- Email: [email protected]
Multiple-grained velocity prediction and energy management strategy for hybrid propulsion systems
Journal of Energy Storage 26 (2019) 100950
Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Multiple-grained velocity prediction and energy management strategy for hybrid propulsion systems
T
⁎
Wang Yujie , Li Xiyun, Wang Li, Sun Zhendong Department of Automation, University of Science and Technology of China, Hefei, 230027, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Hybrid propulsion system Power splitting strategy Energy management Dynamic programming Multiple-grained velocity prediction
The fuel cells have high potential and superiority in future green transportations. The hybridization of the fuel cells with other energy storage devices such as the lithium-ion batteries and supercapacitors provides an effective way to alleviate the burden and prolong the lifespan of the fuel cells. The designs of topology and management strategy are important for fuel cell vehicles. This paper presents an improved power splitting strategy for hybrid propulsion systems by using multiple-grained velocity prediction. In this paper, the dynamic programming strategy is presented to realize optimal power splitting for different power sources. Moreover, the Markov prediction method is employed for the multiple-grained vehicle velocity prediction. In order to verify the proposed method in the hybrid propulsion system, a semi-physical platform is established to realize the hardware-in-loop simulation. The case study of different hybrid electric propulsion structures is analyzed and discussed. The system hydrogen consumption cost and electricity price of different hybrid propulsion systems are compared under the urban dynamometer driving schedule. The paper systematically compares the power splitting strategy used in different hybrid propulsion structures, in hopes of providing some inspirations to the design and control of the hybrid propulsion system.
1. Introduction 1.1. Background and motivations The traditional vehicles around the world bring about the issues of oil consumption, emission of greenhouse gas and global warming. The emerging alternative energy sources are followed closely by the automotive industry to reduce dependence on fossil fuels, thereby reducing global warming. The fuel cell (FC) which produces electricity through chemical reactions between hydrogen and oxygen with water as its only by-product, has the highest potential to compete with other electric propulsion systems in vehicular applications [1,2]. The most promising type of the FC to be utilized in vehicular applications is the polymer electrolyte membrane (PEM) FC because of its high efficiency, relatively lightweight, small size and low reaction temperature [3,4]. However, two main drawbacks of a pure fuel cell vehicle (FCV) are as follows: (1) incapable of energy savings from regenerative braking; (2) slow start-up and power response. Therefore the electric propulsion systems in FCVs are always designed with the support of lithium-ion batteries (LIBs), supercapacitors (SCs), or hybrid configurations [5]. Generally, the LIBs have higher specific energy density than the SCs and hence can provide extra energy [6]. Whereas, the SCs have higher ⁎
specific power density and longer lifetime, which can reduce the burden on the batteries and FCs [7,8]. Moreover, randomness from the power load demand causes frequency oscillations among interconnected power systems [9,10]. The hybridization of FCs with other energy storage devices such as the LIBs and SCs can provide an effective solution to improve the slow dynamic responses of FCs in the vehicular applications, alleviate the burden of the power supply, as well as to reduce frequency oscillations and prolong the lifespan of the FC system [11,12]. 1.2. Literature review There are many topologies of the hybrid energy storage system (HESS), and the most typical three types are the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure [13]. Weyers et al. [14] have proposed the simulation-based energy management concepts for the FC + LIB system in mobile applications, which can control the power distribution between the battery and fuel cell simultaneously. Azib et al. [15] have applied the FC + SC structure with the PWM control strategy for automotive applications. A cascaded control loop with a decoupling strategy in the frequency domain is fully analyzed. Yu et al. [16] have analyzed the benefits of using a combination of FCs,
Corresponding author. E-mail addresses: [email protected] (Y. Wang), [email protected] (X. Li), [email protected] (L. Wang), [email protected] (Z. Sun).
https://doi.org/10.1016/j.est.2019.100950 Received 23 August 2019; Received in revised form 6 September 2019; Accepted 10 September 2019 Available online 17 September 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
health (SOH) [34] of chemical energy systems including lithium-ion batteries, fuel cells, and supercapacitors are usually not known a priori. As reported in Ref. [35], the power prediction will inherently suffer from uncertainties of aging and temperature. Therefore the energy management system would also cover the functions of monitoring and estimating the power capability and key states of the energy storage devices [36,37]. The power capability, as well as other states such as the state-of-charge (SOC), SOH, and terminal voltage, are often used as boundaries or constraints for the energy management strategies. The goal of this work is to systematically compare the economy and practicality of different hybrid propulsion structures based on the optimization-based approach, in hopes of providing some inspirations to the design and management of FCVs.
LIBs, and SCs. A static optimization rule has been developed to meet the requirements of the total energy, peak power and cruising power while minimizing the volume, weight, and cost of the whole system. Li et al. [17] have performed fuzzy logic control strategies on both FC + LIB and FC + LIB + SC structures. The results indicate that minimal hydrogen consumption is required by the FC + LIB + SC structure. Kasimalla et al. [18] have summarized various types of energy management schemes of the FC with other auxiliary energy supply. Thorough investigations on their utilization, configuration, and management are presented and compared. Solero et al. [19] have designed a multipleinput and single-output converter for the FC + LIB + SC structure of an electric vehicle's propulsion system. The selection of auxiliary components is achieved according to the drive requirement of a real urban driving cycle. Gao et al. [20] have employed the FC + LIB + SC structure for a hybrid power bus, where the FC and the SC are regarded as active control power sources, and the battery is considered as a passive control power source. The fuzzy logic algorithm is employed to determine the desired power of each component according to the propulsion power and regenerative braking power. Peng et al. [21] have applied the FC + LIB + SC structure for a powertrain system with three DC/DC converters, where each component can be controlled respectively. Bauman et al. [22] have compared the three typical topologies by objective functions of acceleration time, fuel economy, and power train cost. The results show that the FC + SC structure is the least desirable choice because of low fuel economy and high cost. The FC + LIB structure with less cost and FC + LIB + SC structure with higher fuel economy and longer lifespans are close competitors. The energy management strategy also plays an important role in the HESS [23], which can be divided into two groups: the optimizationbased approach and the rule-based approach. Zhang et al. [24] have proposed a wavelet-transform based strategy for the HESS, which can identify the high-frequency transient of the load, and assign different frequency contents to different energy sources. Vahidi et al. [25] have proposed an optimal power allocation strategy for the FC + LIB + SC system. The distribution of current demand between the FC and the SC is formulated using a model predictive control framework. The optimal strategy can meet different load demands and avoid fuel cell oxygen starvation. Yu et al. [26] have presented an active power-flow control algorithm by using the optimal control theory to meet the different required loads while optimizing energy cost and battery life. Ettihir et al. [27] have presented an optimal tracking method to obtain better performance and minimize hydrogen consumption. Hu et al. [28] have presented a cost-optimal energy management strategy that fully considered the degradation of both fuel cell and battery systems. Moreover, a model predictive control framework was used to minimize the total running cost of the hybrid system, and the effects of driving and pricing scenarios on the optimized vehicular economy were explored. Wu et al. [29] have proposed an optimization method for efficient energy management and components sizing of a plug-in FCV. The convex programming problem was formulated to optimize both the control decision and parameters of the energy devices. The rule-based energy management strategy, namely the logical threshold strategy, are widely used in practical engineering. For instance, Peng et al. [30] have proposed a rule-based energy management strategy using dynamic programming. The optimization-based rule is validated by a hardware-in-loop (HIL) simulation approach. Wang et al. [31] have presented a rule-based power allocation method for the hybrid energy storage system which fully considered the constraints of the power capability and the remaining capacity of different energy storage devices. Lopez et al. [32] have presented a rule-based power management system where a low-pass filter is used to split the power between the FC and SC. The energy management strategy can improve efficiency and decrease undesired transients. The rule-based energy management strategy is widely used in practice because it is reliable and easy to be developed. However, the rules are based on experience and may not get an optimal result. It is noted that the future power [33] and state-of-
1.3. Main work In this paper, three representative hybrid structures of the electric propulsion system commonly used in FCVs including the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure are studied. The multi-state constraints dynamic programming algorithm is implemented to realize the optimal power splitting of different hybrid propulsion systems. The conditions of different working modes have been discussed. A semi-physical platform is established to realize the hardware-in-loop simulation. The case study of different hybrid electric propulsion structures is analyzed and discussed. The system hydrogen consumption cost and electricity price of different hybrid propulsion systems are compared under dynamic road maps. 1.4. Paper organization The remainder of this paper is organized as follows. In Section 2, three representative hybrid structures of the electric propulsion system are introduced. Then, the system configurations of different hybrid structures are presented. In Section 3, the multiple-grained velocity prediction is first presented, then the vehicle working modes and the dynamic programming algorithm are presented. Experiment and simulation are discussed in Section 4, followed by conclusions presented in Section 5. 2. Structures of electric propulsion systems In this section, three representative hybrid structures of the electric propulsion system are introduced. Then, the system configurations of different hybrid structures are given based on the parameters of a lightweight electric vehicle. 2.1. Fuel cell and lithium-ion battery (FC + LIB) structure The FC + LIB structure is one of the most popular hybrid structures used in the vehicular electric propulsion system where the FC and the DC bus are connected by a unidirectional DC/DC converter in order to meet the voltage level of the DC bus. The LIB system is connected to the DC bus through a bidirectional DC/DC converter. In the FC + LIB structure, the FC system is used for vehicular propulsion and the LIB system is employed to provide supplemental power and start-up power for the FC system. The power flow formula of the FC + LIB structure is as follows:
Pload = ηfc Pfc + ηb Pb
(1)
where ηfc denotes the efficiency of the unidirectional DC/DC converter between the FC and DC bus, ηb denotes the efficiency of the bidirectional converter between the LIB system and the DC bus, Pfc denotes the output power of the FC, and Pb denotes the output power of the battery. The advantage of the FC + LIB structure is that low power and transient response are required from the FC system. However frequent 2
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
the multiple-grained velocity prediction and the power splitting strategy using the dynamic programming algorithm are introduced. As a representation, the FC + LIB + SC structure is introduced.
charge and discharge with high rates accelerate the deterioration of the battery system and the maintenance cost of the LIB system is increased. 2.2. Fuel cell and supercapacitor (FC + SC) structure
3.1. Division of vehicle working modes In the FC + SC hybrid structure, the SC system is employed to provide transient high power and recover braking energy so that the burden of the FC system is alleviated. The FC is connected to the DC bus through a unidirectional DC/DC converter and the SC is connected to the DC bus through a bidirectional DC/DC converter. The power flow formula of the FC + SC structure is as follows:
Pload = ηfc Pfc + ηsc Psc
For the FC + LIB + SC structure, the vehicle working modes can be divided into 6 cases: Case 1: FC start-up mode. In this case, all the demand power will be provided by the LIB and SC system. The FC system needs to be activated. The system power relation can be expressed as:
⎧ Pfc = 0 η Pb + ηsc Psc = Pstart + Pload ⎨ b ⎩ Pm = ηac Pload
(2)
where ηsc denotes the efficiency of the bidirectional converter between the SC and DC bus, Psc denotes the output power of the SC system. The advantage of the FC + SC structure is that the SC can provide the transient high power and recover braking energy so that the burden of the FC system is alleviated. Therefore the SC can prolong the lifespan of the FC system by less current shock. However, due to the low energy density of the SC, the charging and discharging time of the SC system is limited. The increment of SC quantity will lead to the lifting of vehicle weight and more power is required in order to satisfy the vehicle propulsion. Moreover, the self-discharge phenomenon of SC also causes a large amount of energy loss.
where Pfc represents the FC power, Pstart represents the FC start-up power, Pload represents the load power, Pm represents the vehicle motor power, Pb and Psc represent the battery power and SC power, ηb, and ηsc represent the efficiency of the bidirectional converters of the LIB and SC systems, ηac represent the efficiency of the DC/AC inverter. The load power of the vehicle can be calculated by:
du Pload = ⎛0.325u2 + 0.936 (Mv + Me ) ⎞ u dt ⎝ ⎠
Aiming at the problems brought by the above two structures, the FC + LIB + SC structure is established. In the FC + LIB + SC structure, the FC provides the main propulsion of the vehicle, the LIB and SC jointly provide supplemental power, such as startup, acceleration, and climbing. The power flow formula of the FC + SC structure is as follows:
⎧ ηfc Pfc = Pload + ηb Pb + ηsc Psc ⎨ ⎩ Pm = ηac Pload
The hybridization of LIB and SC with the FC system can take the advantages of the above two structures. The continuous discharge and regenerative braking time can be extended by the LIB system. Meanwhile, the burden of the FC and LIB systems are alleviated by the SC system.
⎧ ηfc Pfc + ηb Pb = Pload + ηsc Psc ⎨ ⎩ Pm = ηac Pload
2.4. System configuration In this work, a light-weight electric vehicle is used for system simulation. In order to meet the rated power of the vehicle. The system configuration of the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure are shown in Table 1.
⎧ ηfc Pfc + ηsc Psc = Pload + ηb Pb ⎨ ⎩ Pm = ηac Pload
In this section, the vehicle working modes are first presented, then
SC
FC
FC + LIB + SC
Group mode Cell rated values Mass Group mode Cell rated values Mass Group mode Cell rated values Mass
81s3p 3.7 V/12 Ah 80.19 kg 81s9p 3.7 V/12 Ah 240.57 kg / / /
10s1p 2.7 V/3.04 Wh 5.07 kg / / / 30s1p 2.7 V/3.04 Wh 15.2 kg
/ / 165 kg / / 165 kg / / 165 kg
FC + LIB
FC + SC
(8)
Case 5: FC + LIB + SC working mode. In the condition that the demand power is lower than the maximum power of the FC system, and the SOC of the LIB and SC systems are higher than their lower thresholds, the demand power will be provided by the FC, LIB, and SC together:
Table 1 System configuration. LIB
(7)
Case 4: FC + SC working mode. Corresponding to case 3, in the condition that the SOC of the SC is higher than its lower threshold, but the SOC of the LIB is lower than its lower threshold, the FC and battery will provide the demand power and the battery will be charged. The system power relation can be expressed as:
3. Energy management strategy
Parameters
(6)
where ηfc represents the efficiency of the unidirectional converter of the FC system. Case 3: FC + LIB working mode. In the condition that the SOC of the LIB is higher than its lower threshold, but the SOC of the SC is lower than its lower threshold, the FC and LIB will provide the demand power and the SC will be charged. The system power relation can be expressed as:
(3)
Structure
(5)
where Mv denotes the mass of the vehicle, Me denotes the mass of the energy storage system, and u denotes the vehicle speed. Case 2: FC individual working mode. In the condition that the SOC of the LIBs and SCs are lower than their lower thresholds, the batteries and SCs will be charged, and all the demand power will be provided by the FC system. The system power relation can be expressed as:
2.3. Fuel cell, lithium-ion battery, and supercapacitor (FC + LIB + SC) structure
Pload = ηfc Pfc + ηb Pb + ηsc Psc
(4)
⎧ ηfc Pfc + ηb Pb + ηsc Psc = Pload ⎨ ⎩ Pm = ηac Pload
(9)
In the condition that the demand power is higher than the maximum power of the FC system, the FC system will provide its maximum power and the rest of demand power will be provided by the batteries and SCs: 3
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
⎧ ηfc Pfc,max + ηb Pb + ηsc Psc = Pload ⎨ ⎩ Pm = ηac Pload
obtained as shown in Fig. 1(b), and the state transition probability of vehicle velocity based on multiple-grained division is shown in Fig. 1(c).
(10)
where Pfc,max represents the maximum power of the FC system. Case 6: Energy recovery. In the condition that the SOC of the LIB and SC systems are lower than their higher thresholds, the braking energy will be recovered by the LIB and the SC systems. In the condition that the SOC of the battery is lower than its higher threshold, but the SOC of the SC is higher than its higher threshold, the braking energy will be recovered by the battery system only. When the SOC of the battery is higher than its higher threshold, but the SOC of the SC is lower than its higher threshold, the braking energy will be recovered by the SC system only. If the SOC of both the battery and SC systems are over their higher thresholds, the energy recovery will stop.
3.3. Power splitting strategy In order to handle the optimal problem of power splitting in the hybrid propulsion systems, the dynamic programming algorithm is employed. The principle of the power splitting strategy of the FC + LIB + SC structure is to minimize the following cost function:
JA = J1 + J2 + J3 = ξfc + ξe
T
H˙ (Pfc (t ), t ) dt + ξe
∫0
T
Pb (t ) dt
Psc (t ) dt
(16)
where T denotes the operation time, H denotes the hydrogen consumption, Pb and Psc denote the power of the lithium-ion batteries and supercapacitors, ξfc and ξe denote the price of the hydrogen and the electricity price. The power of the FC, LIB, and SC are governed by the vehicle working modes and system power relations introduced in Section 3.1 (from Eqs. (4) to (10)). The power of the LIB and SC can be calculated by:
3.2. Multiple-grained velocity prediction In order to obtain an optimal power splitting strategy, the prediction of velocity is necessary. In the driving process, the future velocity is unknown, however, it can be regarded as a random process with Markov properties where the impact of time is ignored and the next decision is only related to the current state. Definition 1. If the state St at time t satisfies the following equation, then the state is called Markov state, or the state satisfies Markov property.
[St + 1 |St ] = [St + 1 |S1, …, St ]
∫0
T
∫0
(11)
Pb (t ) = Ib (t ) Voc (z (t )) + Ib2 (t ) Rb
(17)
Psc (t ) = Isc (t ) Vsc (t ) + Isc2 (t ) Rsc
(18)
Definition 2. The state transition probability refers to the probability that a Markov state jumping to a subsequent state, which can be expressed by the following equation:
where Ib and Isc denote the current of the LIB and SC, Voc denotes the open-circuit voltage of the LIB, z denotes the state-of-charge (SOC) of the battery, Rb and Rsc denote the internal resistances of the LIB and SC. In this work, the cell open-circuit voltage and SOC of the LIB can be calculated by:
P (s′|s ) = [St + 1 = s′|St = s]
z (t ) = z (0) +
(12)
∫0
t
Ib (τ ) dτ / Cb
(19)
Voc (z ) = 3.99 − 0.5z + 0.688z 2 + 1.468 × 10−5/z + 0.164 ln(z ) The state transition matrix can be expressed by:
⎡ P11 ⋯ P1n ⎤ P=⎢⋮ ⋱ ⋮ ⎥ ⎢ Pn1 ⋯ Pnn ⎥ ⎣ ⎦
− 1.267 × 10−2 ln(1 − z )
where z(0) denotes the initial SOC, Cb denotes the nominal capacity of the LIB. The constraints for the power splitting strategy are as follows:
(13)
where all states constitute the rows, all subsequent states constitute the columns, n denotes the number of the states. For the vehicle's velocity prediction, the state transition probability of vehicle velocity can be calculated by:
Pij = P (vk + 1 |vk ) = [Sk + 1 = vk + 1 |Sk = vk ]
⎧0 ≤ zb ≤ 1 ⎪ 0 ≤ z sc ≤ 1 ⎪ 0 ≤ Pfc ≤ 50kW ⎨ ⎪− 60kW ≤ Psc ≤ 60kW ⎪− 15kW ≤ Pb ≤ 15kW ⎩
(14)
n ∑ j = 1 Pij
where i, j = 1, 2, 3, …, n, and = 1. Then the probability of the vehicle velocity can be expressed by:
Pij = mij / mi
(20)
(21)
where Psc,cell and Pb,cell denote the cell power of the SC and LIB, respectively. The objective and constraints of the power splitting strategy of the FC + LIB structure are to find the control rules that minimize the cost functions of JB and JC and ensure the safety of the FC and LIB system:
(15)
where mij demotes the number of times that the velocity transit from Sk to Sk + 1, mi demotes the sum of times that the velocity transit from Sk n (mi = ∑ j = 1 mij ). The division of the Markov state is important for the vehicle velocity prediction, the fine-grained division can improve the prediction accuracy, but requires more computational resources both in training and prediction process. The coarse-grained division may make the prediction results inaccurate and affect the implementation of power allocation. Taking the above reasons into account, in this work a multiplegrained velocity prediction is presented based on the distribution of the vehicle velocity, and there are three division rules: coarse, middle and fine. With different division rules, the velocity state can be divided into different intervals. Take the urban dynamometer driving schedule as an example. Based on the statistical data of the urban dynamometer driving schedule shown in Fig. 1(a), the distribution of the vehicle velocity can be
obj.:min JB = min(J1 + J2) = min ⎜⎛ξfc ⎝
∫0
T
H˙ (Pfc (t ), t ) dt + ξe
⎧0 ≤ zb ≤ 1 s. t . : 0 ≤ Pfc ≤ 50kW ⎨ ⎩− 15kW ≤ Pb ≤ 15kW
∫0
T
Pb (t ) dt ⎞⎟ ⎠ (22)
(23)
Similarly, the objective and constraints of the FC + SC structure are as follows:
obj. :min JC = min(J1 + J3) = min ⎛⎜ξfc ⎝ 4
∫0
T
H˙ (Pfc (t ), t ) dt + ξe
∫0
T
Psc (t ) dt ⎞⎟ ⎠
(24)
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
Fig. 1. Multiple-grained velocity division: (a) Urban dynamometer driving schedule. (b) Distribution of the vehicle velocity. (b) State transition probability based on multiple-grained division.
Fig. 2. Flow diagram of the velocity prediction and power splitting strategy.
⎧ 0 ≤ z sc ≤ 1 s. t . : 0 ≤ Pfc ≤ 50kW ⎨ ⎩− 60kW ≤ Psc ≤ 60kW
4.1. Results of the FC + LIB structure The power splitting results of the FC + LIB structure under the urban dynamometer driving schedule is shown in Fig. 4. The results of power splitting strategy using the presented dynamic programming algorithm based on multiple-grained velocity prediction are shown in Fig. 4(a). The SOC of the LIB is shown in Fig. 4(b). In the FC + LIB structure, the hybrid propulsion system can satisfy most of the demand power when discharging, and the LIBs can absorb the vehicle braking energy within the battery's power restrictions. Based on the proposed strategy the SOC and power of the FC and LIB are controlled within their limit bounds. The cost of the FC + LIB structure under a 1370s urban dynamometer driving schedule is shown in Table 2. The cost of hydrogen consumption and the electricity price of the LIB are ¥8.55 and ¥0.35, respectively.
(25)
The overall flow diagram of the velocity prediction and power splitting strategy is shown in Fig. 2.
4. Results and discussion In order to compare the proposed power splitting strategy applied on different hybrid structures, the semi-physical experiment and simulation platform is developed as shown in Fig. 3, which includes a host computer, a FC simulation platform, a FC management module, a LIB pack, a SC pack, and an electronic load test system. The host computer is used to build management models in MATLAB/Simulink®, which can communicate with other components based on the controller area network (CAN). The FC simulation platform is used to build the FC and balance of plant (BOP) models using MATLAB/Simulink®, which can cooperate with the FC management module by CAN. The electronic load tester (NEWARE BTS-8000) is used to charge/discharge the LIB and SC systems according to the instruction of the host computer by TCP/IP protocol. In addition, the electronic load tester can monitor the terminal voltage and the load current in real-time and send the data to the host through TCP/IP protocol.
4.2. Results of the FC + SC structure The results of the presented power splitting strategy of the FC + SC structure under the urban dynamometer driving schedule is shown in Fig. 5. The power splitting results using dynamic programming and multiple-grained velocity prediction are shown in Fig. 5(a). The SOC of SC is shown in Fig. 5(b). In the FC + SC structure, the hybrid propulsion system can satisfy most of the demand power and the SC can absorb 5
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
Fig. 3. Semi-physical experiment and simulation platform.
Fig. 4. Power splitting results of the FC + LIB structure under the urban dynamometer driving schedule: (a) Power of the FC and LIB. (b) SOC of the LIB.
most of the regenerative braking energy. Based on the proposed dynamic programming strategy the SOC and power of the FC and SC are controlled within their limit bounds. The cost of the FC + SC structure under a 1370 s urban dynamometer driving schedule is ¥10.31. The cost of hydrogen consumption and the electricity price of the SC are ¥10.22 and ¥0.09, respectively. Compared with the FC + LIB structure, the FC + SC structure can better absorb the regenerative braking energy and satisfy the instantaneous high power. However, the overall cost and the cost of the hydrogen consumption are higher than that of the FC + LIB structure.
Table 2 Cost comparison of different hybrid propulsion systems under the urban dynamometer driving schedule. Structure
J1
J2
J3
JA
JB
JC
FC + LIB FC + SC FC + LIB + SC
¥8.55 ¥10.22 ¥7.54
¥0.35 × ¥0.37
× ¥0.09 ¥0.08
× × ¥7.99
¥8.90 × ×
× ¥10.31 ×
Fig. 5. Power splitting results of the FC + SC structure under the urban dynamometer driving schedule: (a) Power of the FC and SC. (b) SOC of the SC. 6
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
Fig. 6. Power splitting results of the FC + LIB + SC structure under the urban dynamometer driving schedule: (a) Power of the FC, LIB and SC. (b) SOC of the LIB. (c) SOC of the SC.
4.3. Results of the FC + LIB + SC structure
Acknowledgments
The results of the presented power splitting strategy for the FC + LIB + SC structure under the urban dynamometer driving schedule is shown in Fig. 6. The power splitting results of the FC, LIB and SC are shown in Fig. 6(a). The SOC of LIB and SC are shown in Fig. 6(b) and (c). In the FC + LIB + SC structure, the hybrid propulsion system can satisfy most of the demand power and the LIB and SC can absorb most of the regenerative braking energy. Moreover, the LIB and SC are controlled within their limit power and SOC. The cost of the FC + LIB + SC structure under a 1370 s urban dynamometer driving schedule is ¥7.99, which is lower than that of the FC + LIB and FC + SC structure. The cost of hydrogen consumption is ¥7.54. The electricity prices of the LIB and SC are ¥0.37 and ¥0.08, respectively. Compared with the FC + LIB and FC + SC structures, the FC + LIB + SC structure has the lowest cost under the urban dynamometer driving schedule. In addition, the strategy can satisfy the demand power and absorb regenerative energy by the SC and LIB.
This work is supported partly by the National Natural Science Foundation of China (Grant no. 61803359), and partly by the Fundamental Research Funds for the Central Universities (Grant no. WK2100100032). References [1] F. Panik, Fuel cells for vehicle applications in cars-bringing the future closer, J. Power Sources 71 (1–2) (1998) 36–38. [2] P. Corbo, F.E. Corcione, F. Migliardini, et al., Energy management in fuel cell power trains, Energy Convers. Manag 47 (18–19) (2006) 3255–3271. [3] Y. Wang, Z. Sun, Z. Chen, Energy management strategy for battery/ supercapacitor/ fuel cell hybrid source vehicles based on finite state machine, Appl. Energy 254 (2019) 113707. [4] O. Erdinc, M. Uzunoglu, Recent trends in PEM fuel cell-powered hybrid systems: investigation of application areas, design architectures and energy management approaches, Renew. Sustain. Energy Rev. 14 (9) (2010) 2874–2884. [5] C. Capasso, O. Veneri, Experimental analysis on the performance of lithium based batteries for road full electric and hybrid vehicles, Appl. Energy 136 (2014) 921–930. [6] A. Du Pasquier, I. Plitz, S. Menocal, et al., A comparative study of Li-ion battery, supercapacitor and nonaqueous asymmetric hybrid devices for automotive applications, J. Power Sources 115 (1) (2003) 171–178. [7] Y. Wang, C. Liu, R. Pan, et al., Modeling and state-of-charge prediction of lithiumion battery and ultracapacitor hybrids with a co-estimator, Energy 121 (2017) 739–750. [8] Y. Wang, X. Zhang, C. Liu, et al., Multi-timescale power and energy assessment of lithium-ion battery and supercapacitor hybrid system using extended Kalman filter, J. Power Sources 389 (2018) 93–105. [9] C. Mu, Y. Tang, H. He, Improved sliding mode design for load frequency control of power system integrated an adaptive learning strategy, IEEE Trans. Ind. Electron. 64 (8) (2017) 6742–6751. [10] C. Mu, W. Liu, W. Xu, Hierarchically adaptive frequency control for an EV-integrated smart grid with renewable energy, IEEE Trans. Ind. Inform. 14 (9) (2018) 4254–4263. [11] H. Li, A. Ravey, A. N Diaye, et al., Online adaptive equivalent consumption minimization strategy for fuel cell hybrid electric vehicle considering power sources degradation, Energy Convers. Manag 192 (2019) 133–149. [12] S. Ahmadi, S.M.T. Bathaee, A.H. Hosseinpour, Improving fuel economy and performance of a fuel-cell hybrid electric vehicle (fuel-cell, battery, and ultra-capacitor) using optimized energy management strategy, Energy Convers. Manag. 160 (2018) 74–84. [13] A. Kaabeche, Y. Bakelli, Renewable hybrid system size optimization considering various electrochemical energy storage technologies, Energy Convers. Manag. 193 (2019) 162–175. [14] C. Weyers, T. Bocklisch, Simulation-based investigation of energy management concepts for fuel cell–battery–hybrid energy storage systems in mobile applications, Energy Proc. 155 (2018) 295–308. [15] T. Azib, O. Bethoux, G. Remy, et al., An innovative control strategy of a single converter for hybrid fuel cell/supercapacitors power source, IEEE Trans. Ind. Electron. 57 (12) (2010) 4024–4031. [16] Z. Yu, D. Zinger, A. Bose, An innovative optimal power allocation strategy for fuel cell, battery and supercapacitor hybrid electric vehicle, J. Power Sources 196 (4) (2011) 2351–2359. [17] Q. Li, W. Chen, Y. Li, et al., Energy management strategy for fuel cell/battery/ ultracapacitor hybrid vehicle based on fuzzy logic, Internat. J. Electr. Power Energy Syst. 43 (1) (2012) 514–525. [18] V.K.R. Kasimalla, V. Velisala, A review on energy allocation of fuel cell/battery/ ultracapacitor for hybrid electric vehicles, Int. J. Energy Res. 42 (14) (2018) 4263–4283. [19] L. Solero, A. Lidozzi, J.A. Pomilio, Design of multiple-input power converter for
5. Conclusions In this work, the power splitting strategies for different hybrid propulsion systems have been investigated. First, three representative hybrid structures of the electric propulsion system commonly used in FCVs including the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure are presented. Then the dynamic programming strategy with multiple-grained vehicle velocity prediction is presented to realize optimal power splitting for different hybrid structures. In order to verify the proposed method in the hybrid propulsion system, a semi-physical platform is established to realize the hardware-in-loop simulation. The case studies of different hybrid electric propulsion structures are analyzed and discussed. The system hydrogen consumption cost and electricity price of different hybrid propulsion systems are compared and analyzed under the urban dynamometer driving schedule. In the FC + LIB structure, the hybrid propulsion system can satisfy most of the demand power when discharging, and the LIBs can absorb the vehicle braking energy within the battery's power restrictions. Compared with the FC + LIB structure, the FC + SC structure can better absorb the regenerative braking energy and satisfy the instantaneous high power. However, the overall cost and the cost of the hydrogen consumption are higher than that of the FC + LIB structure. The FC + LIB + SC structure has the lowest cost under the urban dynamometer driving schedule. In addition, the strategy can satisfy the demand power and absorb regenerative energy by the SC and LIB. Our future work will focus on real-time energy management strategies used in fuel cell, battery, and supercapacitor hybrid systems by employing advanced control methodology in order to improve the fuel economy and prolong the system lifespan.
7
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
[29] X. Wu, X. Hu, X. Yin, et al., Convex programming energy management and components sizing of a plug-in fuel cell urban logistics vehicle, J. Power Sources 423 (2019) 358–366. [30] J. Peng, H. He, R. Xiong, Rule based energy management strategy for a series–parallel plug-in hybrid electric bus optimized by dynamic programming, Appl Energy 185 (2017) 1633–1643. [31] Y. Wang, Z. Sun, Z. Chen, Development of energy management system based on a rule-based power distribution strategy for hybrid power sources, Energy 175 (2019) 1055–1066. [32] G.L. Lopez, R.S. Rodriguez, V.M. Alvarado, et al., Hybrid PEMFC-supercapacitor system: modeling and energy management in energetic macroscopic representation, Appl. Energy 205 (2017) 1478–1494. [33] Z. Wei, A. Bhattarai, C. Zou, et al., Real-time monitoring of capacity loss for vanadium redox flow battery, J. Power Sources 390 (2018) 261–269. [34] X. Tang, C. Zou, K. Yao, et al., Aging trajectory prediction for lithium-ion batteries via model migration and Bayesian Monte Carlo method, Appl. Energy 254 (2019) 113591. [35] X. Tang, Y. Wang, C. Zou, et al., A novel framework for Lithium-ion battery modeling considering uncertainties of temperature and aging, Energy Convers. Manag. 180 (2019) 162–170. [36] Y. Wang, R. Pan, C. Liu, et al., Power capability evaluation for lithium iron phosphate batteries based on multi-parameter constraints estimation, J. Power Sources 374 (2018) 12–23. [37] C. Zou, A. Klintberg, Z. Wei, et al., Power capability prediction for lithium-ion batteries using economic nonlinear model predictive control, J. Power Sources 396 (2018) 580–589.
hybrid vehicles, IEEE Trans. Power Electron. 20 (5) (2005) 1007–1016. [20] D. Gao, Z. Jin, Q. Lu, Energy management strategy based on fuzzy logic for a fuel cell hybrid bus, J. Power Sources 185 (1) (2008) 311–317. [21] F. Peng, Y. Zhao, T. Chen, et al., Development of robust suboptimal real-time power sharing strategy for modern fuel cell based hybrid tramways considering operational uncertainties and performance degradation, Appl. Energy 226 (2018) 503–521. [22] J. Bauman, M. Kazerani, A comparative study of fuel-cell–battery, fuel-cell–ultracapacitor, and fuel-cell–battery–ultracapacitor vehicles, IEEE Trans. Vehic. Technol. 57 (2) (2008) 760–769. [23] N. Sulaiman, M.A. Hannan, A. Mohamed, et al., Optimization of energy management system for fuel-cell hybrid electric vehicles: issues and recommendations, Appl. Energy 228 (2018) 2061–2079. [24] X. Zhang, C.C. Mi, A. Masrur, et al., Wavelet-transform-based power management of hybrid vehicles with multiple on-board energy sources including fuel cell, battery and ultracapacitor, J. Power Sources 185 (2) (2008) 1533–1543. [25] A. Vahidi, A. Stefanopoulou, H. Peng, Current management in a hybrid fuel cell power system: a model-predictive control approach, IEEE Trans. Control Syst. Technol. 14 (6) (2006) 1047–1057. [26] Z. Yu, D. Zinger, A. Bose, An innovative optimal power allocation strategy for fuel cell, battery and supercapacitor hybrid electric vehicle, J. Power Sources 196 (4) (2011) 2351–2359. [27] K. Ettihir, L. Boulon, K. Agbossou, Optimization-based energy management strategy for a fuel cell/battery hybrid power system, Appl. Energy 163 (2016) 142–153. [28] X. Hu, C. Zou, X. Tang, et al., Cost-optimal energy management of hybrid electric vehicles using fuel cell/battery health-aware predictive control, IEEE Trans. Power Electron. (2019).
8
Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Multiple-grained velocity prediction and energy management strategy for hybrid propulsion systems
T
⁎
Wang Yujie , Li Xiyun, Wang Li, Sun Zhendong Department of Automation, University of Science and Technology of China, Hefei, 230027, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Hybrid propulsion system Power splitting strategy Energy management Dynamic programming Multiple-grained velocity prediction
The fuel cells have high potential and superiority in future green transportations. The hybridization of the fuel cells with other energy storage devices such as the lithium-ion batteries and supercapacitors provides an effective way to alleviate the burden and prolong the lifespan of the fuel cells. The designs of topology and management strategy are important for fuel cell vehicles. This paper presents an improved power splitting strategy for hybrid propulsion systems by using multiple-grained velocity prediction. In this paper, the dynamic programming strategy is presented to realize optimal power splitting for different power sources. Moreover, the Markov prediction method is employed for the multiple-grained vehicle velocity prediction. In order to verify the proposed method in the hybrid propulsion system, a semi-physical platform is established to realize the hardware-in-loop simulation. The case study of different hybrid electric propulsion structures is analyzed and discussed. The system hydrogen consumption cost and electricity price of different hybrid propulsion systems are compared under the urban dynamometer driving schedule. The paper systematically compares the power splitting strategy used in different hybrid propulsion structures, in hopes of providing some inspirations to the design and control of the hybrid propulsion system.
1. Introduction 1.1. Background and motivations The traditional vehicles around the world bring about the issues of oil consumption, emission of greenhouse gas and global warming. The emerging alternative energy sources are followed closely by the automotive industry to reduce dependence on fossil fuels, thereby reducing global warming. The fuel cell (FC) which produces electricity through chemical reactions between hydrogen and oxygen with water as its only by-product, has the highest potential to compete with other electric propulsion systems in vehicular applications [1,2]. The most promising type of the FC to be utilized in vehicular applications is the polymer electrolyte membrane (PEM) FC because of its high efficiency, relatively lightweight, small size and low reaction temperature [3,4]. However, two main drawbacks of a pure fuel cell vehicle (FCV) are as follows: (1) incapable of energy savings from regenerative braking; (2) slow start-up and power response. Therefore the electric propulsion systems in FCVs are always designed with the support of lithium-ion batteries (LIBs), supercapacitors (SCs), or hybrid configurations [5]. Generally, the LIBs have higher specific energy density than the SCs and hence can provide extra energy [6]. Whereas, the SCs have higher ⁎
specific power density and longer lifetime, which can reduce the burden on the batteries and FCs [7,8]. Moreover, randomness from the power load demand causes frequency oscillations among interconnected power systems [9,10]. The hybridization of FCs with other energy storage devices such as the LIBs and SCs can provide an effective solution to improve the slow dynamic responses of FCs in the vehicular applications, alleviate the burden of the power supply, as well as to reduce frequency oscillations and prolong the lifespan of the FC system [11,12]. 1.2. Literature review There are many topologies of the hybrid energy storage system (HESS), and the most typical three types are the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure [13]. Weyers et al. [14] have proposed the simulation-based energy management concepts for the FC + LIB system in mobile applications, which can control the power distribution between the battery and fuel cell simultaneously. Azib et al. [15] have applied the FC + SC structure with the PWM control strategy for automotive applications. A cascaded control loop with a decoupling strategy in the frequency domain is fully analyzed. Yu et al. [16] have analyzed the benefits of using a combination of FCs,
Corresponding author. E-mail addresses: [email protected] (Y. Wang), [email protected] (X. Li), [email protected] (L. Wang), [email protected] (Z. Sun).
https://doi.org/10.1016/j.est.2019.100950 Received 23 August 2019; Received in revised form 6 September 2019; Accepted 10 September 2019 Available online 17 September 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
health (SOH) [34] of chemical energy systems including lithium-ion batteries, fuel cells, and supercapacitors are usually not known a priori. As reported in Ref. [35], the power prediction will inherently suffer from uncertainties of aging and temperature. Therefore the energy management system would also cover the functions of monitoring and estimating the power capability and key states of the energy storage devices [36,37]. The power capability, as well as other states such as the state-of-charge (SOC), SOH, and terminal voltage, are often used as boundaries or constraints for the energy management strategies. The goal of this work is to systematically compare the economy and practicality of different hybrid propulsion structures based on the optimization-based approach, in hopes of providing some inspirations to the design and management of FCVs.
LIBs, and SCs. A static optimization rule has been developed to meet the requirements of the total energy, peak power and cruising power while minimizing the volume, weight, and cost of the whole system. Li et al. [17] have performed fuzzy logic control strategies on both FC + LIB and FC + LIB + SC structures. The results indicate that minimal hydrogen consumption is required by the FC + LIB + SC structure. Kasimalla et al. [18] have summarized various types of energy management schemes of the FC with other auxiliary energy supply. Thorough investigations on their utilization, configuration, and management are presented and compared. Solero et al. [19] have designed a multipleinput and single-output converter for the FC + LIB + SC structure of an electric vehicle's propulsion system. The selection of auxiliary components is achieved according to the drive requirement of a real urban driving cycle. Gao et al. [20] have employed the FC + LIB + SC structure for a hybrid power bus, where the FC and the SC are regarded as active control power sources, and the battery is considered as a passive control power source. The fuzzy logic algorithm is employed to determine the desired power of each component according to the propulsion power and regenerative braking power. Peng et al. [21] have applied the FC + LIB + SC structure for a powertrain system with three DC/DC converters, where each component can be controlled respectively. Bauman et al. [22] have compared the three typical topologies by objective functions of acceleration time, fuel economy, and power train cost. The results show that the FC + SC structure is the least desirable choice because of low fuel economy and high cost. The FC + LIB structure with less cost and FC + LIB + SC structure with higher fuel economy and longer lifespans are close competitors. The energy management strategy also plays an important role in the HESS [23], which can be divided into two groups: the optimizationbased approach and the rule-based approach. Zhang et al. [24] have proposed a wavelet-transform based strategy for the HESS, which can identify the high-frequency transient of the load, and assign different frequency contents to different energy sources. Vahidi et al. [25] have proposed an optimal power allocation strategy for the FC + LIB + SC system. The distribution of current demand between the FC and the SC is formulated using a model predictive control framework. The optimal strategy can meet different load demands and avoid fuel cell oxygen starvation. Yu et al. [26] have presented an active power-flow control algorithm by using the optimal control theory to meet the different required loads while optimizing energy cost and battery life. Ettihir et al. [27] have presented an optimal tracking method to obtain better performance and minimize hydrogen consumption. Hu et al. [28] have presented a cost-optimal energy management strategy that fully considered the degradation of both fuel cell and battery systems. Moreover, a model predictive control framework was used to minimize the total running cost of the hybrid system, and the effects of driving and pricing scenarios on the optimized vehicular economy were explored. Wu et al. [29] have proposed an optimization method for efficient energy management and components sizing of a plug-in FCV. The convex programming problem was formulated to optimize both the control decision and parameters of the energy devices. The rule-based energy management strategy, namely the logical threshold strategy, are widely used in practical engineering. For instance, Peng et al. [30] have proposed a rule-based energy management strategy using dynamic programming. The optimization-based rule is validated by a hardware-in-loop (HIL) simulation approach. Wang et al. [31] have presented a rule-based power allocation method for the hybrid energy storage system which fully considered the constraints of the power capability and the remaining capacity of different energy storage devices. Lopez et al. [32] have presented a rule-based power management system where a low-pass filter is used to split the power between the FC and SC. The energy management strategy can improve efficiency and decrease undesired transients. The rule-based energy management strategy is widely used in practice because it is reliable and easy to be developed. However, the rules are based on experience and may not get an optimal result. It is noted that the future power [33] and state-of-
1.3. Main work In this paper, three representative hybrid structures of the electric propulsion system commonly used in FCVs including the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure are studied. The multi-state constraints dynamic programming algorithm is implemented to realize the optimal power splitting of different hybrid propulsion systems. The conditions of different working modes have been discussed. A semi-physical platform is established to realize the hardware-in-loop simulation. The case study of different hybrid electric propulsion structures is analyzed and discussed. The system hydrogen consumption cost and electricity price of different hybrid propulsion systems are compared under dynamic road maps. 1.4. Paper organization The remainder of this paper is organized as follows. In Section 2, three representative hybrid structures of the electric propulsion system are introduced. Then, the system configurations of different hybrid structures are presented. In Section 3, the multiple-grained velocity prediction is first presented, then the vehicle working modes and the dynamic programming algorithm are presented. Experiment and simulation are discussed in Section 4, followed by conclusions presented in Section 5. 2. Structures of electric propulsion systems In this section, three representative hybrid structures of the electric propulsion system are introduced. Then, the system configurations of different hybrid structures are given based on the parameters of a lightweight electric vehicle. 2.1. Fuel cell and lithium-ion battery (FC + LIB) structure The FC + LIB structure is one of the most popular hybrid structures used in the vehicular electric propulsion system where the FC and the DC bus are connected by a unidirectional DC/DC converter in order to meet the voltage level of the DC bus. The LIB system is connected to the DC bus through a bidirectional DC/DC converter. In the FC + LIB structure, the FC system is used for vehicular propulsion and the LIB system is employed to provide supplemental power and start-up power for the FC system. The power flow formula of the FC + LIB structure is as follows:
Pload = ηfc Pfc + ηb Pb
(1)
where ηfc denotes the efficiency of the unidirectional DC/DC converter between the FC and DC bus, ηb denotes the efficiency of the bidirectional converter between the LIB system and the DC bus, Pfc denotes the output power of the FC, and Pb denotes the output power of the battery. The advantage of the FC + LIB structure is that low power and transient response are required from the FC system. However frequent 2
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
the multiple-grained velocity prediction and the power splitting strategy using the dynamic programming algorithm are introduced. As a representation, the FC + LIB + SC structure is introduced.
charge and discharge with high rates accelerate the deterioration of the battery system and the maintenance cost of the LIB system is increased. 2.2. Fuel cell and supercapacitor (FC + SC) structure
3.1. Division of vehicle working modes In the FC + SC hybrid structure, the SC system is employed to provide transient high power and recover braking energy so that the burden of the FC system is alleviated. The FC is connected to the DC bus through a unidirectional DC/DC converter and the SC is connected to the DC bus through a bidirectional DC/DC converter. The power flow formula of the FC + SC structure is as follows:
Pload = ηfc Pfc + ηsc Psc
For the FC + LIB + SC structure, the vehicle working modes can be divided into 6 cases: Case 1: FC start-up mode. In this case, all the demand power will be provided by the LIB and SC system. The FC system needs to be activated. The system power relation can be expressed as:
⎧ Pfc = 0 η Pb + ηsc Psc = Pstart + Pload ⎨ b ⎩ Pm = ηac Pload
(2)
where ηsc denotes the efficiency of the bidirectional converter between the SC and DC bus, Psc denotes the output power of the SC system. The advantage of the FC + SC structure is that the SC can provide the transient high power and recover braking energy so that the burden of the FC system is alleviated. Therefore the SC can prolong the lifespan of the FC system by less current shock. However, due to the low energy density of the SC, the charging and discharging time of the SC system is limited. The increment of SC quantity will lead to the lifting of vehicle weight and more power is required in order to satisfy the vehicle propulsion. Moreover, the self-discharge phenomenon of SC also causes a large amount of energy loss.
where Pfc represents the FC power, Pstart represents the FC start-up power, Pload represents the load power, Pm represents the vehicle motor power, Pb and Psc represent the battery power and SC power, ηb, and ηsc represent the efficiency of the bidirectional converters of the LIB and SC systems, ηac represent the efficiency of the DC/AC inverter. The load power of the vehicle can be calculated by:
du Pload = ⎛0.325u2 + 0.936 (Mv + Me ) ⎞ u dt ⎝ ⎠
Aiming at the problems brought by the above two structures, the FC + LIB + SC structure is established. In the FC + LIB + SC structure, the FC provides the main propulsion of the vehicle, the LIB and SC jointly provide supplemental power, such as startup, acceleration, and climbing. The power flow formula of the FC + SC structure is as follows:
⎧ ηfc Pfc = Pload + ηb Pb + ηsc Psc ⎨ ⎩ Pm = ηac Pload
The hybridization of LIB and SC with the FC system can take the advantages of the above two structures. The continuous discharge and regenerative braking time can be extended by the LIB system. Meanwhile, the burden of the FC and LIB systems are alleviated by the SC system.
⎧ ηfc Pfc + ηb Pb = Pload + ηsc Psc ⎨ ⎩ Pm = ηac Pload
2.4. System configuration In this work, a light-weight electric vehicle is used for system simulation. In order to meet the rated power of the vehicle. The system configuration of the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure are shown in Table 1.
⎧ ηfc Pfc + ηsc Psc = Pload + ηb Pb ⎨ ⎩ Pm = ηac Pload
In this section, the vehicle working modes are first presented, then
SC
FC
FC + LIB + SC
Group mode Cell rated values Mass Group mode Cell rated values Mass Group mode Cell rated values Mass
81s3p 3.7 V/12 Ah 80.19 kg 81s9p 3.7 V/12 Ah 240.57 kg / / /
10s1p 2.7 V/3.04 Wh 5.07 kg / / / 30s1p 2.7 V/3.04 Wh 15.2 kg
/ / 165 kg / / 165 kg / / 165 kg
FC + LIB
FC + SC
(8)
Case 5: FC + LIB + SC working mode. In the condition that the demand power is lower than the maximum power of the FC system, and the SOC of the LIB and SC systems are higher than their lower thresholds, the demand power will be provided by the FC, LIB, and SC together:
Table 1 System configuration. LIB
(7)
Case 4: FC + SC working mode. Corresponding to case 3, in the condition that the SOC of the SC is higher than its lower threshold, but the SOC of the LIB is lower than its lower threshold, the FC and battery will provide the demand power and the battery will be charged. The system power relation can be expressed as:
3. Energy management strategy
Parameters
(6)
where ηfc represents the efficiency of the unidirectional converter of the FC system. Case 3: FC + LIB working mode. In the condition that the SOC of the LIB is higher than its lower threshold, but the SOC of the SC is lower than its lower threshold, the FC and LIB will provide the demand power and the SC will be charged. The system power relation can be expressed as:
(3)
Structure
(5)
where Mv denotes the mass of the vehicle, Me denotes the mass of the energy storage system, and u denotes the vehicle speed. Case 2: FC individual working mode. In the condition that the SOC of the LIBs and SCs are lower than their lower thresholds, the batteries and SCs will be charged, and all the demand power will be provided by the FC system. The system power relation can be expressed as:
2.3. Fuel cell, lithium-ion battery, and supercapacitor (FC + LIB + SC) structure
Pload = ηfc Pfc + ηb Pb + ηsc Psc
(4)
⎧ ηfc Pfc + ηb Pb + ηsc Psc = Pload ⎨ ⎩ Pm = ηac Pload
(9)
In the condition that the demand power is higher than the maximum power of the FC system, the FC system will provide its maximum power and the rest of demand power will be provided by the batteries and SCs: 3
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
⎧ ηfc Pfc,max + ηb Pb + ηsc Psc = Pload ⎨ ⎩ Pm = ηac Pload
obtained as shown in Fig. 1(b), and the state transition probability of vehicle velocity based on multiple-grained division is shown in Fig. 1(c).
(10)
where Pfc,max represents the maximum power of the FC system. Case 6: Energy recovery. In the condition that the SOC of the LIB and SC systems are lower than their higher thresholds, the braking energy will be recovered by the LIB and the SC systems. In the condition that the SOC of the battery is lower than its higher threshold, but the SOC of the SC is higher than its higher threshold, the braking energy will be recovered by the battery system only. When the SOC of the battery is higher than its higher threshold, but the SOC of the SC is lower than its higher threshold, the braking energy will be recovered by the SC system only. If the SOC of both the battery and SC systems are over their higher thresholds, the energy recovery will stop.
3.3. Power splitting strategy In order to handle the optimal problem of power splitting in the hybrid propulsion systems, the dynamic programming algorithm is employed. The principle of the power splitting strategy of the FC + LIB + SC structure is to minimize the following cost function:
JA = J1 + J2 + J3 = ξfc + ξe
T
H˙ (Pfc (t ), t ) dt + ξe
∫0
T
Pb (t ) dt
Psc (t ) dt
(16)
where T denotes the operation time, H denotes the hydrogen consumption, Pb and Psc denote the power of the lithium-ion batteries and supercapacitors, ξfc and ξe denote the price of the hydrogen and the electricity price. The power of the FC, LIB, and SC are governed by the vehicle working modes and system power relations introduced in Section 3.1 (from Eqs. (4) to (10)). The power of the LIB and SC can be calculated by:
3.2. Multiple-grained velocity prediction In order to obtain an optimal power splitting strategy, the prediction of velocity is necessary. In the driving process, the future velocity is unknown, however, it can be regarded as a random process with Markov properties where the impact of time is ignored and the next decision is only related to the current state. Definition 1. If the state St at time t satisfies the following equation, then the state is called Markov state, or the state satisfies Markov property.
[St + 1 |St ] = [St + 1 |S1, …, St ]
∫0
T
∫0
(11)
Pb (t ) = Ib (t ) Voc (z (t )) + Ib2 (t ) Rb
(17)
Psc (t ) = Isc (t ) Vsc (t ) + Isc2 (t ) Rsc
(18)
Definition 2. The state transition probability refers to the probability that a Markov state jumping to a subsequent state, which can be expressed by the following equation:
where Ib and Isc denote the current of the LIB and SC, Voc denotes the open-circuit voltage of the LIB, z denotes the state-of-charge (SOC) of the battery, Rb and Rsc denote the internal resistances of the LIB and SC. In this work, the cell open-circuit voltage and SOC of the LIB can be calculated by:
P (s′|s ) = [St + 1 = s′|St = s]
z (t ) = z (0) +
(12)
∫0
t
Ib (τ ) dτ / Cb
(19)
Voc (z ) = 3.99 − 0.5z + 0.688z 2 + 1.468 × 10−5/z + 0.164 ln(z ) The state transition matrix can be expressed by:
⎡ P11 ⋯ P1n ⎤ P=⎢⋮ ⋱ ⋮ ⎥ ⎢ Pn1 ⋯ Pnn ⎥ ⎣ ⎦
− 1.267 × 10−2 ln(1 − z )
where z(0) denotes the initial SOC, Cb denotes the nominal capacity of the LIB. The constraints for the power splitting strategy are as follows:
(13)
where all states constitute the rows, all subsequent states constitute the columns, n denotes the number of the states. For the vehicle's velocity prediction, the state transition probability of vehicle velocity can be calculated by:
Pij = P (vk + 1 |vk ) = [Sk + 1 = vk + 1 |Sk = vk ]
⎧0 ≤ zb ≤ 1 ⎪ 0 ≤ z sc ≤ 1 ⎪ 0 ≤ Pfc ≤ 50kW ⎨ ⎪− 60kW ≤ Psc ≤ 60kW ⎪− 15kW ≤ Pb ≤ 15kW ⎩
(14)
n ∑ j = 1 Pij
where i, j = 1, 2, 3, …, n, and = 1. Then the probability of the vehicle velocity can be expressed by:
Pij = mij / mi
(20)
(21)
where Psc,cell and Pb,cell denote the cell power of the SC and LIB, respectively. The objective and constraints of the power splitting strategy of the FC + LIB structure are to find the control rules that minimize the cost functions of JB and JC and ensure the safety of the FC and LIB system:
(15)
where mij demotes the number of times that the velocity transit from Sk to Sk + 1, mi demotes the sum of times that the velocity transit from Sk n (mi = ∑ j = 1 mij ). The division of the Markov state is important for the vehicle velocity prediction, the fine-grained division can improve the prediction accuracy, but requires more computational resources both in training and prediction process. The coarse-grained division may make the prediction results inaccurate and affect the implementation of power allocation. Taking the above reasons into account, in this work a multiplegrained velocity prediction is presented based on the distribution of the vehicle velocity, and there are three division rules: coarse, middle and fine. With different division rules, the velocity state can be divided into different intervals. Take the urban dynamometer driving schedule as an example. Based on the statistical data of the urban dynamometer driving schedule shown in Fig. 1(a), the distribution of the vehicle velocity can be
obj.:min JB = min(J1 + J2) = min ⎜⎛ξfc ⎝
∫0
T
H˙ (Pfc (t ), t ) dt + ξe
⎧0 ≤ zb ≤ 1 s. t . : 0 ≤ Pfc ≤ 50kW ⎨ ⎩− 15kW ≤ Pb ≤ 15kW
∫0
T
Pb (t ) dt ⎞⎟ ⎠ (22)
(23)
Similarly, the objective and constraints of the FC + SC structure are as follows:
obj. :min JC = min(J1 + J3) = min ⎛⎜ξfc ⎝ 4
∫0
T
H˙ (Pfc (t ), t ) dt + ξe
∫0
T
Psc (t ) dt ⎞⎟ ⎠
(24)
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
Fig. 1. Multiple-grained velocity division: (a) Urban dynamometer driving schedule. (b) Distribution of the vehicle velocity. (b) State transition probability based on multiple-grained division.
Fig. 2. Flow diagram of the velocity prediction and power splitting strategy.
⎧ 0 ≤ z sc ≤ 1 s. t . : 0 ≤ Pfc ≤ 50kW ⎨ ⎩− 60kW ≤ Psc ≤ 60kW
4.1. Results of the FC + LIB structure The power splitting results of the FC + LIB structure under the urban dynamometer driving schedule is shown in Fig. 4. The results of power splitting strategy using the presented dynamic programming algorithm based on multiple-grained velocity prediction are shown in Fig. 4(a). The SOC of the LIB is shown in Fig. 4(b). In the FC + LIB structure, the hybrid propulsion system can satisfy most of the demand power when discharging, and the LIBs can absorb the vehicle braking energy within the battery's power restrictions. Based on the proposed strategy the SOC and power of the FC and LIB are controlled within their limit bounds. The cost of the FC + LIB structure under a 1370s urban dynamometer driving schedule is shown in Table 2. The cost of hydrogen consumption and the electricity price of the LIB are ¥8.55 and ¥0.35, respectively.
(25)
The overall flow diagram of the velocity prediction and power splitting strategy is shown in Fig. 2.
4. Results and discussion In order to compare the proposed power splitting strategy applied on different hybrid structures, the semi-physical experiment and simulation platform is developed as shown in Fig. 3, which includes a host computer, a FC simulation platform, a FC management module, a LIB pack, a SC pack, and an electronic load test system. The host computer is used to build management models in MATLAB/Simulink®, which can communicate with other components based on the controller area network (CAN). The FC simulation platform is used to build the FC and balance of plant (BOP) models using MATLAB/Simulink®, which can cooperate with the FC management module by CAN. The electronic load tester (NEWARE BTS-8000) is used to charge/discharge the LIB and SC systems according to the instruction of the host computer by TCP/IP protocol. In addition, the electronic load tester can monitor the terminal voltage and the load current in real-time and send the data to the host through TCP/IP protocol.
4.2. Results of the FC + SC structure The results of the presented power splitting strategy of the FC + SC structure under the urban dynamometer driving schedule is shown in Fig. 5. The power splitting results using dynamic programming and multiple-grained velocity prediction are shown in Fig. 5(a). The SOC of SC is shown in Fig. 5(b). In the FC + SC structure, the hybrid propulsion system can satisfy most of the demand power and the SC can absorb 5
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
Fig. 3. Semi-physical experiment and simulation platform.
Fig. 4. Power splitting results of the FC + LIB structure under the urban dynamometer driving schedule: (a) Power of the FC and LIB. (b) SOC of the LIB.
most of the regenerative braking energy. Based on the proposed dynamic programming strategy the SOC and power of the FC and SC are controlled within their limit bounds. The cost of the FC + SC structure under a 1370 s urban dynamometer driving schedule is ¥10.31. The cost of hydrogen consumption and the electricity price of the SC are ¥10.22 and ¥0.09, respectively. Compared with the FC + LIB structure, the FC + SC structure can better absorb the regenerative braking energy and satisfy the instantaneous high power. However, the overall cost and the cost of the hydrogen consumption are higher than that of the FC + LIB structure.
Table 2 Cost comparison of different hybrid propulsion systems under the urban dynamometer driving schedule. Structure
J1
J2
J3
JA
JB
JC
FC + LIB FC + SC FC + LIB + SC
¥8.55 ¥10.22 ¥7.54
¥0.35 × ¥0.37
× ¥0.09 ¥0.08
× × ¥7.99
¥8.90 × ×
× ¥10.31 ×
Fig. 5. Power splitting results of the FC + SC structure under the urban dynamometer driving schedule: (a) Power of the FC and SC. (b) SOC of the SC. 6
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
Fig. 6. Power splitting results of the FC + LIB + SC structure under the urban dynamometer driving schedule: (a) Power of the FC, LIB and SC. (b) SOC of the LIB. (c) SOC of the SC.
4.3. Results of the FC + LIB + SC structure
Acknowledgments
The results of the presented power splitting strategy for the FC + LIB + SC structure under the urban dynamometer driving schedule is shown in Fig. 6. The power splitting results of the FC, LIB and SC are shown in Fig. 6(a). The SOC of LIB and SC are shown in Fig. 6(b) and (c). In the FC + LIB + SC structure, the hybrid propulsion system can satisfy most of the demand power and the LIB and SC can absorb most of the regenerative braking energy. Moreover, the LIB and SC are controlled within their limit power and SOC. The cost of the FC + LIB + SC structure under a 1370 s urban dynamometer driving schedule is ¥7.99, which is lower than that of the FC + LIB and FC + SC structure. The cost of hydrogen consumption is ¥7.54. The electricity prices of the LIB and SC are ¥0.37 and ¥0.08, respectively. Compared with the FC + LIB and FC + SC structures, the FC + LIB + SC structure has the lowest cost under the urban dynamometer driving schedule. In addition, the strategy can satisfy the demand power and absorb regenerative energy by the SC and LIB.
This work is supported partly by the National Natural Science Foundation of China (Grant no. 61803359), and partly by the Fundamental Research Funds for the Central Universities (Grant no. WK2100100032). References [1] F. Panik, Fuel cells for vehicle applications in cars-bringing the future closer, J. Power Sources 71 (1–2) (1998) 36–38. [2] P. Corbo, F.E. Corcione, F. Migliardini, et al., Energy management in fuel cell power trains, Energy Convers. Manag 47 (18–19) (2006) 3255–3271. [3] Y. Wang, Z. Sun, Z. Chen, Energy management strategy for battery/ supercapacitor/ fuel cell hybrid source vehicles based on finite state machine, Appl. Energy 254 (2019) 113707. [4] O. Erdinc, M. Uzunoglu, Recent trends in PEM fuel cell-powered hybrid systems: investigation of application areas, design architectures and energy management approaches, Renew. Sustain. Energy Rev. 14 (9) (2010) 2874–2884. [5] C. Capasso, O. Veneri, Experimental analysis on the performance of lithium based batteries for road full electric and hybrid vehicles, Appl. Energy 136 (2014) 921–930. [6] A. Du Pasquier, I. Plitz, S. Menocal, et al., A comparative study of Li-ion battery, supercapacitor and nonaqueous asymmetric hybrid devices for automotive applications, J. Power Sources 115 (1) (2003) 171–178. [7] Y. Wang, C. Liu, R. Pan, et al., Modeling and state-of-charge prediction of lithiumion battery and ultracapacitor hybrids with a co-estimator, Energy 121 (2017) 739–750. [8] Y. Wang, X. Zhang, C. Liu, et al., Multi-timescale power and energy assessment of lithium-ion battery and supercapacitor hybrid system using extended Kalman filter, J. Power Sources 389 (2018) 93–105. [9] C. Mu, Y. Tang, H. He, Improved sliding mode design for load frequency control of power system integrated an adaptive learning strategy, IEEE Trans. Ind. Electron. 64 (8) (2017) 6742–6751. [10] C. Mu, W. Liu, W. Xu, Hierarchically adaptive frequency control for an EV-integrated smart grid with renewable energy, IEEE Trans. Ind. Inform. 14 (9) (2018) 4254–4263. [11] H. Li, A. Ravey, A. N Diaye, et al., Online adaptive equivalent consumption minimization strategy for fuel cell hybrid electric vehicle considering power sources degradation, Energy Convers. Manag 192 (2019) 133–149. [12] S. Ahmadi, S.M.T. Bathaee, A.H. Hosseinpour, Improving fuel economy and performance of a fuel-cell hybrid electric vehicle (fuel-cell, battery, and ultra-capacitor) using optimized energy management strategy, Energy Convers. Manag. 160 (2018) 74–84. [13] A. Kaabeche, Y. Bakelli, Renewable hybrid system size optimization considering various electrochemical energy storage technologies, Energy Convers. Manag. 193 (2019) 162–175. [14] C. Weyers, T. Bocklisch, Simulation-based investigation of energy management concepts for fuel cell–battery–hybrid energy storage systems in mobile applications, Energy Proc. 155 (2018) 295–308. [15] T. Azib, O. Bethoux, G. Remy, et al., An innovative control strategy of a single converter for hybrid fuel cell/supercapacitors power source, IEEE Trans. Ind. Electron. 57 (12) (2010) 4024–4031. [16] Z. Yu, D. Zinger, A. Bose, An innovative optimal power allocation strategy for fuel cell, battery and supercapacitor hybrid electric vehicle, J. Power Sources 196 (4) (2011) 2351–2359. [17] Q. Li, W. Chen, Y. Li, et al., Energy management strategy for fuel cell/battery/ ultracapacitor hybrid vehicle based on fuzzy logic, Internat. J. Electr. Power Energy Syst. 43 (1) (2012) 514–525. [18] V.K.R. Kasimalla, V. Velisala, A review on energy allocation of fuel cell/battery/ ultracapacitor for hybrid electric vehicles, Int. J. Energy Res. 42 (14) (2018) 4263–4283. [19] L. Solero, A. Lidozzi, J.A. Pomilio, Design of multiple-input power converter for
5. Conclusions In this work, the power splitting strategies for different hybrid propulsion systems have been investigated. First, three representative hybrid structures of the electric propulsion system commonly used in FCVs including the FC + LIB structure, the FC + SC structure, and the FC + LIB + SC structure are presented. Then the dynamic programming strategy with multiple-grained vehicle velocity prediction is presented to realize optimal power splitting for different hybrid structures. In order to verify the proposed method in the hybrid propulsion system, a semi-physical platform is established to realize the hardware-in-loop simulation. The case studies of different hybrid electric propulsion structures are analyzed and discussed. The system hydrogen consumption cost and electricity price of different hybrid propulsion systems are compared and analyzed under the urban dynamometer driving schedule. In the FC + LIB structure, the hybrid propulsion system can satisfy most of the demand power when discharging, and the LIBs can absorb the vehicle braking energy within the battery's power restrictions. Compared with the FC + LIB structure, the FC + SC structure can better absorb the regenerative braking energy and satisfy the instantaneous high power. However, the overall cost and the cost of the hydrogen consumption are higher than that of the FC + LIB structure. The FC + LIB + SC structure has the lowest cost under the urban dynamometer driving schedule. In addition, the strategy can satisfy the demand power and absorb regenerative energy by the SC and LIB. Our future work will focus on real-time energy management strategies used in fuel cell, battery, and supercapacitor hybrid systems by employing advanced control methodology in order to improve the fuel economy and prolong the system lifespan.
7
Journal of Energy Storage 26 (2019) 100950
Y. Wang, et al.
[29] X. Wu, X. Hu, X. Yin, et al., Convex programming energy management and components sizing of a plug-in fuel cell urban logistics vehicle, J. Power Sources 423 (2019) 358–366. [30] J. Peng, H. He, R. Xiong, Rule based energy management strategy for a series–parallel plug-in hybrid electric bus optimized by dynamic programming, Appl Energy 185 (2017) 1633–1643. [31] Y. Wang, Z. Sun, Z. Chen, Development of energy management system based on a rule-based power distribution strategy for hybrid power sources, Energy 175 (2019) 1055–1066. [32] G.L. Lopez, R.S. Rodriguez, V.M. Alvarado, et al., Hybrid PEMFC-supercapacitor system: modeling and energy management in energetic macroscopic representation, Appl. Energy 205 (2017) 1478–1494. [33] Z. Wei, A. Bhattarai, C. Zou, et al., Real-time monitoring of capacity loss for vanadium redox flow battery, J. Power Sources 390 (2018) 261–269. [34] X. Tang, C. Zou, K. Yao, et al., Aging trajectory prediction for lithium-ion batteries via model migration and Bayesian Monte Carlo method, Appl. Energy 254 (2019) 113591. [35] X. Tang, Y. Wang, C. Zou, et al., A novel framework for Lithium-ion battery modeling considering uncertainties of temperature and aging, Energy Convers. Manag. 180 (2019) 162–170. [36] Y. Wang, R. Pan, C. Liu, et al., Power capability evaluation for lithium iron phosphate batteries based on multi-parameter constraints estimation, J. Power Sources 374 (2018) 12–23. [37] C. Zou, A. Klintberg, Z. Wei, et al., Power capability prediction for lithium-ion batteries using economic nonlinear model predictive control, J. Power Sources 396 (2018) 580–589.
hybrid vehicles, IEEE Trans. Power Electron. 20 (5) (2005) 1007–1016. [20] D. Gao, Z. Jin, Q. Lu, Energy management strategy based on fuzzy logic for a fuel cell hybrid bus, J. Power Sources 185 (1) (2008) 311–317. [21] F. Peng, Y. Zhao, T. Chen, et al., Development of robust suboptimal real-time power sharing strategy for modern fuel cell based hybrid tramways considering operational uncertainties and performance degradation, Appl. Energy 226 (2018) 503–521. [22] J. Bauman, M. Kazerani, A comparative study of fuel-cell–battery, fuel-cell–ultracapacitor, and fuel-cell–battery–ultracapacitor vehicles, IEEE Trans. Vehic. Technol. 57 (2) (2008) 760–769. [23] N. Sulaiman, M.A. Hannan, A. Mohamed, et al., Optimization of energy management system for fuel-cell hybrid electric vehicles: issues and recommendations, Appl. Energy 228 (2018) 2061–2079. [24] X. Zhang, C.C. Mi, A. Masrur, et al., Wavelet-transform-based power management of hybrid vehicles with multiple on-board energy sources including fuel cell, battery and ultracapacitor, J. Power Sources 185 (2) (2008) 1533–1543. [25] A. Vahidi, A. Stefanopoulou, H. Peng, Current management in a hybrid fuel cell power system: a model-predictive control approach, IEEE Trans. Control Syst. Technol. 14 (6) (2006) 1047–1057. [26] Z. Yu, D. Zinger, A. Bose, An innovative optimal power allocation strategy for fuel cell, battery and supercapacitor hybrid electric vehicle, J. Power Sources 196 (4) (2011) 2351–2359. [27] K. Ettihir, L. Boulon, K. Agbossou, Optimization-based energy management strategy for a fuel cell/battery hybrid power system, Appl. Energy 163 (2016) 142–153. [28] X. Hu, C. Zou, X. Tang, et al., Cost-optimal energy management of hybrid electric vehicles using fuel cell/battery health-aware predictive control, IEEE Trans. Power Electron. (2019).
8