cell system means the output power exceeds the affordable ability of the fuel cell. Thus, a lower limit Vfc_min is also required. The output current of the d.c.

Feed forward coefficient Kf


converter should increase if the output voltage exceeds the upper limit. And the current should decrease if the voltage falls below the lower limit. Fig. 8 presents the control logic in the algorithm.


Experimental results


The control algorithm in Matlab/Simulink

Fig. 9 presents the control algorithm developed in Matlab/ Simulink. The algorithm is converted into C-code using the real-time workshop (RTW) tool, integrated with hardware driver codes for MPC5644, and finally downloaded into an embedded controller [46]. The control cycle for the real-time algorithm is 10 ms. Key parameters for the real-time algorithm are listed in Table 2.



Δ Pfc




Fuel cell system Ksys

Fig. 7 e Closed-loop control algorithm for fuel cell output power.

Experiments on test bench

The powertrain system for the plug-in fuel cell city bus was tested on the bench for the “China city bus typical cycles” [47]. Results are shown as follows.


Starting/stopping processes

Fig. 10(a) and (b) presents the transient profiles of the fuel cell system during starting up and shutting down processes. As described in Section 4.1, the output power of the fuel cell system in the starting process is controlled in such a way that the power requirements for both the electric motor and the battery are fulfilled. The starting process takes almost 15 min, so the cooling water temperature increases gradually from 6 to 40  C. The output power of the fuel cell system Pfc is composed of two parts, the feed forward part Pfctg_1, as expressed in Equation (21), and the feed backward part Pfctg_2, as expressed in Equation (22). The three variables are illustrated in the lower part of Fig. 10(a). The output power of the fuel cell system changes between 10 and 40 kW, the feed forward component Pfctg_1 almost always stays between 20 and 40 kW, and the third variable Pfctg_2 fluctuates between e20 and 20 kW. Fig. 10(b) shows the shutting-down process. After receiving the shutting-down command from the vehicle driver at 1301 s, the output power of the fuel cell system decreases linearly at a rate of e1.87 kW s1. The shutting-down process takes about 15 s, and the cooling water temperature keeps almost constant around 39  C. During the shuttingdown process, the voltage increases from 463.5 to 618 V, and the current decreases from 77 to 3.5 A.


Non-linear PI control Kp+KI/s


The normal operating process

Fig. 11(a)e(d) presents system dynamics in the normal operating process for two driving cycles. Fig. 11(a) shows the two profiles for the vehicle velocity and the electric power of the electric motor. The maximal velocity is 60 km h1, and the driving time for one cycle is 21.8 min. The maximal input power of the electric motor is 156 kW, and the maximal recycled power is about 32 kW. Fig. 11(b) illustrates the power split situation in the two cycles. As presented in Section 5.2.1, the starting up process of the fuel cell system takes about 15 min. After start up, the


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Yes Is Vfc

Idctg2(k)= Idctg1(k)

Is Vfc>Vfcmin?

Yes No


Idctg2(k+1)= Idctg2(k)+ΔIdc

Idctg2(k+1)= Idctg2(k)-ΔIdc


No Yes Is Vfc
Is Vfc>Vfcmin?

Fig. 8 e Structure of the voltage regulation logic.

system switches into normal operation mode. Output power of the fuel cell system changes between 15 and 45 kW, and output power of the d.c. converter changes between 10 and 40 kW. The battery provides the dynamic power requirements, and it fluctuates between 64 and 130 kW. The fuel cell system and the battery are the key components in the powertrain. Fig. 11(c) describes the dynamics of the two components. After 15 min, the fuel cell system switches into normal operation mode. The fuel cell voltage was kept between 460 and 530 V, corresponding to 0.74 and 0.85 V for each cell. A small time window of around 20.5 min is enlarged in the figure, in order to show the process of voltage regulation when the fuel cell voltage hits the upper bound. When the voltage exceeded the upper bound, the output current increased so as to pull the voltage down. The average power of the fuel cell system in the enlarged window was

16 kW. The two dashed lines are upper and lower limits for the fuel cell voltage, 527 V (0.85 V for each cell) and 372 V (0.6 V for each cell), respectively. The output current of the fuel cell system changes between 25 and 100 A. In the normal operation mode, the output voltage can be limited within the suitable range so as to avoid performance degradation. The lower part of Fig. 11(c) shows the performance of the battery. As a manganese-based material is used for the battery cell, the maximal allowed discharge current can be 500 A, and the maximal allowed charge current can be 300 A. In cycle testing, the maximal discharge current is 350 A (2 C), and the maximal charge current is 175 A (1 C). The battery works in a safe range. Fig. 11(d) presents the inner statuses of the two components and the distribution of the working points of the fuel cell system. For a plug-in vehicle, the energy management

Fig. 9 e Real-time multi-mode energy management strategy in Matlab/Simulink with a control cycle of 10 ms.

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Table 2 e Parameters for the real-time strategy in Matlab/ Simulink with a control cycle of 10 ms. Name (unit) Step power of fuel cell system in the shutting-down module DPfc_sp (kW) Feed forward coefficient in the closed-loop control algorithm Kf (103 V1) Feedback coefficient in the closed-loop control algorithm Kp (103 V1) Feedback coefficient in the closed-loop control algorithm KI (103 V1 s1) Upper limit of fuel cell voltage in the voltage regulation module Vfcmax (V) Lower limit of fuel cell voltage in the voltage regulation module Vfcmin (V) Step current of d.c. converter in the voltage regulation module DIdc (A)

Value 0.02 2.3e3.7 0.01e0.5 0.01e0.1


Because the battery works in a small discharge/charge rate, a heat balance was obtained. The inner temperature was kept around 27  C. After switching into normal operation mode, the cooling water temperature was kept between 35 and 39  C. The lower part of the figure shows the working points distribution. Two peaks appear when Pfc ¼ 16 and 37 kW. If we only consider system efficiency, the optimal powers should be at 11 kW and 42 kW. However, fuel cell voltage will exceed the upper bound if the output power is 11 kW. Thus, the first peak moves from 11 kW to 16 kW. The second peak shifts from 42 kW to 37 kW because of power limitation.

517 382 0.05

strategy tries to utilize the electric energy in the battery as much as possible, whilst keeping the battery in a health status. Therefore, a relatively low target end value is chosen, SoCtg ¼ 20%. The final two cycles in the testing are selected to show the experimental results. The battery SoC was kept in a low level during these two cycles, around 17%.

Fig. 10 e Test bench results: (a) starting up process, (b) shutting-down process.


Energy flow diagram and performance degradation

Fig. 12(a)e(b) presents some statistical results regarding fuel economy and system durability. Fig. 12(a) shows the energy flow diagram in two testing cycles. The entire testing time was 45.9 min, corresponding to 15.5 km driving distance. In total, 1.18 kg hydrogen gas was consumed by the fuel cell system, while battery SoC was kept at around 17%. Fuel cell system efficiency was 58.4%, and net efficiency was 54.1%. If we take the d.c. conversion to be part of the first power source, total efficiency was 52.1%. Being the second power source, the battery was kept charge-sustaining with an average equivalent charge/discharge resistance of 0.035 U. About 0.56% of the hydrogen energy was consumed by the battery resistance, corresponding to 0.29 kW. The average efficiency of the Li-ion battery was 99%. The electric motor worked as a generator or a motor. The average efficiencies were 91% and 71.4% for the motor mode and the generator mode, respectively. Defined as the following equation, the average powertrain efficiency was 49.6%. The fuel economy is 7.6 kg (100 km)1:   1 hpowertrain ¼ Edrv = EH2 þ Ebat hdis hchg (38) where Edrv is the mechanical energy for driving at the output port of the electric motor, EH2 is the low heat value energy of the hydrogen gas, Ebat is the net discharge/charge energy of the battery, hdis and hchg are discharge/charge efficiencies of the Li-ion battery. Compared to the study in Ref. [48], average powertrain efficiency is relatively high in this paper. This is because 1) average efficiency of the fuel cell system has improved in the last several years, and 2) there is no auxiliary power consumption on bench testing. In a practical situation, assuming the average auxiliary power is around 5 kW, and a regenerative braking technology is applied, and can reduce 7% of hydrogen consumption, then the powertrain efficiency will be 45.4%, and the hydrogen consumption will be 8.3 kg (100 km)1. This fuel economy will correspond to 240 km driving mileage. Fig. 12(b) illustrates the performance evolution of the fuel cell system and the battery packages in the 20 testing cycles. We took the fuel cell voltage when the total output current is 100 A (0.37A cm2) as a standard to evaluate the performance. The value was identified using LSM (Least Square Method). The degradation rate for each cell is 37 mV h1. This value is relatively high than some results reported in literature [49]. According to the results reported in the demonstrational program after the Beijing Olympic Games [50], the degradation rate of a 40 kW PEM fuel cell system was 0.26 W km1 when the fuel


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Fig. 11 e System dynamics in two driving cycles: (a) velocity and power requirement profiles, (b) power split, (c) currents and voltages of the fuel cell and battery systems, (d) temperatures of the fuel cell and battery systems, and distribution of the fuel cell system working points.

cell output power was 100 A. The average velocity of the demonstrational program was 15 km h1, and the fuel cell was composed of 520 cells. Therefore, the degradation rate for one cell was 75 mV h1. Therefore, the performance degradation is greatly reduced. The lower part of Fig. 12(b) shows the performance evolution of the li-ion battery. The average charge/discharge resistance is identified using the same method. The resistance was kept almost in constant in the testing, meaning the performance of the battery was kept unchanged.



This paper proposed a real-time multi-mode energy management strategy for a plug-in fuel cell/battery electric vehicle. In order to reduce fuel consumption and prolong working lifetime of the fuel cell/battery system, a multiobjective optimized problem is first defined. A real-time multi-mode strategy consisting of five blocks is designed. The strategy was applied into the fuel cell powertrain, and tested on the bench for 20 “China city bus typical cycles”. 1) The cooling water temperature of the fuel cell system is strictly controlled in the starting up process while the

power requirement of the electric motor is being fulfilled. Battery SoC will decrease slightly. However, at the beginning of the operation the battery was always charged at a high SoC level, so it will not influence the dynamic performance of the vehicle. 2) In the normal operation mode, the optimization problem is simplified and solved using a PMP algorithm and power/ voltage control algorithm. The working points of the fuel cell system located in the high efficiency range, and the single fuel cell voltage was kept between 0.74 and 0.85 V, so as to avoid carbon corrosion at high potential. The discharge/charge current of the battery was limited within 2 C/1 C, so as to avoid performance degradation caused by large working current. At the end of the operation the battery SoC was kept around 17% so the battery would not be damaged when there was too little energy left in the package. 3) In the shutting-down process, the output power of the fuel cell system decreases linearly, so that no water flooding or drying occur within the fuel cell system. This process will be finished in 15 s. 4) Energy flow analysis shows that, with the proposed strategy, the average net efficiency of the fuel cell system was 54.1%, the average powertrain efficiency in the battery charge-sustaining mode was 49.6%, and the fuel economy

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L=15.5km T=45.9min

Hydrogen tank 1.18kg 142.8MJ (100%, 51.8kW) Fuel cell system (58.4 %) 83.4MJ (58.4%, 30.3kW)

Hydrogen loss, cell efficiency

Fuel cell system net output

Auxiliary components, 2.2 kW

77.3 MJ (54.1%, 28.1kW)

DC converter (96.3%) 0.8 MJ (0.56%, 0.29kW)

Li-ion battery package (99%)

37.2MJ (26.1%, 13.5kW)



74.4 MJ (52.1%, 27.0 kW) No auxiliary power consumption on bench testing

36.6MJ (25.6%, 13.3kW)

3.6 MJ (2.52%, 1.3kW)

77.4MJ (54.2%, 28.1kW)

Electric motor 71.4% 5.0MJ (3.5%, 1.8kW)


Power-train energy efficiency 49.6%

5) Performance evolution analysis shows that, battery performance was kept unchanged, and the degradation rate for each cell was 37 mV h1, which is half than the level in the China demonstrational program in 2009 after the Beijing Olympic Games (75 mV h1). Although the two PEM fuel cell systems were developed in different years, their structures and control strategies in the fuel cell system are similar. The multi-mode energy management strategy has positive influence on the fuel cell durability, but it is difficult to figure out the accurate degree of the contribution of the strategy to the reduction of performance degradation. More testing and validation work needs to be done to improve the strategy. In the near future, a demonstrational program will be carried out to evaluate the proposed strategy, and a small stack (w10 kW) will be built up to study the influences of control strategies on system durability. Dynamics within the fuel cell system will be monitored, and observation algorithms for key states will be studied. A hierarchical control strategy, including energy management level and fuel cell control level, will be developed so as to improve both the system efficiency and the durability.

Acknowledgments This work was funded by the NSFC (National Natural Science Foundation) of China under contract No. 61004075, Tsinghua National Laboratory for Information Science and Technology (TNList) Cross-discipline Foundation, MOST (Ministry of Science and Technology) of China under contract No. 2011AA11A269 and No. 2010DFA72760.

70.4MJ (49.3%, 25.6kW)

(a) 390

Vfc100A (V)



references 370 for single cell 11-37μV.h-1

360 0


4 t (hours)




4 t (hours)



Rbatavg (Ω)

0.04 0.035 0.03

0.025 0

(b) Fig. 12 e Statistic results in the cycling testing: (a) energy flow diagram for two cycles, (b) performance degradation of the fuel cell system and the battery in the 20 cycles.

was 7.6 kg (100 km)1. In a practical situation, these two values will be 45.4% and 8.3 kg (100 km)1, which corresponds to 240 km driving mileage. The electric energy stored in the LIB system (63 kWh) will provide a pure battery driving range of more than 30 km. Thus, the entire driving range will exceed 270 km.

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