# Active Equalization Strategy for Lithium-Ion Battery Packs Based on Multilayer Dual Interleaved Inductor Circuits in Electric Vehicles

Authors: Xu Lei; Jianping He; Linqian Fan; Guiping Wang
Journal: Journal of Advanced Transportation
 (2022)

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## Abstract

Lithium-ion batteries (LIBs) are widely used in electric vehicles (EVs) due to their superior power performance over other batteries. However, when connected in series, overcharged cells of LIBs face the risk of explosion, and undercharged cells decrease the life cycle of the battery. Eventually, the inconsistency phenomenon between cells resulting from manufacturing tolerance and usage process reduces the overall charging capacity of the battery and increases the risk of explosion after long-time use. Research has focused on synthesizing active material to achieve higher energy density and extended life cycle for LIBs while neglecting a comparative analysis of equalization technology on the performance of battery packs. In this paper, a nondissipative equalization structure is proposed to reconcile the inconsistency of series-connected LIB cells. In this structure, a circuit uses high-level equalization units to enable direct energy transfer between any two individual cells, and dual interleaved inductors in each equalization unit increase the equalization speed of a single cell in one equalization cycle by a factor of two. The circuit is compared with the classical inductor equalization circuit (CIEC), dual interleaved equalization circuit (DIEC), and parallel architecture equalization circuit (PAEC) in the states of standing, charging, and discharging, respectively, to validate the advantages of the proposed scheme. Considering the diversity of imbalance states, the state of charge (SOC) and terminal voltage are both chosen as the equalization criterion. The second-order RC model of the LIB and the adaptive unscented Kalman filter (AUKF) algorithm are employed for SOC estimation. For effective equalization, the adaptive fuzzy neural network (AFNN) is utilized to further reduce energy consumption and equalization time. The experiment results show that the AFNN algorithm reduces the total equalization time by approximately 37.4% and improves equalization efficiency by about 4.89% in contrast with the conventional mean-difference algorithm. Particularly, the experiment results of the equalization circuit verification certify that the proposed equalization structure can greatly accelerate the equalization progress and reduce the equalization loss compared to the other three equalization circuits.


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## Body

## 1. Introduction

EVs have attracted increasing attention in recent years due to their efficient energy utilization, zero emissions, and contributions to carbon neutral and green global environment. EVs commonly use LIBs characterized by superior power performance, long life, high-energy density, and no memory effect [1, 2]. However, the electrical capacity, voltage, and instantaneous discharge power of individual LIB cell are far below electricity demand in real-world applications. Thus, LIB cells are often connected in series to boost the voltage and in parallel to increase the capacity [3].Different from cells connected in parallel that are able to self-balance the charge, cells connected in series are faced with the problem of cell charge imbalance that worsen over time [3–5]. In Figure 1, multiple cells are connected in series to form a string with a high voltage level. The charge of cells differs owing to the capacity, self-discharge rate, internal impedance, and temperature mismatch. Manufacturing differences and discrepancies in the usage environment reduce the overall battery performance, which accelerates battery aging and causes safety hazards (e.g., a fire or, in the worst case, an explosion) [6–8]. These issues are worsened by the fact that LIBs are very sensitive to deep discharge and overcharge [9]. Numerous studies have been conducted to improve the capacity and life cycle of LIBs, and the safety issues have not been well addressed [10]. Manufacturing differences are inevitable, and thus a proper equalization technology is needed to make each cell operate safely and reliably.Figure 1
Sources of nonuniform, performance, and an equalization system design.Bi denotes the (i)-th battery cell.The essence of equalization technology is to lower as much as possible the charge variance by equalization circuits and equalization control algorithms. The equalization technology is classified into passive and active according to the energy consumption and energy transfer [11]. The passive equalization technology dissipates the excess power of a higher SOC cell by power resistors, and yet it has two distinct drawbacks: energy waste and thermal imbalance. The delayed thermal consumption results in high local temperature of the battery pack, which may be a safety hazard [12]. The active equalization technology solves these two drawbacks by moving the excess power from higher SOC cells to lower ones via capacitors, inductors, or transformers [12]. The charge imbalance is resolved by energy deallocation. Particularly, the inductor-based active equalization circuit has wide acceptance because of good controllability and reliability [13]. In this paper, based on the CIEC, an inductor-based multilayer dual interleaved equalization circuit (MLDIEC) is proposed. The MLDIEC avoids inefficient transmission of energy when two battery cells are far apart with the aid of a high-level equalization unit. Incorporating dual interleaved inductors into the circuit enhances the equalization efficiency. Meanwhile, theoretical calculations are carried out to explore the relationship among different equalization parameters.An equalization control strategy complementary to the equalization circuit is presented to illustrate the equalization processes. Generally, equalization control strategies can be based on the terminal voltage, SOC, or capacity, depending on the battery characteristics. Note that these variables can also be used as criteria to determine whether the battery pack is balanced. The terminal voltage of the battery is measurable in real time with a simple monitoring system, but it cannot describe the charge in the SOC-open-circuit voltage (OCV) plateau accurately [14]. The SOC takes into account many factors (e.g., the voltage, current, and internal resistance environmental temperature), yet it cannot be measured directly. Instead, the SOC needs to be calculated with various methods, e.g., the electrochemical model, the equivalent circuit method, and neural networks. The complexity of these methods limits their applicability of the SOC-based strategy [13]. The capacity-based strategy considers the aging rate besides SOC. Yet, the battery capacity is only available offline, and thus this method is not suitable for real-time applications [11]. In practice, the terminal voltage and SOC are adopted in different regions of the SOC-OCV characteristic curve of LIBs [15]. In the low and high voltage regions of the curve, the terminal voltage-based strategy is adopted to prevent overcharging or discharging [16]. In the plateau region, the SOC-based strategy is preferred since it describes the battery charge accurately. To achieve high accuracy in real-time applications, the SOC value can be estimated by the Kalman filter algorithm based on an equivalent circuit model. The improved unscented Kalman filter (UKF) proposed by J. C Lv estimates SOC with the error of just 0.63% [17, 18]. Thus, the AUKF is employed for SOC estimation.The equalization control strategy incorporates an equalization algorithm [19, 20]. The mean-difference algorithm is widely applied to the inductor-based equalization circuit due to its simplicity. However, the mean-difference algorithm is inefficient since it cannot maximize the overall performance of the equalization circuit [21]. Therefore, we employ the AFNN to develop the equalization algorithm. This algorithm is suitable for real-time operations, is very adaptive, and realizes nonlinear mapping with arbitrary accuracy. Thus, the AFNN is suitable for complex controlled objects that are challenging to be described by a mathematical model of the battery pack [22].Figure2 shows the overall structure of the proposed MLDIEC and its control strategy. The SOCs and terminal voltages of cells marked in the diagram are chosen to judge the equalization status of the battery pack. The AUKF is used for SOC estimation. The AFNN is adopted to improve the equalization efficiency. The rest of this paper is organized as follows. Section 2 introduces the structure and operating principle of the MLDIEC. Section 3 describes the AUKF to estimate the SOC. Section 4 presents the equalization control algorithm in detail. Section 5 presents the experiment results. Section 6 concludes the paper.Figure 2
Overall structure of the proposed MLDIEC and its control strategy.


## 2. The MLDIEC

[23] proposes a CIEC, where an inductor is put between two adjacent cells to transfer energy from a high SOC cell to a low SOC cell, as illustrated in Figure 3. However, the energy transfer is limited to adjacent cells. Bo Dong et al. [4] proposed a multilayer inductor equalization circuit (MLIEC). With this circuit, energy is exchanged directly between two cells far apart, avoiding intermediate inductors and reducing energy loss during equalization [24, 25]. Inductors in the CIEC and MLIEC are operated with asynchronous current to prevent inductor saturation but make inductor inefficient during equalization [26]. To overcome this drawback, we propose a multilayer dual interleaved equalization circuit (MLDIEC) based on the MLIEC, as shown in Figure 4(a).Figure 3
Classical inductor equalization circuit topology.Figure 4
(a) The equalization circuit topology; (b) the enlargement of the proposed equalization unitEU1-1.
(a)(b)Figure4(b) shows an equalization unit EU1-1 in greater detail, including two inductors (L1 and L2) and four MOSFETs (S1, S2, S3, and S4). High-layer units are utilized to transfer energy between any two cells, which speeds up the equalization, increases the battery energy usage, and reduces energy loss. The dual inductors replace the conventional single inductor and increase the cell operating time during an equalization cycle. This way, the circuit avoids keeping the battery idle for a long time and increases the equalization speed. The layer number and unit number per layer are determined by equations (1) and (2), respectively:(1)m=log2n+1,a=log2ni,where m is the number of equalization layers, n is the number of cells in the series-connected battery, [−] represents the Gaussian rounding function, and a is the number of equalization units in layer i.


### 2.1. Working Principle

The equalization unit is a dual interleaved inductor unit that increases the cell operating time in an equalization cycle. Yet, a battery cell cannot be charged and discharged to two inductors simultaneously, which reduces the energy transfer efficiency. To address this issue, the phase difference between the pulse width modulation (PWM) signals of the two inductors can be set to 180°, so that the two inductors can compensate each other, and the battery operates safely. Take theEU1-1 in Figure 4(b) as an example. The two inductors work in Discontinuous Conduction Mode (DCM), and their operations are the same [27]. Assume that the SOC of B1 is higher than that of B2 to analyze the operating state of inductor L1. The equalization control switch S1 is controlled to achieve battery equalization at first. The equalization process within an equalization cycle T is divided into three stages based on the direction of energy transfer. The signal waveform of the three stages is shown in Figure 5, and the D is the duty cycle.Stage 1: (0-t1(DT)).When the control signal from the equalization control system is set, switchS1 is turned on. Battery B1, inductor L1, and switch S1 make up a closed loop. The electric energy is converted into magnetic energy and stored in L1. According to the Kirchhoff laws (KCLs), the voltage relationship of the loop is obtained by(2)RT−onit+L1ditdt=VB1.The current ofL1 is as follows:(3)it=VB1RT−on1−e−RT−on/L1t,whereRT-on is the total equivalent resistance of L1, S1, and B1 and the wire when S1 is turned on, L1 is the inductance of L1, and VB1 is the battery voltage, which can be regarded as constant because the voltage does not vary much during a single period. When t reaches t1, B1 finishes discharging. The current of L1 reaches the maximum value in this equalization cycle.Stage 2: (t1-t2).When switchS1 is turned off, a loop consists of B2, L1, and S2 is formed. At this stage, the magnetic energy stored in L1 is released. Similarly, the voltage of the loop is given by(4)RT−offit+VB2=L1ditdt+VD.The current ofL1 is found to be(5)it=e−RT−on/L1t−t1imax+VB2−VDRTe−RT−on/L1t−t1−t,whereRT-off is the equivalent internal resistance sum of L1, B2 and the wire when S1 is turned off, which can be approximately as RT-off = RT-on = RT, VB2 is the voltage value of B2 but is a constant, and VD is the on-state voltage drop of the parasitic diode of MOSFET S2 [28].At time 0.5T, switch S3 is turned on. Another loop is made up of B1, L2, S3. The electric energy of B1 is converted into magnetic energy, and stored in L2.Stage 3: (t2-T).At the end of stage 2, all the energy of inductorL1 transfers to B2. Stage 3 aims to prevent stage 1 of the next cycle from overlapping with stage 2 of the current period, which avoids energy accumulation in inductors.Figure 5
Signal waveform of inductors (L)1 and (L)2.


### 2.2. Equalization Circuit Parameters

#### 2.2.1. PWM Duty Cycle

To ensure that the inductor equalization unit operates in DCM, the PWM duty cycle of the MOSFET needs to avoid energy accumulation. Equations (3) and (5) describe the voltage relationship during the discharging and charging operations. Ignoring the equivalent resistance RT-on and the MOSFET on-state voltage drop VD in the two equations, the current of L1 is changed as follows:(6)it=VB1L1t,0<t<t1,it=VB1L1t1−VB2L1t−t1,t1<t<t2.Assuming thatt is equal to T, the duty cycle D and voltages should meet the following requirement:(7)VB1L1DT−VB2L11−DT≤0.A relationship betweenD and voltages is thus developed as(8)D≤VB2VB1+VB2.To make the inductor in DCM,VB2 should equal VB1. Therefore, the maximum theoretical value of duty cycle D is 0.5. Furthermore, based on the inductors operated in DCM and the current of L1 in one equalization cycle, the maximum energy transfer ratio of an individual inductor in the first-level equalization unit can be formulated as(9)QV=VB1D2T2L1f,where Qv can also be interpreted as the average current value of the inductor, and f is the switching frequency.


#### 2.2.2. Inductor and Square Wave Frequency

To avoid battery damage from excessive current during equalization, the maximum current supplied to the battery should be below the peak current. The equalization circuit is designed as a hierarchical structure by considering that the current of different layers may superimpose on the battery. The inductor peak current of the equalization unit per layer is the same as that of the first layer. Thus, we obtain(10)iB−Definem≥VB−MAXDLf,where VB-MAX is the upper limit voltage, iB-Define is the maximum equalization current allowed, m is the number of equalization layers, and f is the square wave frequency reflecting the relationship between the switching frequency of the MOSFET and the losses during equalization.


#### 2.2.3. Switching Voltage

The MOSFET employs switching frequency to control the current during equalization. The maximum withstanding voltage of the MOSFET must be greater than the voltage applied at both ends, preventing it from breaking down. As seen in Figure5, the voltage across the MOSFET at the disconnection moment is the battery voltage. However, the MOSFET in each layer withstands the different voltage, increasing with the number of layers. The maximum withstand voltage of the MOSFET is(11)Vstress=Vmax2m−1,where Vmax is the maximum voltage of an individual cell, and m is the number of equalization layers.


## 2.1. Working Principle

The equalization unit is a dual interleaved inductor unit that increases the cell operating time in an equalization cycle. Yet, a battery cell cannot be charged and discharged to two inductors simultaneously, which reduces the energy transfer efficiency. To address this issue, the phase difference between the pulse width modulation (PWM) signals of the two inductors can be set to 180°, so that the two inductors can compensate each other, and the battery operates safely. Take theEU1-1 in Figure 4(b) as an example. The two inductors work in Discontinuous Conduction Mode (DCM), and their operations are the same [27]. Assume that the SOC of B1 is higher than that of B2 to analyze the operating state of inductor L1. The equalization control switch S1 is controlled to achieve battery equalization at first. The equalization process within an equalization cycle T is divided into three stages based on the direction of energy transfer. The signal waveform of the three stages is shown in Figure 5, and the D is the duty cycle.Stage 1: (0-t1(DT)).When the control signal from the equalization control system is set, switchS1 is turned on. Battery B1, inductor L1, and switch S1 make up a closed loop. The electric energy is converted into magnetic energy and stored in L1. According to the Kirchhoff laws (KCLs), the voltage relationship of the loop is obtained by(2)RT−onit+L1ditdt=VB1.The current ofL1 is as follows:(3)it=VB1RT−on1−e−RT−on/L1t,whereRT-on is the total equivalent resistance of L1, S1, and B1 and the wire when S1 is turned on, L1 is the inductance of L1, and VB1 is the battery voltage, which can be regarded as constant because the voltage does not vary much during a single period. When t reaches t1, B1 finishes discharging. The current of L1 reaches the maximum value in this equalization cycle.Stage 2: (t1-t2).When switchS1 is turned off, a loop consists of B2, L1, and S2 is formed. At this stage, the magnetic energy stored in L1 is released. Similarly, the voltage of the loop is given by(4)RT−offit+VB2=L1ditdt+VD.The current ofL1 is found to be(5)it=e−RT−on/L1t−t1imax+VB2−VDRTe−RT−on/L1t−t1−t,whereRT-off is the equivalent internal resistance sum of L1, B2 and the wire when S1 is turned off, which can be approximately as RT-off = RT-on = RT, VB2 is the voltage value of B2 but is a constant, and VD is the on-state voltage drop of the parasitic diode of MOSFET S2 [28].At time 0.5T, switch S3 is turned on. Another loop is made up of B1, L2, S3. The electric energy of B1 is converted into magnetic energy, and stored in L2.Stage 3: (t2-T).At the end of stage 2, all the energy of inductorL1 transfers to B2. Stage 3 aims to prevent stage 1 of the next cycle from overlapping with stage 2 of the current period, which avoids energy accumulation in inductors.Figure 5
Signal waveform of inductors (L)1 and (L)2.


## 2.2. Equalization Circuit Parameters

### 2.2.1. PWM Duty Cycle

To ensure that the inductor equalization unit operates in DCM, the PWM duty cycle of the MOSFET needs to avoid energy accumulation. Equations (3) and (5) describe the voltage relationship during the discharging and charging operations. Ignoring the equivalent resistance RT-on and the MOSFET on-state voltage drop VD in the two equations, the current of L1 is changed as follows:(6)it=VB1L1t,0<t<t1,it=VB1L1t1−VB2L1t−t1,t1<t<t2.Assuming thatt is equal to T, the duty cycle D and voltages should meet the following requirement:(7)VB1L1DT−VB2L11−DT≤0.A relationship betweenD and voltages is thus developed as(8)D≤VB2VB1+VB2.To make the inductor in DCM,VB2 should equal VB1. Therefore, the maximum theoretical value of duty cycle D is 0.5. Furthermore, based on the inductors operated in DCM and the current of L1 in one equalization cycle, the maximum energy transfer ratio of an individual inductor in the first-level equalization unit can be formulated as(9)QV=VB1D2T2L1f,where Qv can also be interpreted as the average current value of the inductor, and f is the switching frequency.


### 2.2.2. Inductor and Square Wave Frequency

To avoid battery damage from excessive current during equalization, the maximum current supplied to the battery should be below the peak current. The equalization circuit is designed as a hierarchical structure by considering that the current of different layers may superimpose on the battery. The inductor peak current of the equalization unit per layer is the same as that of the first layer. Thus, we obtain(10)iB−Definem≥VB−MAXDLf,where VB-MAX is the upper limit voltage, iB-Define is the maximum equalization current allowed, m is the number of equalization layers, and f is the square wave frequency reflecting the relationship between the switching frequency of the MOSFET and the losses during equalization.


### 2.2.3. Switching Voltage

The MOSFET employs switching frequency to control the current during equalization. The maximum withstanding voltage of the MOSFET must be greater than the voltage applied at both ends, preventing it from breaking down. As seen in Figure5, the voltage across the MOSFET at the disconnection moment is the battery voltage. However, the MOSFET in each layer withstands the different voltage, increasing with the number of layers. The maximum withstand voltage of the MOSFET is(11)Vstress=Vmax2m−1,where Vmax is the maximum voltage of an individual cell, and m is the number of equalization layers.


## 2.2.1. PWM Duty Cycle

To ensure that the inductor equalization unit operates in DCM, the PWM duty cycle of the MOSFET needs to avoid energy accumulation. Equations (3) and (5) describe the voltage relationship during the discharging and charging operations. Ignoring the equivalent resistance RT-on and the MOSFET on-state voltage drop VD in the two equations, the current of L1 is changed as follows:(6)it=VB1L1t,0<t<t1,it=VB1L1t1−VB2L1t−t1,t1<t<t2.Assuming thatt is equal to T, the duty cycle D and voltages should meet the following requirement:(7)VB1L1DT−VB2L11−DT≤0.A relationship betweenD and voltages is thus developed as(8)D≤VB2VB1+VB2.To make the inductor in DCM,VB2 should equal VB1. Therefore, the maximum theoretical value of duty cycle D is 0.5. Furthermore, based on the inductors operated in DCM and the current of L1 in one equalization cycle, the maximum energy transfer ratio of an individual inductor in the first-level equalization unit can be formulated as(9)QV=VB1D2T2L1f,where Qv can also be interpreted as the average current value of the inductor, and f is the switching frequency.


## 2.2.2. Inductor and Square Wave Frequency

To avoid battery damage from excessive current during equalization, the maximum current supplied to the battery should be below the peak current. The equalization circuit is designed as a hierarchical structure by considering that the current of different layers may superimpose on the battery. The inductor peak current of the equalization unit per layer is the same as that of the first layer. Thus, we obtain(10)iB−Definem≥VB−MAXDLf,where VB-MAX is the upper limit voltage, iB-Define is the maximum equalization current allowed, m is the number of equalization layers, and f is the square wave frequency reflecting the relationship between the switching frequency of the MOSFET and the losses during equalization.


## 2.2.3. Switching Voltage

The MOSFET employs switching frequency to control the current during equalization. The maximum withstanding voltage of the MOSFET must be greater than the voltage applied at both ends, preventing it from breaking down. As seen in Figure5, the voltage across the MOSFET at the disconnection moment is the battery voltage. However, the MOSFET in each layer withstands the different voltage, increasing with the number of layers. The maximum withstand voltage of the MOSFET is(11)Vstress=Vmax2m−1,where Vmax is the maximum voltage of an individual cell, and m is the number of equalization layers.


## 3. SOC Estimation Based on AUKF

The SOC estimation accuracy is directly affected by the performance of the equalization control algorithm. To make an accurate estimation, this paper employs a second-order equivalent circuit model considering the battery hysteresis effect and uses AUKF to estimate the SOC. The Kalman filter algorithm combined with the second-order equivalent circuit model estimates the SOC accurately in real-time applications. Meanwhile, the extended Kalman filter (EKF) and cubature Kalman filter (CKF) are employed as benchmarks.


### 3.1. Second-Order Equivalent Circuit Model

Much effort has gone into building battery models, such as the equivalent circuit model, the neural network model, and the electrochemical model. The equivalent circuit model can better respond to the relationship between battery parameters, reflect the dynamic performance of the battery, and facilitate the battery characteristics analysis and parameter identification [26, 29]. Here, we propose a second-order RC equivalent circuit model with hysteresis effects. The two RC networks shown in Figure 6 describe the effects of differential polarization and electrochemical polarization, respectively.Figure 6
Second-order RC equivalent circuit model.LetUoc(t) be the battery OCV. R0 denotes the ohmic internal resistance of the battery [12]. There are four parameters in the two RC networks. Re and Ce denote the electrochemical polarization internal resistance and capacitance of the battery, respectively. Rd and Cd denote the concentration polarization resistance and capacitance, respectively. I(t) is the dry circuit current, positive for discharging and negative for charging.According to KCL and Kirchhoff’s Voltage Law (KVL), the ohmic voltageU0(t), the electrochemical polarization voltage Ue(t), and the concentration polarization voltage Ud(t) can be calculated by(12)U0t=R0It,Uet=ReIt−CedUetdt,Udt=RdIt−CedUdtdt.respectively. And the battery terminal voltageU(t) is(13)Ut=UOCt+UOt+Uet+Udt.By the current integration method, we have(14)SOCt=SOC0−1QN∫0tηItdt.where SOC0 is the initial SOC, QN is the normal capacity of the battery, and η is the charging and discharging efficiency of the battery.The system state-space equations are discretized into(15)Uek=e−τ/τeUek−1+Re1−e−τ/τeIk−1,Udk=e−τ/τdUdk−1+Rd1−e−τ/τdIk−1,SOCk=SOCk−1−ητQNIk−1.where τ, τe and τd are the sampling periods satisfying(16)τe=Re⋅Ce,τd=Rd⋅Cd.Hence, the established discretized state-space equation of the battery system is as follows:(17)SOCkUekUdk=1000e−τ/τe000e−τ/τdSOCk−1Uek−1Udk−1+ητQNIRe1−e−τ/τeRd1−e−τ/τdIk−1+wk−1,where wk−1 is the model observation noise. The discretized state output voltage of the model is(18)Uk=UOCVk+UOk+Uek+UDk+υk−1,where vk−1 is the observation noise of terminal voltage.


### 3.2. SOC Estimation Based on AUKF

The key to the UKF is the unscented transform operation to transform the mean and covariance of the nonlinear system, avoiding linearization operations and retaining the high-order terms of the system. The UKF also improves the transmission accuracy of the system Gaussian density. Further, the AUKF iteratively corrects the system noise covariance and the observed noise covariance using maximum likelihood estimation and expectation maximization, resulting in better adaptability and better estimation results [30].For a nonlinear discrete-time system, the state equation and the measurement equation are as follows:(19)xk=fxk−1,uk−1+wk−1,yk=hxk,uk+vk,where xk is the system state vector, yk is the measurement vector, uk is the known input vector, wk is the process Gaussian noise, vk is the measurement noise Gaussian, and f(xk, uk) is a nonlinear measurement function. The AUKF for the battery SOC estimation is illustrated as follows:Step 1: Initialization and state extension(20)x^0=Ex0,P0=Ex0−x^0x0−x^0T,X^0=EX0=Ex^0,0,0,PX,0=EX0−X^0X0−X^0T,whereX^0 and PX,0 are the initial state estimate and error covariance matrix. The state vector Xk is defined as(21)Xk=SOCkUekUdkT.with the state variables SOC(k),Ue(k) and Ud(k).Step 2: 2L + 1 sampling (Sigma) points establishment(22)X0,k−1=Xk−1,i=0,Xi,k−1=Xk−1+L+λPX,k−1,i=1∼L,Xi,k−1=Xk−1+L+λPX,k−1,i=L+1∼2L.Step 3: The weight calculationThe calculation of the mean weight and covariance weight can be presented as(23)W0m=λn+λ,W0c=λn+λ+1−α2+β,Wim=Wic=λ2n+λ,i=1,2,…2L,whereλ=α2n+ς−n is a scale parameter to eliminate the total prediction error, α determines the distribution of sigma points around X^ and is usually a small positive value ranging from 1 to e−4, ς takes values of 0 to 3-n generally, β is used to integrate the X prior estimation and generally selected to be 2, and Wim and Wic are weighting factors to calculate the mean and covariance of the i-th sigma point, respectively.Step 4: State estimation time updating(24)X^i,k=fXi|k−1,uk−1,i=0,1,…2L,Xk|k−1=∑i=02LWimX^i,k−1.Step 5: Covariance matrix time updating(25)PX,k|k−1=∑i=02LWicX^i,k−Xk|k−1X^i,k−Xk|k−1T+Qk−1.whereQk is the covariance of the process Gaussian noise wk. Rk is the covariance of measurement noise Gaussian vk, without relationship between them.Step 6: New sigma points attainment at timek|k-1(26)X0,k|k−1=Xk|k−1,i=0,Xi,k|k−1=Xk|k−1+L+λPX,k|k−1,i=1∼L,Xi,k|k−1=Xk|k−1+L+λPX,k|k−1,i=L+1∼2L.Step 7: Measurement estimation(27)y^i,k|k−1=hXi,k|k−1,uk,yk|k−1=∑i=02LWimyi,k|k−1.Step 8: Kalman gain matrix(28)K=Pxy⋅≤Pyy−1,where(29)Pyy,k|k−1=∑i=02LWicy^i,k|k−1−yk|k−1y^i,k|k−1−yk|k−1T+Rk−1,Pxy,k|k−1=∑i=02LWicXi,k|k−1−X^k|k−1y^i,k|k−1−yk|k−1T.Step 9: Residual calculating(30)εk=yk−yk|k−1.Step 10: State estimation measurement updating(31)Xk=X^k|k−1+Kεk.Step 11: Covariance matrix measurement updating(32)Pk=Pk|k−1−K⋅Pyy⋅KT.The above steps constitute the UKF. The AUKF contains an additional step to adjust the process noise covariance and measurement noise as follows.Step 12: Adaptive adjustment ofQ and RThe two noise covariance matrices are updated at each iteration using the following two equations in real time:(33)Qk=Qk|k−1+K⋅εk−1⋅K−1+Pk−∑i=02LWicX^i,k−Xk|k−1X^i,k−Xk|k−1T,Rk=Rk|k−1+εk−1+∑i=02LWicXi,k|k−1−X^k|k−1y^i,k|k−1−yk|k−1T.


## 3.1. Second-Order Equivalent Circuit Model

Much effort has gone into building battery models, such as the equivalent circuit model, the neural network model, and the electrochemical model. The equivalent circuit model can better respond to the relationship between battery parameters, reflect the dynamic performance of the battery, and facilitate the battery characteristics analysis and parameter identification [26, 29]. Here, we propose a second-order RC equivalent circuit model with hysteresis effects. The two RC networks shown in Figure 6 describe the effects of differential polarization and electrochemical polarization, respectively.Figure 6
Second-order RC equivalent circuit model.LetUoc(t) be the battery OCV. R0 denotes the ohmic internal resistance of the battery [12]. There are four parameters in the two RC networks. Re and Ce denote the electrochemical polarization internal resistance and capacitance of the battery, respectively. Rd and Cd denote the concentration polarization resistance and capacitance, respectively. I(t) is the dry circuit current, positive for discharging and negative for charging.According to KCL and Kirchhoff’s Voltage Law (KVL), the ohmic voltageU0(t), the electrochemical polarization voltage Ue(t), and the concentration polarization voltage Ud(t) can be calculated by(12)U0t=R0It,Uet=ReIt−CedUetdt,Udt=RdIt−CedUdtdt.respectively. And the battery terminal voltageU(t) is(13)Ut=UOCt+UOt+Uet+Udt.By the current integration method, we have(14)SOCt=SOC0−1QN∫0tηItdt.where SOC0 is the initial SOC, QN is the normal capacity of the battery, and η is the charging and discharging efficiency of the battery.The system state-space equations are discretized into(15)Uek=e−τ/τeUek−1+Re1−e−τ/τeIk−1,Udk=e−τ/τdUdk−1+Rd1−e−τ/τdIk−1,SOCk=SOCk−1−ητQNIk−1.where τ, τe and τd are the sampling periods satisfying(16)τe=Re⋅Ce,τd=Rd⋅Cd.Hence, the established discretized state-space equation of the battery system is as follows:(17)SOCkUekUdk=1000e−τ/τe000e−τ/τdSOCk−1Uek−1Udk−1+ητQNIRe1−e−τ/τeRd1−e−τ/τdIk−1+wk−1,where wk−1 is the model observation noise. The discretized state output voltage of the model is(18)Uk=UOCVk+UOk+Uek+UDk+υk−1,where vk−1 is the observation noise of terminal voltage.


## 3.2. SOC Estimation Based on AUKF

The key to the UKF is the unscented transform operation to transform the mean and covariance of the nonlinear system, avoiding linearization operations and retaining the high-order terms of the system. The UKF also improves the transmission accuracy of the system Gaussian density. Further, the AUKF iteratively corrects the system noise covariance and the observed noise covariance using maximum likelihood estimation and expectation maximization, resulting in better adaptability and better estimation results [30].For a nonlinear discrete-time system, the state equation and the measurement equation are as follows:(19)xk=fxk−1,uk−1+wk−1,yk=hxk,uk+vk,where xk is the system state vector, yk is the measurement vector, uk is the known input vector, wk is the process Gaussian noise, vk is the measurement noise Gaussian, and f(xk, uk) is a nonlinear measurement function. The AUKF for the battery SOC estimation is illustrated as follows:Step 1: Initialization and state extension(20)x^0=Ex0,P0=Ex0−x^0x0−x^0T,X^0=EX0=Ex^0,0,0,PX,0=EX0−X^0X0−X^0T,whereX^0 and PX,0 are the initial state estimate and error covariance matrix. The state vector Xk is defined as(21)Xk=SOCkUekUdkT.with the state variables SOC(k),Ue(k) and Ud(k).Step 2: 2L + 1 sampling (Sigma) points establishment(22)X0,k−1=Xk−1,i=0,Xi,k−1=Xk−1+L+λPX,k−1,i=1∼L,Xi,k−1=Xk−1+L+λPX,k−1,i=L+1∼2L.Step 3: The weight calculationThe calculation of the mean weight and covariance weight can be presented as(23)W0m=λn+λ,W0c=λn+λ+1−α2+β,Wim=Wic=λ2n+λ,i=1,2,…2L,whereλ=α2n+ς−n is a scale parameter to eliminate the total prediction error, α determines the distribution of sigma points around X^ and is usually a small positive value ranging from 1 to e−4, ς takes values of 0 to 3-n generally, β is used to integrate the X prior estimation and generally selected to be 2, and Wim and Wic are weighting factors to calculate the mean and covariance of the i-th sigma point, respectively.Step 4: State estimation time updating(24)X^i,k=fXi|k−1,uk−1,i=0,1,…2L,Xk|k−1=∑i=02LWimX^i,k−1.Step 5: Covariance matrix time updating(25)PX,k|k−1=∑i=02LWicX^i,k−Xk|k−1X^i,k−Xk|k−1T+Qk−1.whereQk is the covariance of the process Gaussian noise wk. Rk is the covariance of measurement noise Gaussian vk, without relationship between them.Step 6: New sigma points attainment at timek|k-1(26)X0,k|k−1=Xk|k−1,i=0,Xi,k|k−1=Xk|k−1+L+λPX,k|k−1,i=1∼L,Xi,k|k−1=Xk|k−1+L+λPX,k|k−1,i=L+1∼2L.Step 7: Measurement estimation(27)y^i,k|k−1=hXi,k|k−1,uk,yk|k−1=∑i=02LWimyi,k|k−1.Step 8: Kalman gain matrix(28)K=Pxy⋅≤Pyy−1,where(29)Pyy,k|k−1=∑i=02LWicy^i,k|k−1−yk|k−1y^i,k|k−1−yk|k−1T+Rk−1,Pxy,k|k−1=∑i=02LWicXi,k|k−1−X^k|k−1y^i,k|k−1−yk|k−1T.Step 9: Residual calculating(30)εk=yk−yk|k−1.Step 10: State estimation measurement updating(31)Xk=X^k|k−1+Kεk.Step 11: Covariance matrix measurement updating(32)Pk=Pk|k−1−K⋅Pyy⋅KT.The above steps constitute the UKF. The AUKF contains an additional step to adjust the process noise covariance and measurement noise as follows.Step 12: Adaptive adjustment ofQ and RThe two noise covariance matrices are updated at each iteration using the following two equations in real time:(33)Qk=Qk|k−1+K⋅εk−1⋅K−1+Pk−∑i=02LWicX^i,k−Xk|k−1X^i,k−Xk|k−1T,Rk=Rk|k−1+εk−1+∑i=02LWicXi,k|k−1−X^k|k−1y^i,k|k−1−yk|k−1T.


## 4. Equalization Control Algorithm

When discharged to a low SOC, the battery voltage decreases sharply [18, 31]. If the current is high, the battery may be damaged because of staying over-discharging for a long time. Likewise, when the battery is charged to a high SOC, its voltage increases significantly. When charged with a high current, the battery can be overcharged for a long time [32]. Besides, the polarization and ohmic effect are more significant if the battery ages severely, resulting in a more pronounced voltage drop at low SOC and voltage rise at high SOC [33–36]. Thus, adopting SOC as the single equalization criterion is not enough; this cannot prevent possible battery damage from overcharging and over-discharging [12, 37, 38].Figure7 is the SOC-OCV characteristic curve of the LIB. Assume that the interval [0.2, 0.8] denotes the SOC value between 0.2 and 0.8, which is considered as the plateau region. The intervals [0, 0.2] and [0.8, 1] are called non-platform interval where the SOC and OCV are approximately linear, and the terminal voltage can be measured online with a simple monitoring system. However, the OCV has little change in the plateau region. Thus, the terminal voltage and SOC are both chosen as the equalization parameters in this paper. The SOC-based equalization control algorithm is used when the SOC is in [0.2, 0.8], while the terminal-voltage-based equalization control algorithm is used when the SOC is below 0.2 or above 0.8. Unfortunately, there are various imbalance states; we cannot use the average SOC as an absolute benchmark for the SOC-based equalization algorithm. Figure 8 shows two battery packs in the imbalanced state. The average SOCs of both battery packs are between 0.2 and 0.8. However, in the battery pack shown in Figure 8(a), there is one cell with low SOC and others with high SOC that are at risk of overcharging. In the battery pack shown in Figure 8(b), there is one cell with high SOC and others with low SOC that needs to avoid over-discharging. Thus, this paper also proposes the SOC difference as another equalization parameter in the SOC-based equalization control algorithm. Similarly, the terminal-voltage-based equalization algorithm adopts the average and difference of terminal voltage between cells as equalization parameters. The specific implementation flow can be seen in Figure 9 where AFNN is an equalization control algorithm based on equalization parameters.Figure 7
OCV versus SOC characteristic of the experimental LIB cell.Figure 8
(a) Imbalanced SOC with one cell of low SOC and others of high SOC; (b) imbalanced SOC with one cell of high SOC and others of low SOC.
(a)(b)Figure 9
Flow chart of the equalization control strategy.The equalization strategy is developed on the basis of the equalization circuit to optimize the performance of the equalization circuit, so that the overall equalization performance can be maximized [39]. However, controlling the magnitude of the equalization current is a very complex nonlinear control problem. Model neural networks (NNs) can achieve nonlinear mapping with arbitrary accuracy. However, the NN requires a large amount of data to train. In this paper, an adaptive fuzzy neural network is used to control the value of the equalization current in the equalization process.The AFNN algorithm is combined with fuzzy logic control (FLC) and neural network to achieve high self-adaptability and good fault tolerance. The AFNN can adjust the membership function parameters as well as the weights between neurons [40]. In the paper, the AFNN is a first-order Takagi-Sugeno (T-S) fuzzy neural network based on the hybrid algorithm based on BP and least squares. It requires learning to determine five parameters including the antecedent and posterior parameters. The antecedent parameters of the network are obtained by BP algorithm, and the posterior parameters are identified by least squares, which greatly improves the learning efficiency. The AFNN is divided into five layers, including a fuzzy layer, a fuzzy rule intensity release layer, a rule strength normalization layer, a fuzzy rule output layer, and an output layer, as shown in Figure 10. The AFNN rules are obtained from the expert knowledge during equalization. The expert knowledge improves the reliability of the algorithm [41–43].Figure 10
Structure of the adaptive fuzzy neural network.Layer 1.
Fuzzy layer
There are two inputs to the fuzzy layer. For the SOC-based fuzzy neural network, the two inputs are △SOC and SOCavg, which can be expressed as(34)ΔSOC=∑i=1mSOCim−∑j=1nSOCjn,SOCavg=∑i=1mSOCi+∑j=1nSOCjm+n,where SOCi is the SOC of the i-th cell among the m cells on the left-hand side of the equalization unit, SOCj is the SOC of the j-th cell among the n cells on the right-hand side of the equalization unit, ∆SOC denotes the difference between the average SOC of the cells on the left-hand side of the equalization unit and the average SOC of the cells on the right-hand sides of the equalization unit, and SOCavg denotes the average SOCs of all cells in the equalization unit.
For the terminal-voltage-based fuzzy neural network, the two inputs are the terminal-voltage difference ∆V and the terminal-voltage average Vavg, which can be presented as follows:(35)ΔV=∑i=1mVim−∑j=1nVjjn,Vavg=∑i=1mVi+∑j=1nVjm+n,where the ∆V represents the difference between the average terminal voltage of the cells on the left-hand side of the equalization unit and the average terminal voltage of the cells on the right-hand side of the equalization unit, and Vavg is the average terminal voltage of all cells in the equalization unit.
Furthermore, the equalization loss [44] of the battery is(36)EL=∑i=1nEibefore−∑i−1nEiafter∑i=1nEibefore−E¯before=∑i=1nSOCibefore−∑i=1nSOCiafter∑i=1nSOCibefore−SOC¯before,where EL is the total energy consumption of the battery, Eibefore is the energy of the i-th battery cell before equalization, Eiafter denotes the energy of the i-th cell after equalization, and E¯ is the average energy of all battery cells.
The number of fuzzy sets of the input parameters determines the number of membership functions in the first layer. The theoretical domain of ∆SOC is 0–0.6, SOCavg is in 0–1, ∆V is in 0 to 1, and Vavg is in 2.6–4.2. In terms of the imbalanced state of the battery and characteristics, the theoretical domain of the inputs is divided into five fuzzy sets of very large (VL), large (L), medium (M), small (S), and very small (VS). A fuzzy rule base is developed through expert knowledge of the battery equalization control process and practical experience. Finally, the number of membership functions is obtained. The membership functions selected are all Gaussian functions, denoted as(37)μx=e−x−a/b2,where a is the center of the membership function, b is the width of the membership function, and a and b, as antecedent parameters of the fuzzy neural network, are obtained via database training and learning.
The input parameters, ∆SOC/∆V and SOCavg/Vavg, are defined as x1 and x2, respectively. The input and output of the first layer are(38)Oi1=μAix1,i=1,2,…5,Oj1=μBjx2,j=1,2,…5,where μAi(x1) is i-th membership function of input parameter x1, and μBj(x) is the j-th membership function of input parameter x2.Layer 2.
Fuzzy rule intensity release layer
The output value can be calculated by(39)Ok2=ωk=μAix1μBjx2,k=1,2,…25,where ωk represents the activation strength of one of the fuzzy rules.Layer 3.
Rule strength normalization layer
By calculating the weight of the activation strength for each fuzzy rule, the output of the layer is given by(40)Ok3=ωk¯=ωk∑k=125ωk.Layer 4.
Fuzzy rule output layer
The output of each fuzzy rule can be expressed as(41)Ok4=ωk¯fk=ωk¯pkx1+qkx2+rk,where pk, qk and rk are used as the posterior parameters of the fuzzy neural network and are obtained by training.Layer 5.
Output layer
The layer is used to calculate the output equalization current value by(42)Ieq=O5=∑k=125ωk¯.


## 5. Experimental Tests

Figure11, a photograph of the experimental setup and associated instruments, is built as the core of experimental test, and the designing of software and hardware is given.Figure 11
Photograph of the experimental setup and associated instruments.Subsection5.1 is done in simulation with estimating the parameters in the second-order RC model and assessing the proposed AUKF in estimating the SOC, using the EKF and CKF as benchmarks. Meanwhile, Subsections 5.2 and 5.3 are based on the hardware experimental platform, including a DC supply power, a host computer, an active equalization controller, six serial connected batteries, an equalization circuit board, and an oscilloscope. For the active equalization controller, the MOSFET switch array is used to generate a pair of PWM signal for the MOSFETs to control the equalization circuit [45, 46]. The oscilloscope shows the control waveform of the inductors, which can be seen specifically in Figure 5 sawtooth wave, completing the equalization monitoring and characterizing the process of energy transfer. The sensors receive the voltage and current information of the batteries and send them to the host computer. The host computer uses these collected data for SOC estimation, monitoring cell voltage and string temperature, and protecting the whole equalization system [47].


### 5.1. SOC Accuracy Validation

We aim to estimate five parameters in the second-order RC model, i.e.,Re, Ce, Rd, Cd, R0. They describe the dynamic behavior of the battery. First of all, we use a specific type of the LIB as the experimental object and analyze the Hybrid Pulse Power Characterization (HPPC) of the battery to obtain the pulse discharge current (as shown in Figure 12) and voltage data. The Parameter Estimation toolbox in MATLAB is then employed to estimate the five parameters. The estimation results conducted on a computer with Intel (R) Core (TM) i7-6700 CPU @ 3.40 GHz 3.41 GHz are shown in Figure 13. With these parameter estimates, a second-order RC equivalent model is built in MATLAB/Simscape.Figure 12
Dynamic stress test (DST) conditions.Figure 13
Model parameter estimation result.We next compare the AUKF algorithm, the EKF, and the CKF in terms of their accuracy in estimating the SOC. The current values in Figure12 are used as the inputs for the built equivalent circuit model. Figure 14(a) and Figure 14(b) present the error curves of the three methods. Table 1 summarizes the mean and standard variances of the errors generated by the three methods. We see that the estimation errors of both the EKF and CKF are larger than the estimation error of the AUKF. The AUKF converges faster, and the error tends to 8% in this condition. There is little doubt that the EKF is simple and suitable for nonlinear systems with a low degree; however, higher order terms of the EKF are ignored, and the filtering accuracy can be immensely reduced. The CKF has high filtering accuracy and good convergence, and yet some of the approximation errors are discarded when estimating the nonlinear system. When it comes down to it, however, the shortcomings of the CKF algorithm may make the filtering fail to meet the proposed consistency, and thus, the state truth cannot be estimated accurately. Sometimes there is also a problem of open-square failure, or even it is scattered when the degree of nonlinearity is high, or the initial error is large. With the advantages of UKF, no linearization error is introduced, and the accuracy can reach the second-order accuracy of Taylor series expansion without calculating Jacobi matrix. However, when the a priori noise statistical properties do not match the actual noise statistical properties, the state estimation performance of the UKF will be poor or even scattered. In the paper, the AUKF can adaptively adjust the process noise variance and measurement noise variance to reduce the model estimation error and suppress the filter divergence [48].Figure 14
(a) SOC estimation results based on AUKF, EKF, and CKF; (b) errors of AUKF, EKF, and CKF in estimating SOC.
(a)(b)Table 1
Summary statistics of the SOC estimation result of the three Kalman filter methods.
SOC estimation methodEKFCKFAUKFMean error0.011790.02378−0.002665Standard variance of the error0.0060760.011830.006611


### 5.2. Performance Evaluation of the Proposed MLDIEC

To analyze the performance of the proposed MLDIEC, we compare it with three other battery equalization circuits: CIEC, PAEC, and DIEC. A comparison between these circuits is carried out in the standing, charging, and discharging states of the battery. The equalization efficiency is measured by two metrics: equalization time and energy loss. The initial values of SOC are listed in Table2. The equalization loss of the battery pack is calculated by equation (38). It is significant to note that the energy losses during experiment will be smaller than that in the actual situation for several reasons. For example, line resistance is often neglected. However, this will not affect the magnitude order of energy loss of the four equalization circuits, and thus, the comparisons are still meaningful.Table 2
The initial SOCs of the six battery cells.
Battery cellB1B2B3B4B5B6Initial SOC (%)424344454647Tables3–5 present the equalization processes of the four equalization circuits in the three states, respectively. The horizontal coordinate is the equalization time, and the vertical one indicates the SOC. The CIEC has cumbersome energy transfer paths and unoptimized equalization units. Hence, its equalization time and energy losses are significantly higher than others. The DIEC adopts the dual parallel method that increases the equalization time by a factor of about one, while the energy can only be transferred between adjacent cells. The PAEC adds a high-level equalization unit to avoid the energy transfer disadvantage of the DIEC. As a result, the equalization time is shorter, and energy losses are lower. The proposed MLDIEC combines the advantages of the PAEC and DIEC. However, it should be noted that because the MLDIEC adopts the dual interleaved inductors that inevitably increase the energy loss from internal resistance of the battery, the energy loss of MLDIEC is slightly higher than that of PAEC. The equalization time and energy loss of the four equalization circuits under the same conditions are given in Figures 15 and 16, respectively. We see that the MLDIEC significantly reduces the energy loss and equalization time at the same time.Table 3
Equalization results of the four equalizing circuits in the standing state.Table 4
Equalization results of the four equalizing circuits in the charging state.Table 5
Equalization results of the four equalizing circuits in the discharging state.Figure 15
Comparisons of equalization time of the four equalization circuits.Figure 16
Comparisons of energy loss of the four equalization circuits.


### 5.3. Performance Evaluation of the Proposed MLDIEC

The network model in this paper is constructed in the fuzzy toolbox in MATLAB, and the network design is completed in three steps: training data import, generation of T-S fuzzy inference system, and learning algorithm selection and training. The generation of the T-S fuzzy inference system and the learning algorithm selection have been described in Section4. The training data in the network are obtained from the battery characterization and the variation of the battery parameters in the experiment. The values of the antecedent parameters in the network are determined, and the membership functions of the 2 input quantities (△SOC and SOCavg) are clarified, as shown in Figure 17. Table 6 shows the 25 groups of 75 identification parameters. The switching surface of the AFNN output corresponding to the input is shown in Figure 18.Figure 17
Membership function of the AFNN (a) SOCavg (b) △SOC.
(a)(b)Table 6
Output node.
Node[P Q R]Node[P Q R]O1[−0.2043, 4.592, 0.687]O14[−0.9794, 0.1179, 2.26]O2[4.73, 4.666, 0.7763]O15[−0.9656, 0.4559, 2.005]O3[−8.91, −0.3964, 1.976]O16[−0.7007, −1.053, 1.295]O4[−0.6012, 3.246, 1.021]O17[5.141, 6.515, −4.145]O5[0.4065, 1.661, 1.983]O18[−5.866, −2.445, 6.494]O6[-0.1581, 4.431, 0.7461]O19[0.6098, 1.579, 0.2385]O7[−0.2639, 1.239, 1.222]O20[0.536, 2.706, −0.2429]O8[−1.508, 6.958, 0.245]O21[−0.5077, 3.491, 0.8377]O9[−5.737, 0.6068, 3.128]O22[0.06906, −0.3967, 0.7745]O10[−4.146, 0.1816, 2.808]O23[0.173, 6.92, −1.074]O11[0.02749, 4.017, 0.6894]O24[−1.84, 0.1639, 3.056]O12[−0.9279, 3.133, 1.288]O25[−0.06897, −0.4748, 1.599]O13[0.1818, 5.581, −0.2427]Figure 18
Switching surface of the AFNN output corresponding to the input.To test and verify the proposed equalization algorithm—the AFNN—for battery equalization, a comparison is made with the mean-difference algorithm in the standing, charging, and discharging state, as shown in Table7. Note that, to emphasize the advantages of the AFNN for battery equalization, the differences of initial SOC between cells are set extremely large. We see that the AFNN improves the equalization times by 35.3%, 39.9%, and 37.1% compared with the mean-difference algorithm in the standing, charging, and discharging states, respectively. Meanwhile, the AFNN decreases the equalization energy losses by 4.9%, 4.4%, and 5.3% compared with the mean-difference algorithm in the standing, charging, and discharging states, respectively. The results of the two algorithms are summarized in Figure 19 to facilitate the comparison.Table 7
Equalization time comparison between mean-difference and AFNN algorithm in three states.
Mean-difference algorithmAFNN algorithmStandingChargingDischargingFigure 19
Equalization results based on mean-difference algorithm and AFNN algorithm in the three states.


## 5.1. SOC Accuracy Validation

We aim to estimate five parameters in the second-order RC model, i.e.,Re, Ce, Rd, Cd, R0. They describe the dynamic behavior of the battery. First of all, we use a specific type of the LIB as the experimental object and analyze the Hybrid Pulse Power Characterization (HPPC) of the battery to obtain the pulse discharge current (as shown in Figure 12) and voltage data. The Parameter Estimation toolbox in MATLAB is then employed to estimate the five parameters. The estimation results conducted on a computer with Intel (R) Core (TM) i7-6700 CPU @ 3.40 GHz 3.41 GHz are shown in Figure 13. With these parameter estimates, a second-order RC equivalent model is built in MATLAB/Simscape.Figure 12
Dynamic stress test (DST) conditions.Figure 13
Model parameter estimation result.We next compare the AUKF algorithm, the EKF, and the CKF in terms of their accuracy in estimating the SOC. The current values in Figure12 are used as the inputs for the built equivalent circuit model. Figure 14(a) and Figure 14(b) present the error curves of the three methods. Table 1 summarizes the mean and standard variances of the errors generated by the three methods. We see that the estimation errors of both the EKF and CKF are larger than the estimation error of the AUKF. The AUKF converges faster, and the error tends to 8% in this condition. There is little doubt that the EKF is simple and suitable for nonlinear systems with a low degree; however, higher order terms of the EKF are ignored, and the filtering accuracy can be immensely reduced. The CKF has high filtering accuracy and good convergence, and yet some of the approximation errors are discarded when estimating the nonlinear system. When it comes down to it, however, the shortcomings of the CKF algorithm may make the filtering fail to meet the proposed consistency, and thus, the state truth cannot be estimated accurately. Sometimes there is also a problem of open-square failure, or even it is scattered when the degree of nonlinearity is high, or the initial error is large. With the advantages of UKF, no linearization error is introduced, and the accuracy can reach the second-order accuracy of Taylor series expansion without calculating Jacobi matrix. However, when the a priori noise statistical properties do not match the actual noise statistical properties, the state estimation performance of the UKF will be poor or even scattered. In the paper, the AUKF can adaptively adjust the process noise variance and measurement noise variance to reduce the model estimation error and suppress the filter divergence [48].Figure 14
(a) SOC estimation results based on AUKF, EKF, and CKF; (b) errors of AUKF, EKF, and CKF in estimating SOC.
(a)(b)Table 1
Summary statistics of the SOC estimation result of the three Kalman filter methods.
SOC estimation methodEKFCKFAUKFMean error0.011790.02378−0.002665Standard variance of the error0.0060760.011830.006611


## 5.2. Performance Evaluation of the Proposed MLDIEC

To analyze the performance of the proposed MLDIEC, we compare it with three other battery equalization circuits: CIEC, PAEC, and DIEC. A comparison between these circuits is carried out in the standing, charging, and discharging states of the battery. The equalization efficiency is measured by two metrics: equalization time and energy loss. The initial values of SOC are listed in Table2. The equalization loss of the battery pack is calculated by equation (38). It is significant to note that the energy losses during experiment will be smaller than that in the actual situation for several reasons. For example, line resistance is often neglected. However, this will not affect the magnitude order of energy loss of the four equalization circuits, and thus, the comparisons are still meaningful.Table 2
The initial SOCs of the six battery cells.
Battery cellB1B2B3B4B5B6Initial SOC (%)424344454647Tables3–5 present the equalization processes of the four equalization circuits in the three states, respectively. The horizontal coordinate is the equalization time, and the vertical one indicates the SOC. The CIEC has cumbersome energy transfer paths and unoptimized equalization units. Hence, its equalization time and energy losses are significantly higher than others. The DIEC adopts the dual parallel method that increases the equalization time by a factor of about one, while the energy can only be transferred between adjacent cells. The PAEC adds a high-level equalization unit to avoid the energy transfer disadvantage of the DIEC. As a result, the equalization time is shorter, and energy losses are lower. The proposed MLDIEC combines the advantages of the PAEC and DIEC. However, it should be noted that because the MLDIEC adopts the dual interleaved inductors that inevitably increase the energy loss from internal resistance of the battery, the energy loss of MLDIEC is slightly higher than that of PAEC. The equalization time and energy loss of the four equalization circuits under the same conditions are given in Figures 15 and 16, respectively. We see that the MLDIEC significantly reduces the energy loss and equalization time at the same time.Table 3
Equalization results of the four equalizing circuits in the standing state.Table 4
Equalization results of the four equalizing circuits in the charging state.Table 5
Equalization results of the four equalizing circuits in the discharging state.Figure 15
Comparisons of equalization time of the four equalization circuits.Figure 16
Comparisons of energy loss of the four equalization circuits.


## 5.3. Performance Evaluation of the Proposed MLDIEC

The network model in this paper is constructed in the fuzzy toolbox in MATLAB, and the network design is completed in three steps: training data import, generation of T-S fuzzy inference system, and learning algorithm selection and training. The generation of the T-S fuzzy inference system and the learning algorithm selection have been described in Section4. The training data in the network are obtained from the battery characterization and the variation of the battery parameters in the experiment. The values of the antecedent parameters in the network are determined, and the membership functions of the 2 input quantities (△SOC and SOCavg) are clarified, as shown in Figure 17. Table 6 shows the 25 groups of 75 identification parameters. The switching surface of the AFNN output corresponding to the input is shown in Figure 18.Figure 17
Membership function of the AFNN (a) SOCavg (b) △SOC.
(a)(b)Table 6
Output node.
Node[P Q R]Node[P Q R]O1[−0.2043, 4.592, 0.687]O14[−0.9794, 0.1179, 2.26]O2[4.73, 4.666, 0.7763]O15[−0.9656, 0.4559, 2.005]O3[−8.91, −0.3964, 1.976]O16[−0.7007, −1.053, 1.295]O4[−0.6012, 3.246, 1.021]O17[5.141, 6.515, −4.145]O5[0.4065, 1.661, 1.983]O18[−5.866, −2.445, 6.494]O6[-0.1581, 4.431, 0.7461]O19[0.6098, 1.579, 0.2385]O7[−0.2639, 1.239, 1.222]O20[0.536, 2.706, −0.2429]O8[−1.508, 6.958, 0.245]O21[−0.5077, 3.491, 0.8377]O9[−5.737, 0.6068, 3.128]O22[0.06906, −0.3967, 0.7745]O10[−4.146, 0.1816, 2.808]O23[0.173, 6.92, −1.074]O11[0.02749, 4.017, 0.6894]O24[−1.84, 0.1639, 3.056]O12[−0.9279, 3.133, 1.288]O25[−0.06897, −0.4748, 1.599]O13[0.1818, 5.581, −0.2427]Figure 18
Switching surface of the AFNN output corresponding to the input.To test and verify the proposed equalization algorithm—the AFNN—for battery equalization, a comparison is made with the mean-difference algorithm in the standing, charging, and discharging state, as shown in Table7. Note that, to emphasize the advantages of the AFNN for battery equalization, the differences of initial SOC between cells are set extremely large. We see that the AFNN improves the equalization times by 35.3%, 39.9%, and 37.1% compared with the mean-difference algorithm in the standing, charging, and discharging states, respectively. Meanwhile, the AFNN decreases the equalization energy losses by 4.9%, 4.4%, and 5.3% compared with the mean-difference algorithm in the standing, charging, and discharging states, respectively. The results of the two algorithms are summarized in Figure 19 to facilitate the comparison.Table 7
Equalization time comparison between mean-difference and AFNN algorithm in three states.
Mean-difference algorithmAFNN algorithmStandingChargingDischargingFigure 19
Equalization results based on mean-difference algorithm and AFNN algorithm in the three states.


## 6. Conclusion

This paper presents an AFNN-based multideck dual interleaved inductor active equalization circuit to reconcile the inconsistency of series-connected LIBs. The circuit provides an optimal path and energy transfer scheme between two nonadjacent cells by a high-level equalization unit. Dual inductors replace the single inductor in the equalization unit, allowing a cell to operate twice in one equalization cycle and avoiding the battery to be idle for a long time. Comparisons with other three equalization circuits show that the proposed equalization structure can greatly accelerate the equalization speed and reduce the equalization loss. The SOC and terminal voltage are chosen as the equalization criterion in different intervals of the SOC-OCV characteristic curve of LIBs, and the AUKF is used for SOC estimation. The AFNN algorithm is employed for effective equalization. Experimental results show that the AFNN algorithm increases the equalization efficiency by about 4.89% and saves the equalization time by about 37.4% compared with the mean-difference algorithm under the same operating conditions. In the future, the battery pack model will be further developed and widely used with more accurate SOC estimation values and less computational burden.



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*Source: 8653547-2022-03-20.xml*