supercapacitor hybrid energy storage systems for electric vehicles using perturbation observer based robust control

supercapacitor hybrid energy storage systems for electric vehicles using perturbation observer based robust control

Journal of Power Sources xxx (xxxx) xxx Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/locate...

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Journal of Power Sources xxx (xxxx) xxx

Contents lists available at ScienceDirect

Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

Applications of battery/supercapacitor hybrid energy storage systems for electric vehicles using perturbation observer based robust control Bo Yang a, Jingbo Wang a, Xiaoshun Zhang c, *, Junting Wang a, Hongchun Shu a, Shengnan Li b, Tingyi He b, Chaofan Lan d, Tao Yu d a

Faculty of Electric Power Engineering, Kunming University of Science and Technology, 650500, Kunming, China Electric Power Research Institute of Yunnan Power Grid Co., Ltd., Kunming, 650217, China College of Engineering, Shantou University, 515063, Shantou, China d College of Electric Power, South China University of Technology, 510640, Guangzhou, China b c

H I G H L I G H T S

� Anovel NRFOCis designed for BSM-HESSused inEVs application. � RBS is used to optimally assign power between battery and SMES. � Bio-inspired MSSA is used to optimally tune the NRFOC parameters. � Satisfactory control performance is realized under various operation conditions. � dSpace based HIL experiment validates the implementation feasibility. A R T I C L E I N F O

A B S T R A C T

Keywords: Battery/supercapacitor hybrid energy storage system Electric vehicles Robust fractional-order sliding-mode control Perturbation observer

This paper designs a robust fractional-order sliding-mode control (RFOSMC) of a fully active battery/super­ capacitor hybrid energy storage system (BS-HESS) used in electric vehicles (EVs), in which two bidirectional DC/ DC converters are employed to decouple battery pack and supercapacitor pack from DC bus based on the classical 5th-order averaged model. Rule-based strategy (RBS) is firstly employed as the energy management strategy (EMS) to generate the battery current reference. Then, RFOSMC scheme is developed as the underlying controller to globally compensate nonlinearities and various uncertainties of BS-HESS by the real-time perturbation esti­ mation via a sliding-mode state and perturbation observer (SMSPO). Two outputs are chosen, e.g., battery current and DC bus voltage, which are also the only states that need to be measured for the control system design, thus RFOSMC is relatively easy to be implemented. The control performance of RFOSMC is thoroughly inves­ tigated in comprehensive case studies to that of other three typical controllers. Finally, a hardware-in-the-loop (HIL) test is undertaken to validate the effectiveness of the proposed control scheme.

1. Introduction In the past decade, electric energy storage system (EESS) has played a paramount role in smart grid and energy internet thanks to its elegant merits of power system stability enhancement, auxiliary control of renewable energy, generation efficiency improvement, and greenhouse gas emission reduction [1–3], which can provide a powerful and effec­ tive supplement for renewable energy system (RES) [4–7] to handle its inherent weakness of high intermittency and ubiquitous randomness. EESS technologies can be typically classified into three categories

according to the type of stored energy, e.g., mechanical (flywheel, pumped hydro, and compressed air), electrical (superconducting mag­ netic and supercapacitor), as well as chemical (battery and fuel cell) [8]. Generally speaking, they own various features for different applications, such as power rating, charging/discharging time, power/energy density, and life time in both years and cycles [9]. Based on different time and size scales, EESS can be further divided into two groups, that is, (a) energy-type storage systems which are characterized by high energy capacity and long storage duration and (b) power-type storage systems which are characterized by high power ca­ pacity and quick response time [10]. Thus far, hybrid energy storage

* Corresponding author. E-mail address: [email protected] (X. Zhang). https://doi.org/10.1016/j.jpowsour.2019.227444 Received 5 August 2019; Received in revised form 2 November 2019; Accepted 10 November 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Bo Yang, Journal of Power Sources, https://doi.org/10.1016/j.jpowsour.2019.227444

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Nomenclature Variables v1, v2, vo i1, i2 E vu

BS-HESS parameters C1, C2, Co filter capacitances of battery side, supercapacitor side and supercapacitor load CSC capacitance of supercapacitor inductances of battery side and supercapacitor side L1, L2 Re, Ru inner series resistances of battery and supercapacitor RL1, RL2 series resistances of battery side and supercapacitor side Ron1, Ron2, Ron3, Ron4 MOSFET on-resistances for S1, S2, S3, and S4 Ro equivalent load of EVs D1, D2 duty cycle for the on-state of S1 and S3

voltages corresponding to C1, C2 and Co currents flowing through L1 and L2 open-circuit voltage of battery open-circuit voltage of supercapacitor

Abbreviations BS-HESS battery/superconductor hybrid energy storage system EV electric vehicle EMS energy management strategy RBS rule-based strategy PID proportional-integral-derivative SMC sliding-mode control ASMC adaptive sliding mode control RFOSMC robust fractional-order SMC SMSPO sliding-mode state and perturbation observer HIL hardware-in-the-loop IAE integral of absolute error

RFOSMC parameters b11, b22 controller gains k11, k12, k13, k21, k22, k23, k24, α11, α12, α13, α21, α22, α23, α24 observer gains α1α2 fractional differential order λc1 , λc2 fractional-order PDα sliding surface gains ς 1 , ς 2 , φ1 , φ2 sliding-mode control gains εo thickness layer boundary of observer εc thickness layer boundary of controller

system (HESS) incorporating the aforementioned two types of EESS has been widely and popularly applied, which is capable of simultaneously satisfying the rigorous requirements of both high energy capacity and rapid response time in some specific applications [11], upon which the power-type storage devices will supply short-term power demands while the energy-type storage devices will satisfy long-term energy require­ ment [12]. On the other hand, electric vehicles (EVs) are well known for their high efficiency and zero local emissions, while a long cruising mileage is expected as an ultimate goal for EVs [13]. However, the widespread of EVs is mainly restricted by energy storage technologies that deliver lower range, weight and cost performance than the users may desire, which application focuses on the battery as they consume a significant fraction of energy stored in the battery [14,15]. In practice, battery lifespan is relatively short and its performance will be inevitably degraded after numerous times of charging/discharging, which usually limits the efficient operation of EVs [16]. In contrast, supercapacitor lifespan is much longer (over one million cycles) and owns a much higher power density, which is also able to supply a rapid and effective energy output [17]. As a consequence, battery/supercapacitor HESS (BS-HESS) becomes a prominent solution to prolong the lifespan of batteries in EVs [18]. In recent years, numerous EVs applications have been investigated. For example, in Ref. [19], decentralized vehicle-to-grid control methods were developed to achieve a short-term interaction between EVs and microgrid, such that a smoother power regulation could be realized. Meanwhile, literature [20] proposed a stochastic collaborative planning for EV charging stations and power distribution system, which can significantly enhance the charging efficiency under various stochastic operation conditions. Besides, Probabilistic modelling of EV charging pattern in residential distribution networks was carried out to thor­ oughly study the effect of uncertainties on EV charging performance in practice [21]. In addition, performance-based settlement of frequency regulation for EV aggregators was investigated for an optimal frequency regulation by the participation of EVs [22]. In order to effectively protect the battery by using supercapacitor, an enormous variety of energy management strategy (EMS) has been pro­ posed, which can be categorized into online EMC and offline EMS. The former one can be regarded as semi-empirical strategies including rulebased strategy (RBS) [23], filtration based strategy (FBS) [24], model predictive strategy (MPS) [25], fuzzy logic strategy (FLS) [26], and “all

or nothing” strategy [27], while the latter one can be considered as global optimization strategies consisting of dynamic programming (DP) approach [28] and Pontryagin’s minimum principle [29]. Various EMSs attempt to generate current reference for battery and supercapacitor via an optimal assignment of total power demand. After the current refer­ ence is obtained by a specific EMS, appropriate design of underlying controller is of great importance for the reference tracking as there normally exists complex interactions between different components, strong nonlinearities, parameter uncertainties, as well as unmodelled dynamics in BS-HESS. Conventional linear proportional-integral-derivative (PID) control has been applied for BS-HESS of EVs thanks to its high reliability and simplicity. Nevertheless, its control performance might be considerably degraded when operation condition varies due to local linearization [30]. To remedy this difficulty, plenty of nonlinear control schemes have been developed. In Ref. [31], a sliding-mode control (SMC) and Lya­ punov function-based control was proposed for BS-HESS used in EVs to effectively track the current reference and to regulate DC bus voltage. Moreover, work [32] designed an estimator-based adaptive sliding mode control (ASMC) strategy for BS-HESS applications of EVs, which can estimate the load variations and unknown external input voltages via state observers and Lyapunov function. Besides, a novel controller was employed, which harnesses the low-frequency component of the supercapacitor voltage to simultaneously allocate the low-frequency power to the battery and to maintain the supercapacitor voltage and the battery current within their limits [33]. Meanwhile, literature [34] converted the control design problems into a numerically efficient optimization problem with linear matrix inequality (LMI) constraints, in which two state feedback control laws are employed to regulate the battery current and DC bus voltage, as well as to ensure the controller stability. However, the aforementioned nonlinear controllers are relatively complicated which usually require several state measurement and an accurate BS-HESS model, thus their applications are limited in practice. In order to handle this thorny issue, this paper attempts to design a robust fractional-order SMC (RFOSMC) strategy for a fully active BSHESS utilized in EVs applications, which main contributions/novelties can be summarized into the following four aspects:

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Fig. 1. The equivalent circuit diagram of BS-HESS used in EVs.

� RBS is adopted to obtain the battery current reference by an optimal assignment of power demand for EVs, such that the lifespan of bat­ tery can be considerably extended; � A sliding-mode state and perturbation observer (SMSPO) [35,36] is used to estimate the combinatorial effect of complex interactions of different components, nonlinearities, and unmodelled dynamics of BS-HESS in the real-time, which is able to realize a global control consistency and to offer a great robustness under various operation conditions; � A fractional-order PDα sliding surface is employed which can further improve the reference tracking performance, while the overconservativeness of conventional SMC could be largely reduced due to the fact that the upper bound of perturbation is replaced by its real-time estimation; � RFOSMC does not require an accurate BS-HESS model while only the measurement of battery current and DC bus voltage is needed, which is relatively easy to be implemented. A dSpace based hardware-inloop (HIL) test is undertaken to validate its implementation feasibility.

Basically, there are three topologies of BS-HESS as follows: (a) Passive BS-HESS: battery and supercapacitor are connected in parallel and directly coupled at DC bus, which has the simplest structure and lowest costs without any additional electronic components. However, the supercapacitor is not utilized effectively; (b) Semi-active: one DC/DC converter is employed to realize a proper trade-off between performance and costs, which has been employed in many applications; (c) Fully active: two DC/DC converters are adopted to achieve the most satisfactory performance but also associated with the highest costs. It is the only choice for applications when DC bus voltage is required to be larger than that of battery/ supercapacitor. For EVs applications, the fully active BS-HESS configuration is fav­ oured whose equivalent circuit diagram is demonstrated by Fig. 1. It contains a battery pack, a supercapacitor pack, two standard bidirectional DC/DC converters (including two insulated gate bipolar translators (IGBTs), one capacitor, and one inductor), an inverter, and a motor. In particular, the load of EVs is normally motors connected with an inverter. When the motor starts, the equivalent load resistance is much smaller than that in other operation conditions. Here, the inverter and motor are equivalent to a resistor which resistance varies within a certain range. Note that two MOSFETs S1 (S3) and S2 (S4) cannot flow current at the same time, that is, when one is off, the other must be on. In order to develop a reliable BS-HESS model for the purpose of control system design, the following three assumptions are made: (a) Both the battery and supercapacitor merely contain parasitic series resistances Re and Ru ; (b) Supercapacitor Csc is replaced by an ideal voltage source Eu so as to determine the input/output current or voltage after the tran­ sience of DC-DC converters. (c) Supercapacitor dynamics is ignored when discharging at a high current due to the slow decrease of its voltage in comparison to that of other elements. Based on the above discussion, the classical 5th-order averaged BS-HESS model can be

The rest of this paper is organized as follows: Section 2 gives the classical 5th-order averaged BS-HESS model; In Section 3, RFOSMC design is provided for BS-HESS; Section 4 and Section 5 present the simulation and HIL results, respectively; At last, conclusions are sum­ marized in Section 6. 2. Modelling of battery/supercapacitor hybrid energy storage systems BS-HESS can minimize the battery stress/size and the total capital cost, which generally contains two bidirectional buck-boost converters in parallel on the load side and powered by supercapacitors and batte­ ries, respectively [37]. Such system can simultaneously own the elegant merits of excellent power density from supercapacitors and high energy density from batteries, which can usually compensate the power fluc­ tuations in EVs and extend battery lifetime [38].

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developed by Ref. [34]. 2

3.1. Energy management strategy via rule-based strategy

1 1 0 0 0 6 Re C 1 C1 6 6 6 1 1 2 3 6 0 0 0 6 v_1 R C C u 2 2 6 � � 6 v_2 7 6 6_ 7 6 1 RL1 þ Ron2 Ron2 Ron1 6 i_1 7 ¼ 6 0 þ D 0 ðD1 1 6 7 6 L1 L1 L1 4 i__ 5 6 2 6 � � 6 RL2 þ Ron4 Ron4 Ron3 v_o 60 1 0 þ D2 ðD2 6 L L2 L2 2 6 6 4 1 1 1 0 0 ð1 D1 Þ ð1 D2 Þ Co C o Ro C o 2 3 1 6R C 07 6 e 1 7 6 7 6 7 60 1 7 6 Ru C2 7� � 6 7 6 7 E þ6 0 0 7 6 7 Eu 6 7 6 0 0 7 6 7 6 7 6 0 0 7 4 5 0 0

3



1 L1



1 L2

Before the underlying controller design, a proper EMS needs to be decided based on the load power Pdemand, such that an optimal power assignment between the battery and supercapacitor can be achieved while the battery current reference i*1 could be generated. The specific criteria of RBS [23] according to the load power demand and supercapacitor voltage are listed as follows:

7 7 7 7 72 3 7 v1 7 76 v2 7 76 7 76 i1 7 76 7 74 i2 5 7 7 vo 7 7 7 7 5

(a) Traction condition (Pdemand�0): the supercapacitor will not support any power to load if power demand Pdemand is smaller than the power threshold Pmin. Otherwise, the battery is going to generate a constant power Pmin while the supercapacitor tends to supply the remained power demand, e.g., Pdemand-Pmin; (b) Regenerative condition (Pdemand<0): the supercapacitor will absorb all regenerative energy until being fully charged, such that possible frequent battery charges can be avoided; (c) State of charge (SOC) of supercapacitor: which is calculated through dividing its voltage by its maximum voltage, and is strictly regulated above 0.5 to ensure a high power conversion efficiency. Meanwhile, around 75% of the energy stored in the supercapacitor is released when its SOC reduces to 0.5; (d) SOC of battery: which is regulated from 0.2 to 0.9 according to its recommended SOC usage window; (e) Voltage of supercapacitor (Vsc): which is strictly controlled above half of its maximum voltage, e.g., Vsc,max, to guarantee a high efficiency. Otherwise, the battery tends to charge the supercapacitor with a constant value Pch.

(1) where Re and Ru represent the inner series resistances of battery and supercapacitor; C1 and C2 are the filter capacitances of battery side and supercapacitor side while v1 and v2 are the voltages across them; L1 and L2 are the inductances of battery side and supercapacitor side while i1 and i2 are the currents flowing through them; RL1 and RL2 denote the inductor series resistances of battery side and supercapacitor side; D1 and D2 denote the duty cycles for the on-state of S1 and S3 which are restricted in a subset of (0, 1) for the sake of safety and efficiency; Ron1, Ron2, Ron3, and Ron4 mean the MOSFET on-resistances for MOSFETs S1, S2, S3, and S4; Csc and Co are the capacitances of supercapacitor and DC bus; Ro denotes the equivalent load resistance of EVs; v1, v2 and vo represent the voltages corresponding to capacitors C1, C2, and Co; E and Eu denote the open-circuit voltages of battery and supercapacitor, respectively.

3.2. Underlying controller design For BS-HESS (1), define the state vector as x ¼ ðx1 ; x2 ; x3 ; x4 ; x5 ÞT ¼

ðv1 ; v2 ; i1 ; i2 ; vo ÞT , output y ¼ ðy1 ; y2 ÞT ¼ ði1 ; vo ÞT , and control input u ¼

ðu1 ; u2 ÞT ¼ ðE; Eu ÞT , respectively. Then, one can obtain the state equa­ tion of BS-HESS (1), as follows

where

3. RFOSMC design for BS-HESS

0

0

f1 B f2 B f ðxÞ ¼ B f3 @f 4 f5

B B B B 1 B B B � C B 1 C B x1 þ C¼B B A B L1 B � B1 B x2 þ BL B 2 B @

1 x1 Re C 1

1 x3 C1

1 x2 Ru C2

1 x4 C2

1

� RL1 þ Ron2 Ron2 Ron1 þ D1 x3 þ ðD1 L1 L1 � RL2 þ Ron4 Ron4 Ron3 þ D2 x4 þ ðD2 L2 L2 ð1

D1 Þ

(2)

x_ ¼ f ðxÞ þ gðxÞu

1 x3 þ ð1 Co

D2 Þ

1 x4 Co

1 x5 Ro C o

C C C C C C C C 1 C 1Þ x5 C ; gðxÞ ¼ L1 C C C 1 C 1Þ x5 C L2 C C C A

2

1 6RC 0 e 1 6 6 6 1 60 6 Ru C2 6 6 ​6 0 0 6 6 6 0 0 6 6 6 0 0 4 0 0

3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5

(3)

Differentiate the output y until the control input u being explicitly appeared in the matrix form, yields � � � � � � €y1 h1 ðxÞ u ⋯ ¼ (4) þ BðxÞ 1 h2 ðxÞ y2 u2

The RFOSMC design aims to realize a robust tracking of the battery current and load voltage, as well as to achieve a smooth transition during load variation or faults. In this paper, ~ x¼x b x is denoted as the estimation error of variable x and b x means the estimate of x, while x* represents the reference of variable x, respectively.

where

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1 RL1 þ Re C1 L1

h1 ðxÞ ¼ �

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RL1

Ron2 þ ðRon2 L1

Ron2 þ ðRon2 L21 Ron1 ÞD1

Ron1 ÞD1

1 Ro C o



� � ðD1 v1 þ

1Þð1 L1 Co

� � D2 Þ i2 þ

1 þ C1 L1



RL1

Ron2 þ ðRon2 L1

Ron1 ÞD1

�2

� ðD1 1Þ2 i1 L1 Co

ðD1 1Þ vo L1

(5)

with

� � 1 RL1 Ron2 þ ðRon2 Ron1 ÞD1 ð1 D1 Þ 1 1 þ v1 þ Ro Co L 1 Co Ru C2 Ro Co L1 �� � �2 RL2 Ron4 þ ðRon4 Ron3 ÞD2 ð1 D2 Þ RL1 Ron2 þ ðRon2 Ron1 ÞD1 RL1 þ Ron2 ðRon2 Ron1 ÞD1 þ v2 þ þ Co L2 L2 L1 Ro Co L1 �2 � �2 � �� 2 2 ðD1 1Þ ðD2 1Þ 1 ð1 D1 Þ RL2 Ron4 þ ðRon4 Ron3 ÞD2 RL2 Ron4 þ ðRon4 Ron3 ÞD2 þ i1 þ Ro C o Co L1 Co L2 Co L2 Ro Co L2 � � �2 � � � 2 ðD2 1Þ 1 1 ð1 D2 Þ RL1 þ Ron2 ðRon2 Ron1 ÞD1 1 þ i2 þ ðD1 1Þ2 þ Ro C o L2 C2 Co Ro C o L2 Co Co L21 �

h2 ðxÞ ¼



þðD2

1 Re C 1

� 2 RL2 þ Ron4

2

1 6 RCL 6 e 1 1 BðxÞ ¼ 6 4 1 D1 Re C1 Co L1

Ron3 ÞD2

ðRon4 Co L22

þ

1 Ro C o



ðD1 1Þ2 ðD2 1Þ2 þ L1 Co L2 Co þ Ro C o



1 Ro C o

0 1 D2 Ru C2 Co L2

7 7 7 5

The inverse of control gain matrix B(x) can be calculated by 3 2 0 Re C1 L1 7 6 B 1 ðxÞ ¼ 4 ð1 D1 ÞRu C2 L2 Ru C2 L2 Co 5 1 D2 1 D2

B0 ¼ (7)

Re Ru C1 C2 Co L1 L2 6¼ 0 1 D2

b11 0

0 b22

� (11)

where b11 and b22 are the user-defined constant control gains. Note that the selection of such control gain matrix B0 (11) can fully decouple the control of battery and supercapacitor, which are actually coupled in the original control matrix BðxÞ, as shown in Eq. (7). Define the tracking error as e ¼ [e1, e2]T ¼ [i1 -i*1 , ​ vo -v*o ]T, differen­ tiate the tracking error e until the control input u is appeared explicitly, yields

(8)

To guarantee the above input-output linearization to be valid, the control gain matrix B(x) must be nonsingular among the whole opera­ tion range. Calculate its determinant, gives det½BðxÞ� ¼

(6)

�2 9 > > = vo > > ;



3

ðD1 1Þ2 L1 Co



� � � � � €e1 u ψ 1 ð⋅Þ ⋯ ¼ þ B0 1 e2 ψ 2 ð⋅Þ u2

"

€i_* 1

⋯ * vo

# (12)

Define z11 ¼ i1 and z12 ¼ z_11 , apply a third-order SMSPO [35,36] to estimate the perturbation ψ 1 ð⋅Þ, yields 8 bz_ 11 ¼ bz 12 þ α11~z11 þ k11 tanhð~z11 ; εo Þ < (13) b 1 ð⋅Þ þ α12~z11 þ k12 tanhð~z11 ; εo Þ þ b11 u1 bz_ 12 ¼ ψ : ψb_ 1 ð⋅Þ ¼ α13~z11 þ k13 tanhð~z11 ; εo Þ

(9)

As discussed before, duty cycle D2 is always different from zero for the purpose of operation safety and efficiency, thus the above lineari­ zation can always be satisfied. Besides, functions h1 ðxÞ, h2 ðxÞ and matrix BðxÞ aggregate the nonlinearities, parameter uncertainties, unmodelled dynamics, and external disturbances of BS-HESS, which also involve a huge number of states and parameters measurement. In practice, their accurate values are very hard, if not impossible, to be measured/known. To tackle this challenge, SMSPO is applied to effectively and efficiently estimate their real values in the real-time. Define the perturbations ψ 1 ð⋅Þ and ψ 2 ð⋅Þ for BS-HESS system (4), obtains � � � � � � ψ 1 ð⋅Þ u h ðxÞ (10) ¼ 1 þ ðBðxÞ B0 Þ 1 ψ 2 ð⋅Þ h2 ðxÞ u2

where observer gains k11, k12, k13, α11, α12, and α13, are all positive constants. Similarly, define z21 ¼ vo , z22 ¼ z_21 , and z23 ¼ z_22 , a fourth-order SMSPO is used for the estimation of the perturbation ψ 2 ð⋅Þ by 8 bz_ 21 ¼ bz 22 þ α21~z21 þ k21 tanhð~z21 ; εo Þ > > < bz_ 22 ¼ bz 23 þ α22~z21 þ k22 tanhð~z21 ; εo Þ (14) _ > b > : bz 23 ¼ ψ 2 ð⋅Þ þ α23~z21 þ k23 tanhð~z21 ; εo Þ þ b22 u2 ψb_ 2 ð⋅Þ ¼ α24~z21 þ k24 tanhð~z21 ; εo Þ where observer gains k21, k22, k23, k24, α21, α22, α23, and α24, are all positive observer gains.

with the constant control gain matrix B0 being given by 5

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Fig. 2. Overall RFOSMC structure for BS-HESS used in EVs.

Design a fractional-order PDα sliding surface of tracking error dy­ namics (12), as follows � �# � � " α1 * * b S FO1 ¼ D bz 11 z11 þ λc1 bz 11 z11 (15) � � b S FO2 Dα2 bz 21 z*21 þ λc2 bz 21 z*21

Table 1 The BS-HESS parameters [34].

where α1 and α2 represent the fractional differential orders, while positive gains λc1 and λc2 are the fractional-order PDα sliding surface gains, respectively. Here, Riemann-Liouville (RL) definition [39] for fractional-order derivative is adopted. Remark 1. Let b S FO1 ¼ 0 and b S FO2 ¼ 0, yields (

Dα1 bz 11 Dα2 bz 21

� z*11 ¼ � z*21 ¼

λc1 bz 11 λc2 bz 21

z*11 z*21

� (16)



" * � €i_ u1 ¼ B0 1 1* ⋯ u2 vo

ψb 1 ð⋅Þ

ς1 bS FO1

ϕ1 tanhðb S FO1 ; εc Þ

ψb 2 ð⋅Þ

ς2 bS FO2

ϕ2 tanhðb S FO2 ; εc Þ

Description

Value

Unit

L1 Re RL1 C1 L2 Ru RL2 C2 Csc Ron C0

Battery side inductance Battery series resistance Battery side inductor series resistance Battery side filter capacitance Supercapacitor side inductance Supercapacitor serial resistance Supercapacitor side inductor series resistance Supercapacitor side filter capacitance Supercapacitor capacitance MOSFET on-resistance Load side capacitance

680 0.04 0.25 1 39 0.011 0.114 0.22 116 0.021 1

[μH] [Ω] [Ω] [mF] [mH] [Ω] [Ω] [mH] [F] [Ω] [mF]

the tracking performance. As a consequence, appropriate tuning of the aforementioned control gains is of great importance for a proper tradeoff between control cost and tracking performance. It is worth noting that continuous and smooth tanh(~ x1 ; ​ εo ) function and tanhðb S FO1 ; εc Þ function (εo and εc represent the thickness layer

According to Ref. [40], one can obtain that C1 ¼ λc1 and C2 ¼ λc2 , which can directly lead to jargðeigðC1 ÞÞj ¼ jargðeigðC2 ÞÞj ¼ π. When 0 < α1 < 2 and 0 < α2 < 2, then jargðeigðC1 ÞÞj > α1*π =2 and jargðeigðC2 ÞÞj > α2*π=2 can be consistently constructed. As a conse­ quence, fractional-order PDα sliding surface dynamics (15) is asymp­ totically stable. At last, the overall RFOSMC for BS-HESS (1) can be designed as



Symbol

boundary of the observer and controller, respectively) is adopted to ~1 ) function used in conventional SMC, such replace discontinuous sgn(x

# (17)

where sliding-mode control gains ς1 , ς2 , ϕ1 , and ϕ2 ​ are all positive, which are chosen to guarantee the convergence of tracking error dy­ namics. Here, a larger value of sliding-mode control gains ς1 , ς2 , ϕ1 , and ϕ2 will lead to a faster tracking rate and smaller tracking error, but also cause a higher control cost; While a smaller value of them will result in a slower tracking rate and larger tracking error, but also cause a lower control cost. Besides, a larger value of constant control gain matrix B0 1 will reduce the control cost but also degrade the tracking performance; While a larger value of it will increase the control cost but also improve

Table 2 The RFOSMC parameters. Battery current controller Load voltage control

b11 ¼ 350

ς1 ¼30

k11 ¼20

ϕ1 ¼25

α13 ¼1000 λc1 ¼ 30

εo ¼0.2

εc ¼0.2

b22 ¼ 550

α23 ¼4000

k24 ¼40000

6

ς2 ¼25 α24 ¼10000 α2 ¼ 1:4

k12 ¼600

ϕ2 ¼20

k21 ¼10

λc2 ¼ 25

α11 ¼30

k13 ¼6000

α21 ¼40

α12 ¼300

α1 ¼ 1:6 α22 ¼600

k22 ¼400

k23 ¼6000

εo ¼0.2

εc ¼0.2

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Fig. 3. System responses obtained under heavy load condition. (a) Load power P, (b) DC bus voltage vo, (c) Battery current i1, (d) Supercapacitor current i2, (e) Battery voltage E, and (f) Supercapacitor voltage Eu.

αnþ1 ¼ (s þλα )nþ1 ¼ 0 in the open left-half complex plane at λα, with

that the malignant chattering effect can be noticeably reduced, which is defined as x

eε e tanhðx; εÞ ¼ x eε þ e

x

ε x

ε

αi ¼ Cinþ1 λiα ; i ​ ¼ 1; 2; ⋯; n þ 1

(18)

(19)

Meanwhile, the ratio of sliding-mode observer gains, i.e., ki/k1 (i ¼ 2, 3,⋯, n þ 1) are chosen to locate the poles of polynomial pn þ (k2/k1)pn 1 þ ⋯ ​ þ (kn/k1)p þ (knþ1/k1) ¼ (p þ λk )n ¼ 0 in the open left-half complex plane at λk , with

Remark 2. [41]. Luenberger observer gains, i.e., αi, (i ¼ 1, 2,⋯, n þ 1), are selected to place the poles of polynomial snþ1 þ α1sn þ α2sn 1 þ ⋯ þ 7

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Fig. 4. System responses obtained under light load condition. (a) Load power P, (b) DC bus voltage vo, (c) Battery current i1, (d) Supercapacitor current i2, (e) Battery voltage E, and (f) Supercapacitor voltage Eu.

kiþ1 ¼ Cin λik ; i ¼ 1; 2; ⋯; n: k1

estimation error, but also cause a lower control cost. In order to achieve a trade-off between perturbation estimation performance and control costs, they must be properly tuned.

(20)

Here, a larger value of Luenberger observer gain λα and sliding-mode gain λk will result in a higher perturbation estimation rate and smaller estimation error (they can be considered as perturbation estimation performance), but also cause a higher control cost; While a smaller value of them will lead to a lower perturbation estimation rate and larger

Remark 3. Battery current regulation tends to minimize the battery degradation, while supercapacitor current regulation aims to compen­ sate the load power demand as much as possible and to maintain a constant DC bus voltage. In particular, during heavy load condition, the 8

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Fig. 5. Peak value of active power |P| obtained under a 40% load drop lasting 100 ms with 20% variation of the battery/supercapacitor series resistances RL1 and RL2 as well as inductances L1 and L2. Table 3 IAE indices of each controllers obtained in both cases (in p.u.).

Table 4 Overall control costs required by each controllers in both cases (in p.u.).

Scenarios

IAE Indices

PID

SMC

ASMC

RFOSMC

Scenarios

PID

SMC

ASMC

RFOSMC

Heavy load condition

IAEI IAEv IAEI IAEV

0.3785 0.3152 0.3128 0.2571

0.3218 0.2697 0.2634 0.2093

0.2951 0.2214 0.2382 0.1735

0.2463 0.1775 0.1827 0.1489

Heavy load condition Light load condition

0.8657 0.7538

0.9542 0.8316

0.9317 0.8259

0.8216 0.7103

Light load condition

peaking phenomenon that would amplify the perturbation estimation error when discontinuity occurs.

supercapacitor will supply most of the current while its voltage de­ creases rapidly, which however cannot last for a long period of time. In contrast, during light load condition, the supercapacitor is recharged while the charging rate is relied on the battery current, which can last much longer. Besides, RFOSMC can be directly incorporated with any existing EMS, such as those reported in literatures [23–29], to achieve a satisfactory tracking performance only if the reference is calculated by EMS.

To this end, the overall RFOSMC structure for BS-HESS is demon­ strated in Fig. 2. Here, only two states, e.g., battery current i1 and DC bus voltage vo , must be measured without an accurate BS-HESS model. Note that hysteresis control [26] is employed in RFOSMC to prevent the DC/DC converters from frequent starts/stops. 4. Case studies

Remark 4. Note that this paper adopts nonlinear sliding-mode PO instead of linear PO (e.g., high-gain PO) due to the fact that nonlinear PO can avoid the use of high-gain in linear PO, which might often result in

The studied BS-HESS parameters are given in Table 1. Meanwhile Table 2 tabulates the RFOSMC parameters which values are determined 9

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Fig. 6. The configuration and platform of HIL test. (a) configuration and (b) plaform

Matlab/Simulink 2016b with a fixed-step size of 10

Table 5 The error specification of DS 1104 controller [46]. Parameters Offset error Gain error Offset drift Gain drift Signal-to-noise ratio

4

.

4.1. Heavy load condition

Component A/D converter

D/A converter

�5 mV Multiplexed channels: �0.25% Parallel channels: �0.5% 40 μV/K 25 ppm/K Multiplexed channels: >80 dB Parallel channels: >65 dB

�1 mV �0.1%

A series of step changes of power demand, which corresponds to different operation conditions of EVs, e.g., sudden acceleration/decel­ eration, starting/stoping, etc., are firstly applied on BS-HESS to inves­ tigate the tracking performance of RFOSMC under heavy load condition. Note that a negative load power means the regenerative braking con­ dition while the DC bus voltage reference is chosen as 160 V. Fig. 3 demonstrates the system responses of BS-HESS, from which one can readily see that RFOSMC can smoothly track the variation of power demand and maintain the DC bus voltage with the minimal tracking error (without any overshoot) and fastest tracking rate in comparison to that of other controllers, which is due to the real-time compensation of perturbation. Note that such smooth tracking is very important for an economic and reliable EVs operation as well as extending the lifespan of battery.

130 μV/K 25 ppm/K >80 dB

through trial-and-error. Three case studies, e.g., (a) Heavy load condi­ tion, (b) Light load condition, and (c) robustness with uncertain BSHESS parameters, are carried out, which aim to study the tracking performance of RFOSMC against that of conventional PID control [30], SMC [31], and ASMC [32], respectively. The initial SOC of battery is chosen to be 90%. The minimum and maximum voltage of battery pack is 36 V and 144 V, while the rated voltage of supercapacitor pack is 125 V. Besides, parameters Pmin and Pch in RBS are selected to be 2 kW and 100 W, respectively. Simulations are undertaken by

4.2. Light load condition In this section, a series of step changes of power demand are applied 10

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Fig. 7. Comparison of simulation and HIL test obtained under heavy load condition. (a) Load power P, (b) DC bus voltage vo, (c) Battery current i1, (d) Supercapacitor current i2, (e) Battery voltage E, and (f) Supercapacitor voltage Eu.

to further evaluate the tracking performance of RFOSMC under light load condition, in which the DC bus voltage is regulated at 100 V. The obtained system responses are depicted in Fig. 4, in which it is clear that RFOSMC can achieve the most satisfactory tracking performance against to that of other three controllers.

battery/supercapacitor series resistances RL1 and RL2 as well as in­ ductances L1 and L2 with �20% variation around their nominal value are investigated. Then, a 40% load drop lasting 100 ms occurs, while the peak value of active power |P| is recorded, which variation is demon­ strated by Fig. 5. It can be seen that such variation under series re­ sistances uncertainties obtained by PID control, SMC, ASMC, and RFOSMC is 26.23%, 18.54%, 14.79%, and 10.46%, respectively. Consequently, RFOSMC can offer the highest robustness among all controllers in the presence of uncertain BS-HESS parameters thanks to its real-time perturbation compensation.

4.3. Robustness with uncertain BS-HESS parameters The robustness of RFOSMC is studied in the presence of uncertain BSHESS parameters. Here, a series of plant-model mismatches of the 11

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Fig. 8. Comparison of simulation and HIL test obtained under light load condition. (a) Load power P, (b) DC bus voltage vo, (c) Battery current i1, (d) Supercapacitor current i2, (e) Battery voltage E, and (f) Supercapacitor voltage Eu.

4.4. Quantitative analysis

voltage vo) is only 55.29%, 73.90%, and 66.01% of that of PID control, SMC, and ASMC in the light load condition, respectively. RT Finally, the overall control costs, i.e., 0 ðju1 j þju2 jÞdt [44,45], of each controllers required in both cases are compared in Table 4. One can readily observe that RFOSMC merely requires the minimal overall control costs in both cases. In particular, its control costs calculated in the heavy load condition are only 94.91%, 86.10%, and 88.18% to that of PID control, SMC, and ASMC, respectively.

This section provides quantitative analysis of the control perfor­ mance of each controller, upon which the integral of absolute error (IAE) RT indices [42,43], e.g., IAEx ¼ 0 jx x* jdt, are presented in Table 3. Clearly, RFOSMC owns the lowest IAE indices in both cases thus it can realize the lowest tracking error. More specifically, its IAEI (which corresponds to battery current i1) is merely 65.07%, 76.54%, and 83.46% of that of PID control, SMC, and ASMC in the heavy load con­ dition, respectively. Besides, its IAEV (which corresponds to DC bus 12

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5. HIL test

Acknowledgments

A dSpace based HIL test is undertaken while its configuration and platform are depicted by Fig. 6(a) and (b), respectively. Here, RFOSMC (13)–(17) is embedded on DS1104 board with a sampling frequency fc ¼ 5 kHz. Meanwhile, BS-HESS (1) is implemented on DS1006 board with a limit sampling frequency fs ¼ 100 kHz to simulate the real BSHESS as close as possible. Specifically, battery current i1 and DC bus voltage vo are measured from the real-time calculation of BS-HESS embedded on DS1006 board, which are then transmitted to RFOSMC embedded on DS1104 board through cables for a real-time calculation of controller outputs, e.g., battery voltage E and supercapacitor voltage Eu, respectively. Lastly, the guaranteed measurement error of DS1104 controller board is provided in Table 5.

The authors appreciatively acknowledge the support of Research and Development Start-Up Foundation of Shantou University (NTF19001), and National Natural Science Foundation of China (61963020, 51907112, 51777078, 51977102), the Fundamental Research Funds for the Central Universities (D2172920), the Key Projects of Basic Research and Applied Basic Research in Universities of Guangdong Province (2018KZDXM001), and the Science and Technology Projects of China Southern Power Grid (GDKJXM20172831). References [1] S.W. Liao, W. Yao, X.N. Han, J.Y. Wen, S.J. Cheng, Chronological operation simulation framework for regional power system under high penetration of renewable energy using meteorological data, Appl. Energy 203 (2017) 816–828. [2] J. Liu, J.Y. Wen, W. Yao, Y. Long, Solution to short-term frequency response of wind farms by using energy storage systems, IET Renew. Power Gener. 10 (5) (2016) 669–678. [3] R. Faisal, P.D. Badal, K. Subrata, Sarker, K.D. 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5.1. HIL results of heavy load condition Fig. 7 compares the simulation results and HIL results obtained under heavy load condition, by which one can observe that their system re­ sponses are very close. 5.2. HIL results of light load condition The comparison between the simulation results and HIL test results obtained in the presence of light load condition is presented in Fig. 8, from which it is clear that their responses match each other very well. 6. Conclusions The fully active BS-HESS plays a very crucial role in the applications of EVs which can significantly extend the lifespan of batteries. This paper develops a novel RFOSMC strategy for BS-HESS used in EVs to achieve a fast and smooth tracking, which main findings/contributions can be concluded into the following four aspects: (1) Based on the classical 5th-order averaged model, RBS is employed to optimally assign the power demand of EVs between the battery and supercapacitor. Once the output reference is ob­ tained, an SMSPO is applied to estimate the nonlinearities and various uncertainties of BS-HESS online, which is then fully compensated by an FOSMC. Therefore, great robustness can be realized, together with more reasonable control efforts as the upper bound of perturbation is replaced by its real-time estimate; (2) Only two states measurement is needed, e.g., battery current and DC bus voltage, which leads to a relatively easy implementation of RFOSMC. Besides, the use of fractional-order sliding surface is capable of significantly enhancing the dynamic responses. Moreover, the continuous function tanh(.) is adopted to largely suppress the malignant effect of chattering. Hence, a smooth tracking performance can be realized; (3) Three cases are undertaken which verify the satisfactory tracking performance and noticeable robustness of RFOSMC against that of other controllers. Moreover, a dSpace based HIL test is carried out to further validate the implementation feasibility of RFOSMC; (4) Simulation results demonstrate that RFOSMC is able to consid­ erably improve the tracking performance compared to that of other approaches in terms of tracking rate, tracking error, as well as overall control costs. In particular, its battery current tracking error is only 65.07%, 76.54%, and 83.46% of that of PID control, SMC, and ASMC in the heavy load condition, while its corre­ sponding control costs are merely 94.91%, 86.10%, and 88.18% to the above three alternatives in the same scenario. In future studies, RFOSMC will be applied on a real BS-HESS for EVs applications. 13

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