- Email: [email protected]
A comparative study of power allocation strategies used in fuel cell and ultracapacitor hybrid systems
Energy 189 (2019) 116142
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
A comparative study of power allocation strategies used in fuel cell and ultracapacitor hybrid systems Yujie Wang a, Zhendong Sun a, Xiyun Li a, Xiaoyu Yang b, Zonghai Chen a, * a
Department of Automation, University of Science and Technology of China, Hefei, Anhui, 230027, PR China National Experimental Teaching Demonstrating Center of Information and Computer, University of Science and Technology of China, Hefei, Anhui, 230027, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 July 2019 Received in revised form 13 September 2019 Accepted 16 September 2019 Available online 19 September 2019
The proton exchange membrane fuel cell is a good candidate for the future green transportation. In the vehicle applications, the fuel cell systems are always grouped with other energy storage devices such as the lithium-ion batteries and ultracapacitors in order to enhance their dynamic performance. The energy management strategy, especially the power allocation strategy plays an important role in the energy management system of the vehicles. This paper presents a comparative study of the power allocation strategies used in different hybrid structures. First, a framework of the fuel cell and ultracapacitors hybrid system is established considering the models of the ultracapacitor, fuel cells, and vehicle dynamics. Then the suboptimal on-line power allocation strategies based on classical cybernetics and rules are presented. The off-line dynamic program algorithm is employed as an optimal solution in order to compare with the proposed suboptimal on-line power allocation strategies. After that, simulations are put forward to compare the performance of the presented power allocation strategies. Finally, experimental studies are conducted to compare the fuel economy and the dynamic property of different hybrid structures using a semi-physical experimental platform. Compared with the fuel cell and batteries hybrid structure, the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 21.03%e26.70% under the PID-based power allocation strategy, and improved by 21.86%e30.48% under the rule-based power allocation strategy. The results indicate that the proposed rule-based strategy can achieve a near optimal performance compared with the dynamic programming algorithm and is easily applied online. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Power allocation strategy System modeling Dynamic programming Rule-based strategy
1. Introduction 1.1. Background and motivation Due to the environmental pollution and the shortage of petrochemical resources, the development of sustainable and clean new energy has risen in the world's agenda. The fuel cells have attracted much attention because of their high efficiency and environmental friendship [1]. A fuel cell is an electrochemical device that converts the chemical energy of the fuel and oxidant directly into electrical energy [2]. In the automotive industry, the most widely used fuel cells are the proton exchange membrane fuel cells which produce
* Corresponding author. E-mail addresses: [email protected] (Y. Wang), [email protected] (Z. Sun), [email protected] (X. Li), [email protected] (X. Yang), chenzh@ ustc.edu.cn (Z. Chen). https://doi.org/10.1016/j.energy.2019.116142 0360-5442/© 2019 Elsevier Ltd. All rights reserved.
electricity with water as their only by-products [3]. Compared with other kinds of the fuel cells, e.g. solid oxide fuel cells, molten carbonate fuel cells and phosphoric acid fuel cells, the proton exchange membrane fuel cells have specialties of low start-up temperature, lightweight and long endurance. The fuel cell vehicles have great superiorities in energy efficiency, endurance mileage, charging speed and climate tolerance compared with the electrified vehicles powered by the secondary batteries. However, there are several significant disadvantages. Firstly, the dynamic response of the fuel cell system is not as fast as that of the electrified vehicles, and it is difficult to track the peak power when the external demand power changes dramatically. Moreover, the fuel cell system cannot recover the braking energy, which causes energy waste and reduces the system efficiency in the frequently braking urban traffic conditions. Therefore the fuel cells are often used in conjunction with other energy storage devices, e.g. the lithium-ion batteries [4] or the ultracapacitors. The ultracapacitors or the so called “electrochemical double-
2
Y. Wang et al. / Energy 189 (2019) 116142
layer capacitors (EDLC)”, are another type of electrochemical energy storage devices which share some similarities to the lithiumion batteries. The difference is that their energy densities are about one tenth that of the lithium-ion batteries, but their power densities are of more than ten times that of the lithium-ion batteries which can quickly response instantaneous high power to meet external demand for peak power. Moreover, the lifespans of the ultracapacitors are longer than most batteries which are appropriate to applications requiring high power and long cycle life. The hybrid use of the fuel cells and ultracapacitors can effectively improve the system performance of the fuel cell vehicles. Wang et al. [5] proposed a multi-timescale power and energy evaluation approach for the lithium-ion battery and ultracapacitor hybrid system. Compared with the lithium-ion batteries, the ultracapacitors can provide fast and effective energy outputs. 1.2. Literature review One of the key problem when the fuel cells are used in a hybrid system is how to allocate power to fuel cells and energy storage devices (ultracapacitors or batteries) and ensure the safety and efficiency of the power system. A variety of energy management strategies can be found in the literature. Azib et al. [6] proposed a decoupling strategy in the frequency domain which can make the high-frequency part of the demand energy shared by ultracapacitors to prolong the lifespan of the fuel cell system. Zandi et al. [7] developed a method which is based on the flatness control technique and fuzzy logic control. The main feature of this strategy is to use a single general control algorithm to manage the power of the power supply in different operating modes, avoiding any algorithm commutation. Li et al. [8] proposed a power allocation strategy based on wavelet transform and fuzzy logic control, the burden of the fuel cell caused by rapid changes of large current was reduced. Rodatz et al. [9] developed an equivalent consumption minimization strategy to determine the real-time optimal power allocation which can improve fuel efficiency along with robustness. Thounthong et al. [10] proposed a control strategy for a fuel cell and ultracapacitor hybrid vehicle based on direct current link voltage regulation. This method can minimize the mechanical stresses of fuel cell and ensure a good synchronization between the fuel flow and the fuel cell current. Payman et al. [11] proposed a flatnessbased nonlinear control method and designed an observer to estimate parameters of the fuel cell which varies with the environment. Experimental results demonstrated that the proposed method was robust both in the normal and overload modes. Xu et al. [12] presented an optimal energy management strategy based on dynamic programming and Pontryagin's minimal law. The fuel economy of the presented strategy is analyzed with simulation models. Wang et al. [13] developed an energy management strategy for the battery, ultracapacitor, and fuel cell hybrid power source vehicles based on finite state machine. The presented strategy is compared with the dynamic programming algorithm, and the fuel economy and dynamic property are analyzed. Lopez et al. [14] employed a rule-based power management strategy where a low pass filter is used to split the power between different power sources. The benefits of the energy management strategy with respect to the prevention of oxygen starvation and reduction of start and stop times are analyzed. The above-mentioned literature both the rule-based approaches and the optimization-based approaches can achieve good expected control requirements. However, a comparative study of the power allocation strategies for the fuel cell and ultracapacitor hybrid system has not been reported in the existing literature. Moreover, strategies with low computation complexity and calculation cost which are suitable for practical applications need to be developed.
1.3. Objectives and contributions Because of the high power density and energy recovery capability of the ultracapacitors, the hybrid of ultracapacitors and fuel cells has better robustness in power control [15]. To fulfill the power balance between the load power and the energy storage devices, the energy management strategy plays an important role in the hybrid energy storage system. This work is committed to proposing appropriate power allocation strategies based on rules and classical cybernetics with low computation complexity. The main contributions of this paper are as follows: First, the framework of the fuel cell and ultracapacitor hybrid power system is established with accurate modeling of the ultracapacitors, fuel cells, and vehicle dynamics. Second, the power allocation strategies based on rules and classical cybernetics are put forward. Moreover, the dynamic programming algorithm is used as a benchmark to verify the effectiveness of the proposed strategies. Third, the performance of the proposed power allocation strategies has been compared systematically with simulations and experiments under different working conditions using a semi-physical experimental platform. Simulation results show that the proposed strategies can achieve a near optimal performance when comparing with dynamic programming algorithm. The proposed suboptimal strategies are moreover easily applied online. 1.4. Outline of the paper The remainder of this paper is organized as follows. In Section 2, the framework of the system structure and the models of the ultracapacitors, fuel cells, and vehicle dynamics are introduced. In Section 3, the power allocation strategies based on rules and classical cybernetics are introduced. The off-line dynamic programming algorithm is presented as a benchmark compared with the proposed suboptimal strategies. In Section 4, experiments are conducted under different working conditions using a semiphysical experimental platform. Finally, the conclusions and potential future work are given in Section 5. 2. System structure and modeling In this section, the overall framework of the system structure and the models of the ultracapacitor, the fuel cell, and the vehicle dynamics will be introduced. 2.1. System structure The overall framework of the vehicle structure is shown in Fig. 1. The ultracapacitors are used to provide supplemental power for starting, accelerating, climbing, and recover energy from vehicle braking. A bidirectional DC/DC converter is used to connect the ultracapacitors with the DC/AC inverter. The fuel cell system is used to convert the chemical energy to electrical energy through an electrochemical reaction of the hydrogen and oxygen. A unidirectional DC/DC converter is used to connect the fuel cell system and the DC/AC inverter. Compared with the battery and fuel cell hybrid system, the ultracapacitors have higher power densities, which can better alleviate the burden of the fuel cell system when the load power fluctuates violently. Moreover, the ultracapacitors have longer lifespans than lithium-ion batteries. Therefore the replacement and maintenance costs can be saved. 2.2. Model description 2.2.1. Model description of the ultracapacitor The structure of ultracapacitors is essentially the same as a
Y. Wang et al. / Energy 189 (2019) 116142
Physical connection Ultracapacitor
H2
Cooler
Hydrogen Tank
Air O2 Compressor Fuel cell system
Humidifier
Signal connection
3
Bidirectional
Bidirectional
Convertor DC/DC
Invertor DC/AC
Unidirectional Fuel Cell Stack
Convertor DC/DC
Motor
Energy management system
H2O
Fig. 1. Structure of the fuel cell and ultracapacitor hybrid system.
lithium-ion battery. There are negative and positive electrodes, current collectors, and a separator. The electrodes are composed of small particles, within their voids filled by an electrolyte solution [16]. Diverse models have been developed in the literature to describe the internal and external behaviors of the ultracapacitors, e.g. the physics-based models (PBMs) [17,18] and the equivalentcircuit models (ECMs) [19]. The PBMs have high accuracy describing the potential of the solid particles and electrolyte. However, the partial differential equations of the PBMs are complex and the model parameters are difficult to identify in practical applications. The ECMs are widely used in practice because they can approximate the input and output behaviors with simple structures. For the ultracapacitors, three representative ECMs with different computational demands and prediction accuracies are the classic model, the multi-stage ladder model and the dynamic model [20]. In this work, the classic model with sufficiently simple structure yet capturing the key dynamics of the ultracapacitor is employed. The structure of the classic model is shown in Fig. 2. The dynamic behavior and the output of the model can be described by Eqs. (1) and (2) according to Ref. [21].
2.2.2. Model description of the fuel cell The fuel cell model [22] can be described by:
Vfc ¼ Voc Vact Vohm Vconc
where Vfc represents the model output of the fuel cell, Voc represents the open-circuit voltage (OCV) of the fuel cell, Vact represents the activation loss, Vohm represents the ohmic loss, and Vconc represents the concentration loss. The OCV of the fuel cell can be expressed by Eq. (4) according to Ref. [22].
Voc ¼ 1:229 0:85 103 Tfc 298:15 þ 4:309 105 1 298:15 lnðpH2 Þ þ lnðpO2 Þ 2
(1)
VT ¼ Vp þ Rs IL
(2)
where VT represents the terminal voltage, Rs represents the internal series resistance which includes the electrolyte resistance and contact resistance, Cp represents the equivalent capacitor, Rp represents the self-discharge resistance, Vp denotes the voltage across the capacitor and IL represents the current of the ultracapacitor (define positive for charge and negative for discharge).
V
Rs
C 0
0 IL
VT
Vp
I t
IL
Fig. 2. The classic model of the ultracapacitor.
(5)
where v0 denotes the voltage drop at zero current density, Ifc represents the current of the fuel cell, A represents the active area of the fuel cell, va and c1 are model coefficients. The ohmic loss of the fuel cell can be expressed by:
Vohm ¼ Ifc Rohm
(6)
where Rohm represents the internal ohmic resistance depends on the temperature and membrane humidity of the fuel cell. Finally, the concentration loss of the fuel cell can be expressed by:
Vconc
t
1
Ifc B C Vact ¼ v0 þ va @1 ec1 A A
Rp
VT
(4)
where Tfc represents the Kelvin temperature of the fuel cell, pH2 represents the pressure of hydrogen, and pO2 represents the pressure of oxygen. The activation loss of the fuel cell can be expressed by:
0 dVp 1 1 ¼ Vp þ IL Rp Cp Cp dt
(3)
I ¼ fc A
c2
Ifc ADfc;max
!c3 (7)
where Dfc,max represents the current density causes precipitous voltage drop, c2 and c3 are model coefficients. 2.2.3. Model description of the vehicle dynamics The aggregate demand power of the vehicle power system needs to overcome the rolling frictional resistance, the component resistance of the vehicle's weight acting on the road with slope q,
4
Y. Wang et al. / Energy 189 (2019) 116142
the air resistance, and the acceleration resistance. Therefore the power requirement can be calculated by:
Pm ¼ h mMgsinq þ Mgsinq þ 0:5rair Aw Cair u2 þ
du dM u dt
(8)
where h denotes the efficiency of the transmission system, m denotes the rolling resistance coefficient, M denotes the vehicle mass, g denotes the gravitational acceleration, rair denotes the density of air, Aw denotes the windward area of the vehicle, Cair denotes the coefficient of air resistance, d denotes the correction coefficient of the rotation mass, and u denotes the vehicle speed. In order to verify the accuracy of the presented models of the ultracapacitor and the fuel cell, experiments are conducted with a real ultracapacitor (Maxwell BCAP3000) (1.35 Ve2.7 V @25 C). The model prediction results of the ultracapacitor are compared with the measured values as shown in Fig. 3 (a). The mean absolute error (MAE) of the ultracapacitor model is 2.4 mV and the root mean square error (RMSE) is 2.9 mV. The results indicate that the presented ultracapacitor model can accurately simulate the real voltage with maximum absolute error (MaxE) less than 10 mV. To verify the accuracy of the fuel cell model, we conduct experiments and draw a current vs. power diagram shown in Fig. 3(b) in which the model outputs are compared with the experiment results with an error less than 0.5 kW. The polarization voltage curve (0.6 Ve1 V @60 C) of the fuel cell stack model is shown in Fig. 3(d), and the specifics of the OCV, activation loss, ohmic loss, and concentration loss are plotted in Fig. 3(c). From the figures, we can see that the prediction results of the fuel cell stack model are accordant with the experiment results.
3. Energy management strategy The energy management strategy is important in the hybrid energy storage system. In order to rationally assign the load power of the designed vehicle model, the on-line power allocation strategy based on classical cybernetics and the strategy based on criterion rules are introduced in this section. The off-line dynamic program algorithm is employed as an optimal solution in order to compare with the proposed suboptimal on-line power allocation strategies. 3.1. PID-based power allocation strategy 3.1.1. Design of the PID controller In classical cybernetics, the PID control has been widely used owing to its quick response speed, high steady accuracy and good robustness [23]. In order to make the fuel cell system and ultracapacitors work together and meet the demand power of the vehicle motor, a PID control algorithm is proposed for the power allocation of the hybrid power source system. The principle of the control strategy is to keep the state-ofcharge (SOC) of the ultracapacitors near its enactment value so that the system can calculate the required power of the fuel cell system and ultracapacitors adaptively through the closed-loop control algorithm. In the fuel cell system, the PID controller functions the hydrogen flow valve by the residual of the stated and estimated SOC of the ultracapacitors, which changes the power output of the fuel cell. The diagram of the PID-based power allocation strategy for the fuel cell and ultracapacitor hybrid power source system is shown in Fig. 4. Specifically, based on the model of
Fig. 3. Experimental results of the ultracapacitor and fuel cell system: (a) Model prediction of the ultracapacitor (1.35 Ve2.7 V @25 C). (b) Output power of the fuel cell system. (c) Model prediction of fuel cell system (OCV, activation loss, ohmic loss, and concentration loss). (d) Polarization voltage curve of the fuel cell (0.6 Ve1 V @60 C).
Y. Wang et al. / Energy 189 (2019) 116142
5
Fig. 4. Diagram of the PID-based power allocation strategy.
the ultracapacitors introduced in Section 2.2.1, the discrete time state-space equation for the ultracapacitors state estimation can be established as follows:
3.1.2. Simulation results of the PID controller The simulation results of the PID-based power allocation strategy under the New European Driving Cycle (NEDC) are shown in Fig. 5. The power allocation results of the fuel cell and ultra-
8 3 3 2 2 hDt=CN 1 0 " # # " > > > zk z 7 7 6 6 > k1 > 7 7I < ¼6 þ6 5 5 L;k1 4 4 Vp;k Vp;k1 0 exp Dt R C 1 exp Dt R C Rp > p p p p > > > > : VT;k ¼ Vp;k þ Rs IL;k
where zk represents the SOC of the ultracapacitors, h represents the coulombic efficiency, Dt represents the sample time, and CN represents the nominal capacity of the ultracapacitor. Then the SOC can be observed by the model-based state estimation algorithms, e.g. unscented Kalman filter (UKF) or particle filter (PF) which can be found in our previous work [19,24]. and the control algorithm of the PID controller can be expressed as:
ð _ uðtÞ ¼ kp eðtÞ þ ki eðtÞdt þ kd eðtÞ
(10)
where e(t) ¼ z(t)-z*, z* denotes the set value of the ultracapacitor's SOC (z* ¼ 0.6), kp, ki and kd are proportion, integration, and differentiation parameters of the PID controller. In this work, the parameters kp, ki, and kd are 1 105, 9 103, and 1 102.
(9)
capacitors are shown in Fig. 5 (a) and the SOC of the ultracapacitors are shown in Fig. 5 (b). From the simulation results, we can see that the PID-based power allocation strategy can satisfy the demand power, and the ultracapacitors can absorb most of the regenerated energy. However, both the power of the fuel cell and the ultracapacitors have a certain amount of overshoots when the demand power changes. Moreover, the fuel cell still suffers from high peak power shocks. From the variation curve of the SOC, the residual capacity of the ultracapacitors has not been used in full range.
3.2. Rule-based power allocation strategy 3.2.1. Design of the rule-based controller In order to overcome the drawbacks of the PID controller, a rule-
Fig. 5. Simulation results of the PID-based power allocation strategy: (a) power allocation of the fuel cell and ultracapacitors. (b) SOC of the ultracapacitors.
6
Y. Wang et al. / Energy 189 (2019) 116142
Strategy
Criterion Start
Pm>0?
Yes
Power allocation strategy
Yes
Fuel cell Ready?
No
Fuel cell startup mode
Puc =Pm+Paux Pfc =0
No
ultracapacitor s are full
No
Energy recovery mode (A)
Puc =-Pm Pfc =0
Energy recovery mode (B)
Puc =0 Pfc =0
FC and UC combined operating mode
Puc =Pm-Pfc,max Pfc =Pfc,max
Fuel cell individual operating mode (A)
Puc =0 Pfc =Pm
Fuel cell individual operating mode (B)
Puc =0 Pfc =Pfc,max
Fuel cell individual operating mode (C)
Puc =-|Pfc,max-Pm| Pfc =Pfc,max
Yes
ultracapacitor s are empty
Operating modes
Yes
No
Pm>Pfc,max
Yes
No
Pm>Pfc,max
Yes
No
Fig. 6. Rule-based power allocation strategy.
based power allocation strategy is presented for the fuel cell and ultracapacitor hybrid system. The control principle of the rulebased power allocation strategy is the fuel cell system provides a relatively stable power whereas the ultracapacitors provide the transient peak power. Therefore the burden of the fuel cell can be alleviated by the ultracapacitors. The rule-based power allocation strategy is shown in Fig. 6. According to this rule-based power allocation strategy, the operating modes of the fuel cell and ultracapacitor hybrid system can be divided into 4 cases: Case 1. Fuel cell startup mode. In this operating mode, the fuel cell system needs to be activated by auxiliary power in order to finish gas purging and preheating. Therefore all the demand power Pm of the motor and the startup power of the fuel cell Paux should be provided by the ultracapacitors. Case 2. Fuel cell and ultracapacitor combined operating mode. After the fuel cell finish gas purging and preheating and the ultracapacitors have enough residual capacity, whereas the demand power is higher than the fuel cell maximum output power Pfc,max, the system turns into the fuel cell and ultracapacitor combined operating mode. The fuel cell provides its maximum power output, and the residual power (Pm - Pfc,max) is provided by the ultracapacitors. Case 3. Fuel cell individual operating mode. In the condition that the demand power is lower than the fuel cell maximum output power the fuel cell individually provides the demand power. When the ultracapacitors do not have enough residual capacity, the demand power should be provided by the fuel cell individually. Moreover, in order to maintain a stable output of the fuel cell and charge the empty ultracapacitors, the ultracapacitors are used to absorb excess power (-|Pfc,max - Pm|) provided by the fuel cell system. Case 4. Energy recovery mode. In this operating mode, the controller controls the regenerated energy feeding to the ultracapacitors due to the residual capacity of the ultracapacitors. If the ultracapacitors are full, the controller cuts off the DC/DC converter and the ultracapacitors stop absorb the regenerated energy.
The hybrid use of the fuel cells and ultracapacitors can effectively improve the system performance of the fuel cell vehicles. If the SOC of the ultracapacitors is too high, the braking energy cannot be absorbed, if the SOC of the ultracapacitors is too low, it will not help the system to share the peak power, so the proposed strategy based on the SOC variation range of the ultracapacitors is helpful to keep the SOC of ultracapacitors in an appropriate range and balance between the load power and the energy storage devices. The superiority of the rule-based power allocation strategy is that the stable power can be provided by the fuel cell whereas the instantaneous peak power can be provided by the ultracapacitors. Moreover, the ultracapacitors can also recover most of the regenerated energy when the vehicle brakes. 3.2.2. Simulation results of the rule-based controller The simulation results of the proposed rule-based power allocation strategy under the NEDC are shown in Fig. 7. The power allocation results of the fuel cell and ultracapacitors under NEDC are shown in Fig. 7 (a) and the SOC of the ultracapacitor is shown in Fig. 7 (b). The proposed rule-based power allocation strategy can satisfy the demand power with a rational allocation of the fuel cell's power and the ultracapacitors' power as shown in Fig. 7 (a). The ultracapacitors can also absorb most of the regenerated energy from vehicle breaks. It can overcome the problem of overshoots in the PID-based power allocation strategy. Moreover, the SOC utilization range of ultracapacitors has increased by 35%. 3.3. Dynamic programming strategy 3.3.1. Design of dynamic programming algorithm The dynamic programming algorithm based on Bellman's optimality principle is widely used for solving multistage decisionmaking problems [25], and it is suitable for energy management problems especially the power allocation problem. The dynamic programming algorithm is presented as an optimal solution for the power allocation of the fuel cell and ultracapacitors hybrid energy storage system. In this work, the dynamic programming method is used as a benchmark to verify the effectiveness of the proposed strategies.
Y. Wang et al. / Energy 189 (2019) 116142
7
Fig. 7. Simulation results of the rule-based power allocation strategy: (a) power allocation of the fuel cell and ultracapacitors. (b) SOC of the ultracapacitors.
For the fuel cell and ultracapacitor hybrid energy storage system, we choose the fuel cell output power Pfc as the control variable and the SOC of the ultracapacitors as the state variable. The cost function J to be minimized is the total hydrogen consumption, which is given as follows:
ðtf J¼
m_ Pfc ðtÞ; t dt
(11)
0
where tf denotes the break up time, m denotes the hydrogen consumption. Then the problem can be described as follows:
ðf minJ ¼ min m_ Pfc ðtÞ; t dt t
obj :
0
st: :
8_ zðtÞ ¼ f ðzðtÞ; IL ðtÞÞ > > > > > > zð0Þ ¼ z tf > > > < Pfc ðtÞ ¼ Pm ðtÞ IL ðtÞVT ðtÞ > > z > min zðtÞ zmax > > > > > Puc;min Puc Puc;max > : Pfc;min Pfc Pfc;max
(12)
In order to calculate the hydrogen consumption more
accurately, the equation z(0) ¼ z(tf) is added as a constraint when applying the dynamic programming algorithm.
3.3.2. Simulation results of the dynamic programming algorithm The simulation results of the dynamic programming power allocation strategy under the NEDC are shown in Fig. 8. The power allocation results of the fuel cell and ultracapacitors under NEDC are shown in Fig. 8 (a) and the SOC of the ultracapacitor is shown in Fig. 8 (b). Fig. 8(b) illustrates that based on the dynamic programming power allocation strategy, the ultracapacitors can absorb most of the peak power. The fuel cell provides a relatively stable power output, which matches the results of the presented rulebased power allocation strategy. The simulation results also show that the proposed rule-based power allocation strategy can achieve a near optimal performance compared with the dynamic programming algorithm.
4. Experimental verification and analysis In this section, to further analyze the performance of the presented power allocation strategies, experiments are conducted on a semi-physical experimental platform. The dynamic property and fuel economy of the presented power allocation strategies are compared with different hybrid structures under different road maps.
Fig. 8. Simulation results of the dynamic programming power allocation strategy: (a) power allocation of the fuel cell and ultracapacitors. (b) SOC of the ultracapacitors.
8
Y. Wang et al. / Energy 189 (2019) 116142
Fig. 9. Semi-physical experimental platform.
4.1. Semi-physical experimental platform In order to apply the power allocation strategies with the hybrid power source system, a semi-physical experimental platform is developed as shown in Fig. 9. The electronic load tester NEWARE BTS-4000 can communicate with the host computer through TCP/ IP protocol and is used to test the ultracapacitors and monitor the voltage and current of the ultracapacitors in real time. The host computer is used to develop the models and power allocation strategies using MATLAB/Simulink® where the vehicle dynamic simulation platform and the fuel cell simulation platform are included. The parameters of the fuel cell simulation platform and the vehicle dynamics are shown in Table 1 and Table 2, respectively. It also should be pointed out that the energy density and power
Table 1 Parameters of the fuel cell simulation platform. Parameters
Values
Maximum current density Charge transfer coefficient Volume of anode Volume of cathode Hydrogen gas constant Oxygen gas constant Ideal gas constant Faraday constant Reference temperature
2.2 A/cm2 0.5 0.005 m3 0.01 m3 4124.36 J/(mol$K) 259.81 J/(mol$K) 8.31 J/(mol$K) 96485.33 C/mol 298.15 K
Table 2 Parameters of the vehicle dynamics. Parameters
Values
Vehicle mass Efficiency of the transmission system Rolling resistance coefficient Density of air Gravitational acceleration Windward area of the vehicle Coefficient of air resistance Correction coefficient of the rotation mass
1480 kg 0.9 0.015 1.202 kg/m3 9.8 m/s2 2 m2 0.3 1.04
density of the ultracapacitors are quite different with the lithiumion batteries, which means that the size of ultracapacitors is larger than the lithium-ion batteries for the same energy requirements. However, as a kind of power output device, the power capability of the ultracapacitor is much higher than the battery. In the configuration of the hybrid energy storage systems, the ultracapacitors are used to provide and absorb instantaneous high energy, and the fundamental and stable output is provided by the fuel cell system. The difference in energy/power density between the battery and ultracapacitor is reflected in the weight of the energy storage system, which should be considered in the vehicle mass in the vehicle dynamic model. 4.2. Results and discussions In order to compare the performance of the proposed PID-based and rule-based power allocation strategies, the dynamic property and fuel economy of the presented power allocation strategies are compared with different hybrid structures under different road maps. Moreover, the results of the dynamic programming strategy are presented as a benchmark. The results of the PID-based and rule-based power allocation strategies are compared with the dynamic programming strategy which is recognized as an optimal solution for power allocation of hybrid power source system. The qualitative and quantitative analysis results are presented as follows. 4.2.1. Results of road map A The results of the presented power allocation strategies with different hybrid structures under the EPA Highway Fuel Economy Test Cycle [26] (road map A) are shown in Fig. 10. The PID-based power allocation results of the fuel cell and ultracapacitors hybrid structure are shown in Fig. 10 (a). The SOC curve of the ultracapacitors based on PID control is shown in Fig. 10 (b). It can be seen that the PID-based power allocation strategy can satisfy the demand power, and the ultracapacitors can absorb most of the regenerated energy. However, the power output of the fuel cell is not stable. The rule-based power allocation results of the fuel cell and ultracapacitors hybrid structure are shown in Fig. 10 (e) and the SOC curve of the ultracapacitors is shown in Fig. 10 (f). Compared with
Y. Wang et al. / Energy 189 (2019) 116142
9
Fig. 10. Results of power allocation strategies with different hybrid structures under EPA Highway Fuel Economy Test Cycle: (a) PID-based power allocation of the fuel cell and ultracapacitors hybrid structure. (b) SOC of the ultracapacitors based on PID control. (c) PID-based power allocation of the fuel cell and batteries hybrid structure. (d) SOC of the batteries based on PID control. (e) Rule-based power allocation of the fuel cell and ultracapacitors hybrid structure. (f) SOC of the ultracapacitors based on rule-based control. (g) Rule-based power allocation of the fuel cell and batteries hybrid structure. (h) SOC of the batteries based on rule-based control. (i) Dynamic programming power allocation of the fuel cell and ultracapacitors hybrid structure. (j) SOC of the ultracapacitors based on dynamic programming. (k) Dynamic programming power allocation of the fuel cell and batteries hybrid structure. (l) SOC of the batteries based on dynamic programming.
the PID-based power allocation strategy, the rule-based strategy provides more optimized power allocation of the fuel cell and ultracapacitors where the fuel cell system provides stable power outputs and the ultracapacitors take responsibility to provide peak power and absorb regenerated energy. In addition, the SOC operating range of the rule-based power allocation strategy has been expanded. The PID-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 10 (c) and the SOC curve of the batteries based on the PID control is shown in Fig. 10 (d). In this structure, the batteries take the role of the ultracapacitors. Similar to the fuel cell and ultracapacitors hybrid system, the power output of the fuel cell is also erratic. The rule-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 10 (g), and the SOC curve of the batteries is shown in Fig. 10 (h). In the rule-based power allocation strategy, power constraints
have been added to prevent the batteries from over-charging and over-discharging, therefore the regenerated energy cannot be absorbed in very high levels of SOC. The hydrogen consumptions of the fuel cell and ultracapacitors hybrid structure and the fuel cell and batteries hybrid structure under road map A are compared in Table 3. The hydrogen consumptions of the fuel cell and ultracapacitors hybrid structure with the PID-based and rule-based power allocation strategies are 0.507 kg and 0.529 kg, respectively. Whereas the hydrogen consumptions of the fuel cell and batteries hybrid structure with the PID-based and rule-based power allocation strategies are 0.642 kg and 0.677 kg, respectively. The fuel cell and ultracapacitors hybrid structure has higher fuel economy than the fuel cell and batteries hybrid structure. Compared with the fuel cell and batteries hybrid structure, the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 21.03% under the PID-based
Table 3 Hydrogen consumptions under road map A.
Fuel cell & ultracapacitors Fuel cell & batteries
PID-based Strategy
Rule-based Strategy
Dynamic programming
0.507 kg 0.642 kg
0.529 kg 0.677 kg
0.499 kg 0.502 kg
Y. Wang et al. / Energy 189 (2019) 116142
4.2.2. Results of road map B The results of the presented power allocation strategies with different hybrid structures under the EPA Urban Dynamometer Driving Schedule [27] (road map B) are shown in Fig. 11. The PIDbased power allocation of the fuel cell and ultracapacitors hybrid structure is shown in Fig. 11 (a). The SOC curve of the ultracapacitors based on PID control is shown in Fig. 11 (b). The PIDbased power allocation strategy can satisfy demand power. But the power output of the fuel cell is unstable especially when the load power changes dramatically. The SOC of the ultracapacitors can track the set target and meet the control requirements. The rule-based power allocation results of the fuel cell and ultracapacitors hybrid structure are shown in Fig. 11 (e) and the SOC curve of the ultracapacitors is shown in Fig. 11 (f). It can be seen that the power output of the fuel cell is much more stable than that of the PID-based power allocation strategy. Moreover, the ultracapacitors can suffer most of the instantaneous surges of high power and absorb all regenerated energy. The PID-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 11 (c) and the SOC curve of the batteries based on the PID control is shown in Fig. 11 (d). In the fuel cell and ultracapacitors hybrid structure, the power output of the fuel cell is unstable when the batteries are not full. When the
power allocation strategy, and improved by 21.86% under the rulebased power allocation strategy. In order to further compare the proposed on-line power allocation strategies with the off-line optimal approach. The dynamic programming algorithm is conducted, as shown in Fig.10 (i)e(l). The power allocation results of the fuel cell and ultracapacitors hybrid structure using the dynamic programming algorithm are shown in Fig. 10 (i), and the SOC curve of the ultracapacitors is shown in Fig. 10 (j). The power allocation results of the fuel cell and batteries hybrid structure using the dynamic programming algorithm are shown in Fig. 10 (k) and the SOC of the batteries is shown in Fig. 10 (l). As an optimal solution, the hydrogen consumption of dynamic programming is less than the PID and rule-based strategy. The hydrogen consumption of the fuel cell and ultracapacitors hybrid structure is 0.499 kg, and that of the fuel cell and batteries hybrid structure is 0.502 kg. Compared with the fuel cell and batteries hybrid structure, the fuel cell and ultracapacitors hybrid structure has better fuel economy. Moreover, in the cases of dynamic programming and rule-based strategy, the power allocation and SOC of the ultracapacitors are approximated which indicate that the presented rule-based strategy can obtain near optimal results.
PID-based
(c)
SOC PID-based Time (s) (f)
Time (s) (g)
Time (s) (h) Rule-based
Rule-based Time (s)
SOC
Power (W)
SOC
Power (W)
Rule-based
(i)
Rule-based
(j)
Time (s)
(k)
Time (s)
(l)
SOC
Power (W)
SOC
Power (W)
Dynamic programming
Time (s) Dynamic programming
Dynamic programming
Time (s)
PID-based
PID-based
Time (s) (e)
(d)
Power (W)
(b)
Power (W)
(a)
SOC
10
Dynamic programming Time (s)
Time (s)
Time (s)
Fig.11. Results of power allocation strategies with different hybrid structures under EPA Urban Dynamometer Driving Schedule: (a) PID-based power allocation of the fuel cell and ultracapacitors hybrid structure. (b) SOC of the ultracapacitors based on PID control. (c) PID-based power allocation of the fuel cell and batteries hybrid structure. (d) SOC of the batteries based on PID control. (e) Rule-based power allocation of the fuel cell and ultracapacitors hybrid structure. (f) SOC of the ultracapacitors based on rule-based control. (g) Rule-based power allocation of the fuel cell and batteries hybrid structure. (h) SOC of the batteries based on rule-based control. (i) Dynamic programming power allocation of the fuel cell and ultracapacitors hybrid structure. (j) SOC of the ultracapacitors based on dynamic programming. (k) Dynamic programming power allocation of the fuel cell and batteries hybrid structure. (l) SOC of the batteries based on dynamic programming.
Y. Wang et al. / Energy 189 (2019) 116142
11
Table 4 Hydrogen consumptions under road map B.
Fuel cell & ultracapacitors Fuel cell & batteries
PID-based Strategy
Rule-based Strategy
Dynamic programming
0.593 kg 0.809 kg
0.568 kg 0.817 kg
0.456 kg 0.457 kg
SOC of the batteries arrives the higher threshold (>0.95), the batteries stop absorbing the regenerated energy and start to discharge. The rule-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 11 (g) and the SOC curve of the batteries is shown in Fig. 11 (h). Because the power capability of the batteries is much lower than the ultracapacitors, the batteries need to operate with the fuel cell in most of the cycles. Moreover, at high levels of the SOC, the batteries should stop absorbing regenerated energy in order to prevent over-charging. The hydrogen consumptions of Road map B are shown in Table 4. The hydrogen consumptions of the fuel cell and ultracapacitors hybrid structure with the PID-based and rule-based power allocation strategies under road map B are 0.593 kg and 0.568 kg. The hydrogen consumptions of the fuel cell and batteries hybrid structure with the PID-based and rule-based power allocation strategies are 0.809 kg and 0.817 kg, respectively. In road map B, compared with the fuel cell and batteries hybrid structure, the fuel economy of the fuel cell and ultracapacitors hybrid structure has an improvement of 26.70% under the PID-based power allocation strategy, and an improvement of 30.48% under the rule-based power allocation strategy. The fuel cell and ultracapacitors hybrid structure can save more hydrogen than the fuel cell and batteries hybrid structure. The power allocation results of the fuel cell and ultracapacitors hybrid structure using the dynamic programming algorithm under road map B are shown in Fig. 11 (i), and the SOC curve of the ultracapacitors is shown in Fig. 11 (j). The power allocation results of the fuel cell and batteries hybrid structure using the dynamic programming algorithm are shown in Fig. 11 (k) and the SOC of the batteries is shown in Fig. 11 (l). The hydrogen consumption of the fuel cell and ultracapacitors hybrid structure is 0.456 kg, and that of the fuel cell and batteries hybrid structure is 0.457 kg. From the results, we can see that the power outputs of the fuel cell system in the fuel cell and ultracapacitors hybrid structure are stable both in the dynamic programming and rule-based strategy. In addition, the ultracapacitors can absorb most of the regenerated energy and provide peak power. The proposed rule-based power allocation strategy with the fuel cell and ultracapacitors hybrid structure can achieve a suboptimal performance under the road map B.
5. Conclusions This paper presents a comparative study on the power allocation strategies used in different hybrid structures. First, the framework of a fuel cell and ultracapacitors hybrid system is established with accurate modeling of the ultracapacitors, fuel cells, and vehicle dynamics. Then the PID-based power allocation strategy and the rule-based power allocation strategy are presented. To verify the effectiveness of the proposed strategies, the dynamic programming algorithm is presented as a benchmark. Simulation studies are put forward to compare the performance of the presented power allocation strategies. In order to further verify the power allocation strategies with the hybrid power source systems, a semi-physical experimental platform is developed. Experiments are conducted to compare the fuel economy and dynamic property of the presented power allocation strategies with different hybrid structures under two typical dynamic road maps. In road map A, compared with the fuel cell and batteries hybrid structure,
the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 21.03% under the PID-based power allocation strategy, and improved by 21.86% under the rule-based power allocation strategy. In road map B, the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 26.70% under the PID-based power allocation strategy, and improved by 30.48% under the rule-based power allocation strategy. The results indicate that the proposed rule-based power allocation strategy with the fuel cell and ultracapacitors hybrid structure has good performance and fuel economy compared with the fuel cell and batteries hybrid structure, which can achieve a near optimal performance compared with the dynamic programming algorithm. Our future work will focus on the algorithm improvement and application of the presented power allocation strategy. CRediT authorship contribution statement Yujie Wang: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing original draft. Zhendong Sun: Conceptualization, Writing - review & editing. Xiyun Li: Conceptualization, Writing - review & editing. Xiaoyu Yang: Conceptualization, Writing - review & editing. Zonghai Chen: Funding acquisition, Project administration, Supervision, Writing - review & editing. Acknowledgment This work is supported by the National Natural Science Foundation of China (Grant No. 61803359). References [1] Peighambardoust SJ, Rowshanzamir S, Amjadi M. Review of the proton exchange membranes for fuel cell applications[J]. Int J Hydrogen Energy 2010;35(17):9349e84. [2] Kirubakaran A, Jain S, Nema RK. A review on fuel cell technologies and power electronic interface[J]. Renew Sustain Energy Rev 2009;13(9):2430e40. [3] Wang Y, Chen KS, Mishler J, et al. A review of polymer electrolyte membrane fuel cells: technology, applications, and needs on fundamental research[J]. Appl Energy 2011;88(4):981e1007. [4] Weyers C, Bocklisch T. Simulation-based investigation of energy management concepts for fuel cellebatteryehybrid energy storage systems in mobile applications[J]. Energy Procedia 2018;155:295e308. [5] Wang Y, Zhang X, Liu C, et al. Multi-timescale power and energy assessment of lithium-ion battery and supercapacitor hybrid system using extended Kalman filter[J]. J Power Sources 2018;389:93e105. [6] Azib T, Bethoux O, Remy G, et al. An innovative control strategy of a single converter for hybrid fuel cell/supercapacitor power source[J]. IEEE Trans Ind Electron 2010;57(12):4024e31. [7] Zandi M, Payman A, Martin JP, et al. Energy management of a fuel cell/ supercapacitor/battery power source for electric vehicular applications[J]. IEEE Trans Veh Technol 2011;60(2):433e43. [8] Li Q, Chen W, Liu Z, et al. Development of energy management system based on a power sharing strategy for a fuel cell-battery-supercapacitor hybrid tramway[J]. J Power Sources 2015;279:267e80. [9] Rodatz P, Paganelli G, Sciarretta A, et al. Optimal power management of an experimental fuel cell/supercapacitor-powered hybrid vehicle[J]. Contr Eng Pract 2005;13(1):41e53. €l S, Davat B. Control strategy of fuel cell/supercapacitors [10] Thounthong P, Rae hybrid power sources for electric vehicle[J]. J Power Sources 2006;158(1): 806e14. [11] Payman A, Pierfederici S, Meibody-Tabar F. Energy management in a fuel cell/ supercapacitor multisource/multiload electrical hybrid system[J]. IEEE Trans Power Electron 2009;24(12):2681e91. [12] Xu L, Ouyang M, Li J, et al. Application of Pontryagin's Minimal Principle to the
12
[13]
[14]
[15]
[16] [17] [18]
[19]
Y. Wang et al. / Energy 189 (2019) 116142 energy management strategy of plugin fuel cell electric vehicles[J]. Int J Hydrogen Energy 2013;38(24):10104e15. Wang Y, Sun Z, Chen Z. Energy management strategy for battery/supercapacitor/fuel cell hybrid source vehicles based on finite state machine[J]. Appl Energy 2019;254:113707. Lopez GL, Rodriguez RS, Alvarado VM, et al. Hybrid PEMFC-supercapacitor system: modeling and energy management in energetic macroscopic representation[J]. Appl Energy 2017;205:1478e94. Thounthong P, Chunkag V, Sethakul P, et al. Comparative study of fuel-cell vehicle hybridization with battery or supercapacitor storage device[J]. IEEE Trans Veh Technol 2009;58(8):3892e904. Burke A. Ultracapacitors: why, how, and where is the technology[J]. J Power Sources 2000;91(1):37e50. Srinivasan V, Weidner JW. Mathematical modeling of electrochemical capacitors[J]. J Electrochem Soc 1999;146(5):1650e8. Lin C, Ritter JA, Popov BN, et al. A mathematical model of an electrochemical capacitor with double-layer and faradaic processes[J]. J Electrochem Soc 1999;146(9):3168e75. Wang Y, Liu C, Pan R, et al. Modeling and state-of-charge prediction of lithium-ion battery and ultracapacitor hybrids with a co-estimator[J]. Energy
2017;121:739e50. [20] Zhang L, Wang Z, Hu X, et al. A comparative study of equivalent circuit models of ultracapacitors for electric vehicles[J]. J Power Sources 2015;274:899e906. [21] Zhang L, Hu X, Wang Z, et al. A review of supercapacitor modeling, estimation, and applications: a control/management perspective[J]. Renew Sustain Energy Rev 2018;81:1868e78. [22] Mann RF, Amphlett JC, Hooper MAI, et al. Development and application of a generalised steady-state electrochemical model for a PEM fuel cell[J]. J Power Sources 2000;86(1e2):173e80. [23] Ang KH, Chong G, Li Y. PID control system analysis, design, and technology[J]. IEEE Trans Control Syst Technol 2005;13(4):559e76. [24] Wang Y, Zhang C, Chen Z. A method for state-of-charge estimation of LiFePO4 batteries at dynamic currents and temperatures using particle filter[J]. J Power Sources 2015;279:306e11. [25] PenCg S. A generalized dynamic programming principle and Hamilton-JacobiBellman equation[J]. Stochastics: Int J Prob Stoch Process 1992;38(2):119e34. [26] EPA Highway fuel economy test cycle (HFETC). Available online: https://www. dieselnet.com/standards/cycles/hwfet.php. [Accessed 5 March 2019]. [27] EPA urban dynamometer driving Schedule (UDDS). Available online: https:// www.dieselnet.com/standards/cycles/ftp72.php. [Accessed 5 March 2019].
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
A comparative study of power allocation strategies used in fuel cell and ultracapacitor hybrid systems Yujie Wang a, Zhendong Sun a, Xiyun Li a, Xiaoyu Yang b, Zonghai Chen a, * a
Department of Automation, University of Science and Technology of China, Hefei, Anhui, 230027, PR China National Experimental Teaching Demonstrating Center of Information and Computer, University of Science and Technology of China, Hefei, Anhui, 230027, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 July 2019 Received in revised form 13 September 2019 Accepted 16 September 2019 Available online 19 September 2019
The proton exchange membrane fuel cell is a good candidate for the future green transportation. In the vehicle applications, the fuel cell systems are always grouped with other energy storage devices such as the lithium-ion batteries and ultracapacitors in order to enhance their dynamic performance. The energy management strategy, especially the power allocation strategy plays an important role in the energy management system of the vehicles. This paper presents a comparative study of the power allocation strategies used in different hybrid structures. First, a framework of the fuel cell and ultracapacitors hybrid system is established considering the models of the ultracapacitor, fuel cells, and vehicle dynamics. Then the suboptimal on-line power allocation strategies based on classical cybernetics and rules are presented. The off-line dynamic program algorithm is employed as an optimal solution in order to compare with the proposed suboptimal on-line power allocation strategies. After that, simulations are put forward to compare the performance of the presented power allocation strategies. Finally, experimental studies are conducted to compare the fuel economy and the dynamic property of different hybrid structures using a semi-physical experimental platform. Compared with the fuel cell and batteries hybrid structure, the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 21.03%e26.70% under the PID-based power allocation strategy, and improved by 21.86%e30.48% under the rule-based power allocation strategy. The results indicate that the proposed rule-based strategy can achieve a near optimal performance compared with the dynamic programming algorithm and is easily applied online. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Power allocation strategy System modeling Dynamic programming Rule-based strategy
1. Introduction 1.1. Background and motivation Due to the environmental pollution and the shortage of petrochemical resources, the development of sustainable and clean new energy has risen in the world's agenda. The fuel cells have attracted much attention because of their high efficiency and environmental friendship [1]. A fuel cell is an electrochemical device that converts the chemical energy of the fuel and oxidant directly into electrical energy [2]. In the automotive industry, the most widely used fuel cells are the proton exchange membrane fuel cells which produce
* Corresponding author. E-mail addresses: [email protected] (Y. Wang), [email protected] (Z. Sun), [email protected] (X. Li), [email protected] (X. Yang), chenzh@ ustc.edu.cn (Z. Chen). https://doi.org/10.1016/j.energy.2019.116142 0360-5442/© 2019 Elsevier Ltd. All rights reserved.
electricity with water as their only by-products [3]. Compared with other kinds of the fuel cells, e.g. solid oxide fuel cells, molten carbonate fuel cells and phosphoric acid fuel cells, the proton exchange membrane fuel cells have specialties of low start-up temperature, lightweight and long endurance. The fuel cell vehicles have great superiorities in energy efficiency, endurance mileage, charging speed and climate tolerance compared with the electrified vehicles powered by the secondary batteries. However, there are several significant disadvantages. Firstly, the dynamic response of the fuel cell system is not as fast as that of the electrified vehicles, and it is difficult to track the peak power when the external demand power changes dramatically. Moreover, the fuel cell system cannot recover the braking energy, which causes energy waste and reduces the system efficiency in the frequently braking urban traffic conditions. Therefore the fuel cells are often used in conjunction with other energy storage devices, e.g. the lithium-ion batteries [4] or the ultracapacitors. The ultracapacitors or the so called “electrochemical double-
2
Y. Wang et al. / Energy 189 (2019) 116142
layer capacitors (EDLC)”, are another type of electrochemical energy storage devices which share some similarities to the lithiumion batteries. The difference is that their energy densities are about one tenth that of the lithium-ion batteries, but their power densities are of more than ten times that of the lithium-ion batteries which can quickly response instantaneous high power to meet external demand for peak power. Moreover, the lifespans of the ultracapacitors are longer than most batteries which are appropriate to applications requiring high power and long cycle life. The hybrid use of the fuel cells and ultracapacitors can effectively improve the system performance of the fuel cell vehicles. Wang et al. [5] proposed a multi-timescale power and energy evaluation approach for the lithium-ion battery and ultracapacitor hybrid system. Compared with the lithium-ion batteries, the ultracapacitors can provide fast and effective energy outputs. 1.2. Literature review One of the key problem when the fuel cells are used in a hybrid system is how to allocate power to fuel cells and energy storage devices (ultracapacitors or batteries) and ensure the safety and efficiency of the power system. A variety of energy management strategies can be found in the literature. Azib et al. [6] proposed a decoupling strategy in the frequency domain which can make the high-frequency part of the demand energy shared by ultracapacitors to prolong the lifespan of the fuel cell system. Zandi et al. [7] developed a method which is based on the flatness control technique and fuzzy logic control. The main feature of this strategy is to use a single general control algorithm to manage the power of the power supply in different operating modes, avoiding any algorithm commutation. Li et al. [8] proposed a power allocation strategy based on wavelet transform and fuzzy logic control, the burden of the fuel cell caused by rapid changes of large current was reduced. Rodatz et al. [9] developed an equivalent consumption minimization strategy to determine the real-time optimal power allocation which can improve fuel efficiency along with robustness. Thounthong et al. [10] proposed a control strategy for a fuel cell and ultracapacitor hybrid vehicle based on direct current link voltage regulation. This method can minimize the mechanical stresses of fuel cell and ensure a good synchronization between the fuel flow and the fuel cell current. Payman et al. [11] proposed a flatnessbased nonlinear control method and designed an observer to estimate parameters of the fuel cell which varies with the environment. Experimental results demonstrated that the proposed method was robust both in the normal and overload modes. Xu et al. [12] presented an optimal energy management strategy based on dynamic programming and Pontryagin's minimal law. The fuel economy of the presented strategy is analyzed with simulation models. Wang et al. [13] developed an energy management strategy for the battery, ultracapacitor, and fuel cell hybrid power source vehicles based on finite state machine. The presented strategy is compared with the dynamic programming algorithm, and the fuel economy and dynamic property are analyzed. Lopez et al. [14] employed a rule-based power management strategy where a low pass filter is used to split the power between different power sources. The benefits of the energy management strategy with respect to the prevention of oxygen starvation and reduction of start and stop times are analyzed. The above-mentioned literature both the rule-based approaches and the optimization-based approaches can achieve good expected control requirements. However, a comparative study of the power allocation strategies for the fuel cell and ultracapacitor hybrid system has not been reported in the existing literature. Moreover, strategies with low computation complexity and calculation cost which are suitable for practical applications need to be developed.
1.3. Objectives and contributions Because of the high power density and energy recovery capability of the ultracapacitors, the hybrid of ultracapacitors and fuel cells has better robustness in power control [15]. To fulfill the power balance between the load power and the energy storage devices, the energy management strategy plays an important role in the hybrid energy storage system. This work is committed to proposing appropriate power allocation strategies based on rules and classical cybernetics with low computation complexity. The main contributions of this paper are as follows: First, the framework of the fuel cell and ultracapacitor hybrid power system is established with accurate modeling of the ultracapacitors, fuel cells, and vehicle dynamics. Second, the power allocation strategies based on rules and classical cybernetics are put forward. Moreover, the dynamic programming algorithm is used as a benchmark to verify the effectiveness of the proposed strategies. Third, the performance of the proposed power allocation strategies has been compared systematically with simulations and experiments under different working conditions using a semi-physical experimental platform. Simulation results show that the proposed strategies can achieve a near optimal performance when comparing with dynamic programming algorithm. The proposed suboptimal strategies are moreover easily applied online. 1.4. Outline of the paper The remainder of this paper is organized as follows. In Section 2, the framework of the system structure and the models of the ultracapacitors, fuel cells, and vehicle dynamics are introduced. In Section 3, the power allocation strategies based on rules and classical cybernetics are introduced. The off-line dynamic programming algorithm is presented as a benchmark compared with the proposed suboptimal strategies. In Section 4, experiments are conducted under different working conditions using a semiphysical experimental platform. Finally, the conclusions and potential future work are given in Section 5. 2. System structure and modeling In this section, the overall framework of the system structure and the models of the ultracapacitor, the fuel cell, and the vehicle dynamics will be introduced. 2.1. System structure The overall framework of the vehicle structure is shown in Fig. 1. The ultracapacitors are used to provide supplemental power for starting, accelerating, climbing, and recover energy from vehicle braking. A bidirectional DC/DC converter is used to connect the ultracapacitors with the DC/AC inverter. The fuel cell system is used to convert the chemical energy to electrical energy through an electrochemical reaction of the hydrogen and oxygen. A unidirectional DC/DC converter is used to connect the fuel cell system and the DC/AC inverter. Compared with the battery and fuel cell hybrid system, the ultracapacitors have higher power densities, which can better alleviate the burden of the fuel cell system when the load power fluctuates violently. Moreover, the ultracapacitors have longer lifespans than lithium-ion batteries. Therefore the replacement and maintenance costs can be saved. 2.2. Model description 2.2.1. Model description of the ultracapacitor The structure of ultracapacitors is essentially the same as a
Y. Wang et al. / Energy 189 (2019) 116142
Physical connection Ultracapacitor
H2
Cooler
Hydrogen Tank
Air O2 Compressor Fuel cell system
Humidifier
Signal connection
3
Bidirectional
Bidirectional
Convertor DC/DC
Invertor DC/AC
Unidirectional Fuel Cell Stack
Convertor DC/DC
Motor
Energy management system
H2O
Fig. 1. Structure of the fuel cell and ultracapacitor hybrid system.
lithium-ion battery. There are negative and positive electrodes, current collectors, and a separator. The electrodes are composed of small particles, within their voids filled by an electrolyte solution [16]. Diverse models have been developed in the literature to describe the internal and external behaviors of the ultracapacitors, e.g. the physics-based models (PBMs) [17,18] and the equivalentcircuit models (ECMs) [19]. The PBMs have high accuracy describing the potential of the solid particles and electrolyte. However, the partial differential equations of the PBMs are complex and the model parameters are difficult to identify in practical applications. The ECMs are widely used in practice because they can approximate the input and output behaviors with simple structures. For the ultracapacitors, three representative ECMs with different computational demands and prediction accuracies are the classic model, the multi-stage ladder model and the dynamic model [20]. In this work, the classic model with sufficiently simple structure yet capturing the key dynamics of the ultracapacitor is employed. The structure of the classic model is shown in Fig. 2. The dynamic behavior and the output of the model can be described by Eqs. (1) and (2) according to Ref. [21].
2.2.2. Model description of the fuel cell The fuel cell model [22] can be described by:
Vfc ¼ Voc Vact Vohm Vconc
where Vfc represents the model output of the fuel cell, Voc represents the open-circuit voltage (OCV) of the fuel cell, Vact represents the activation loss, Vohm represents the ohmic loss, and Vconc represents the concentration loss. The OCV of the fuel cell can be expressed by Eq. (4) according to Ref. [22].
Voc ¼ 1:229 0:85 103 Tfc 298:15 þ 4:309 105 1 298:15 lnðpH2 Þ þ lnðpO2 Þ 2
(1)
VT ¼ Vp þ Rs IL
(2)
where VT represents the terminal voltage, Rs represents the internal series resistance which includes the electrolyte resistance and contact resistance, Cp represents the equivalent capacitor, Rp represents the self-discharge resistance, Vp denotes the voltage across the capacitor and IL represents the current of the ultracapacitor (define positive for charge and negative for discharge).
V
Rs
C 0
0 IL
VT
Vp
I t
IL
Fig. 2. The classic model of the ultracapacitor.
(5)
where v0 denotes the voltage drop at zero current density, Ifc represents the current of the fuel cell, A represents the active area of the fuel cell, va and c1 are model coefficients. The ohmic loss of the fuel cell can be expressed by:
Vohm ¼ Ifc Rohm
(6)
where Rohm represents the internal ohmic resistance depends on the temperature and membrane humidity of the fuel cell. Finally, the concentration loss of the fuel cell can be expressed by:
Vconc
t
1
Ifc B C Vact ¼ v0 þ va @1 ec1 A A
Rp
VT
(4)
where Tfc represents the Kelvin temperature of the fuel cell, pH2 represents the pressure of hydrogen, and pO2 represents the pressure of oxygen. The activation loss of the fuel cell can be expressed by:
0 dVp 1 1 ¼ Vp þ IL Rp Cp Cp dt
(3)
I ¼ fc A
c2
Ifc ADfc;max
!c3 (7)
where Dfc,max represents the current density causes precipitous voltage drop, c2 and c3 are model coefficients. 2.2.3. Model description of the vehicle dynamics The aggregate demand power of the vehicle power system needs to overcome the rolling frictional resistance, the component resistance of the vehicle's weight acting on the road with slope q,
4
Y. Wang et al. / Energy 189 (2019) 116142
the air resistance, and the acceleration resistance. Therefore the power requirement can be calculated by:
Pm ¼ h mMgsinq þ Mgsinq þ 0:5rair Aw Cair u2 þ
du dM u dt
(8)
where h denotes the efficiency of the transmission system, m denotes the rolling resistance coefficient, M denotes the vehicle mass, g denotes the gravitational acceleration, rair denotes the density of air, Aw denotes the windward area of the vehicle, Cair denotes the coefficient of air resistance, d denotes the correction coefficient of the rotation mass, and u denotes the vehicle speed. In order to verify the accuracy of the presented models of the ultracapacitor and the fuel cell, experiments are conducted with a real ultracapacitor (Maxwell BCAP3000) (1.35 Ve2.7 V @25 C). The model prediction results of the ultracapacitor are compared with the measured values as shown in Fig. 3 (a). The mean absolute error (MAE) of the ultracapacitor model is 2.4 mV and the root mean square error (RMSE) is 2.9 mV. The results indicate that the presented ultracapacitor model can accurately simulate the real voltage with maximum absolute error (MaxE) less than 10 mV. To verify the accuracy of the fuel cell model, we conduct experiments and draw a current vs. power diagram shown in Fig. 3(b) in which the model outputs are compared with the experiment results with an error less than 0.5 kW. The polarization voltage curve (0.6 Ve1 V @60 C) of the fuel cell stack model is shown in Fig. 3(d), and the specifics of the OCV, activation loss, ohmic loss, and concentration loss are plotted in Fig. 3(c). From the figures, we can see that the prediction results of the fuel cell stack model are accordant with the experiment results.
3. Energy management strategy The energy management strategy is important in the hybrid energy storage system. In order to rationally assign the load power of the designed vehicle model, the on-line power allocation strategy based on classical cybernetics and the strategy based on criterion rules are introduced in this section. The off-line dynamic program algorithm is employed as an optimal solution in order to compare with the proposed suboptimal on-line power allocation strategies. 3.1. PID-based power allocation strategy 3.1.1. Design of the PID controller In classical cybernetics, the PID control has been widely used owing to its quick response speed, high steady accuracy and good robustness [23]. In order to make the fuel cell system and ultracapacitors work together and meet the demand power of the vehicle motor, a PID control algorithm is proposed for the power allocation of the hybrid power source system. The principle of the control strategy is to keep the state-ofcharge (SOC) of the ultracapacitors near its enactment value so that the system can calculate the required power of the fuel cell system and ultracapacitors adaptively through the closed-loop control algorithm. In the fuel cell system, the PID controller functions the hydrogen flow valve by the residual of the stated and estimated SOC of the ultracapacitors, which changes the power output of the fuel cell. The diagram of the PID-based power allocation strategy for the fuel cell and ultracapacitor hybrid power source system is shown in Fig. 4. Specifically, based on the model of
Fig. 3. Experimental results of the ultracapacitor and fuel cell system: (a) Model prediction of the ultracapacitor (1.35 Ve2.7 V @25 C). (b) Output power of the fuel cell system. (c) Model prediction of fuel cell system (OCV, activation loss, ohmic loss, and concentration loss). (d) Polarization voltage curve of the fuel cell (0.6 Ve1 V @60 C).
Y. Wang et al. / Energy 189 (2019) 116142
5
Fig. 4. Diagram of the PID-based power allocation strategy.
the ultracapacitors introduced in Section 2.2.1, the discrete time state-space equation for the ultracapacitors state estimation can be established as follows:
3.1.2. Simulation results of the PID controller The simulation results of the PID-based power allocation strategy under the New European Driving Cycle (NEDC) are shown in Fig. 5. The power allocation results of the fuel cell and ultra-
8 3 3 2 2 hDt=CN 1 0 " # # " > > > zk z 7 7 6 6 > k1 > 7 7I < ¼6 þ6 5 5 L;k1 4 4 Vp;k Vp;k1 0 exp Dt R C 1 exp Dt R C Rp > p p p p > > > > : VT;k ¼ Vp;k þ Rs IL;k
where zk represents the SOC of the ultracapacitors, h represents the coulombic efficiency, Dt represents the sample time, and CN represents the nominal capacity of the ultracapacitor. Then the SOC can be observed by the model-based state estimation algorithms, e.g. unscented Kalman filter (UKF) or particle filter (PF) which can be found in our previous work [19,24]. and the control algorithm of the PID controller can be expressed as:
ð _ uðtÞ ¼ kp eðtÞ þ ki eðtÞdt þ kd eðtÞ
(10)
where e(t) ¼ z(t)-z*, z* denotes the set value of the ultracapacitor's SOC (z* ¼ 0.6), kp, ki and kd are proportion, integration, and differentiation parameters of the PID controller. In this work, the parameters kp, ki, and kd are 1 105, 9 103, and 1 102.
(9)
capacitors are shown in Fig. 5 (a) and the SOC of the ultracapacitors are shown in Fig. 5 (b). From the simulation results, we can see that the PID-based power allocation strategy can satisfy the demand power, and the ultracapacitors can absorb most of the regenerated energy. However, both the power of the fuel cell and the ultracapacitors have a certain amount of overshoots when the demand power changes. Moreover, the fuel cell still suffers from high peak power shocks. From the variation curve of the SOC, the residual capacity of the ultracapacitors has not been used in full range.
3.2. Rule-based power allocation strategy 3.2.1. Design of the rule-based controller In order to overcome the drawbacks of the PID controller, a rule-
Fig. 5. Simulation results of the PID-based power allocation strategy: (a) power allocation of the fuel cell and ultracapacitors. (b) SOC of the ultracapacitors.
6
Y. Wang et al. / Energy 189 (2019) 116142
Strategy
Criterion Start
Pm>0?
Yes
Power allocation strategy
Yes
Fuel cell Ready?
No
Fuel cell startup mode
Puc =Pm+Paux Pfc =0
No
ultracapacitor s are full
No
Energy recovery mode (A)
Puc =-Pm Pfc =0
Energy recovery mode (B)
Puc =0 Pfc =0
FC and UC combined operating mode
Puc =Pm-Pfc,max Pfc =Pfc,max
Fuel cell individual operating mode (A)
Puc =0 Pfc =Pm
Fuel cell individual operating mode (B)
Puc =0 Pfc =Pfc,max
Fuel cell individual operating mode (C)
Puc =-|Pfc,max-Pm| Pfc =Pfc,max
Yes
ultracapacitor s are empty
Operating modes
Yes
No
Pm>Pfc,max
Yes
No
Pm>Pfc,max
Yes
No
Fig. 6. Rule-based power allocation strategy.
based power allocation strategy is presented for the fuel cell and ultracapacitor hybrid system. The control principle of the rulebased power allocation strategy is the fuel cell system provides a relatively stable power whereas the ultracapacitors provide the transient peak power. Therefore the burden of the fuel cell can be alleviated by the ultracapacitors. The rule-based power allocation strategy is shown in Fig. 6. According to this rule-based power allocation strategy, the operating modes of the fuel cell and ultracapacitor hybrid system can be divided into 4 cases: Case 1. Fuel cell startup mode. In this operating mode, the fuel cell system needs to be activated by auxiliary power in order to finish gas purging and preheating. Therefore all the demand power Pm of the motor and the startup power of the fuel cell Paux should be provided by the ultracapacitors. Case 2. Fuel cell and ultracapacitor combined operating mode. After the fuel cell finish gas purging and preheating and the ultracapacitors have enough residual capacity, whereas the demand power is higher than the fuel cell maximum output power Pfc,max, the system turns into the fuel cell and ultracapacitor combined operating mode. The fuel cell provides its maximum power output, and the residual power (Pm - Pfc,max) is provided by the ultracapacitors. Case 3. Fuel cell individual operating mode. In the condition that the demand power is lower than the fuel cell maximum output power the fuel cell individually provides the demand power. When the ultracapacitors do not have enough residual capacity, the demand power should be provided by the fuel cell individually. Moreover, in order to maintain a stable output of the fuel cell and charge the empty ultracapacitors, the ultracapacitors are used to absorb excess power (-|Pfc,max - Pm|) provided by the fuel cell system. Case 4. Energy recovery mode. In this operating mode, the controller controls the regenerated energy feeding to the ultracapacitors due to the residual capacity of the ultracapacitors. If the ultracapacitors are full, the controller cuts off the DC/DC converter and the ultracapacitors stop absorb the regenerated energy.
The hybrid use of the fuel cells and ultracapacitors can effectively improve the system performance of the fuel cell vehicles. If the SOC of the ultracapacitors is too high, the braking energy cannot be absorbed, if the SOC of the ultracapacitors is too low, it will not help the system to share the peak power, so the proposed strategy based on the SOC variation range of the ultracapacitors is helpful to keep the SOC of ultracapacitors in an appropriate range and balance between the load power and the energy storage devices. The superiority of the rule-based power allocation strategy is that the stable power can be provided by the fuel cell whereas the instantaneous peak power can be provided by the ultracapacitors. Moreover, the ultracapacitors can also recover most of the regenerated energy when the vehicle brakes. 3.2.2. Simulation results of the rule-based controller The simulation results of the proposed rule-based power allocation strategy under the NEDC are shown in Fig. 7. The power allocation results of the fuel cell and ultracapacitors under NEDC are shown in Fig. 7 (a) and the SOC of the ultracapacitor is shown in Fig. 7 (b). The proposed rule-based power allocation strategy can satisfy the demand power with a rational allocation of the fuel cell's power and the ultracapacitors' power as shown in Fig. 7 (a). The ultracapacitors can also absorb most of the regenerated energy from vehicle breaks. It can overcome the problem of overshoots in the PID-based power allocation strategy. Moreover, the SOC utilization range of ultracapacitors has increased by 35%. 3.3. Dynamic programming strategy 3.3.1. Design of dynamic programming algorithm The dynamic programming algorithm based on Bellman's optimality principle is widely used for solving multistage decisionmaking problems [25], and it is suitable for energy management problems especially the power allocation problem. The dynamic programming algorithm is presented as an optimal solution for the power allocation of the fuel cell and ultracapacitors hybrid energy storage system. In this work, the dynamic programming method is used as a benchmark to verify the effectiveness of the proposed strategies.
Y. Wang et al. / Energy 189 (2019) 116142
7
Fig. 7. Simulation results of the rule-based power allocation strategy: (a) power allocation of the fuel cell and ultracapacitors. (b) SOC of the ultracapacitors.
For the fuel cell and ultracapacitor hybrid energy storage system, we choose the fuel cell output power Pfc as the control variable and the SOC of the ultracapacitors as the state variable. The cost function J to be minimized is the total hydrogen consumption, which is given as follows:
ðtf J¼
m_ Pfc ðtÞ; t dt
(11)
0
where tf denotes the break up time, m denotes the hydrogen consumption. Then the problem can be described as follows:
ðf minJ ¼ min m_ Pfc ðtÞ; t dt t
obj :
0
st: :
8_ zðtÞ ¼ f ðzðtÞ; IL ðtÞÞ > > > > > > zð0Þ ¼ z tf > > > < Pfc ðtÞ ¼ Pm ðtÞ IL ðtÞVT ðtÞ > > z > min zðtÞ zmax > > > > > Puc;min Puc Puc;max > : Pfc;min Pfc Pfc;max
(12)
In order to calculate the hydrogen consumption more
accurately, the equation z(0) ¼ z(tf) is added as a constraint when applying the dynamic programming algorithm.
3.3.2. Simulation results of the dynamic programming algorithm The simulation results of the dynamic programming power allocation strategy under the NEDC are shown in Fig. 8. The power allocation results of the fuel cell and ultracapacitors under NEDC are shown in Fig. 8 (a) and the SOC of the ultracapacitor is shown in Fig. 8 (b). Fig. 8(b) illustrates that based on the dynamic programming power allocation strategy, the ultracapacitors can absorb most of the peak power. The fuel cell provides a relatively stable power output, which matches the results of the presented rulebased power allocation strategy. The simulation results also show that the proposed rule-based power allocation strategy can achieve a near optimal performance compared with the dynamic programming algorithm.
4. Experimental verification and analysis In this section, to further analyze the performance of the presented power allocation strategies, experiments are conducted on a semi-physical experimental platform. The dynamic property and fuel economy of the presented power allocation strategies are compared with different hybrid structures under different road maps.
Fig. 8. Simulation results of the dynamic programming power allocation strategy: (a) power allocation of the fuel cell and ultracapacitors. (b) SOC of the ultracapacitors.
8
Y. Wang et al. / Energy 189 (2019) 116142
Fig. 9. Semi-physical experimental platform.
4.1. Semi-physical experimental platform In order to apply the power allocation strategies with the hybrid power source system, a semi-physical experimental platform is developed as shown in Fig. 9. The electronic load tester NEWARE BTS-4000 can communicate with the host computer through TCP/ IP protocol and is used to test the ultracapacitors and monitor the voltage and current of the ultracapacitors in real time. The host computer is used to develop the models and power allocation strategies using MATLAB/Simulink® where the vehicle dynamic simulation platform and the fuel cell simulation platform are included. The parameters of the fuel cell simulation platform and the vehicle dynamics are shown in Table 1 and Table 2, respectively. It also should be pointed out that the energy density and power
Table 1 Parameters of the fuel cell simulation platform. Parameters
Values
Maximum current density Charge transfer coefficient Volume of anode Volume of cathode Hydrogen gas constant Oxygen gas constant Ideal gas constant Faraday constant Reference temperature
2.2 A/cm2 0.5 0.005 m3 0.01 m3 4124.36 J/(mol$K) 259.81 J/(mol$K) 8.31 J/(mol$K) 96485.33 C/mol 298.15 K
Table 2 Parameters of the vehicle dynamics. Parameters
Values
Vehicle mass Efficiency of the transmission system Rolling resistance coefficient Density of air Gravitational acceleration Windward area of the vehicle Coefficient of air resistance Correction coefficient of the rotation mass
1480 kg 0.9 0.015 1.202 kg/m3 9.8 m/s2 2 m2 0.3 1.04
density of the ultracapacitors are quite different with the lithiumion batteries, which means that the size of ultracapacitors is larger than the lithium-ion batteries for the same energy requirements. However, as a kind of power output device, the power capability of the ultracapacitor is much higher than the battery. In the configuration of the hybrid energy storage systems, the ultracapacitors are used to provide and absorb instantaneous high energy, and the fundamental and stable output is provided by the fuel cell system. The difference in energy/power density between the battery and ultracapacitor is reflected in the weight of the energy storage system, which should be considered in the vehicle mass in the vehicle dynamic model. 4.2. Results and discussions In order to compare the performance of the proposed PID-based and rule-based power allocation strategies, the dynamic property and fuel economy of the presented power allocation strategies are compared with different hybrid structures under different road maps. Moreover, the results of the dynamic programming strategy are presented as a benchmark. The results of the PID-based and rule-based power allocation strategies are compared with the dynamic programming strategy which is recognized as an optimal solution for power allocation of hybrid power source system. The qualitative and quantitative analysis results are presented as follows. 4.2.1. Results of road map A The results of the presented power allocation strategies with different hybrid structures under the EPA Highway Fuel Economy Test Cycle [26] (road map A) are shown in Fig. 10. The PID-based power allocation results of the fuel cell and ultracapacitors hybrid structure are shown in Fig. 10 (a). The SOC curve of the ultracapacitors based on PID control is shown in Fig. 10 (b). It can be seen that the PID-based power allocation strategy can satisfy the demand power, and the ultracapacitors can absorb most of the regenerated energy. However, the power output of the fuel cell is not stable. The rule-based power allocation results of the fuel cell and ultracapacitors hybrid structure are shown in Fig. 10 (e) and the SOC curve of the ultracapacitors is shown in Fig. 10 (f). Compared with
Y. Wang et al. / Energy 189 (2019) 116142
9
Fig. 10. Results of power allocation strategies with different hybrid structures under EPA Highway Fuel Economy Test Cycle: (a) PID-based power allocation of the fuel cell and ultracapacitors hybrid structure. (b) SOC of the ultracapacitors based on PID control. (c) PID-based power allocation of the fuel cell and batteries hybrid structure. (d) SOC of the batteries based on PID control. (e) Rule-based power allocation of the fuel cell and ultracapacitors hybrid structure. (f) SOC of the ultracapacitors based on rule-based control. (g) Rule-based power allocation of the fuel cell and batteries hybrid structure. (h) SOC of the batteries based on rule-based control. (i) Dynamic programming power allocation of the fuel cell and ultracapacitors hybrid structure. (j) SOC of the ultracapacitors based on dynamic programming. (k) Dynamic programming power allocation of the fuel cell and batteries hybrid structure. (l) SOC of the batteries based on dynamic programming.
the PID-based power allocation strategy, the rule-based strategy provides more optimized power allocation of the fuel cell and ultracapacitors where the fuel cell system provides stable power outputs and the ultracapacitors take responsibility to provide peak power and absorb regenerated energy. In addition, the SOC operating range of the rule-based power allocation strategy has been expanded. The PID-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 10 (c) and the SOC curve of the batteries based on the PID control is shown in Fig. 10 (d). In this structure, the batteries take the role of the ultracapacitors. Similar to the fuel cell and ultracapacitors hybrid system, the power output of the fuel cell is also erratic. The rule-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 10 (g), and the SOC curve of the batteries is shown in Fig. 10 (h). In the rule-based power allocation strategy, power constraints
have been added to prevent the batteries from over-charging and over-discharging, therefore the regenerated energy cannot be absorbed in very high levels of SOC. The hydrogen consumptions of the fuel cell and ultracapacitors hybrid structure and the fuel cell and batteries hybrid structure under road map A are compared in Table 3. The hydrogen consumptions of the fuel cell and ultracapacitors hybrid structure with the PID-based and rule-based power allocation strategies are 0.507 kg and 0.529 kg, respectively. Whereas the hydrogen consumptions of the fuel cell and batteries hybrid structure with the PID-based and rule-based power allocation strategies are 0.642 kg and 0.677 kg, respectively. The fuel cell and ultracapacitors hybrid structure has higher fuel economy than the fuel cell and batteries hybrid structure. Compared with the fuel cell and batteries hybrid structure, the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 21.03% under the PID-based
Table 3 Hydrogen consumptions under road map A.
Fuel cell & ultracapacitors Fuel cell & batteries
PID-based Strategy
Rule-based Strategy
Dynamic programming
0.507 kg 0.642 kg
0.529 kg 0.677 kg
0.499 kg 0.502 kg
Y. Wang et al. / Energy 189 (2019) 116142
4.2.2. Results of road map B The results of the presented power allocation strategies with different hybrid structures under the EPA Urban Dynamometer Driving Schedule [27] (road map B) are shown in Fig. 11. The PIDbased power allocation of the fuel cell and ultracapacitors hybrid structure is shown in Fig. 11 (a). The SOC curve of the ultracapacitors based on PID control is shown in Fig. 11 (b). The PIDbased power allocation strategy can satisfy demand power. But the power output of the fuel cell is unstable especially when the load power changes dramatically. The SOC of the ultracapacitors can track the set target and meet the control requirements. The rule-based power allocation results of the fuel cell and ultracapacitors hybrid structure are shown in Fig. 11 (e) and the SOC curve of the ultracapacitors is shown in Fig. 11 (f). It can be seen that the power output of the fuel cell is much more stable than that of the PID-based power allocation strategy. Moreover, the ultracapacitors can suffer most of the instantaneous surges of high power and absorb all regenerated energy. The PID-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 11 (c) and the SOC curve of the batteries based on the PID control is shown in Fig. 11 (d). In the fuel cell and ultracapacitors hybrid structure, the power output of the fuel cell is unstable when the batteries are not full. When the
power allocation strategy, and improved by 21.86% under the rulebased power allocation strategy. In order to further compare the proposed on-line power allocation strategies with the off-line optimal approach. The dynamic programming algorithm is conducted, as shown in Fig.10 (i)e(l). The power allocation results of the fuel cell and ultracapacitors hybrid structure using the dynamic programming algorithm are shown in Fig. 10 (i), and the SOC curve of the ultracapacitors is shown in Fig. 10 (j). The power allocation results of the fuel cell and batteries hybrid structure using the dynamic programming algorithm are shown in Fig. 10 (k) and the SOC of the batteries is shown in Fig. 10 (l). As an optimal solution, the hydrogen consumption of dynamic programming is less than the PID and rule-based strategy. The hydrogen consumption of the fuel cell and ultracapacitors hybrid structure is 0.499 kg, and that of the fuel cell and batteries hybrid structure is 0.502 kg. Compared with the fuel cell and batteries hybrid structure, the fuel cell and ultracapacitors hybrid structure has better fuel economy. Moreover, in the cases of dynamic programming and rule-based strategy, the power allocation and SOC of the ultracapacitors are approximated which indicate that the presented rule-based strategy can obtain near optimal results.
PID-based
(c)
SOC PID-based Time (s) (f)
Time (s) (g)
Time (s) (h) Rule-based
Rule-based Time (s)
SOC
Power (W)
SOC
Power (W)
Rule-based
(i)
Rule-based
(j)
Time (s)
(k)
Time (s)
(l)
SOC
Power (W)
SOC
Power (W)
Dynamic programming
Time (s) Dynamic programming
Dynamic programming
Time (s)
PID-based
PID-based
Time (s) (e)
(d)
Power (W)
(b)
Power (W)
(a)
SOC
10
Dynamic programming Time (s)
Time (s)
Time (s)
Fig.11. Results of power allocation strategies with different hybrid structures under EPA Urban Dynamometer Driving Schedule: (a) PID-based power allocation of the fuel cell and ultracapacitors hybrid structure. (b) SOC of the ultracapacitors based on PID control. (c) PID-based power allocation of the fuel cell and batteries hybrid structure. (d) SOC of the batteries based on PID control. (e) Rule-based power allocation of the fuel cell and ultracapacitors hybrid structure. (f) SOC of the ultracapacitors based on rule-based control. (g) Rule-based power allocation of the fuel cell and batteries hybrid structure. (h) SOC of the batteries based on rule-based control. (i) Dynamic programming power allocation of the fuel cell and ultracapacitors hybrid structure. (j) SOC of the ultracapacitors based on dynamic programming. (k) Dynamic programming power allocation of the fuel cell and batteries hybrid structure. (l) SOC of the batteries based on dynamic programming.
Y. Wang et al. / Energy 189 (2019) 116142
11
Table 4 Hydrogen consumptions under road map B.
Fuel cell & ultracapacitors Fuel cell & batteries
PID-based Strategy
Rule-based Strategy
Dynamic programming
0.593 kg 0.809 kg
0.568 kg 0.817 kg
0.456 kg 0.457 kg
SOC of the batteries arrives the higher threshold (>0.95), the batteries stop absorbing the regenerated energy and start to discharge. The rule-based power allocation results of the fuel cell and batteries hybrid structure are shown in Fig. 11 (g) and the SOC curve of the batteries is shown in Fig. 11 (h). Because the power capability of the batteries is much lower than the ultracapacitors, the batteries need to operate with the fuel cell in most of the cycles. Moreover, at high levels of the SOC, the batteries should stop absorbing regenerated energy in order to prevent over-charging. The hydrogen consumptions of Road map B are shown in Table 4. The hydrogen consumptions of the fuel cell and ultracapacitors hybrid structure with the PID-based and rule-based power allocation strategies under road map B are 0.593 kg and 0.568 kg. The hydrogen consumptions of the fuel cell and batteries hybrid structure with the PID-based and rule-based power allocation strategies are 0.809 kg and 0.817 kg, respectively. In road map B, compared with the fuel cell and batteries hybrid structure, the fuel economy of the fuel cell and ultracapacitors hybrid structure has an improvement of 26.70% under the PID-based power allocation strategy, and an improvement of 30.48% under the rule-based power allocation strategy. The fuel cell and ultracapacitors hybrid structure can save more hydrogen than the fuel cell and batteries hybrid structure. The power allocation results of the fuel cell and ultracapacitors hybrid structure using the dynamic programming algorithm under road map B are shown in Fig. 11 (i), and the SOC curve of the ultracapacitors is shown in Fig. 11 (j). The power allocation results of the fuel cell and batteries hybrid structure using the dynamic programming algorithm are shown in Fig. 11 (k) and the SOC of the batteries is shown in Fig. 11 (l). The hydrogen consumption of the fuel cell and ultracapacitors hybrid structure is 0.456 kg, and that of the fuel cell and batteries hybrid structure is 0.457 kg. From the results, we can see that the power outputs of the fuel cell system in the fuel cell and ultracapacitors hybrid structure are stable both in the dynamic programming and rule-based strategy. In addition, the ultracapacitors can absorb most of the regenerated energy and provide peak power. The proposed rule-based power allocation strategy with the fuel cell and ultracapacitors hybrid structure can achieve a suboptimal performance under the road map B.
5. Conclusions This paper presents a comparative study on the power allocation strategies used in different hybrid structures. First, the framework of a fuel cell and ultracapacitors hybrid system is established with accurate modeling of the ultracapacitors, fuel cells, and vehicle dynamics. Then the PID-based power allocation strategy and the rule-based power allocation strategy are presented. To verify the effectiveness of the proposed strategies, the dynamic programming algorithm is presented as a benchmark. Simulation studies are put forward to compare the performance of the presented power allocation strategies. In order to further verify the power allocation strategies with the hybrid power source systems, a semi-physical experimental platform is developed. Experiments are conducted to compare the fuel economy and dynamic property of the presented power allocation strategies with different hybrid structures under two typical dynamic road maps. In road map A, compared with the fuel cell and batteries hybrid structure,
the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 21.03% under the PID-based power allocation strategy, and improved by 21.86% under the rule-based power allocation strategy. In road map B, the fuel economy of the fuel cell and ultracapacitors hybrid structure has improved by 26.70% under the PID-based power allocation strategy, and improved by 30.48% under the rule-based power allocation strategy. The results indicate that the proposed rule-based power allocation strategy with the fuel cell and ultracapacitors hybrid structure has good performance and fuel economy compared with the fuel cell and batteries hybrid structure, which can achieve a near optimal performance compared with the dynamic programming algorithm. Our future work will focus on the algorithm improvement and application of the presented power allocation strategy. CRediT authorship contribution statement Yujie Wang: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing original draft. Zhendong Sun: Conceptualization, Writing - review & editing. Xiyun Li: Conceptualization, Writing - review & editing. Xiaoyu Yang: Conceptualization, Writing - review & editing. Zonghai Chen: Funding acquisition, Project administration, Supervision, Writing - review & editing. Acknowledgment This work is supported by the National Natural Science Foundation of China (Grant No. 61803359). References [1] Peighambardoust SJ, Rowshanzamir S, Amjadi M. Review of the proton exchange membranes for fuel cell applications[J]. Int J Hydrogen Energy 2010;35(17):9349e84. [2] Kirubakaran A, Jain S, Nema RK. A review on fuel cell technologies and power electronic interface[J]. Renew Sustain Energy Rev 2009;13(9):2430e40. [3] Wang Y, Chen KS, Mishler J, et al. A review of polymer electrolyte membrane fuel cells: technology, applications, and needs on fundamental research[J]. Appl Energy 2011;88(4):981e1007. [4] Weyers C, Bocklisch T. Simulation-based investigation of energy management concepts for fuel cellebatteryehybrid energy storage systems in mobile applications[J]. Energy Procedia 2018;155:295e308. [5] Wang Y, Zhang X, Liu C, et al. Multi-timescale power and energy assessment of lithium-ion battery and supercapacitor hybrid system using extended Kalman filter[J]. J Power Sources 2018;389:93e105. [6] Azib T, Bethoux O, Remy G, et al. An innovative control strategy of a single converter for hybrid fuel cell/supercapacitor power source[J]. IEEE Trans Ind Electron 2010;57(12):4024e31. [7] Zandi M, Payman A, Martin JP, et al. Energy management of a fuel cell/ supercapacitor/battery power source for electric vehicular applications[J]. IEEE Trans Veh Technol 2011;60(2):433e43. [8] Li Q, Chen W, Liu Z, et al. Development of energy management system based on a power sharing strategy for a fuel cell-battery-supercapacitor hybrid tramway[J]. J Power Sources 2015;279:267e80. [9] Rodatz P, Paganelli G, Sciarretta A, et al. Optimal power management of an experimental fuel cell/supercapacitor-powered hybrid vehicle[J]. Contr Eng Pract 2005;13(1):41e53. €l S, Davat B. Control strategy of fuel cell/supercapacitors [10] Thounthong P, Rae hybrid power sources for electric vehicle[J]. J Power Sources 2006;158(1): 806e14. [11] Payman A, Pierfederici S, Meibody-Tabar F. Energy management in a fuel cell/ supercapacitor multisource/multiload electrical hybrid system[J]. IEEE Trans Power Electron 2009;24(12):2681e91. [12] Xu L, Ouyang M, Li J, et al. Application of Pontryagin's Minimal Principle to the
12
[13]
[14]
[15]
[16] [17] [18]
[19]
Y. Wang et al. / Energy 189 (2019) 116142 energy management strategy of plugin fuel cell electric vehicles[J]. Int J Hydrogen Energy 2013;38(24):10104e15. Wang Y, Sun Z, Chen Z. Energy management strategy for battery/supercapacitor/fuel cell hybrid source vehicles based on finite state machine[J]. Appl Energy 2019;254:113707. Lopez GL, Rodriguez RS, Alvarado VM, et al. Hybrid PEMFC-supercapacitor system: modeling and energy management in energetic macroscopic representation[J]. Appl Energy 2017;205:1478e94. Thounthong P, Chunkag V, Sethakul P, et al. Comparative study of fuel-cell vehicle hybridization with battery or supercapacitor storage device[J]. IEEE Trans Veh Technol 2009;58(8):3892e904. Burke A. Ultracapacitors: why, how, and where is the technology[J]. J Power Sources 2000;91(1):37e50. Srinivasan V, Weidner JW. Mathematical modeling of electrochemical capacitors[J]. J Electrochem Soc 1999;146(5):1650e8. Lin C, Ritter JA, Popov BN, et al. A mathematical model of an electrochemical capacitor with double-layer and faradaic processes[J]. J Electrochem Soc 1999;146(9):3168e75. Wang Y, Liu C, Pan R, et al. Modeling and state-of-charge prediction of lithium-ion battery and ultracapacitor hybrids with a co-estimator[J]. Energy
2017;121:739e50. [20] Zhang L, Wang Z, Hu X, et al. A comparative study of equivalent circuit models of ultracapacitors for electric vehicles[J]. J Power Sources 2015;274:899e906. [21] Zhang L, Hu X, Wang Z, et al. A review of supercapacitor modeling, estimation, and applications: a control/management perspective[J]. Renew Sustain Energy Rev 2018;81:1868e78. [22] Mann RF, Amphlett JC, Hooper MAI, et al. Development and application of a generalised steady-state electrochemical model for a PEM fuel cell[J]. J Power Sources 2000;86(1e2):173e80. [23] Ang KH, Chong G, Li Y. PID control system analysis, design, and technology[J]. IEEE Trans Control Syst Technol 2005;13(4):559e76. [24] Wang Y, Zhang C, Chen Z. A method for state-of-charge estimation of LiFePO4 batteries at dynamic currents and temperatures using particle filter[J]. J Power Sources 2015;279:306e11. [25] PenCg S. A generalized dynamic programming principle and Hamilton-JacobiBellman equation[J]. Stochastics: Int J Prob Stoch Process 1992;38(2):119e34. [26] EPA Highway fuel economy test cycle (HFETC). Available online: https://www. dieselnet.com/standards/cycles/hwfet.php. [Accessed 5 March 2019]. [27] EPA urban dynamometer driving Schedule (UDDS). Available online: https:// www.dieselnet.com/standards/cycles/ftp72.php. [Accessed 5 March 2019].