ultracapacitor hybrid energy storage system using dynamic programming optimization

Journal of Power Sources 438 (2019) 227024

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Load-adaptive real-time energy management strategy for battery/ ultracapacitor hybrid energy storage system using dynamic programming optimization Chang Liu, Yujie Wang, Li Wang, Zonghai Chen * Department of Automation, University of Science and Technology of China, Hefei, 230027, PR China

H I G H L I G H T S

G R A P H I C A L A B S T R A C T

� A practical load-adaptive real-time en­ ergy management strategy is designed. � Control rules are extracted from the optimization results of 4 load cycles. � Real-time power splitting factors are decided by functions of load statistics. � Near optimal results are given under unknown cycles by the proposed strategy.

A R T I C L E I N F O

A B S T R A C T

Keywords: Hybrid energy storage system Energy management strategy Load-adaptive Rule based control Optimal analysis

Energy management is crucial in battery/ultracapacitor hybrid energy storage systems in electric vehicles. Rule based control is one typical strategy in real-time management, but its adaptability in dynamic load is quite poor. This paper aims to develop a practical energy management strategy with near-optimal performance in both energy-saving and battery life extending. Firstly, dynamic programming (DP) analysis is used to find out the optimal control mode. Three-segment control rules are then extracted from the DP results. A functional rela­ tionship is established between the power splitting parameters and load statistics. Finally, a load-adaptive rule based control strategy is proposed based on that. Two composite load cycles are tested for verification. Results show that compared with the ordinary rule based control strategy, the proposed strategy has the stronger capability of battery protecting and energy-saving under unknown load patterns, where the battery Ah throughput and total energy loss are reduced by 3.4%–15.7% and 3.0%–15.1%, respectively. The results are quite close to DP results, showing that the proposed strategy can achieve near-optimal energy management in real time with low computational cost.

1. Introduction In electric vehicles (EVs), lithium-ion batteries (LIB) play an important role in energy storage. However, limited cycle life and weak

power output capability gradually become the main drawbacks of LIBs in EV applications [1]. As a solution, the hybrid energy storage system (HESS) has been proposed [2], which consists of multiple energy storage devices. An ultracapacitor (UC) has the characteristic of fast charge/­ discharge with high power density and long cycle life, which can

* Corresponding author. E-mail address: [email protected] (Z. Chen). https://doi.org/10.1016/j.jpowsour.2019.227024 Received 13 April 2019; Received in revised form 13 August 2019; Accepted 14 August 2019 Available online 17 August 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.

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Nomenclature Ahthp B bα C c CC,cell Ea EB,cell EBr,cell EC,cell Eloss Epeak Erange Eregn EWLTP gk IB,k IC,k J Jk Jk(fk) k kα M N NB,p NB,s NC,p NC,s Pavg PB PB,k PB,n PBloss,k PB,thd PC PC,k PC,chg Pchgavg PCloss,k PDC,k PDCloss,k Pdisavg PL Ploss,k PWLTP p1 p2 p3 QB

R RB RB,cell RC RC,cell SOCB ΔSOHB Srange SWLTP Tchg Tdis Te Ttol Ts tp,i

Ah throughput of the battery module The pre-exponential factor in the battery capacity fade model A parameter in the linear function between α and PB,thd Nominal capacitance of the UC module The rate of the battery current (c ¼ 1 means the current is 2A) Nominal capacitance of the UC cell The activation energy in J/mol Stored energy of the battery cell The extra energy waste per cell from the mass increase of the battery module Stored energy of the UC cell Energy loss of the HESS The maximum energy to cover the peak load period in the WLTP cycle The energy to cover the vehicle’s nominal range in WLTP The maximum regenerative energy in the WLTP cycle The required energy for one WLTP cylcle The cost of step k Current of the battery module at step k Current of the UC module at step k The optimization objective function The cumulative cost function at step k The optimization objective function with the best energy consumption at step k Denotes the kth sample time A parameter in the linear function between α and PB,thd Number of the discrete states for UC in the DP analysis Number of the total time steps in the DP analysis Parallel number of battery cells Series number of battery cells Parallel number of UC cells Series number of UC cells The average power of a period of driving cycle Power of the battery module Power of the battery module at step k The nominal power of the battery module Power loss of the battery module at step k A negative constant in the control rules which means the threshold power of the battery module Power of the UC module Power of the UC module at step k A positive constant in the control rules which means the charging power of the UC module The charge average power during a period of driving cycle Power loss of the UC module at step k Power of the DC-DC converter at step k (load side) Power loss of the DC-DC converter at step k The discharge average power during a period of driving cycle Power of the load Power loss of the HESS at step k The power demand of WLTP An auxiliary variable for generating PB,thd An auxiliary variable for generating kα An auxiliary variable for generating bα Ah throughput of the battery module

tr,i UB UB,DC UB,cell UC,cell UC,high UC,low Uk ui w1 w2 xj z

α

ηDC

The gas constant Internal resistance of the battery module Internal resistance of the battery cell Internal resistance of the UC module Internal resistance of the UC cell The state of charge of the battery module Percentage capacity loss of the battery cell The vehicle’s nominal range in WLTP The range of one WLTP cycle The charge time during a period of driving cycle The discharge time during a period of driving cycle The absolute temperature The total time of a period of driving cycle Sample time of each step The ith continuous time period during which PWLTP is larger than PB,n in the WLTP cycle The ith continuous regenerative time period in the WLTP cycle Nominal voltage of the battery module Lowest voltage requirement of the battery module Nominal voltage of the battery cell Nominal voltage of the UC cell Nominal voltage/highest working voltage of the UC module Lowest working voltage of the UC module The set of control variables at step k The ith control variable of Uk The weight factor of Eloss in the optimization objective function The weight factor of QB in the optimization objective function The jth discrete point of state variable The power law factor in the battery capacity fade model A factor in the range of (0,1] in the control rules which means the power splitting ratio of the UC module when the power exceeds PB,thd Energy efficiency of the DC-DC converter

Abbreviations aRBC load adaptive rule based control BTO battery-only system CLC combined load cycle DP dynamic programming EMS energy management strategy ESS energy storage system EV electric vehicle GA genetic algorithm HESS hybrid energy storage system HWFET Highway Fuel Economy Test LIB lithium-ion battery MPC model predictive control PSO particle swarm optimization RBC rule based control RLC random load cycle RMS root mean square UC ultracapacitor UDDS Urban Dynamometer Driving Schedule US06 US06 Supplemental Federal Test Procedure WLTP Worldwide harmonized Light-duty vehicles Test Procedure

2

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compensate for the weak points of LIB [3]. Thus, the LIB/UC hybrid has been widely discussed and studied for years [4–6]. There exist two main goals of LIB/UC HESS, to reduce the energy waste in energy storage devices, and to extend the cycle life of the battery by cutting down the dynamic current for the battery. For LIB/UC HESS, different hybrid to­ pologies can be found in the literature. Among them, the semi-active topologies with one DC-DC converter connecting the different sides seem to be the optimal trade-off between energy efficiency and controllability [7,8]. The use of the DC-DC converter brings the issue of energy management, which means to fulfill the HESS goals by splitting the load power properly. An ideal energy management strategy (EMS) can take full advantage of the features of battery and UC, which requires the UC to serve the short-time peak power or high-frequency power, whereas the battery provides the average power or low frequency power. Then the battery current can be controlled to be less fluctuant, which is believed to help extend the cycle life of the battery. Addition­ ally, sufficient management is required to minimize the gross energy loss. The current EMSs published in the literature can be categorized into two main types: rule based control (RBC) strategy and optimization based control strategy. For the first type, the control strategy is based on certain rules which come from heuristics or empirical experience. Spe­ cific control methods of this type include rule based control [9,10], fuzzy logic control [11], filtration based control [12], and wavelet transform [13] amongst others. The advantages of this type of strategy are obvious: low computational cost, low control complexity, strong robustness and simple implementation. However, the disadvantages are also clear. Due to the control rules being pre-set, they lack the adaptability to variable load conditions. The most frequent problem is that the UC is controlled to release its limited energy too early and fails to cut down the peak power for the battery, along with the inefficient energy storage in the HESS. The second type of strategy aims to find out the optimal control mode directly. This type of strategy requires a cost function to evaluate the performance of HESS of some aspects include the battery current level and the gross energy loss. By using optimization methods, the optimal solution can be solved according to the load power demand. The methods of this type include dynamic programming (DP) [14], genetic algorithm (GA) [15], model predictive control (MPC) [16], and particle swarm optimization (PSO) [17] amongst others. Among them, DP is one widely used method to provide the optimal power splitting mode based on already known load cycles. Santucci et al. [14] use DP to optimize the battery lifetime and system costs based on a battery lifetime degradation model, and the performance is compared to a rule based control (RBC) strategy. Song et al. [18] give the optimal HESS power distribution ac­ cording to two different driving cycles using DP, where a battery degradation model considering temperatures and discharge depths is applied. However, the use of DP also has drawbacks. For instance, the global load information must be known in advance, which is probably not suitable for real-time management. Moreover, the computational cost of DP can be really high, especially when the discretization grid is too thin or too many variables need to be considered [19]. Other opti­ mization methods have similar problems in real-time applications. In order to generate a control strategy that is wise enough and suitable for real-time management, a number of approaches have been proposed by combining the two types of strategies. For example, Zhang et al. [20] use DP to develop suboptimal control strategies for different driving blocks, and a fuzzy logic controller is employed to classify the drive blocks and identify the driving types. Song et al. [21] extract several control rules from the DP results, and a near-optimal rule-based strategy is proposed. Shen and Khaligh [22] use various drive cycle data sets to get the DP results, and an effective and intelligent online implementation of the optimal power split is realized based on neural networks. Castaings et al. [10] propose an optimization-based strategy (λ-control) with active limitation of UC voltage, and experimental re­ sults show it has equivalent performance to a rule-based strategy

(filtering) in real-time management. Xiong et al. [23] propose a real-time strategy based on DP results, where a reinforcement learning algorithm is used to identify the load changes. The results show the superiority of the proposed strategy to the others. This paper aims to find out a practical energy management strategy in real-time applications, which means the computational cost should be low enough to meet the real-time control requirement. The aforemen­ tioned methods, unfortunately, cannot keep their good performance in unknown load situations, or have a relatively high computational cost. Hence, this paper proposes a novel real-time management strategy based on optimization results, with high adaptability to load changes and low computational cost. The contributions of this paper can be summarized as follows. (1) Based on the DP results for multiple load cycles, the three-segment rule based control mode is set up. (2) A loadadaptive parameter adjusting method is proposed based on the func­ tional relationship between the power splitting parameters and the load statistics, to satisfy the requirement of real-time management. (3) The proposed load adaptive rule based control (aRBC) strategy is verified to be near optimal via two composite load cycle tests, in which the per­ formance of aRBC is compared with ordinary rule based control (RBC) results and DP results. The major content of the rest of the paper is as follows. Section 2 gives the modeling and DP analysis for HESS, and the three-segment rule based control mode is summarized. In Section 3, the relationship be­ tween the power splitting parameters and the load statistics is studied. Based on that, the load adaptive rule based control strategy is proposed for real-time management. Section 4 verifies the proposed strategy by using two composite load cycles. The performance of aRBC, ordinary RBC and DP are compared. Section 5 gives the final conclusions. 2. DP based power splitting rules This section provides the modeling of the battery/ultracapacitor hybrid energy storage system used in electric vehicles. Then the DP analysis is given for 4 different driving cycles to formulate the optimal control rules. 2.1. HESS design and modeling in EV The EV studied in this work is selected as a typical road car. The parameters of the vehicle are listed in Table 1, which can refer to Ref. [15]. The configuration of the HESS can be designed according to the standard based on the Worldwide harmonized Light-duty vehicles Test Procedure (WLTP). The HESS must be designed to satisfy the power and energy requirement of the EV. The battery module is first designed, whose minimum energy storage must cover the nominal range Srange of the vehicle. Here the ANR26650M1-A LiFePO4 (LFP) battery of A123 system [24] is selected, whose cell parameters can be found in Table 2. The energy consumption of the whole range can be calculated as follows. Erange ¼ EWLTP

Srange SWLTP

(1)

Table 1 EV parameters.

3

Parameter

Value

Unit

Mass without energy storage system Rotating mass coefficient Aerodynamic drag coefficient Frontal area Air density Rolling resistance coefficient Motor transmission efficiency Nominal range in WLTP (Srange) Battery module voltage (UB,DC)

1360 1.04 0.3 2.0 1.202 0.015 0.9 150 >400

kg – – m2 kg/m3 – – km V

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Table 2 Parameters of the battery cell, the UC cell and the HESS configuration.

Z Eregn ¼ max jPWLTP ðtÞjdt

Item

Parameter

Value

Unit

Battery cell [24]

Mass Charge cut-off voltage Nominal voltage (UB,cell) Nominal capacity Stored energy (EB,cell) Specific energy

72 3.6 3.3 2.2 7.6 105.6

Nominal charge current Maximum discharge current Internal resistance (RB,cell) Nominal cycle life (@10C discharge, 100%DOD)

3 70 8 >1000

g V V Ah Wh Wh/ kg A A mΩ –

Mass Nominal voltage (UC,cell) Nominal capacitance (CC,cell) Maximum Continuous Current Internal resistance (RC,cell) Stored energy (EC,cell) Specific power

510 2.7 3000 130 0.29 3.04 5.9

Nominal cycle life

1,000,000

g V F A mΩ Wh kW/ kg –

Series number of battery cells (NB,s) Parallel number of battery cells (NB,p) Series number of UC cells (NC,s) Parallel number of UC cells (NC,p) Total module mass of battery module Total module mass of UC module Nominal voltage of battery module (UB) Nominal voltage of UC module (UC) Internal resistance of battery module (RB) Internal resistance of UC module (RC) Nominal capacitance of UC module (C) Stored energy in battery module Useable energy in UC module Nominal power of battery module Nominal power of UC module Energy efficiency of DC-DC (ηDC)

125 25 112 2 265.4 139.8 412.5

– – – – kg kg V

302.4 40

V mΩ

16.24 53.57 23.75 510.3 18.5 674.02 0.95

mΩ F kWh Wh kW kW –

UC cell [25]

HESS configuration

i

where tr,i denotes the ith continuous time period during which PWLTP is positive in the WLTP cycle. Along with the DC link voltage requirement, the following criteria are given.

EBr;cell Þ � Erange

NB;s UB;cell > UB;DC

(6)

1 UB < NC;s UC;cell < UB 2

(7)

NB;s RB;cell NB;p

(8)

UB ¼ NB;s UB;cell

(9)

RB ¼

The behavior of the battery module can be consequently described by the following equations. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi UB;k þ U 2B;k þ 4PB;k RB;k IB;k ¼ (10) 2RB;k

(2)

PB;k ¼ ðUB;k þ IB;k RB;k ÞIB;k

(11)

(3)

PBloss;k ¼ I 2B;k RB;k

(12)

where k denotes the time series. Similarly, the UC module is represented by an equivalent series resistance and an equivalent series capacitance. The connection between the cell and the module can be described as follows.

where EBr,cell denotes the extra energy waste per cell from the mass in­ crease of the battery module. According to our assessment, when the mass of the battery module increases by 72 g (the mass of one battery cell), it will require about 0.07 Wh additional energy, which is almost 1% of the energy storage of a battery cell. As for the UC module, the energy storage should partly cover the demand of the peak power period. Also, the energy storage of the UC module should be large enough to cover the regenerative energy every time the load power is positive in the WLTP cycle. The Maxwell BCAP3000 ultracapacitor [25] is selected, whose cell parameters can be found in Table 2. The maximum energy demand of the peak power period can be calculated as follows. Z � � Epeak ¼ max �PWLTP ðtÞ PB;n �dt (4) i

� 3 NC;s NC;p EC;cell � max Eregn ; Epeak 4

where the voltage of the UC module is required to be in the range of (1/ 2UB, UB), to avoid the inefficient operation of the DC-DC converter. This is because when the DC-DC converter is operating in buck mode, the too low output voltage will reduce the energy efficiency. Based on the above analysis (Eqs. (1)–(7)), the configuration of HESS can be determined. Table 2 gives the size information of the battery module and the UC module. This paper focuses on energy management optimization, and no optimization of HESS size has been done. The battery semi-active hybrid topology is selected in this work, in which the battery module is connected to the DC bus via a bidirectional DC/DC converter while the UC module is connected to the DC bus directly. In order to better describe the behavior of the HESS, an equivalent circuit model is provided as shown by Fig. 1(a). It is notable that the current is defined as positive when the battery or UC is charging, and negative when discharging. As can be seen in Fig. 1(a), the battery module is represented by an equivalent series resistance and a controlled voltage source. The connection between the cell and the module can be described as follows.

Thus, the total energy storage of the battery module should be no less than Erange. Also, the series voltage of the battery module should be no less than the DC link voltage. The following criteria are given. NB;s NB;p ðEB;cell

(5)

tr;i

NC;s RB;cell NC;p

(13)

UC ¼ NC;s UC;cell

(14)

RC ¼

C¼

NC;p CC;cell NC;s

(15)

The behavior of the UC module can be consequently described by the following equations.

tp;i

where tp,i denotes the ith continuous time period during which PWLTP is larger than PB,n, the nominal power of battery module, in the WLTP cycle. Similarly, the maximum energy demand of the regenerative period is defined as follows.

4

IC;k ¼

C ðUC;k Ts

PC;k ¼

C � 2 U C;k 2Ts

(16)

UC;k 1 Þ � U 2C;k

1

þ I 2C;k RC

(17)

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Fig. 1. Model for the battery semi-active HESS. (a) Equivalent circuit model. (b) Flowchart of DP optimization.

law factor, c is the rate of the battery current (c ¼ 1 means the current is 2A). The values of the parameters above can refer to Ref. [27]. To simplify the calculation, we choose to minimize QB instead of ΔSOHB. It can be seen that when other parameters remain unchanged, the smaller the QB is, the smaller the capacity loss of the battery. The total Ah throughput of the battery QB can be calculated by the time integration of the absolute value of current IB,k, which can be expressed as follows. X� � �IB;k �Ts QB ¼ (25)

(18)

PCloss;k ¼ I 2C;k RC

The bidirectional DC/DC converter is used for connecting the battery and the DC bus, and the energy efficiency of the converter is our concern. The power transfer relationship in the topology can be described as follows. PDC;k ¼ PL;k

PB;k

PC;k

8 > < PDC;k ηDC;k ðPDC;k � 0Þ ¼ PDC;k > ðPDC;k < 0Þ :

(19) (20)

k

ηDC;k

PDCloss;k ¼ PB;k

PDC;k

Therefore, the optimization objective function J can be established as follows.

(21)

¼

2.2. DP analysis

Eloss

X ¼ Ploss;k Ts

(26)

k

where w1 and w2 denote the weight factors of each part in the optimi­ zation objective function. From the above equations, it can be seen that once the voltage variation of the UC is determined, all the system parameters can be calculated according to the HESS model in 2.1. Therefore, the UC voltage UC is selected as the state variable for the DP search. The operation range of UC is discretized to M separated states, which constitute the whole state space for decision. It is worth noting that in order to simplify the calculation, some assumptions are made: 1. the variations of RB and RC due to the state of charge or state of health changes are not considered in this work; 2. UB,cell is considered as a constant of 3.3 V, rather than changing with the state of charge. The search process of DP can be explained by Fig. 1(b). The search is executed according to a certain load cycle. It is notable that the initial state and the final state of the UC voltage should be the same across a certain test cycle. That is because the energy stored in the UC is quite limited compared to the battery, and for the safety and long-term functioning consideration of the UC, it is preferable to make the UC self-recover to its initial state after the whole cycle. Since the UC module works between NC;s UC;cell and 12NC;s UC;cell , the median energy voltage is pffiffiffiffi therefore 410NC;s UC;cell . Thus the initial state and the final state of UC voltage can be set as this value to allow the UC module to fully utilize its capability. Suppose the cycle lasts N seconds and the sample time interval Ts is 1s, then the DP search process can be divided into N steps according to Bellman’s optimization theory. For the first DP step (k ¼ N), the cost function can be calculated as follows.

The dynamic programming can determine the optimal control input via the designed optimization objective function. For the battery/ ultracapacitor HESS, the optimization goals of this work include the following two points: 1. Minimize the total energy loss, 2. Minimize the capacity fade of the battery. For the first point, the general energy loss condition can be evaluated by the real-time power loss of the HESS, which can be expressed by the following equations. Ploss;k ¼ PBloss;k þ PCloss;k þ PDCloss;k

J ¼ w1 Eloss þ w2 QB X � � ðw1 Ploss;k þ w2 �IB;k �ÞTs

(22) (23)

k

where Ts is the sample time interval, Ploss,k, PBloss,k, PCloss,k, PDCloss,k are the power loss of the HESS, the battery module, the UC module, and the DC-DC converter at step k, respectively, Eloss is the general energy loss of the HESS. As for the second point, Ref. [26–28] has pointed out that the ca­ pacity fade of the battery is directly connected with its Ah throughput. The following equation gives the relationship between the percentage capacity loss of the battery ΔSOHB and the Ah throughput of the battery QB [27]. � � � � Ea ðcÞ z QB ΔSOHB ¼ B c exp (24) RTe where B is the pre-exponential factor, Ea is the activation energy in J/ mol, R is the gas constant, Te is the absolute temperature, z is the power 5

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�

Journal of Power Sources 438 (2019) 227024

JN xj ¼ gN xj

�

WLTP consists of different types of driving scenarios, it is divided into a low speed part and a high speed part in the DP analysis. The speed file of each type of load cycle is plotted by Fig. 2(a)-(e). According to the vehicle parameters and kinetics analysis, the power demand for the HESS can be obtained under each load cycle. The optimal power splitting results for different load cycles are given by Fig. 2(f)–(j). From the figure, it can be seen that the UC serves all the regenerative power and part of the peak power, while the battery serves all the low-power demand and part of the peak power demand. With the help of the UC, the battery is allocated with smoother power than the load power and lower peak power requirements. It is worth noting that, sometimes when the negative load power demand is very small or close to zero, the battery charges the UC. That is because the final state of UC voltage is required to recover to its initial state. The DP analysis is based on the assumption that the current test cycle will be performed again and again, and the initial and final states of UC voltage are set to be the median energy state, in order to have a relatively large charging or discharging workspace. Thus the UC is charged sometimes when it is not working, to store additional energy for the future demand. Here how much the UC should be charged is unknown and depends on the particular test cycle. In order to better understand the UC’s behavior, the relationship

(27)

For the subsequent DP steps (1 � k � N 1), the cumulative cost function at each step can be calculated as follows. � � � � Jk xj ¼ min gk xj ; ui þ Jkþ1 ðfkþ1 Þ (28) ui 2Uk ðxj Þ where gN(xj) denotes the cost of the end step, gk(xj, ui) denotes the cost of step k, fkþ1 denotes the state variable at the step kþ1, Jkþ1(fkþ1) denotes the optimization objective function with the best energy consumption at step kþ1, Uk denotes the set of control variables, i and j denote the discrete points of the control variables and state variables, respectively. 2.3. Three-segment rule based control Based on the DP analysis discussed in 2.2, the optimal power splitting mode can be provided for a certain load cycle. Here, different load cycles are analyzed to develop some common control rules. There are in total 4 types of load cycles being considered, namely the Urban Dynamometer Driving Schedule (UDDS), the Worldwide harmonized Light-duty vehi­ cles Test Procedure (WLTP), the Highway Fuel Economy Test (HWFET) and the US06 Supplemental Federal Test Procedure (US06). Since the

Fig. 2. Speed files and DP power splitting results of different types of load cycles. (a)–(e) Speed files. (f)–(j) DP power splitting results. 6

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Journal of Power Sources 438 (2019) 227024

between UC power and load power is plotted as Fig. 3 shown. As can be seen from the figure, for all cycle types, the distribution of the entire points can be roughly fitted by three line segments. According to the fitted line segments, the relationship between the UC power and the load power can be described by three segments as follows:

PL SOCB UC

s1. If PL < PB;thd , then PC ¼ αðPL PB;thd Þ; PB ¼ ðPL PC Þ= ηDC . s2. If PB;thd � PL � PC;chg , then PC ¼ 0; PB ¼ PL =ηDC . PC;chg , then PC ¼ PL þ PC;chg ; PB ¼ PC;chg = ηDC . s3. If PL >

UC≤ UC,low

Y Y SOCB≤ SOCB,low

Y

N

N

UC≥ UC,high

Y

PL>0

N SOC and voltage protection

Where PB,thd is a negative constant which means the discharge threshold power for the battery, PC,chg is a positive constant which means the charge power for the UC, and α is a factor in the range of (0,1]. The values of PB,thd and α are different for different load cycles. It is apparent that the above behavior of the UC can be converted into a set of control rules. Considering the SOC and voltage limitation, the rele­ vant control rules can be generated as shown in Fig. 4.

PL> PC,chg

N

PB=0 PC=0 PB=PL/η DC PC=0

Y

PB=PLη DC PC=0 PB=0 PC=PL

Y

PB = PC,chg/η DC PC = PL+PC,chg

Y

PB = PL/η DC PC = 0

N PL>PB,thd

3. Design of real-time energy management strategy From DP analysis, the optimal power splitting mode for certain load cycles can be acquired. But when the load pattern is unknown in advance, which is common in practical applications, the DP analysis can be useless. Similarly, the three-phase rule based control strategy cannot work well if the power splitting parameters are decided only by one certain load cycle. It is reasonable that the power splitting parameters should be adjusted according to the real-time load pattern. Therefore, a load-adaptive rule based control strategy is proposed in this section, to satisfy the requirement of online management in practical applications.

N Load power splitting

PB = (PL PC)/η DC PC = α (PL PB,thd)

Fig. 4. The flowchart of three-segment rule based control.

values of the power splitting parameters should change accordingly. In order to get the optimal parameters under different load cycles conve­ niently, a genetic algorithm (GA) based parameter optimization is proposed. The optimization problem using the GA method is described as fol­ lows.

3.1. GA based parameter optimization According to section 2.3, the performance of the three-phase rule based control strategy is directly decided by the values of the power splitting parameters. Therefore, when the load pattern changes, the

Fig. 3. The relationship between the UC power and the load power in DP results. (a) UDDS. (b) WLTP low speed part. (c) WLTP high speed part. (d) HWFET. (e) US06. (f) The three-segment power splitting diagram. 7

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Journal of Power Sources 438 (2019) 227024

X

� � ðw1 Ploss;k þ w2 �IB;k �ÞTs

8 def: > <

Jðα; PB;thd Þ ¼

> : min s:t:

Jðα; PB;thd Þ 0:5 � α � 1; 15000W � PB;thd �

Table 4 GA parameter optimization results.

(29)

k

Load cycle

2500W

Where J(α, PB,thd) is the optimization objective function, which is defined exactly the same with Eq. (13). α and PB,thd are the optimization variables, and their ranges are given respectively. Here, the value of PC, chg is not taken as an optimization variable, but set as a constant, to find out the relationship between α and PB,thd. Once the values of α and PB,thd are given, the three-phase rule based control strategy can provide the power splitting result, and the corresponding J(α, PB,thd) can be evalu­ ated according to its definition. The detailed GA optimization process is described by Table 3. The GA optimization will be repeated 10 times for each different load cycle. The GA optimization results of four types of load cycles are listed in Table 4, where the value of PC,chg is set to be 1200 W. For each type of load cycle, the results of five best GA attempts are given. It can be found that multiple pairs of parameters can achieve similar performance that is close to the optimal cost. For each type of load cycle, the relationship between the two parameters is plotted by Fig. 5(a). It is clear that the value of α can be fitted by a linear function of the value of PB,thd as follows. The detailed linear function fitting factors are listed in Table 5. Furthermore, the selected PB,thd value of each load cycle type is the average of the middle three values from the GA results since they have relative high α values, which helps to reduce the battery power.

4300.6 4290.7 4171.2 3555.7 3149.8

0.687 0.686 0.675 0.621 0.588

14.6147 14.6145 14.6127 14.6037 14.5984

WLTP-low speed part

4156.0 3403.4 3111.3 2521.9 2500.0

0.764 0.696 0.672 0.626 0.625

9.0205 9.0173 9.0163 9.0149 9.0148

WLTP-high speed part

13690.9 13778.8 14088.9 14133.7 14828.4

0.513 0.517 0.533 0.535 0.573

25.5398 25.5398 25.5396 25.5396 25.5396

HWFET

13092.8 12751.6 12642.8 12245.3 11816.0

0.694 0.643 0.628 0.576 0.525

23.5161 23.5154 23.5153 23.5148 23.5144

US06

12647.7 11883.7 11448.8 11445.9 11270.7

0.609 0.577 0.560 0.560 0.553

19.3408 19.3344 19.3326 19.3326 19.3319

p2 ¼ Pavg

In order to generate a load-adaptive parameter adjusting mechanism, the connection between the load pattern and the optimal power splitting parameters is studied. As shown in the aforementioned work, the value of α can be expressed by a linear function of PB,thd. Thus, the value of PB, thd should be determined firstly. For a deeper understanding of the different load patterns, the statistic information of four types of load cycles is listed in Table 5. It can be discovered that there exists a positive correlation between PB, thd and p1, where p1 is defined as follows. � Pavg Ttol Pavg Pdisavg Tdis � p1 ¼ Pavg ⋅ (31) Pdisavg Tdis Pchgavg Pavg Tchg

(33)

Pdisavg

Besides, there exists a negative correlation between bα and p3, where p3 is defined as follows. p3 ¼

Pchgavg Tchg Pdisavg Tdis

(34)

The above relationship can be fitted by quadratic functions as follows. kα ¼

9:627 � 10

bα ¼

15:95p23

13 2 p2

þ 2:397 � 10 8 p2

12:24p3

1:972

1:828 � 10

4

(35) (36)

The relationship between power splitting parameters and load sta­ tistics is illustrated by Fig. 5(b)–(d). Finally, the splitting parameters can be determined, once the statistic information of the actual load pattern is acquired. In order to get the statistic information of load pattern in real time, a slide counting window is applied in this work. The size of the window can be set as 800s, which is comparable with the 4 load cycle types. Furthermore, in order to update the load statistics more frequently, the relevant information will be recalculated when the counting window moves for 50s. Once the latest load statistics are acquired, the new splitting parameters can be produced according to Eqs. (30)-(36). The strategy proposed above can be illustrated by Fig. 6. For the first 800s, the initial power splitting parameters are tuned according to the WLTP cycle. As for the value of PC,chg, it is not generated directly from the load pattern, but is adjusted according to the voltage of the UC. In order to prevent the UC from reaching the highest voltage or the lowest voltage too early and not working properly, it is preferable to maintain the UC voltage at a middle level. The proposed load-adaptive rule based control strategy will adjust the value of PC,chg via a negative feedback mechanism, simultaneously with other parameter adjustments. For the first 800s, the initial value of PC,chg can be set as a constant of 1200 W. It is tuned according to the WLTP cycle in this work.

Then the relationship between PB,thd and p1 can be fitted by a quadratic function, as follows. 1:102 � 103

Jmin ( � 105)

PB,thd, also need to be adjusted when the load pattern changes. It can be discovered that there exists a positive correlation between kα and p2, where p2 is defined as follows.

3.2. Load-adaptive rule based control

7:993 � 10 5 p21 þ 0:525p1

α

UDDS

(30)

α ¼ kα PB;thd þ bα

PB;thd ¼

PB,thd (W)

(32)

Moreover, the two fitting factors in the linear function between α and Table 3 Process of GA algorithm. Step 1: Initialization (1) Load the test cycle data into the program. (2) Key parameters of GA are set as follows: Generations ¼ 200, Penalty Factor ¼ 100, Migration Fraction ¼ 0.2, Population Size ¼ 50, Crossover Fraction ¼ 0.8, Mutation Probability ¼ 0.025. Step 2: GA optimization (1) An initial population is generally created at random and represented in binary form. (2) The optimization objective function J(α, PB,thd) is evaluated via each individual population based on the correspondingly obtained model parameters. (3) If Generation is less than 200, a roulette game is employed to generate a new population based on reproduction, crossover and mutation. The new result based on the updated population is compared with the old result obtained in (2). (4) Return to (2) until Generation reach 200 or the min J(α, PB,thd) is obtained under the constraint in Eq. (29).

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Journal of Power Sources 438 (2019) 227024

(a) WLTP - low speed part

HWFET

α

WLTP - high speed part

US06

UDDS

GA results fit curves

PB,thd (W) (b)

(c)

kα

bα

true value fit curve

PB,thd (W)

true value fit curve

(d)

true value fit curve

p1

p2

p3

Fig. 5. The GA results for different load cycles and the relationship between splitting parameters and load statistics. (a) The GA results for different load cycles. (b) Relationship between PB,thd and p1. (c) Relationship between kα and p2. (d) Relationship between bα and p3. Table 5 Statistics and parameters of four types of load cycles. Parameter

UDDS

WLTP low speed

WLTP high speed

HWFET

US06

Discharge time Tdis(s) Charge time Tchg(s) Total time Ttol(s) Discharge average power Pdisavg(W) Charge average power Pchgavg(W) Average power Pavg(W) p1 p2 p3 PB,thd(W)

791 320 1370 8876.72 7489.99 3375.69 2782.47 5501.04 0.341 3149.8 0.588 8.588 � 10 0.317

1000 546 278 8713.56 6860.51 2850.38 2025.07 5863.18 0.401 2500.0 0.625 8.376 � 10 0.414

800 585 155 16663.09 10669.37 10117.70 9984.09 6545.39 0.170 14828.4 0.573 5.302 � 10 0.213

686 74 766 12067.60 10323.04 9810.01 8203.30 2257.59 0.092 11816.0 0.525 1.321 � 10 1.040

414 142 600 19995.30 15827.41 10050.94 9256.58 9944.37 0.272 11270.7 0.553 4.121 � 10 0.088

α

kα bα

5

5

5

4

5

4. Verification

4.1. Combined load cycle

To verify the performance of the proposed load-adaptive rule based control strategy, tests need to be performed under dynamic load cycles. Two kinds of composite load cycles are provided here. One kind of test cycle is the combined load cycle (CLC), which is generated by splicing the 4 types of load cycles namely WLTP, UDDS, HWFET and US06 in series. Another kind of test cycle is the random load cycle (RLC) generated by splicing the micro-trips and micro-idles randomly, where the micro-trips and micro-idles come from the aforementioned 4 types of load cycles. The definition of the micro-trips and micro-idles comes from Ref. [29]. Two RLCs are generated to test different driving scenarios. For RLC1, it reflects a city-like driving scenario with speed below 80 km/h in over 70% of the time. The RLC2 reflects driving scenarios similar to rural or highways, with more than 40% of the time being faster than 80 km/h. The overall information of CLC and RLCs is given by Table 6.

The proposed load-adaptive rule based control (aRBC) strategy is firstly verified by the CLC test. The result of ordinary rule based control (RBC) and DP methods are also provided, as well as the performance of a battery-only system (BTO). The parameters of ordinary RBC is tuned under the WLTP load cycle, while the detailed information of CLC is supposed to be unknown before the test. As for the configuration of the BTO system, it is set to be the same as the battery module in HESS to provide a comparable vision of performance. The performance of different options in the CLC test is listed by Table 7, and the detailed power splitting results are plotted as Fig. 7 shown. From the table, it is clear that the application of HESS has cut down the energy loss, RMS current and Ah throughput (Ahthp) of the battery significantly compared with the BTO system. This has proven that the use of the UC helps to protect the battery and prolong the cycle life of the system. Furthermore, aRBC reaches a much closer perfor­ mance to DP, which is considered to be the optimal equivalence between the total energy loss and the battery Ah throughput, than ordinary RBC 9

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Journal of Power Sources 438 (2019) 227024

Power Splitting Rules Load Power File

Split power PB, thd

PC, chg

Power Splitting Results

charge Load power

N

t > 1200

Initial Parameters

discharge

PC PL PC

Y Slide the Load Power Window (with size of 1200s) Update the Splitting Parameters N

t mod 50 = 0

Update the Statistical Features of the Load Power Window

Y

Fig. 6. Flowchart of the load-adaptive rule based control.

Table 8, and the detailed power splitting condition of RLC is plotted as Fig. 8(a)-(e) shown. From the table, a similar conclusion can be found that the proposed aRBC method has near optimal performance. Compared with the BTO system, the maximum battery current is reduced by 58.6%, the RMS battery current is reduced by 36.4%, and the Ah throughput is reduced by 35.6%. Compared with the ordinary RBC, the maximum battery current is reduced by 22.3%, the Ah throughput is reduced by 15.7%, and the total energy loss is reduced by 15.1%, showing the better capability of aRBC in battery protecting and energysaving. The performance of different options in the RLC2 test is given by Table 9, and the detailed power splitting condition of RLC is plotted as Fig. 8(f)–(j) shown. From the table, similar conclusions can be found. Compared with the BTO system, the maximum battery current is reduced by 47.9%, the RMS battery current is reduced by 29.3%, and the Ah throughput is reduced by 29.6%. Compared with the ordinary RBC, the battery current performance is almost the same, the Ah throughput is reduced by 3.4%, and the total energy loss is reduced by 3.0%. The results of RLCs show that aRBC generally performs better than RBC in battery protecting and energy-saving. In a city-like driving sce­ nario the improvement is obvious, while in a rural or highway-like scenario the improvement is slight. This is because when the driving scenario has a relatively high average speed and little acceleration or deceleration, it is more suitable for the battery to work, and the UC contributes relatively little. As a result, the change in EMS can only bring about little improvement.

Table 6 Cycle information of CLC and RLCs. Load cycle

CLC

RLC1

RLC2

Distance (km) Total time (s) Max speed (km/h) Average speed (km/h) Time percentage of idles (0 km/h) Time percentage of high speed (�80 km/h) Time percentage of low speed (>0 km/h and <80 km/h)

64.63 4536 131.30 51.30 12.01% 25.73% 62.26%

57.60 5117 97.40 40.52 14.64% 12.55% 72.82%

70.90 3778 131.30 67.56 7.04% 42.93% 50.03%

Table 7 Performance of different options in the CLC test. Parameters Battery energy loss (Wh) UC energy loss (Wh) DC-DC energy loss (Wh) Total energy loss (Wh) Max battery current (A) RMS battery current (A) Battery Ah throughput (Ah)

BTO 61.34 – – – 200.49 34.89 31.78

HESS RBC

aRBC

DP

33.02 13.86 504.67 551.55 102.16 25.60 24.46

29.39 23.47 450.57 503.43 104.67 24.15 21.88

24.87 19.01 426.74 470.61 110.40 22.21 20.75

does. In conclusion, aRBC provides a near optimal result, when the maximum battery current is reduced by 47.8%, the RMS battery current is reduced by 30.8%, and the Ah throughput is reduced by 31.1%, compared with the BTO system. Also, aRBC provides better performance in battery protecting and energy-saving than ordinary RBC, when the battery current performance is almost the same, the Ah throughput is reduced by 10.5%, and the total energy loss is reduced by 8.7%. These have proven that the proposed aRBC has a strong capability of load adapting and battery protection with low energy consumption.

5. Conclusions This paper proposes a load-adaptive rule based control (aRBC) strategy for the real-time energy management of HESS. The work starts with the DP analysis. Three-segment control rules are extracted from the DP results of 4 different types of load cycles. Then the connection be­ tween the power splitting parameters and the load pattern is studied. GA searching is applied to get the optimal power splitting parameters conveniently. After relevant calculations, the functional relationship between power splitting parameters and load statistics is set up. The load-adaptive parameter adjusting mechanism can be consequently founded. To verify the effectiveness of the proposed method, two

4.2. Random load cycle The performance of different options in the RLC1 test is given by 10

Journal of Power Sources 438 (2019) 227024

C. Liu et al.

Fig. 7. Power splitting performance of aRBC in CLC. (a) Speed file of CLC. (b) Power splitting result of aRBC in CLC. (c) UC voltage comparison in CLC. (d) Battery current comparison in CLC. (e) Normalized accumulated Ah throughput comparison in CLC.

composite load cycles are tested, namely the combined load cycle and the random load cycle. Results show that the energy waste and battery current conditions are much better in aRBC than ordinary RBC, while the battery Ah throughput is reduced by 3.4%–15.7% and the total en­ ergy loss is reduced by 3.0%–15.1%. In particular, the city-like driving scenarios with relatively low average speeds and many idles will benefit more from the improvement of EMS. Also, the performance of aRBC in battery protecting and energy-saving is quite near the DP result, which is considered as the optimal equivalence between energy-saving and bat­ tery life-prolonging. Hence, the effectiveness of aRBC is proven, and the superiority of it under unknown load patterns is highlighted. Moreover, the computational cost of aRBC is really low, which means it has good adaptability in practical applications. Our future work is to implement the application of the proposed aRBC in EVs, and to develop more

Table 8 Performance of different options in the RLC1 test. Parameters Battery energy loss (Wh) UC energy loss (Wh) DC-DC energy loss (Wh) Total energy loss (Wh) Max battery current (A) RMS battery current (A) Ah throughput (Ah)

BTO 46.37 – – – 200.49 28.56 29.34

HESS RBC

aRBC

DP

25.34 9.46 463.43 498.22 106.86 21.11 22.40

18.75 14.87 389.48 423.11 83.04 18.16 18.89

15.07 16.43 348.99 380.49 91.81 16.28 16.96

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Journal of Power Sources 438 (2019) 227024

Fig. 8. Power splitting performance of aRBC in RLCs. (a) Speed file of RLC1. (b) Power splitting result of aRBC in RLC1. (c) UC voltage comparison in RLC1. (d) Battery current comparison in RLC1. (e) Normalized accumulated Ah throughput comparison in RLC1. (f) Speed file of RLC2. (g) Power splitting result of aRBC in RLC2. (h) UC voltage comparison in RLC2. (i) Battery current comparison in RLC2. (j) Normalized accumulated Ah throughput comparison in RLC2. [2] 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. [3] C. Liu, Y. Wang, Z. Chen, et al., A variable capacitance based modeling and power capability predicting method for ultracapacitor, J. Power Sources 374 (2018) 121–133. [4] R. Xiong, H. Chen, C. Wang, et al., Towards a smarter hybrid energy storage system based on battery and ultracapacitor-A critical review on topology and energy management, J. Clean. Prod. 202 (2018) 1228–1240. [5] 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. [6] W. Jing, C.H. Lai, W.S.H. Wong, et al., A comprehensive study of batterysupercapacitor hybrid energy storage system for standalone PV power system in rural electrification, Appl. Energy 224 (2018) 340–356. [7] J. Cao, A. Emadi, A new battery/ultracapacitor hybrid energy storage system for electric, hybrid, and plug-in hybrid electric vehicles, IEEE Trans. Power Electron. 27 (1) (2012) 122–132. [8] Z. Song, J. Li, X. Han, et al., Multi-objective optimization of a semi-active battery/ supercapacitor energy storage system for electric vehicles, Appl. Energy 135 (2014) 212–224. [9] 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. [10] A. Castaings, W. Lhomme, R. Trigui, et al., Comparison of energy management strategies of a battery/supercapacitors system for electric vehicle under real-time constraints, Appl. Energy 163 (2016) 190–200. [11] S.T. Sisakat, S.M. Barakati, Fuzzy energy management in electrical vehicles with different hybrid energy storage topologies, in: 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), IEEE, 2015, pp. 1–6. [12] X. Huang, T. Hiramatsu, H. Yoichi, Energy management strategy based on frequency-varying filter for the battery supercapacitor hybrid system of electric vehicles, in: 2013 World Electric Vehicle Symposium and Exhibition (EVS27), IEEE, 2013, pp. 1–6. [13] M. Ibrahim, S. Jemei, G. Wimmer, et al., Nonlinear autoregressive neural network in an energy management strategy for battery/ultra-capacitor hybrid electrical vehicles, Electr. Power Syst. Res. 136 (2016) 262–269. [14] A. Santucci, A. Sorniotti, C. Lekakou, Power split strategies for hybrid energy storage systems for vehicular applications, J. Power Sources 258 (2014) 395–407. [15] M. Wieczorek, M. Lewandowski, A mathematical representation of an energy management strategy for hybrid energy storage system in electric vehicle and real time optimization using a genetic algorithm, Appl. Energy 192 (2017) 222–233.

Table 9 Performance of different options in the RLC2 test. Parameters Battery energy loss (Wh) UC energy loss (Wh) DC-DC energy loss (Wh) Total energy loss (Wh) Max battery current (A) RMS battery current (A) Ah throughput (Ah)

BTO 70.47 – – – 200.49 40.97 33.51

HESS RBC

aRBC

DP

35.26 24.60 502.29 562.15 102.16 28.98 24.41

35.20 25.49 484.82 545.51 104.47 28.96 23.59

32.91 17.75 484.61 535.27 121.26 28.00 23.58

intelligent strategies considering more impacting factors. Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 61803359). References [1] X. Li, Z. Wang, L. Zhang, et al., State-of-health estimation for Li-ion batteries by combing the incremental capacity analysis method with grey relational analysis, J. Power Sources 410 (2019) 106–114.

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C. Liu et al.

Journal of Power Sources 438 (2019) 227024 [22] J. Shen, A. Khaligh, A supervisory energy management control strategy in a battery/ultracapacitor hybrid energy storage system, IEEE Trans. Transp. Electrification 1 (3) (2015) 223–231. [23] R. Xiong, J. Cao, Q. Yu, Reinforcement learning-based real-time power management for hybrid energy storage system in the plug-in hybrid electric vehicle [J], Appl. Energy 211 (2018) 538–548. [24] https://www.buya123products.com/uploads/vipcase/844c1bd8bdd1190ebb364d 572bc1e6e7.pdf accessed by July 2019. [25] https://www.maxwell.com/images/documents/k2series_ds_10153704.pdf accessed by July 2019. [26] I. Baghdadi, O. Briat, J.Y. Del�etage, et al., Lithium battery aging model based on Dakin’s degradation approach, J. Power Sources 325 (2016) 273–285. [27] J. Wang, P. Liu, J. Hicks-Garner, et al., Cycle-life model for graphite-LiFePO4 cells, J. Power Sources 196 (8) (2011) 3942–3948. [28] C. Liu, Y. Wang, Z. Chen, Degradation model and cycle life prediction for lithiumion battery used in hybrid energy storage system, Energy 166 (2019) 796–806. [29] D. Feroldi, M. Carignano, Sizing for fuel cell/supercapacitor hybrid vehicles based on stochastic driving cycles, Appl. Energy 183 (2016) 645–658.

[16] O. Gomozov, J.P.F. Trov~ ao, X. Kestelyn, et al., Adaptive energy management system based on a real-time model predictive control with nonuniform sampling time for multiple energy storage electric vehicle, IEEE Trans. Veh. Technol. 66 (7) (2017) 5520–5530. [17] Z. Chen, R. Xiong, J. Cao, Particle swarm optimization-based optimal power management of plug-in hybrid electric vehicles considering uncertain driving conditions, Energy 96 (2016) 197–208. [18] Z. Song, H. Hofmann, J. Li, et al., Optimization for a hybrid energy storage system in electric vehicles using dynamic programing approach[J], Appl. Energy 139 (2015) 151–162. [19] P. Elbert, S. Ebbesen, L. Guzzella, Implementation of dynamic programming for ndimensional optimal control problems with final state constraints, IEEE Trans. Control Syst. Technol. 21 (3) (2013) 924–931. [20] S. Zhang, R. Xiong, Adaptive energy management of a plug-in hybrid electric vehicle based on driving pattern recognition and dynamic programming, Appl. Energy 155 (2015) 68–78. [21] Z. Song, J. Hou, S. Xu, et al., The influence of driving cycle characteristics on the integrated optimization of hybrid energy storage system for electric city buses, Energy 135 (2017) 91–100.

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