A review of equalization strategies for series battery packs: variables, objectives, and algorithms

Renewable and Sustainable Energy Reviews 116 (2019) 109464

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A review of equalization strategies for series battery packs: variables, objectives, and algorithms Fei Feng a, *, 1, Xiaosong Hu a, **, 1, Jianfei Liu a, Xianke Lin b, Bo Liu c a

State Key Laboratory of Mechanical Transmissions, Department of Automotive Engineering, Chongqing University, Chongqing, 400044, China Department of Automotive, Mechanical and Manufacturing Engineering, University of Ontario Institute of Technology, Oshawa, ON, L1G 0C5, Canada c Chongqing Chang’an New Energy Vehicle Technology Co., Ltd, Chongqing, 401120, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Series battery packs Equalization strategies Equalization objectives Equalization variables Energy storage Electric vehicles

Inconsistency in the internal parameters and external environments of lithium-ion cells after they are connected as a battery pack may greatly limit the pack’s capacity, power capability, and lifetime. Equalization management systems (EMSs) are necessary to mitigate such inter-cell inconsistency. Due to the complexity of application scenarios and the cost of EMSs, the speed, accuracy, and stability of EMSs need to be comprehensively consid­ ered. Unlike the research on equalization circuit architectures, studies on equalization control strategies are far from mature. This paper, for the first time, presents a critical summary and analysis of currently available equalization strategies. They are elaborated and categorized based on the main components of a controller formulation, including equalization variables, equalization objectives, and equalization algorithms. Finally, some insights and thinking about technical challenges and opportunities for the development of equalization strategies are provided. This work could be beneficial to the selection and design of appropriate control strategies for different equalization applications. It spurs new expansive research routes and forward-looking visions for re­ searchers and practitioners in this field.

1. Introduction 1.1. Motivations Electric vehicles (EVs) are environmentally friendly and thereby have received widespread attention from academic, industrial, and government sectors. Batteries and their battery management systems constitute key EV technologies. Compared with other types of batteries, lithium-ion batteries have salient advantages of high cycle lifetime, high energy density, low self-discharge rate, no memory effect, and low environmental pollution [1,2]. With increasingly mature manufacturing and falling cost, lithium-ion batteries have become the mainstream en­ ergy storage technology widely used in EVs [3]. However, due to the potential limitations of the anode and cathode materials, a single lithium-ion cell can only produce a limited voltage range, e.g., from 2.4 to 4.2 V, which obviously cannot meet the energy and power demands of EVs. Thus, an EV battery pack is usually needed, which consists of hundreds or even thousands of cells connected in series and/or parallel

[4]. However, inter-cell inconsistency becomes problematic, as the number of cells increases. This is exacerbated by charging and dis­ charging cycles repeated in realistic battery operations, which may cause the battery pack longevity to decrease exponentially [5,6]. To reduce such inconsistency and extend the capacity and cycle life of a battery pack, an equalization management system (EMS) is an integral part of a battery management system (BMS). Presently, a battery pack typically accounts for one-third or more of the total cost of an EV, such that EMSs are of great significance in decreasing EV operational expenditure, via prolonging battery pack lifetime. 1.2. Inconsistency in battery packs The causes of battery pack inconsistency are quite complicated. They are often dependent on the materials, assembly techniques, and fabri­ cation factors, etc., which can be mainly categorized as internal, external, and coupled causes. Internal factors include the internal resistance, ca­ pacity, and self-discharge rate [7]; external factors include the charging

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (F. Feng), [email protected] (X. Hu). 1 Equally contributed to this work. https://doi.org/10.1016/j.rser.2019.109464 Received 1 July 2019; Received in revised form 28 September 2019; Accepted 3 October 2019 Available online 9 October 2019 1364-0321/© 2019 Elsevier Ltd. All rights reserved.

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and discharging current, ambient temperature, and depth of discharge [8,9]. During the normal operation of a battery pack, the coupled effect of internal and external factors often incur inter-cell inconsistency [10, 11], inducing some unfavorable consequences. First, overly-deep charging can give rise to unwanted internal chemical reactions and the generation of CO2, which increases internal cell pressure and tem­ perature [11–13]. This can accelerate battery aging and damage, even trigger fires and/or explosions in some extreme cases. Second, due to the inter-cell inconsistency and charge/discharge cut-off voltages, the overall charge/discharge capacity of a series battery pack is limited by the weakest cell that first reaches the cut-off voltages [14,15]. As shown in Fig. 1, charging a 4-cell series battery pack must stop when any one cell reaches the upper cut-off voltage. Hence, the pack total capacity (CT ) is determined by the cell with the smallest chargeable capacity (CC ) when no equalization circuit or strategy is applied [16]. Similarly, when any one cell reaches the lower cut-off voltage during discharging, dis­ charging the pack must stop, and the pack’s CT is determined by the cell with the smallest releasable capacity (CR ). Therefore, in case of considerable inconsistency, the capacity utilization rate of a pack is very likely to be largely reduced, and the available capacity drops consider­ ably, which lowers the overall service performance of battery packs. Finally, owing to the so-called “barrel effect”, battery pack cycle life is generally limited by that of the cell with the shortest life [8]. To ensure the uniformity of definition and expression in this paper, CT ,CC , CR and state of charge (SOC) [17] are all defined in Fig. 1. All of these incen­ tivize seeking effective ways to address inter-cell inconsistency, in order to ensure the safety, service performance, and cycle life of battery packs.

fixed shunt resistors and switch shunt resistors, whereas active cir­ cuits include capacitance-based, inductor-based, transformer-based, and converter-based solutions [20–22]. ● According to the circuit topology, equalization circuits are mainly categorized in five types, including cell bypass, cell-to-cell, cell-topack, pack-to-cell, and cell-to-pack-to-cell schemes [19,23]. Passive equalization, also called dissipative equalization [24], involves using a resistor connected to some cells in parallel to consume excess energy [25] and release heat into the air. Due to its simplicity, reli­ ability, and low cost, it has been applied in EVs [26]. However, passive equalization is only applicable to charging conditions [27] and uses a relatively small equalization current. It has several issues, such as low equalization efficiency, long equalization time [22,28], and relatively large heat generation [29] in large battery packs with high internal inconsistency. Active equalization, also called non-dissipative equal­ ization, transfers the energy from cells with higher energy to cells with lower energy via an equalization circuit. Active equalization is a more advanced equalization technology with less power loss and has attracted increasing attention recently [30]. However, active equalization is costly, complex, and unreliable. A previous study performed a theoret­ ical comparative study of active and passive equalizations [31]. In general, each circuit scheme exhibits its own advantages and disad­ vantages, in terms of equalization speed, accuracy, cost, and efficiency, as shown in the blue section of Fig. 2. Equalization circuit topology can be described by the control plant model (CPM). The CPM describes the equalization current flowing in and out of a battery pack based on the electrical energy conversion components of the circuit (e.g., resistors, capacitors, inductors, or con­ verters), circuit topologies, and circuit parameters [32,33]. In the equalization system, the CPM is hardware-dependent and it provides the model information to the upper equalization strategies, as shown in the green section of Fig. 2. Equalization strategies make the control de­ cisions based on the inputs from the CPM. Therefore, the equalization strategies do not interact with hardware directly and can be abstracted into hardware-independent software. In this review, our focus will be on the equalization strategies. On the hardware-independent software side, equalization strategies are responsible for dealing with various control problems of timevariance, nonlinearity, and uncertainty in the entire equalization pro­ cess [34]. As such, control speed, accuracy, and stability [35] of equalization strategies have become the main difficulties. In addition, since the regenerative braking and rapid acceleration conditions of EVs lead to transient changes in current and voltage measurements [11],

1.3. EMS frameworks An EMS monitors the external characteristics of a battery pack in use, estimates and identifies its internal states and parameters, and measures inter-cell inconsistency via internal and external features. When an inconsistency is detected, EMS can redistribute the energy among the cells that have too high or too low releasable capacities. After redistri­ bution, the overall performance of the battery pack can be equalized. An EMS is mainly composed of a hardware equalization circuit and a soft­ ware equalization strategy [18]. An overall EMS framework is shown in Fig. 2. Hardware equalization circuits can be primarily categorized in two ways: ● According to the power transfer mode, equalization circuits are divided into passive and active circuits [18,19]. Passive circuits have

Fig. 1. Schematic of a series battery pack during charging and discharging, and the definitions of capacity. 2

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Fig. 2. An overall EMS framework.

investigations of equalization strategies are extremely challenging. The accuracy and stability of state estimation in BMSs still need improve­ ments, and equalization objectives under different application scenarios must be further enhanced.

1.5. Paper organization The rest of this paper is arranged as follows. Section 2 gives the scope of the survey. Section 3 classifies equalization strategies based on the main components of a controller formulation, including equalization variables, objectives, and algorithms. Details of equalization strategies, and their benefits and drawbacks are elaborated and compared. The main challenges and future prospects for equalization strategies are presented in Section 4. Lastly, the paper is concluded in Section 5.

1.4. Objectives and contributions This paper presents a critical review of the state of the art on battery pack equalization strategies. After a thorough literature survey, it was found that there are many battery pack equalization strategies devel­ oped, but the systematic review and classification are missing. Some studies simply classify the equalization strategies based on the equal­ ization variable, such as voltage, SOC, and capacity. However, many equalization strategies have the same equalization variable but are completely different from each other. This review paper proposes a new classification method based on variables, objectives, and algorithms. It provides a comprehensive review and detailed analysis of existing methods, and in-depth discussions and comparisons of the advantages and disadvantages of different methods. The issues and challenges inherent in equalization strategies are reviewed and identified, along with possible solutions, to provide a basis for the selection and design of equalization strategies according to various scenarios. Moreover, some important promising research explorations are discussed, with an overarching goal of inspiring more innovative concepts, ideas, designs, and tools for continual advances and growth in equalization strategies.

2. Scope of the survey This survey has been carried out with a focus on equalization stra­ tegies. In this paper, the advantages and disadvantages of different strategies are presented, compared and analyzed. Future research di­ rections are also provided and discussed. We used the search terms “electric vehicle” “battery”, “equalization” or “balancing”, “control algorithm” or “strategy” to collect highly rele­ vant journal articles between 2005 and April 2019. Many of those papers are about equalization circuits. Articles that were clearly out of the stated review scope were removed by screening the abstracts. Articles related to battery equalization strategies were collected in the following online journal databases, including IEEE Xplore Digital Library, Science Direct, EI Compendex, IET Digital Library, SAE Mobilus, ResearchGate, Springer Link & Wiley Online Library, CNKI Digital Library, IOS Press 3

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Content Library. Articles in languages other than English and Chinese were excluded. Finally, 105 articles for equalization strategies were selected and reviewed in this paper. 3. Taxonomy of equalization strategies Equalization strategies can be developed by formulating optimal control problems that maximize certain performance indexes during the equalization process. An optimal control system includes the following main components: 1) a mathematical model; 2) an objective function; and 3) quality indicators. In the mathematical model of the equalization system, the output is always the equalization current. However, the inputs can be voltage, SOC, capacity, and other variables. The equal­ ization strategy can be developed based on certain output variables directly, which is called a variable-based equalization strategy. The equalization strategy can also be developed based on the objective function (such as capacity maximization, time minimization, and energy consumption minimization), which is called an objective-based equal­ ization strategy. For the evaluation of equalization control systems, the commonly-used quality indexes are stability, accuracy, and transition time. These quality indexes are highly related to the control algorithms and their parameters. The equalization strategy developed to achieve the above quality indexes is called an algorithm-based equalization strategy. Therefore, equalization strategies can be divided into three categories: variable-based, objective-based, and algorithm-based. An overall equalization strategy framework is shown in the red section of Fig. 2. According to the control method used, equalization variables can be often used as input for an equalization objective and an equalization algorithm. Equalization variables and objectives are necessary inputs for an equalization algorithm. In this section, equalization variables are introduced first, followed by equalization objectives, and then various control algorithms to achieve equalization.

Fig. 3. Battery pack equalization in charge/discharge control based on the operating voltage.

charging and discharging operating voltage curves, a small difference in operating voltage during the plateau may correspond to a large CR dif­ ference, leading to overbalance or underbalance. Z. Li et al. [39] established an equalization strategy in the initial and final stages to avoid the plateau stage. In their study, cell-to-pack equalization strategy was used to redistribute the energy from high voltage cells to the pack, pack-to-cell equalization strategy transfers the energy from the pack to the low voltage cell. When both low voltage cells and high voltage cells exist, cell-to-cell equalization strategy is used to transfer the energy between these cells. Otherwise, over-potential exists in operating voltage during charging and discharging. During the equalization pro­ cess, there are both charging cells and discharging cells. Therefore, inconsistency will still exist after the current is terminated. Considering the existence of over-potential, J. Chen [40] and H. Yang [41] proposed the use of hysteresis control to improve voltage consistency and avoid waiting time. M. Kim et al. [42] proposed the reference voltage modu­ lation scheme. It considered the influence of equalization circuit voltage drop on the reference voltage, thus reasonable equalization reference voltage can be obtained under different charging and discharging sce­ narios. In addition, over-potential varies according to different charging and discharging currents; thus, the over-potential under different cur­ rents needs to be considered. T. Li [43] proposed utilizing the variation of operating voltage difference in a certain time to obtain rates of charging and discharging. Based on these rates, a reasonable equaliza­ tion strategy was developed by operating voltage. The charging and discharging curves of cells with different aging rates are also different, therefore, even cells with the same voltage may have CT inconsistencies. L. Dung [44] proposed a charging equalization method that adapts itself to the aging conditions. It used the voltage difference among cells to adjust the equalization current, which not only maximized the total capacity but also slowed down the battery pack aging rate. However, the operating voltage value is easily interfered, which leads to voltage jump [45] that exceeds the threshold, resulting in equalization errors. Operating voltage-based equalization strategies have been applied in EVs. They have the following advantages: 1) The operating voltage can be measured directly and easily, avoiding complex estimation of other variables, which is much simpler and computationally efficient, and the voltage data is more accurate and reliable. 2) Using operating voltage as the equalization variable can prevent overcharge and discharge of the battery pack to ensure safety. However, there are also disadvantages to operating voltage equalization strategies: 1) Operating voltage is affected by internal parameters (capacity, internal resistance, coulomb efficiency, etc.) and external environmental factors (charge/discharge rate, temperature, aging, etc.) [45]. Hence, it cannot accurately reflect the internal state of the battery [46]. 2) The operating voltage platform span is wide, and voltage fluctuations easily occur due to dis­ charging/charging current in actual vehicle operating conditions that

3.1. Classification based on equalization variable Equalization variables are the output of equalization strategies. They are used to determine whether a battery pack is in a consistent state. At present, equalization variables often include operating voltage, SOC and open circuit voltage (OCV), and capacity [36]. Recently, multivariate fusion, i.e., a combination of multiple variables, has also been used. Selecting reasonable equalization variables forms the basis for formu­ lating a rational equalization strategy. In this subsection, common equalization variables and their advantages and disadvantages are introduced. 3.1.1. Operating voltage-based equalization strategies Operating voltage-based equalization strategies use the voltage be­ tween the positive and negative electrodes as an equalization variable. They aim to make the operating voltage of each cell consistent or within a reasonable range. As shown in Fig. 3, when a pack has three cells connected in series, with different initial operating voltages, the oper­ ating voltage is used as an equalization variable to achieve operatingvoltage equalization during charging and discharging. When taking operating voltage as an equalization variable, whether the EMS needs to be performed or not is determined by comparing the operating voltage differences between cells to a preset voltage threshold. Cells with higher operating voltages are discharged, while those with lower ones are charged to equalize the operating voltages in a battery pack [25,37]. M. Uno et al. [38] considered operating voltage as an equalization variable and preferentially redistributed energy to the cell with the lowest operating voltages to carry out “filling in”, eventually eliminating inter-cell voltage imbalances. P. Guo [14] and R. Ugle et al. [28] compared any two cells’ voltages, and transferred energy between cells when voltage difference exceeds a threshold. This method is simple. However, comparing every pair of cells is complicated and computa­ tionally intensive. In addition, since there is a plateau section in 4

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operation. However, there are also the following disadvantages: 1) using OCV as the equalization variable is only applicable to cells at rest, which limits its application [15]; 2) due to the hysteretic characteristics of OCV, some cells are in a charging state while others are discharging during the equalization process, so cells with the same OCV may have different CR [46]; 3) the OCV-SOC curves also vary from cell to cell due to manufacturing processes; and 4) very flat OCV-SOC curve of some batteries, such as LFP batteries, leads to inaccurate SOC estimation. Energy is transferred from cells with high SOC to cells with low SOC [41,54] if the EMS detects that the difference between cell SOCs exceeds the threshold. The accuracy of SOC estimation plays an important role in the performance of equalization strategy. Besides the OCV-based methods, various other SOC estimation methods (see reviews such as [55,56]) have been extensively studied and applied to equalization al­ gorithms. X. Liu et al. [49] used a current integration method to estimate the SOC of the individual cell. The difference between the individual cell SOC and the average SOC was used to calculate equalization current for accurate control and rapid equalization. However, the Ah integration method has some disadvantages, such as high dependence on the ac­ curate initial SOC and current accumulative error. Q. Sun [57] estimated SOC by Kalman filter, then cells were sorted by SOC, the energy to be transferred was calculated, achieving equalization by controlling the equalization current. Y. Wang et al. [58] proposed an active equalization algorithm based on the real-time observation of SOC and CT , where a particle filter was used to reduce the impact of current drift on SOC estimation. F. Feng et al. [59] unified OCV-based and Ah integral methods, establishing the relationship between the thermodynamic SOC and dynamic SOC of the battery. These were used to establish equal­ ization strategies for two scenarios—battery resting and equalization processes—to achieve a good equalization effect. When it comes to ac­ curate SOC estimation, many previous studies [60–62] have proposed SOC estimation methods that consider aging or temperature. They have achieved more accurate SOC estimation, whereas temperature and aging models are relatively complex, which greatly increases computational complexity. Therefore, estimating SOC while considering aging and temperature remains difficult. SOC represents the ratio of releasable capacity to total capacity. Taking SOC as an equalization variable has the following advantages: 1) The difference in the total capacity of the cells can be ignored, so that all the cells reach fully charged and discharged states at the same time, allowing full pack power to be utilized. 2) SOC consistency means the discharge depths are consistent, which avoids differences in aging rate caused by discharge depth [15,46], thereby extending battery life. 3) SOC can express the releasable capacity of cells so that the power dif­ ference between cells can be transferred once, thus shortening equal­ ization time [63]. However, there are also some drawbacks in using SOC as an equalization variable: 1) At present, it is relatively difficult to achieve real-time accurate SOC estimation while considering tempera­ ture and aging [64]. 2) Although complex SOC estimation can achieve high precision, it increases computational complexity, requiring the controller to have high computing power [48]. Hence, it is difficult to apply to the vehicles currently.

will lead to repeated equalization and over-equalization [47], which increases equalization time and energy consumption. Here, repeated equalization means that, at the end of the equalization process, the equalization variable exceeds the threshold value temporarily, which triggers the equalization process. As described in point 1) above, the operating voltage is affected by many internal and external factors that often trigger the threshold, leading to frequent re-equalization. To sum up, taking operating voltage as the equalization variable is easy, but it is also susceptible to external influences [48,49], which increases error [50]. Therefore, optimal equalization performance cannot always be achieved. 3.1.2. SOC- and OCV-based equalization strategies SOC-based equalization strategies take the SOC as the equalization variable to ensure that each cell’s SOC is consistent with others or within a range. When the initial SOCs of three cells in a series pack are inconsistent. Then, consistent SOC is achieved through equalization during charging and discharging, as shown in Fig. 4. SOC estimation is needed in SOC-based equalization strategies. The OCV-SOC relationship has been used to estimate SOC in some research, which reduces the error probability and computational load of SOC estimation. Some researchers have used OCV only or the OCV-SOC relationship for equalization. X. Hao et al. [15] considered the OCV differences between adjacent cells at rest, and “peak clipping” was adopted to balance cells with high voltage during charging, while “valley filling” was adopted to balance cells with low voltage during discharging to maximize capacity. In Ref. [51], OCV was used to esti­ mate SOC, an energy transfer path for the pack was optimized using the heuristic search A* algorithm, which reduced energy consumption and accelerated equalization speed. However, OCV-based equalization only applies to cells at rest. In addition, the long plateau stage in OCV-SOC curves leads to inaccurate SOC estimation. Thus, some researchers proposed equalization strategies for only the linear region of charge/­ discharge curves to avoid equalization errors such as overcharging. S. Li [52] established a relationship between OCV, polarization voltage, and SOC at the end of charging, avoiding the impact of polarization voltage on SOC estimation. For the flat OCV-SOC curves of some batteries such as LiFePO4 (LFP) batteries, Tang et al. [53] proposed that using balancing current ratio-based and voltage-based algorithms inside and outside the voltage platform, respectively, can overcome the problem of the plateau of the OCV-SOC curve and achieve higher efficiency. In summary, SOC estimation based on OCV-SOC relationship does not require a complex algorithm. Compared with the operating voltage, the OCV can reflect the internal state of the battery more accurately by avoiding the influences of dynamic electrochemical factors (ohmic voltage drop, polarization voltage, and diffusion voltage) during battery

3.1.3. Capacity-based equalization strategies Capacity-based equalization strategies take CT , CR , or CC as an equalization variable to improve the capacity utilization of a battery pack [65]. In passive equalization, the maximum battery pack’s CT is, theoretically, its minimum cell’s capacity. While in active equalization, when the EMS achieves an optimal state of full-charge or full-discharge of all cells at the same time, the CT reaches its theoretical maximum, which is the average capacity of all cells, avoiding the short plate effect of low-capacity cells. Fig. 5 shows capacity changes of cells and a series pack in the processes of charging and discharging in an active capacity-based equalization strategy. Capacity-based equalization strategies take CC during charging and CR during discharging as equalization variables to determine whether a

Fig. 4. Equalization charge and discharge control of a battery pack based on SOC. 5

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3.1.4.1. Voltage and SOC fusion. H. M. A et al. [71] presented a battery charge equalization strategy where cells are sorted by voltage in descending order, and overcharged cells are discharged first. Then, differences between cells’ SOC and average SOC are used to control the EMS to achieve equalization. Voltage and SOC are combined to ensure battery safety, and the method performed well in terms of equalization speed and consistency. However, it is complex and requires a high controller load. W. Chen et al. [72] used combined OCV and SOC as the charging equalization variable. Using OCV can effectively avoid misjudgment caused by over-potential and improve consistency. Meanwhile, using SOC can accelerate the equalization speed. 3.1.4.2. Voltage and capacity fusion. S. Wang et al. [73] designed an equalization strategy based on optimal path selection. The relative voltage deviation degree was obtained by calculating the relative devi­ ation between the sum of a single voltage and the terminal voltage of the battery pack. Then, the standard deviation of capacity was compared with the threshold to determine the combination of two inconsistent cells to achieve the correct energy transfer path and realize fast and efficient equalization.

Fig. 5. Active equalization based on capacity during charging and discharging.

battery pack is consistent or not, and then equalize based on capacity. R. Tian et al. [66] carried out equalization in the form of shunting, with capacity used as the equalization variable, to achieve consistency among cells. However, only a theoretical simulation was carried out and no experimental verification was performed. M. Einhorn et al. [48] pro­ posed a method of controlling the equalization current according to each cell’s capacity in a series pack. It compared and analyzed the advantages and disadvantages of capacity-based and voltage-based equalization strategies through experiments, concluding that using capacity as the equalization variable can better reflect the battery state. However, ca­ pacity is difficult to estimate. For this problem, Y. Zheng et al. [67] used charge-discharge voltage curves to estimate CT online. It proposed dissipative energy equalization based on CT , and capacity maximization was achieved. However, the equalization result was slightly different from the theoretical capacity of the battery pack, so fuzzy logic control (FLC) was utilized to effectively reduce battery pack capacity deviations. However, the existence of a plateau stage prevents accurate equaliza­ tion. Y. Zhao et al. [68] proposed an equalization strategy based on the dynamic estimation of battery model parameters, which were estimated by a nonlinear least-squares method to improve the accuracy of capacity estimation. W. Diao et al. [69] proposed a CR estimation method considering changes in internal resistance, charging and discharging currents, and controlled the equalization current based on CR , thereby maximizing the battery pack’s CR . When it comes to capacity estimation, many methods have been proposed in Refs. [16,61,70]; however, ac­ curate capacity estimation remains difficult. Taking battery capacity as an equalization variable has many ad­ vantages: 1) The battery pack’s CT can be significantly improved and maximized under ideal conditions [31]. 2) Using voltage as a variable will lead to repeated equalization, but using capacity can avoid this, thus shortening the equalization time. 3) It can slow down battery pack aging and prolong its cycle life [48]. However, there are also some short­ comings in using battery capacity as an equalization variable: 1) Online capacity estimation is difficult and complex as it requires high accuracy, stability, and computing resources, which increases hardware costs. 2) Most capacity estimation methods highly depend on accurate SOC estimation. 3) The balancing current also needs to be measured and adding current sensors increases hardware cost, which restricts equal­ ization applications.

3.1.4.3. SOC and temperature fusion. D. Docimo et al. [74] proposed an equalization strategy to tradeoff SOC and temperature. Model predictive control (MPC) was used to control the load current and limit tempera­ ture rises. A. Faisal et al. [75] proposed a rule-based proportional equalization strategy and presented two balancing modes: SOC equal­ ization in the low current range, and thermal equalization in the high current range. This reduced the controller load while taking SOC and temperature equalization into account. An equalization strategy based on thermal and SOC was proposed in Ref. [76]. A linear-quadratic MPC was adopted to control load current and avoid heat being generated by excess current. However, current-limiting control is greatly affected by the load, and load power cannot be adjusted in a wide range. Hence, it can only be slightly adjusted and the equalization speed is slow. Im­ balances of SOC and/or temperature will damage battery pack perfor­ mance and accelerate aging. Therefore, a SOC-temperature fusion equalization strategy can prolong battery pack cycle life. 3.1.4.4. Pros and cons of multivariate fusion. Multivariable fusion can take advantages of multiple variables to compensate for potential de­ fects in a single variable method, thereby improving equalization speed and accuracy. However, multivariate fusion methods still need to esti­ mate variables, and the problems of variable estimation still exist. These control strategies are complex, which increases control difficulty and computational complexity, resulting in high system load and requirements. 3.1.5. Summary This section summarized the basic principles, advantages and dis­ advantages of equalization strategies based on operating voltage, SOC, OCV, and capacity variables and their combinations. Using operating voltage as the equalization variable is convenient as it is easy to measure and avoids the computational complexity brought about by variables estimation; whereas it easily leads to repeated equalization. Using SOC as the equalization variable can avoid repeated equalization and make full use of battery pack capacity; however, SOC estimation is complex. Capacity utilization can be maximized by using capacity as the variable; nevertheless, it is difficult to achieve online capacity estimation at present. For a clearer comparison of the various strategies, the princi­ ples, advantages, and disadvantages of each are summarized in Table 1.

3.1.4. Multivariate fusion-based equalization strategies Multivariate fusion-based equalization strategies exploit the advan­ tages of each variable and select the best ones to achieve the optimal effect. This section reviews several multivariate fusion-based equaliza­ tion strategies in the literature, including SOC and voltage fusion, voltage and capacity fusion, and SOC and temperature fusion.

3.2. Classification based on equalization objective Equalization objectives are reflected in the objective function of equalization algorithms. The objectives of equalization strategies are to 6

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3.2.1. Variable threshold rationalization Equalization starts when the difference in the equalization variables exceeds a threshold. When the cell variation difference is less than the threshold, equalization stops. Threshold selection is one of the key fac­ tors affecting equalization speed and consistency. Equalization thresholds are divided into single, multiple, and adap­ tive thresholds. Setting equalization variables to a single threshold can shorten equalization time and improve stability; however, threshold setting largely depends on prior experience. And setting it to a fixed value may lead to wrong equalization [77], frequent open equalization circuits, repeated equalization, increased energy consumption, and the need to fully consider the trade-off between equalization time and consistency. Therefore, some studies have proposed setting the equal­ ization variable as a multi-threshold or adaptive threshold. G. Qi et al. [78] proposed setting the threshold as a linear function. In Ref. [77], FLC was adopted to dynamically calculate the threshold by taking into ac­ count equalization consistency and equalization time, and an adaptive equalization threshold solution was realized for equalization. The equalization variable threshold can be dynamically adjusted according to the battery state to ensure consistency of the equalization variable, shorten the equalization time, and achieve stable and reliable equalization. However, equalization variables are affected by factors such as charging and discharging current, operating temperature, and aging. It is necessary to set a reasonable equalization variable threshold according to the actual application. This requires not only theoretical calculation but also engineering experience.

Table 1 Principles, advantages, and disadvantages of various battery pack equalization strategies. Equalization variables

Equalization principles

Advantages

Disadvantages

Operating voltage

The inter-cell voltages are consistent or within a certain range

● Vulnerable to external influences, poor stability ● Repeated equalization and slow speed

SOC and OCV

The inter-cell SOC is consistent or within a certain range

● Direct and precise measurement, easy to access and computationally efficient ● Limit over-charging and overdischarging to ensure safety ● Makes full use of battery pack power ● Avoids battery pack aging caused by different discharge depths ● Short equalization time and fast equalization speed ● SOC estimation by SOC-OCV do not need complex algorithm ● OCV can reflect the internal state of the battery

Capacity

Multi-variate

Total capacity, chargeable capacity, or releasable capacity are used to maximize battery capacity

Considers the advantages of each variable, allowing the selection of the optimal variables

● Maximizes battery pack capacity utilization ● High equalization efficiency, avoids repeated equalization as using voltage variable ● Delays battery pack aging and prolongs cycle life ● Combines the advantages of several variables ● Faster equalization speed ● High equalization accuracy

● SOC is difficult to obtain accurately in real-time ● High-precision SOC estimation algorithms are complex and require a powerful controller ● OCV measurement needs to be set aside, low efficiency ● The same OCV may correspond to different CR values due to hysteresis ● The OCV-SOC curves vary from cell to cell ● The flat OCVSOC curve of some batteries, such as LFP bat­ teries leads to inaccurate SOC estimation ● Difficult capacity estimation and high accuracy ● High algorithm complexity ● Measuring current will increase the cost

3.2.2. Battery pack capacity maximization The concept of using battery pack capacity as the equalization objective is that all cells are theoretically fully charged or discharged at the same time. Thereby it can avoid reaching cell cut-off voltages and make the battery stop charging or discharging even when the capacity or SOC is not zero [69], thus maximizing capacity utilization. The method of using capacity as the equalization variable was introduced in Section 2.1.3. This section only discusses the advantages and disadvantages of using capacity maximization as the equalization objective. It contributes to power throughput, equalization energy consumption decline, and the economy of the equalization system. However, to maximize the battery pack capacity, constant equalization is required during the equalization process, which will increase energy consumption in the energy transfer process. The objective of maximizing battery pack capacity also requires greater stability, reliability, and power from the equalization circuit [79], which greatly increases the cost. 3.2.3. Equalization time minimization Equalization time is the duration of the equalization process. It is limited by the cell with the slowest equalization speed. Equalization time is related to the equalization objective, the current capacity of the equalization circuit, the degree of imbalance, and the equalization path. It is necessary to optimize these different objectives and variables. Equalization time increases as battery imbalance increases [80]. The equalization rate is also related to the hardware circuit. Capacitor-based equalization controllers take longer than energy conversion-type con­ trollers (inductor/transformer-based controllers) [81]. In a circuit with an unsteady equalization current, the equalization current is propor­ tional to the voltage difference and gradually becomes zero as equal­ ization progresses [20,26]. Therefore, as the voltage difference decreases, equalization time increases exponentially in flying-capacitor-based hardware [82]. Equalization threshold selection is also a factor that affects equalization time [83]. Thus, adopting a reasonable threshold, use of a strong tolerance circuit, maximization of equalization current, selection of a rational equalization threshold, and use of a control algorithm for the path optimization equalization steps can reduce equalization time under the conditions of constant energy consumption [80]. However, there are many factors affecting

● Difficulties in variables estimation ● Complex control strategies ● High system load and requirements

ensure that the equalization process is fast, accurate and stable, and maximizing the battery energy utilization rate and prolonging battery service life are also their objectives. According to these equalization objectives, this section divides equalization strategies into the following categories: variable threshold rationalization, battery capacity maxi­ mization, equalization time minimization, and equalization energy consumption minimization.

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equalization time, such as the degree of inconsistency, equalization circuit elements and topologies, thresholds, and control algorithms. Shortening the equalization time and increasing the equalization speed inappropriately can lead to large equalization currents, which may in­ crease energy consumption.

Table 2 Principles, advantages, and disadvantages of objective-based equalization strategies.

3.2.4. Equalization energy consumption minimization Equalization energy consumption is mainly comprised of battery energy consumption and equalization circuit energy consumption. Bat­ tery energy consumption is related to charge/discharge efficiency, while the energy consumption of the equalization circuit is related to its working efficiency. Taking equalization energy consumption as the equalization objec­ tive can reduce energy consumption during equalization. Passive equalization dissipates all unbalanced electrical energy through dissi­ pating elements, and the energy utilization rate is zero. Active equal­ ization carries out power transfer through the equalization circuit, and energy is mainly consumed during power transfer, including charge/ discharge losses and equalization circuit losses. In the case of a small battery pack, the equalization energy consumption is also small and can be ignored. However, as the battery pack size increases, energy con­ sumption becomes noticeable. Therefore, by considering the energy ef­ ficiency of the battery and equalization circuit, optimization for energy consumption [84] can reduce equalization energy consumption, improve energy throughput and reduce cost. However, it is difficult to accurately obtain the current of each equalizing circuit. In addition, the energy efficiencies of batteries and electronic components in equaliza­ tion circuits are also difficult to obtain accurately. Due to the above limitations in practical applications, it is difficult to estimate the equalization energy consumption in a real vehicle.

Equalization objective

Equalization principle

Advantages

Disadvantages

Variable threshold rationalization (Single threshold)

A fixed range of equalization variables that control the start and end of equalization

● Accelerates equalization speed ● Improves equalization stability

Multi-threshold

A range of equalization variables that control the start and end of equalization

● Increased consistency ● Shortens the equalization time

Battery pack capacity maximization

All the cells are fully charged and discharged at the same time to maximize capacity utilization of the battery pack Optimal equalization operation is selected to achieve the shortest equalization time Considers the energy consumption of the battery and equalization circuit during equalization

● Maximizes capacity utilization ● Reduces energy consumption

● Repeated equalization, energy consumption increases ● Consider tradeoff between equalization effect and time ● Need to be familiar with battery condition ● Increases algorithm complexity ● Increased energy consumption ● Increased hardware costs

Equalization time minimization

3.2.5. Summary In this section, equalization strategies were divided into four cate­ gories according to the equalization objective: threshold rationalization, battery pack’s CT maximization, equalization time minimization, and equalization energy consumption minimization. A threshold rationalization-based equalization strategy can save equalization time and ensure consistency. A battery pack capacity maximization-based equalization strategy can maximize capacity, but capacity is difficult to estimate in real-time. An equalization time minimization-based equalization strategy can shorten equalization time, but the influence of equalization time is greater and it is easy to increase the equalization energy consumption. Taking equalization energy consumption minimi­ zation as the objective can improve the energy utilization rate and reduce use cost, but it increases computational complexity and hard­ ware costs. These principles, advantages, and disadvantages of objective-based equalization strategies are briefly summarized in Table 2.

Equalization energy consumption minimization

● Shortens equalization time

● Improves energy utilization ● Reduces usage costs

● Equalization time has many influences ● Equalization energy consumption increases ● Equalization energy consumption data is difficult to obtain ● Increased hardware costs

(SIC), FLC, genetic algorithms (GAs) and neural networks (NNs). 3.3.1.1. Classical PID control algorithms. PID control is introduced in the classical control theory. Because of its simple structure, closed-loop stability, reliability, convenient adjustment, and other advantages, it is widely used in the field of industrial control. The key to PID controller design is in selecting the proper proportional, integral, and differential coefficients [85]. Once the parameters of a traditional PID controller are selected, they are fixed. When the disturbance is small, the stability is satisfactory; however, once mutations occur, the system cannot be sta­ bilized quickly. Aiming at rectifying the defects of traditional PID, intelligent PID optimizes PID control parameters through an intelligent algorithm to achieve optimal control. Due to its advantages of stable intelligent control, automation, and simple implementation, particle swarm optimization (PSO) was used to optimize the proportions and integral parameters of the controller. H. Mohammad M et al. [86,87] have applied PSO to equalization strategies. H. Mohammad M et al. [86] took the ratio of feedback voltage to current and the mean absolute error of a reference value as the objective func­ tion. They [87] presented a charge equalization controller model using the mean absolute error of cell SOC and reference SOC as an objective function, and obtained control models for estimating equalization time and current. The method was iterated through PSO to generate regulated optimized PI controller parameters. It had a simple design, excellent equalization performance, and low power loss compared to PID control. Intelligent PID can dynamically change the controller parameters according to the running state, so that the controller can achieve better

3.3. Classification based on equalization algorithm Equalization algorithms are developed to achieve the quality indexes for equalization systems. Selecting an appropriate equalization algo­ rithm can avoid over-equalization and repeated equalization, greatly shorten the equalization time, improve efficiency, and achieve the ob­ jectives in a stable manner. There are many different equalization al­ gorithms. This section classifies the equalization algorithms reported in the literature, including control algorithm-based, data driven-based, and fusion-based algorithms. 3.3.1. Control algorithm-based equalization strategies This section reviews the latest common equalization algorithms. They range from proportion integration differentiation (PID) (classical control theory) to the modern control theory, which includes optimal control (OC), MPC and sliding mode control (SMC). Finally, we review the intelligent control theories, including swarm intelligent control 8

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and its constraint was equalization current. A current discontinuity model was established with the objective of SOC difference to achieve SOC consistency. Through Lyapunov mathematical analysis, SOC can converge to a small scope and verify the convergence and stability of a discrete-time adaptive sliding-mode observer and controller. In this strategy, the maximum allowable equalization current varies with the charge and discharge current, avoiding overcurrent and achieving rapid equalization. SMC is more suitable for establishing nonlinear models of equalization systems owing to its accurate and fast solutions. However, it is also necessary to reconstruct models for different systems. It is difficult to slide strictly along a stable point and easy to generate chat­ tering, resulting in equalization error. 3.3.1.2.3. Model predictive control algorithms. The MPC approach solves open-loop optimization problems in a finite time domain online at each sampling timestep according to the measurement information. It applies the first element of the obtained control sequence to the controlled object and repeats this process with new measurements at the next sampling moment [95]. Compared with PID control, it does not need transfer function derivation, and PID controller selection [96]. Compared with OC, it has low requirements for model accuracy and can deal with time-varying or non-time-varying, and linear or nonlinear data, and system constraints and optimal control problems with or without delay. MPC has a good performance in solving multi-variable and multiconstraint problems, and scholars have applied it to equalization stra­ tegies to improve model constructions and objective functions. L. McCurlie et al. [97] established a system dynamic model considering time changes and the average equalization current. Meanwhile, it took equalization time as the objective function and used fast MPC to solve for time and current to achieve single-point convergence of the equal­ ization variable. M. Preindl [98] divided a battery model into high-voltage battery equalization and a low-voltage battery charging module. Two MPC strategies were used to solve for the optimal equal­ ization current and time. A decoupling method was proposed to solve for slow equalization sampling frequency and achieve rapid equalization charging. Q. Wei et al. [99] proposed duty-based MPC equalization, which established a discrete-time model and optimized the prediction of switching duties by taking input voltage as a cost function. This reduced switching frequency and cost, and improved overall dynamic perfor­ mance. J. Liu et al. [100] proposed an MPC-based active equalization strategy that aimed at SOC consistency and energy consumption mini­ mization. It used nonlinear MPC to achieve multi-objective equalization. L. Zheng et al. [101] considered the impact of aging on inconsistency. It constructed an equalization strategy with MPC, took the difference be­ tween the average and predicted equalization currents as an objective function, and verified the effectiveness of MPC, which was found to fully avoid overbalancing and reduce energy consumption. In addition, some scholars have used thermal equalization as an objective. D. Docimo et al. [74] established a linear time-varying differences model by MPC. This model is applicable to the analysis of inter-cell charge and temperature heterogeneity and is capable of retaining accuracy under the approxi­ mation of small charge, temperature, and current differences. Mini­ mizing charge and temperature heterogeneity was the objective and, by constant evaluation, the optimization process was repeated until the change in the function was negligible. F. Altaf et al. [76] proposed an equalization strategy based on heat and SOC. A linear-quadratic MPC was adopted to realize the management and control of voltage and balanced loads. F. Altaf et al. [75] proposed a constrained proportional controller with gain scheduling constraints for simultaneous SOC and thermal equalization. It uses a linear quadratic and solves control pro­ jection problems to approximate linear quadratic control gains using a simple algorithm, and easily achieves the same performance as MPC. MPC aims to achieve multi-variable constraint optimal control. It uses established equalization models to control equalization circuit switching to control the whole process and achieve optimal control. MPC-based equalization strategies can avoid repeated equalization and

effects in complex, dynamic, and uncertain systems. It has the advan­ tages of simple design, fast speed, high efficiency, and low power con­ sumption. However, an equalization strategy based on intelligent PID requires high computational complexity. 3.3.1.2. Modern control algorithms. Modern control algorithms are based on the state-space model. Modern control algorithms are mainly used to analyze and design control systems by their state variables. This section summarizes the modern control algorithms used in equalization strategies, including OC, SMC, MPC, and run-to-run control. 3.3.1.2.1. Optimal control algorithms. Optimal control (OC) algo­ rithms determine a control law for a controlled system under a given condition, so the system has an optimal solution for a pre-specified performance index [88]. OC is mainly composed of state equations, control variables, constraint conditions, and objective functions. The performance index largely determines OC performance and form. The most commonly-used dynamic programming (DP) and minimum prin­ ciples from modern variation theory can be widely used in equalization strategies. Due to the convenience and high accuracy of OC, many researchers have applied it to equalization strategies. Some studies selected different objective functions for OC to achieve different effects. W. Chen et al. [72] proposed maximizing the sum of battery pack voltages as an objective function. This improved energy transfer efficiency and short­ ened charge equalization time. While Q. Ouyang et al. [89] proposed that the objective function of OC equalization is to minimize differences between cells’ SOC and average SOC to regulate the equalization cur­ rent, thereby equalizing the pack SOC in a relatively short time. Some literature has not only improved objective functions but also proposed different OC models for equalization systems. N. Bouchhima et al. [90] described a novel equalization strategy where the discharge and charge rates of each cell can be controlled. Equalization problems were described as a nonlinear OC problem in a finite domain. BMS was modeled as a network to carry out DP using power dissipation as an objective function and reconfigurable cell number as a constraint. It achieved rapid equalization with high efficiency and strong robustness. M. Caspar et al. [17] introduced a nonlinear average mean current model that is applicable to any equalization topology. It used releasable capacity as the objective and used OC to optimize the switching sequence of the equalization circuit to shorten the equalization time and reduce energy losses caused by repeated equalization. C. Danielson et al. [91] presented a simple discrete time integrator dynamic equalization model that maximizes the total battery capacity as the objective function to maximize the energy utilization of a battery network based on con­ strained optimization techniques. Q. Ouyang et al. [92] used OC to propose a SOC-based equalization strategy that modeled a multibody system with cells as nodes and equalization circuits as boundary con­ ditions to achieve SOC consistency. The effectiveness of the algorithm was validated via theoretical derivation, simulation, and experiments. OC is very effective and simple for use in dynamic and complex systems requiring coupling of an equalization circuit and battery mod­ ule. However, it is difficult to solve accurately while considering nonlinearity or constraints. Moreover, due to the differences between equalization systems, each equalization system needs to be reconstructed. 3.3.1.2.2. Sliding-mode control algorithms. Also known as variable structure control, SMC is, in essence, a special type of nonlinear control [93]. In dynamic processes, SMC changes the system state (e.g. deviation and its various derivatives, etc.) constantly, forces the system to move in a predetermined state trajectory. It has good control performance for nonlinear system, can be applied to multi-input and multi-output sys­ tem, and has design standard for discrete-time system, quick response, no online identification of system, simple physical implementation and good robustness. Q. Ouyang et al. [94] proposed a discrete-time quasi-SMC strategy, 9

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over-equalization, and improve equalization efficiency. However, it needs to make predictions based on known operating conditions and the model of an EMS is complex for MPC. The modeling work is very complicated due to the large variations among EMSs, therefore this method is not widely used. 3.3.1.2.4. Run-to-run control algorithms. Run-to-run control algo­ rithms are a type of optimal control method for batch processes, which are updated according to the feedback and analysis of historical batch information. Then, the process model and plan are adjusted to reduce inter-batch product differences [102–104]. Many equalization control algorithms work within one charging/discharging cycle. However, the equalization process could take longer than one charging/discharging cycle, and it should be allowed for the controller to equalize the battery over cycles. Tang et al. [53] proposed using balancing current ratio-based and voltage-based algorithms inside and outside the voltage platform of a LFP battery. Within each batch run, time-wise control was carried out, then batch-wise control was performed at the end of each batch. This is a model-free and SOC independent algorithm, which is not complex and has higher efficiency. However, there are difficulties in theoretical analysis.

is superior to traditional methods in terms of equalization time, energy loss, and equalization performance. Z. Liu et al. [111] regarded the equalization problem in terms of path selection and applied an ant colony algorithm to optimize path selection with the objective of minimizing equalization energy consumption. It also analyzed multi-objective optimization and the factors affecting efficiency in detail. However, the optimization objective function only considers energy consumption, and the study only used simulation without experimental verification. PSO has advantages in the formulation of equalization strategies, such as simple coding and few parameters, and has been widely used in the field of function optimization. However, it requires a lot of data, which makes it difficult to train an accurate equalization model. Moreover, it is necessary to distinguish between single- and multiobjective optimization, which is relatively complex in the formulation of multi-objective equalization strategies. 3.3.1.3.3. Neural network-based algorithms. Neural network-based algorithms (NNs) simulate the human brain’s functions of information processing, storage, and retrieval. It learns knowledge through training data and obtains optimized output [112]. It has the advantages of nonlinearity, strong learning ability, good adaptability, and does not need an accurate mathematical model, so it is suitable for equalization systems with complexity, nonlinearity, and dynamic changes. It is composed of many simple computing units, which are easily realized by software and hardware. N. Nguyen et al. [18] proposed an equalization strategy based on an adaptive NN. Considering the impacts of temperature and different charge/discharge current on voltage, it took voltage and a voltage de­ rivative as inputs, and the current was the output. An adaptive fuzzy NN was divided into five layers, and an offline training model was used for system tracking of battery pack dynamic reactions. The method maxi­ mized battery capacity and minimized equalization time. However, due to the limited availability of experimental EMS data, it is difficult to train NN models accurately and it is time-consuming. Because of the differ­ ences between equalization systems, it is necessary to train a NN for each one, leading to complex processes. 3.3.1.3.4. Fuzzy logic control algorithms. A typical FLC can be divided into four components: fuzzification, fuzzy rule base, inference engine, and defuzzification [113], as shown in Fig. 6. The rule base is used to collect knowledge and experience of battery equalization. So far, some researchers have applied FLC to the equalization threshold and equalization current. The input for the former is the data values, char­ acteristic values, and relevant parameters of influencing factors, and its output is the equalization threshold and its dynamic adjustment. Input for the equalization current approach is the same that for equalization threshold, and the output is a pulse width modulation (PWM) signal that controls the equalization circuit and regulates the current. Currently, a large number of studies use fixed variable thresholds as battery equalization control indexes, which are prone to judgment errors and frequent switching of the equalization circuit. To resolve this problem, Z. Li et al. [77] proposed a dynamic equalization strategy where the fuzzy threshold, polarization voltage, internal ohmic resis­ tance, and charge and discharge currents are analyzed. It uses FLC to set the voltage threshold dynamically, which effectively reduces the battery terminal voltage difference and shortens the equalization time. How­ ever, the rule base is formulated by human experience, so the process is relatively complicated and there may be subjective errors. FLC has not only been applied to equalization threshold solutions but also to equalization current and other parameters in equalization stra­ tegies with good results. Y. Lee et al. [11] and M. Cheng et al. [114] proposed an FLC equalization system to adjust equalization current by using voltage as a variable, which decreased the equalization and charging times. Y. Lee et al. [115] took the voltage difference between two cells and the cell voltage as two inputs for FLC. Inference results were converted into numerical output equalization current to reduce equalization time, increase equalization efficiency and battery pack

3.3.1.3. Intelligent control algorithms. Intelligent control theory is an automatic control technology that can drive control objectives autono­ mously without human intervention. It does not need to establish complex models artificially, so it is suitable for systems that cannot be accurately modeled due to highly mathematical complexity, nonline­ arity, time-variability, and uncertainty. This section summarizes appli­ cations of intelligent control algorithms [105–107] in equalization strategies, including GA, PSO, NN, and FLC. 3.3.1.3.1. Genetic algorithms. Genetic algorithms (GAs) are a prob­ abilistic global and optimization method that mimics natural biological evolution [108]. GAs are composed of an iterative procedure of the following five main steps [96]: 1) Create an initial population; 2) eval­ uate the performance of each individual population by means of a fitness function; 3) select individuals and reproduce a new population; 4) apply the genetic operators of crossover and mutation; 5) iterate steps 2–4 until the termination criterion is fulfilled. GAs have the characteristics of self-organization, self-adaptation and self-study, reduced risk of falling into a local optimal solution, and easy realization of parallelization. S. Zhang et al. [84] presented a GA-based battery equalization strategy for energy consumption and equalization time. It takes the Coulomb efficiency and energy consumption of equalization circuit as the objective function and formulates the optimal selection of parame­ ters as a constrained optimization problem within a specific time limit. It achieved a satisfactory trade-off which achieved the lowest energy consumption. However, when a GA is applied to an unconstrained optimization problem, the constraints are included in the penalty functions, which penalizes the unfeasible solutions by reducing their fitness values. It can easily lead to premature convergence of the GA and long equalization times in complicated problems. 3.3.1.3.2. Swarm intelligent control algorithms. The classical swarm intelligent control algorithm is inspired by bird behavior and is an optimization algorithm that can iteratively optimize a solution as a particle of a given problem [109,110]. PSO algorithms use three quan­ tities: swarm size, iteration number, and dimension. The main idea is that each solution is considered a particle with n-dimensional space and a fitness function is used to evaluate the degree of superiority of each particle. It then searches for an optimal solution of swarm particles through particle movement in the search space with optimized position and velocity. It has the advantages of using a simple algorithm and a few parameters, and fast convergence. J. Sun et al. [80] put forward an equalization strategy where a fitness function is determined by equalization time and SOC inconsistency. As the input of PSO, SOC is employed to find the global optimal solution and optimal equalization time and direction. It requires fewer steps and 10

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Renewable and Sustainable Energy Reviews 116 (2019) 109464

Fig. 6. Structure of fuzzy controller.

This method is simple, easy to implement, and widely used. In this section, it is divided into statistics-based algorithms and data-mining algorithms.

capacity. However, the influences of fuzzy rules were not considered. D. Cadar et al. [116] proposed an FLC-based equalization method for series batteries that use two inputs to control equalization current: an error associated with the voltage difference between cells, and the derivative of the error, which reduced the equalization time. D. Jia et al. [117] considered internal voltage differences and coupling relationships be­ tween load current, and average voltage, It used cell voltage and load current as two input, duty as the single output and proposed a closed-loop energy model for FLC to achieve accurate real-time equal­ ization. F. Feng [118] took cell SOC and SOC differences as input, with the output being the actual SOC after equalization. It achieved SOC consistency based on FLC in a short time. J. Qin et al. [119] presented a battery equalization system based on FLC. Model inputs of battery ca­ pacity, voltage, and voltage difference were used to generate an opti­ mized equalization current and time to complete equalization faster and more effectively. To ensure the speed when consistency is poor, much FLC input is needed; but when consistency is good, the input only needs to be large enough to achieve accurate control, so the FLC needs a huge rule base. J. Zheng [120] proposed an FLC equalization strategy with a variable range. The input variables are average voltage and cell voltage difference, and it realizes equalization current regulation according to the degree of imbalance. It can avoid overbalancing and repeated equalization when there is low inconsistency, and avoid long equaliza­ tion times due to low equalization currents when there is high incon­ sistency, thereby providing circuit protection. Y. Ma et al. [121] proposed a two-stage equalization algorithm based on FLC that was constructed with fuzzification of the averages and differences of the variables used to control the equalization current, which was able to reduce energy consumption and equalization time. Because an EMS is a nonlinear system, internal resistance, capacity, and other charging/discharging process parameters vary dynamically [11]. The characteristics of charging and discharging also vary greatly due to the number of cycles, current ratio, and environmental temper­ ature, making it difficult to establish an accurate mathematical model. Since FLC does not require an exact mathematical model [122], it is suitable for nonlinear behavior [115] and for making rational decisions under uncertainty in the EMS. FLC can shorten equalization times [11, 123] and it has strong robustness, good real-time performance, simple control parameters, dynamic adjustment of current, good fault toler­ ance, and can greatly improve equalization efficiency. However, since the formulation of fuzzy rules depends on knowledge and experience of the equalization strategy, insufficient and inappropriate knowledge may lead to output oscillation, decreased equalization precision, and incor­ rect equalization. The difficulty lies in the different FLC design rules for different types of lithium-ion batteries. Therefore, application flexibility and portability are poor.

3.3.2.1. Statistics-based algorithms. Statistics-based algorithms are relatively simple, easy to implement, and have high data accuracy. Ac­ cording to differences in the reference statistics, they can be divided into the maximum and minimum method, mean method, and difference method. 3.3.2.1.1. Maximum and minimum algorithms. Maximum and mini­ mum algorithms control equalization according to cell equalization variables, which are divided into maximum and minimum equalization according to the equalization scenario. In maximum equalization, the range of cell variables is calculated and compared with a threshold as per Eq. (2). It takes the cell with the maximum value of a certain equalization variable as the equalization object, discharges cell through a circuit, dissipates excess power or releases it to cells with smaller equalization variables, until reaching a set threshold. Minimum equal­ ization strategies are similar to maximum ones. The cell with the min­ imum variable is detected dynamically. When it reaches the startup condition of EMSs, it is charged by an external power supply or maximum cell until the minimum cell reaches a threshold. Maximum and minimum equalization strategies are generally used for charging. A flow chart of a maximum and minimum equalization strategy is shown in Fig. 7.where cellmax is the maximum value of the cell equalization variable; cellmin is the minimum value of the cell equalization variable; Δ is the difference between battery variables; and ε is the threshold. Due to its simple logic and easy implementation, the maximum and minimum algorithm is widely used. M. Uno et al. [38] and H. Liu et al. [124] proposed that SOC and voltage were taken as equalization vari­ ables, and consistency was achieved by equalizing the cell with the lowest variable in a series battery pack. S. Ye et al. [83] used an array selector switch to select the battery with a higher or lower deviation from the mean value to form an equalization pair. An equalization threshold was used as the judgment condition for starting and stopping equalization. In paper [48], as a battery was discharging, electrical en­ ergy was transferred to the cell with the lowest voltage through a transformer. While charging, the energy was transferred from the cell with the highest terminal voltage to the battery pack through a transformer. The data accuracy of maximum and minimum equalization strategies is relatively high. It only needs to equalize the cells with maximum or minimum values beyond the threshold, which is simple to control and easy to achieve. However, when battery pack consistency is very poor, logical errors, repeated equalization, and overbalance are likely to occur. 3.3.2.1.2. Mean algorithms. Mean algorithms take the average equalization variables of all cells in a battery pack as the equalization reference object, compare the voltage, SOC, or capacity of each battery with the average, and charge batteries with low variable value or discharge higher ones through an equalization circuit to achieve equalization. As shown in Eq. (3), the variance in equalization variables

3.3.2. Data-driven equalization strategies Data-driven equalization strategies use the voltage, SOC, and ca­ pacity estimated by the EMS or BMS to sort, compare, find the variance of equalization variables, and other operations to obtain eigenvalues to judge the degree of battery pack imbalance and realize equalization. 11

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is also the expected value. M. Hoque et al. [125] compared variable ranges and averages to determine when equalization should start and stop. When the battery is discharged, equalization energy is transferred from the battery pack to the cell with the lowest voltage through a transformer. When the battery is charged, equalization energy is transferred from the cell with the highest terminal voltage to the battery pack through a transformer. Z. Li et al. [76] took the range of equalization variables and working current as the basis of when equalization should start and stop, and divided unbalanced situations into three types according to battery pack voltage: too high, too low, or both too high and too low, to formulate different strategies. F. Feng et al. [118] estimated SOC by considering the bat­ tery’s internal changes, and calculated the average and inter-cell dif­ ference in SOC as FLC double input for equalization. F. Feng et al. [126], average SOC was calculated and the SOC differences of all inconsistent cells were obtained. Then, energy transfer between cells was controlled to avoid overbalance and improve equalization efficiency. A mean algorithm can achieve battery pack consistency well and its operation is simple. However, this method often needs to be compared with average variables, which requires high computing resources for embedded systems, and repeated equalization and overbalance may occur. 3.3.2.1.3. Difference algorithms. Difference algorithms compare the equalization variables (i.e. voltage, SOC, or capacity) of two cells. When the difference exceeds a threshold, equalization is carried out to discharge higher cells to lower ones to achieve power transfer until meeting the equalization threshold. The method of calculating the dif­ ference is shown in Eq. (4). A flow chart of the difference equalization strategy is shown in Fig. 9.where celli ; ​ cellj are the variable values of the ith and jth cells, and 1 � i; j � N i 6¼ j . Because difference equalization algorithms are simple and easy to implement [127], they have been adopted by many researchers in their

Fig. 7. Flow chart of a maximum and minimum equalization strategy. Δ ¼ ​ j ​ cellmax ​

​ cellmin j � ε

(2)

is calculated to obtain the degree of imbalance. A flow chart of a mean algorithm is shown in Fig. 8.where N is the number of cells in the battery pack; celli is the value of the ith cell’s equalization variable (1 � i � N); and cellave is the average of the battery pack equalization variable, which

Fig. 8. Flow chart of a mean algorithm. N X

Δ¼

ðcelli

cellave Þ2 � ε

Fig. 9. Flow chart of a difference algorithm. � � Δ ¼ max�celli cellj � � ε

(3)

i¼1

12

(4)

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equalization strategies. Z. Fan et al. [128] proposed a non-dissipative equalization scheme with a voltage-difference method, and realized excellent voltage equalization performance. Other scholars compared the differences in equalization variables and thresholds to determine equalization on-off, and realized objective consistency by controlling switching duties. Z. Liu et al. [111] and Kim et al. [129] used a differ­ ence algorithm to maintain cell variables within an average threshold range. This method is easy to implement and has good expandability, so it is widely used now. However, it has a high requirement for embedded system resources and needs to be frequently compared with the average voltage, making it easy to produce overbalance and repeated equalization.

equalization current as output. An equalization circuit was controlled by adjusting the switching cycle and keeping the duty cycle constant. FLC is usually chosen when errors are large. A PI controller is selected when errors are small to eliminate the steady-state error. H. Qin et al. [132] proposed an FLC-PI equalization strategy, as shown in Fig. 10. It ach­ ieved the requirements of equalization efficiency and precision by tak­ ing advantage of an independent FLC mathematical model and the fast, stable, and accurate control of PI, taking full advantage of the two al­ gorithms in different situations. 3.3.3.2. Adaptive fuzzy neural network-based algorithms. FLC provides a reasoning mechanism under cognitive uncertainty, and NNs provide advantages such as learning and adaptation. The limitation of FLC is that it cannot automatically obtain rules to make output decisions. Tradi­ tional FLC-based modeling of small changes in equalization variable offsets is a challenge because they will reduce the accuracy of the sys­ tem. The limitation of NNs is that large amounts of data are needed to train accurate models. NN and FLC can be combined to optimize the membership function of FLC to give it self-adaptability and learning ability. The resulting hybrid system is called adaptive neural network fuzzy control [18]. Due to its adaptivity and convenience, some scholars have applied it to equalization strategies. H. Yoo et al. [133] proposed a nonlinear dynamic control method for the voltage equalization of series battery systems. To equalize two neighboring batteries, battery voltage and its derivative were used for the input and output to change the duty of the transistors to drive the current of PWM. It uses the advantages of NN and FLC and has the ability to learn and adapt to dynamic changes. Fusion methods overcome the shortcomings of single equalization al­ gorithms, give full play to each algorithm’s advantages, or make full use of their characteristics in different stages to select the best algorithm. However, it is easy to lose data during data processing, resulting in inaccurate estimates.

3.3.2.2. Data mining-based algorithms. Data stream mining (DSM) is a process of extracting knowledge from rapidly- or continuously-produced data [130]. Due to its strong learning ability, some scholars have applied it to equalization strategy research. C. Lin et al. [131] introduced a novel battery equalization method that shuttles capacity among cells. It cal­ culates the DSM automatically to determine equalization charge under conditions of interference and inconsistency. It has the capability of equalizing individual cells in noisy conditions with large in­ consistencies. It not only equalizes cells’ CR online but also reports their health state indirectly. DSM can automatically obtain parameters and equalization operations through data and is suitable for complex sys­ tems. However, DSM requires the discovery of existing data, so it is difficult to obtain, and DSM has difficulty avoiding interference, which requires data preprocessing. 3.3.3. Fusion-based equalization strategies Fusion-based equalization algorithms use multiple variable features or algorithms to decide equalization operations and achieve accurate and convenient EMS. Such equalization algorithms can be divided into data-level fusion, feature-level fusion, and decision-level fusion. Data-level fusion uses the direct fusion of sensor data as the basis for equalization. In the equalization algorithm, the measured voltage can be sorted or pairwise compared in various ways to realize equalization judgment. This type is the lowest level of fusion. The main advantage is its high accuracy using raw data. However, large data volumes lead to high processing costs and times. In addition, due to the dynamic nature of equalization systems and external interference, effective data error correction is required. In feature-level fusion, each sensor abstracts its own feature vector first, then carries on fusion processing to achieve equalization optimi­ zation. The general feature information includes the statistics of the data, e.g. SOC and capacity and their variances and ranges. Feature extraction can reduce the number of variables, which has a small amount of calculation, however, it requires accurate data, otherwise is prone to errors in equalization. Decision-level fusion directly integrates data and features into con­ trol algorithms for specific balancing objectives. It applies multiple variables and control methods to battery equalization strategies to achieve better equalization. Decision-level fusion can give full play to the advantages of different algorithms, and has less equalization time, however, large data loss, low accuracy, and complex algorithms cannot be avoided.

3.3.4. Summary This section summarized algorithm-based equalization strategies, which can be divided into three categories: control theory-based, datadriven, and fusion algorithm-based. Equalization strategies based on control algorithms were categorized according to the development of control theories Among these, modern control theory is widely used, including MPC, SMC, and OC techniques. However, model development is complicated. Equalization strategies based on intelligent control theory do not need complex models and their control is simple; however, a large amount of data is required for support. At present, it is relatively difficult to obtain equalization data and train high-precision models. Data-driven methods are relatively simple, easy to implement and have high data accuracy. However, accurate acquisition and estimation are needed, otherwise control logic chaos such as overbalance and repeated equalization can easily occur, increasing equalization time and reducing equalization efficiency. Fusion-based equalization algorithms overcome the shortcomings of single algorithms and can achieve rapid equaliza­ tion and greatly improved consistency. There are few existing studies on these topics and they may become future research directions. Their basic principles, advantages, and disadvantages are summarized in Table 3.

3.3.3.1. PI-FLC control algorithms. PI can be combined with FLC to make full use of its advantages. PI control applies to accurate solutions for a steady state, and fuzzy control is suitable for nonlinear dynamic conditions. PI-FLC chooses a control algorithm according to the battery state to achieve better equalization performance. The rationale is shown in Fig. 10. To improve dynamic performance, R. Ling et al. [20] com­ bined traditional PI and FLC to design a triangle membership function. The voltage difference and average voltage were taken as input, and

Fig. 10. Block diagram of a fuzzy-PI controller. 13

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Renewable and Sustainable Energy Reviews 116 (2019) 109464

4. Challenges and prospects

equalization strategies are needed to solve the problem of equalization strategies lacking reasonable constraints. Considering the input and output of equalization systems over the whole cycle life, it is expected that a future research direction will be to develop strategies aiming at the comprehensive economy of equalization systems.

Currently, equalization strategies have made some progress. How­ ever, some problems remain in terms of accurate variable sensing and fetching, equalization objective formulation, and algorithm selection. In this section, challenges and prospects are introduced from three aspects: equalization variables, equalization objectives, and equalization algorithms.

4.3. Equalization algorithms Battery pack equalization management requires efficient control to increase discharge cycles, decrease the memory effect, and increase lifespan [138]. Intelligent equalization algorithms are essential. These have some problems, such as complex system modeling, requiring large amounts of effective experimental data, and rational algorithm selec­ tion. Both classical control theory and modern control theory are based on accurate system modeling. Battery packs are complex nonlinear time-varying systems. Knowing how to build a system model that can accurately describe the dynamic behavior of a battery pack and also take into account computational complexity is a big challenge [139]. Both intelligent control theory and data-driven methods require a large amount of effective data. Building a large number of effective battery databases is another challenge [140]. The disadvantages of single al­ gorithms are relatively prominent, which lack the complementarity of advantages between algorithms. Selection of control algorithms ac­ cording to actual application scenarios is also a challenge. Considering battery pack’s complexity in equalization processes, the development of battery pack models with acceptable precision and computational complexity needs to be researched to achieve complex battery system modeling. It is necessary to simplify the multi-cycle equalization of the battery pack and establish the multi-step batch equalization strategy [53]. Owing to the popularization and application of connected and automated vehicle technology, the development of vehicle battery database technology is a focus of current research. Due to the advantages of multiple equalization algorithms, developing a reasonable fusion equalization algorithm according to application sce­ narios to overcome the shortcomings of a single algorithm will be another research direction. However, the present study is qualitative. A quantitative comparative study of the performance of strategies based on different control theories but using the same plant model is required.

4.1. Equalization variables Measuring and estimating battery pack equalization variables have many problems, such as accuracy and computational complexity. It is difficult to ensure the accuracy and reliability of battery voltage, tem­ perature, and current measurements due to multi-physical field inter­ ference in the operating environments of EMSs. Improving the accuracy and reliability of battery parameters without significant increases in sensor cost is currently the major challenge. Online estimation of SOC and capacity is easily affected by charge/discharge currents, tempera­ ture, and aging degree, etc. Accuracy and stability do not meet the re­ quirements of real vehicle applications. Improving the accuracy and stability of battery SOC and capacity estimates under multiple stresses over the whole life cycle is another huge challenge [134]. Large numbers of battery cells increase the computational complexity of algorithms, which leads to an aggravation of the controller load and makes it diffi­ cult to apply to real vehicles. It is also a great challenge to reduce the computational complexity of state estimation without affecting accuracy [135]. Solving the problems of battery parameter measurement, analysis of the interference sources in balanced system working environments, and development of advanced sensing technologies that have high precision and reliability and low cost are current research directions. Considering the influences of multiple external stresses on batteries, the establish­ ment of electric-thermal-aging multi-dimensional coupled models and multi-state joint parameter estimates is needed to solve the problems of accuracy and stability in battery state estimation over the whole life cycle. Another potential research direction is to analyze the inconsistent characteristic performance of battery packs under different external stresses, different SOC states, and different ages, and to establish the battery pack inconsistent evaluation. Establishing general and person­ alized battery pack models and developing multi-state co-estimation methods for different time scales may be able to solve the computational complexity of multi-state co-estimates of battery packs.

5. Conclusions In this paper, the current literature on battery pack equalization strategies was reviewed. Equalization strategies were introduced from the perspectives of equalization variables, equalization objectives, and equalization algorithms, and the advantages and disadvantages of each equalization strategy were summarized. Finally, the challenges and prospects of research on equalization strategies were discussed. Equalization variables based on operating voltage have the advan­ tages of convenient acquisition, safe battery pack use, low computa­ tional complexity, and have been reported in relevant literature. Equalization variables based on SOC and capacity can be used as more essential representations of battery consistency state. However, both SOC and capacity are susceptible to external environments and aging, and it is difficult to guarantee the accuracy, stability, and computational complexity of current relevant algorithms. This is also a current equal­ ization variable research hotspot. It is difficult for a single equalization variable to meet the needs of a battery pack. Equalization strategies based on multi-variable fusion have been reported, and are expected to continue to be a topic of research in the future. Equalization objectives based on a single technical index have the advantages of simple formulation, easy implementation, low computa­ tional complexity, and have been reported in many studies. However, comprehensive performance demands cannot be met based on a single technical index. Considering the tradeoff between multiple objectives and multiple constraints, the establishment of a reasonable equalization objective under actual application scenarios is highly needed. Currently,

4.2. Equalization objectives Battery pack equalization objectives have many problems, such as singularity, lacking reasonable constraints, and cost. Currently, most equalization strategies take a single technical index as the objective. While one single technical index is maximized, other technical indexes are difficult to satisfy. Knowing to equalize each technical index reasonably and improve the comprehensive performance of equalization strategies remain great challenges [136]. The application scenarios of equalization systems are complex and diverse. Setting constraints reasonably according to application scenarios is another challenge. In the existing literature, equalization strategies have certain technical aims, such as variable consistency or short equalization time. However, they ignore the comprehensive economy of input cost and output energy of EMSs. It is also a great challenge to improve the comprehensive economy of BMS by taking the whole life cycle service economy as the objective [137]. Establishing more comprehensive equalization strategy objectives and developing multi-objective optimal equalization strategies may be able to solve the problems of using singular objectives. Studying the actual application of equalization systems, setting reasonable con­ straints and control variables, and developing multi-constraint 14

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Renewable and Sustainable Energy Reviews 116 (2019) 109464

Table 3 Principles, advantages, and disadvantages of equalization strategies based on control algorithms. Control theory

Equalization algorithm

Ref.

Year

Principles

Advantages

Disadvantages

Classical control algorithm

PID-based

[86, 87]

2016, 2017

● Suitable for complex, dynamic and uncertain systems

● Increased complexity of system control

Modern control algorithm

OC-based

[17] [72] [89] [90] [91] [92] [94]

2012–2017

Intelligent algorithm optimizes PID parameters: proportional, integral and differential coefficients Under given conditions, a control law is determined for a given controlled system so that the system has an optimal value for the pre-specified performance index

● Suitable for complex system control with equalization circuit and cell module coupling

● Nonlinearity, difficult to solve accurately ● Requires model building

2017

Purposefully changes according to the current state of the system, the system is forced to follow the predetermined “sliding mode” state trajectory

● Required accurate modeling

[97] [98] [99] [100] [101] [74] [75] [76] [53]

2016–2018

The optimal solution is obtained by searching the optimal position and velocity of the population particle by moving the particle in the search space

● Quick response, insensitive to parameter changes and disturbance ● No system online identification, simple physical implementation ● Small signal modeling and transfer function derivation are not needed ● Suitable for time-varying, nonlinear and time-delay sys­ tem constraints

2019

Uses the balancing results of previous cycles to enhance the control scheme for the current cycle in a batch-to-batch manner

● Difficulty in theoretical analysis

SIC-based

[80] [111]

2015, 2017

FLC-based

[11] [77, 114] [115] [116] [117] [118] [119] [120] [121] [18]

2005–2018

Searches an optimal solution of swarm particles through particle movement in the search space with optimized positions and velocities According to battery knowledge and equalization experience, a rule base is established, output control is carried out, and an optimized solution is obtained

● Model-free and SOC independent ● Higher efficiency and not complex ● Simple coding and few parameters ● High equalization speed ● Robust, real-time, simple con­ trol parameters ● Good fault tolerance, high equalization efficiency

● Rules depend on knowledge and experience ● Poor flexibility, portability

● Suitable for complex, nonlinear, and dynamic systems ● Easy to implement in hardware and software ● Relatively simple and easy to implement ● High data accuracy ● Good expansibility

● Insufficient data makes it difficult to train highprecision models ● Poor portability

● Database is hard to obtain ● Required data preprocessing ● High processing cost and time ● Required high data error correction ● Accurate data, prone to errors in equalization

SMC-based

MPC-based

Run-to-run

Intelligent control algorithm

NN-based

Data driven-based equalization algorithm

Statisticsbased

Data miningbased Fusion-based equalization algorithm

Data-level fusion Feature-level fusion Decision-level fusion

2014

Simulates human intelligence, which obtains knowledge from training data and produces optimized output

2011–2018

Equalization start/stop and energy transfer can be determined directly by comparing and sorting individual state quantities to solve variance and extreme values

2015

A process of extracting knowledge from rapidly changing or continuous data records

● Simple implementation, suitable for complex systems, convenient

[72] [74] [75, 76] [73]

2013–2018

The measured data are fused directly, and then feature extraction is used as the basis of equalization judgment

● High precise data without processing

2013

● Variable reduction, small amount of calculation

[41] [133]

2012,2015

A feature vector is abstracted from the sensor and then fused with different variables to achieve optimal control Multi-equalization variables and multiequalization algorithms are applied to achieve better equalization in different stages of battery operation

[83] [38, 124] [48] [20] [125] [77] [39] [128] [129] [131]

15

● Fully uses the advantages of different algorithms ● Less bandwidth, saves equalization time

● Model construction is complex ● Need to know the operating conditions

● Need a lot of data

● Overbalancing and repeated equalization ● Easy to cause logical chaos, long equalization time

● Large data loss, low accuracy ● Complex algorithm

F. Feng et al.

Renewable and Sustainable Energy Reviews 116 (2019) 109464

equalization objectives only achieve some technical indicators on a technical level. From the perspective of the battery life cycle, the equalization objectives should be to maximize the EMS input cost and output energy ratio. Relevant research has not been reported and it is expected to become a future research direction. Equalization strategies based on control algorithms have the ad­ vantages of high algorithm theory maturity, multiple references for system models, moderate computational complexity, and have been reported in many studies. With the popularization of 5G communication technology and the development of connected and automated vehicle technologies, data-driven equalization strategies have become a research hotspot. Artificial intelligence technology has been increas­ ingly applied in vehicles. Equalization strategies based on artificial in­ telligence fusion have been reported and are expected to continue to be a

topic of research in the future. Declaration of competing interest As Xiaosong Hu, a co-author on this paper, is an Associate Editor of RSER, he was blinded to this paper during review, and the paper was independently handled by Songyan Wang. Acknowledgments This work was supported in part by NSF of China (Grant No. 51807017), NSF of China (Grant No. 51875054), Chinese Postdoctoral Science Foundation (Grant No. 2018M643404) and Special Foundation of Chongqing Postdoctoral Science (Grant No. XmT2018036).

List of symbols CT CC CR cellave cellmax cellmin celllow cellhigh celli Ibal

total capacity (Ah) chargeable capacity (Ah) releasable capacity (Ah) average value of the cell equalization variable maximum value of the cell equalization variable minimum value of the cell equalization variable cells with equalization variable less than cellave ε cells with equalization variable less than cellave þ ε variable value of the ith cells balancing current

Abbreviations BMS battery management system CPM control plant model DP dynamic programming DSM data stream mining EV electric vehicle FLC fuzzy logic control GA genetic algorithm LFP LiFePO4 MPC model predictive control NN neural network OC optimal control OCV open-circuit voltage PID proportion integration differentiation PSO particle swarm optimization SIC swarm intelligent control SMC sliding mode control SOC state of charge Subscripts T C R ave max min low high i, j bal

total chargeable releasable average value maximum value minimum value variable value less than cellave ε variable value less than cellave þ ε ith or jth cells balancing

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