an active and passive hybrid battery equalization strategy

electronics

Article

An Active and Passive Hybrid Battery EqualizationStrategy Used in Group and between Groups

Mingyu Gao 1,2, Jifeng Qu 1,2, Hao Lan 1,2, Qixing Wu 1,2,3, Huipin Lin 1,2,*, Zhekang Dong 1,2

and Weizhong Zhang 3

1 College of Electronic Information, Hangzhou Dianzi University, Hangzhou 310018, China;[email protected] (M.G.); [email protected] (J.Q.); [email protected] (H.L.);[email protected] (Q.W.); [email protected] (Z.D.)

2 Zhejiang Provincial Key Lab of Equipment Electronics, Hangzhou Dianzi University, Hangzhou 310018, China3 Faculty of Automation, Zhejiang Institute of Mechanical and Electrical Engineering,

Hangzhou 310018, Zhejiang, China; [email protected]* Correspondence: [email protected]

Received: 2 September 2020; Accepted: 19 October 2020; Published: 21 October 2020

Abstract: Active battery equalization and passive battery equalization are two important methodswhich can solve the inconsistency of battery cells in lithium battery groups. In this paper, a newhybrid battery equalization strategy combinfigureing the active equalizing method with a passiveequalizing method is proposed. Among them, the implementation of the active equalizing methoduses the bidirectional Flyback converter and Forward converter. This hybrid equalizing strategyadopts the concept of hierarchical equilibrium: it can be divided into two layers, the top layer is theequalization between groups, and the bottom layer is the equalization of group. There are three activeequilibrium strategies and one passive equilibrium strategy. For verification purposes, a series ofexperiments were conducted in MATLAB 2018b/Simulink platform. The simulation and experimentresults show that this hybrid battery equalizing method is efficient and feasible.

Keywords: hybrid battery equalization; Li-ion battery; passive equalization; active equalization;bidirectional flyback converter; bidirectional forward converter

1. Introduction

The advantages of a lithium-ion battery are its high-energy density, low self-discharge rate, cyclingdurability, and wide temperature range [1]. Due to its excellent performance, lithium-ion battery hasbecome the best choice for electric vehicles and other energy storage systems. Due to the differences inthe manufacturing and operating environment, inconsistency between the different batteries in thesame battery group is existed [2]. The inconsistency brings about a loss of capacity of the battery group,and it eventually leads to shorter battery life. A statistic shows that the capacity difference in differentbatteries of the same model can reach 20% [3], bcause the capacity loss of one battery group can reach40%. As time goes on, the inconsistency of batteries will increase. Battery equalizing is an effective wayto reduce the battery decay rate in battery management systems (BMSs). Battery equalizing mainlyfocuses on the investigation of equalization topology and control algorithms [4–6].

The battery equalizing technology plays a vital role in the performance improvement for lithium-ionbatteries. Nowadays, there are two main battery-balancing methods: passive equalizing and activeequalizing [7–10]. The passive equalizing method is that the energy of higher-power batteries isdissipated by one simple resistive circuit, and the energy is wasted in passive equalizing [11–14]. Activeequalizing mainly realizes the non-dissipative transfer of energy in the battery group through energystorage components. The main active equalization methods are shown in Figure 1 [1]. In traditional

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active equalization, the topology usually adopts a single equalization method. One active equalizingmethod that one cell transfers energy to adjacent cells step by step, thus the equalizing speed is veryslow. Another active equalizing method is that the energy is transferred between the battery cell and thebattery group [15–18]. However, it has a disadvantage of repeated energy transfer. All of these activeequalizing methods have significant limitations in their equalization speed and equalization efficiency.The equalization topology regularly adopts the Flyback converter or the Forward converter [19].In these two topologies, a large amount of MOSFETs swiches are turned on or off at the same time,which may increase cost and reduce reliability. It is evident that using a single active or passiveequalizing topology cannot meet actual needs [20,21]. For these reasons, a hybrid equalization topologyis proposed in this paper. By combining multi-layer active equalization with passive equalization,the energy equalization of the battery group can be realized in different situations. The paper mainlyincludes the principle of the hybrid equalization topology, equalization efficiency analysis/calculation,experimental verification and conclusion [22].

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through energy storage components. The main active equalization methods are shown in Figure 1 [1]. In traditional active equalization, the topology usually adopts a single equalization method. One active equalizing method that one cell transfers energy to adjacent cells step by step, thus the equalizing speed is very slow. Another active equalizing method is that the energy is transferred between the battery cell and the battery group [15–18]. However, it has a disadvantage of repeated energy transfer. All of these active equalizing methods have significant limitations in their equalization speed and equalization efficiency. The equalization topology regularly adopts the Flyback converter or the Forward converter [19]. In these two topologies, a large amount of MOSFETs swiches are turned on or off at the same time, which may increase cost and reduce reliability. It is evident that using a single active or passive equalizing topology cannot meet actual needs [20,21]. For these reasons, a hybrid equalization topology is proposed in this paper. By combining multi-layer active equalization with passive equalization, the energy equalization of the battery group can be realized in different situations. The paper mainly includes the principle of the hybrid equalization topology, equalization efficiency analysis/calculation, experimental verification and conclusion [22]

Active equalization methods

Cell to cell Cell to pack Pack to cell

Adjacent cell to cell

Direct cell to

cell

Cell to the

whole battery

pack

Cell to some of

the battery

pack

The whole battery pack to

cell

Some of the

battery pack to

cell

Pack to pack

Figure 1. Classification of active equalization methods.

Figure 2 shows the system architecture of the proposed battery equalization topology. The topology contains the bidirectional forward and bidirectional flyback converters. The structure can be divided into two layers, the top layer is the between-group equalization, and the bottom layer is the in-group equalization. There are m × n battery cells in the system, each n cells forming one battery group, with m groups in total. So, the sub-circuits between the battery groups constitute the between-group equalization system, and the sub-circuits internal to the battery group form the between-group equalization system.

The in-group equalization system is composed of active and passive equalization. The active equalization sub-circuit consists of two reverse-series MOSFETs, a winding of the transformer, an auxiliary MOSFET, and a capacitor. The equalization sub-circuits of different batteries are connected by a multi-winding transformer. The turns ratio of the transformer is 1:1:1:1. The MOSFET interconnected to the battery can replace the diode of the traditional Flyback converter or the Forward converter. In addition, the conduction loss of the MOSFET is much less than that of the diode in the traditional converter topology. The passive equalization sub-circuit of each battery includes a MOSFET and a dissipative resistor. The energy of the higher-capacity cell can be released through the dissipative resistor by changing the switching states of the MOSFET.

The between-group equalization is adopted on the bi-drectional Flyback converter. Each battery group in this layer can charge to any battery cell with higher voltage and larger capacity, and the Flyback converter and the battery group are connected one to one. The primary side of the equalizer is the corresponding battery group, and the secondary side is the entire power supply system. The between-group equalization can realize bidirectional energy flow between the battery group and the entire power supply system.

This topology is a double-layer hybrid topology. It adopts an equalization strategy which combines active and passive balancing to improve the balancing efficiency. In addition, because of

Figure 1. Classification of active equalization methods.

Figure 2 shows the system architecture of the proposed battery equalization topology. The topologycontains the bidirectional forward and bidirectional flyback converters. The structure can be dividedinto two layers, the top layer is the between-group equalization, and the bottom layer is the in-groupequalization. There are m × n battery cells in the system, each n cells forming one battery group,with m groups in total. So, the sub-circuits between the battery groups constitute the between-groupequalization system, and the sub-circuits internal to the battery group form the between-groupequalization system.

The in-group equalization system is composed of active and passive equalization. The activeequalization sub-circuit consists of two reverse-series MOSFETs, a winding of the transformer,an auxiliary MOSFET, and a capacitor. The equalization sub-circuits of different batteries areconnected by a multi-winding transformer. The turns ratio of the transformer is 1:1:1:1. The MOSFETinterconnected to the battery can replace the diode of the traditional Flyback converter or the Forwardconverter. In addition, the conduction loss of the MOSFET is much less than that of the diode in thetraditional converter topology. The passive equalization sub-circuit of each battery includes a MOSFETand a dissipative resistor. The energy of the higher-capacity cell can be released through the dissipativeresistor by changing the switching states of the MOSFET.

The between-group equalization is adopted on the bi-drectional Flyback converter. Each batterygroup in this layer can charge to any battery cell with higher voltage and larger capacity, and theFlyback converter and the battery group are connected one to one. The primary side of the equalizeris the corresponding battery group, and the secondary side is the entire power supply system.The between-group equalization can realize bidirectional energy flow between the battery group andthe entire power supply system.

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the double-layer design, it can be used in scenarios where the number of cells is large, and different layers can be balanced at the same time, which significantly reduces the time required for equalization. The bidirectional flyback converter can complete the energy equalization at a higher power level. The active equalization sub-circuit in each group can flexibly realize the energy exchange between cells. Besides, it is supplemented by a passive equalization circuit. The passive equalization method was used as when the voltage difference between battery cells is small, it can accelerate equalization. Specifically, there are four equalization modes (containing three in-group equalization modes and one between-group equalization circuit mode). The corresponding mode description is introduced below.

B12

B11

B1(n-1)

B1nQ111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

B1k Q1k1 Q1k2Q1k3

L1k B1(k+1)

Q1(k+1)1 Q1(k+1)2

Q1(k+1)3L1(k+1)

L2(k+1)

Bm2

Bm1

Bmk

Q1(n-1)1 Q1(n-1)2

R(n-1)1

Q1(n-1)3L1(n-1)

Q1n1 Q1n2

R1n

Q1n3L1n

B22

B21

B2(n-1)

B2nQ211 Q212

Q221 Q222

Q213

Q223

L21

L22

B2k Q2k1 Q2k2

Q2k3

L2k B2(k+1)

Q2(k+1)1 Q2(k+1)2

R2(k+1)

Q2(k+1)3

Q2(n-1)1 Q2(n-1)2

R2(n-1)

Q2(n-1)3

Q2n1 Q2n2

R2n

Q2n3L2n

L2(n-1)

L3(n-1)

L3(k+1)

B3(n-1)

B3nQ311 Q312

Q321 Q322

Q313

Q323

L31

L32

Q3k1 Q3k2

Q3k3

L3k B3(k+1)

Q3(k+1)1 Q3(k+1)2

R3(k+1)

Q3(k+1)3

Q3(n-1)1 Q3(n-1)2

R3(n-1)

Q3(n-1)3

Q3n1 Q3n2

R3n

Q3n3L3n

B32

B31

B3k

Lm(k+1)

Bm(n-1)

BmnQm11 Qm12

Qm21 Qm22

Qm13

Qm23

Lm1

Lm2

Qmk1 Qmk2Qmk3

Lmk Bm(k+1)

Qm(k+1)1 Qm(k+1)2

Rm(k+1)

Qm(k+1)3

Qm(n-1)1 Qm(n-1)2

Rm(n-1)

Qm(n-1)3

Qmn1 Qmn2

Rmn

Qmn3Lmn

Q11 Q12 Q13 Q14L1

L2

Q21 Q22 Q23 Q24L3

L4

Q31 Q32 Q43 Q44L5

L6

Qm1 Qm2 Qm3 Qm4L2m-1

L2m

R11

Rm2

Rm1

Rmk

R3k

R32

R31

R1k

R21

R12

R2k

R(k+1)1

G2

G3

Gm

G1

Figure 2. Overall battery equalization circuit topology. Figure 2. Overall battery equalization circuit topology.

This topology is a double-layer hybrid topology. It adopts an equalization strategy whichcombines active and passive balancing to improve the balancing efficiency. In addition, because ofthe double-layer design, it can be used in scenarios where the number of cells is large, and differentlayers can be balanced at the same time, which significantly reduces the time required for equalization.The bidirectional flyback converter can complete the energy equalization at a higher power level.The active equalization sub-circuit in each group can flexibly realize the energy exchange betweencells. Besides, it is supplemented by a passive equalization circuit. The passive equalization method

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was used as when the voltage difference between battery cells is small, it can accelerate equalization.Specifically, there are four equalization modes (containing three in-group equalization modes and onebetween-group equalization circuit mode). The corresponding mode description is introduced below.

In the schematic diagram of in-group equalization in each group, taking four cells as an example,the cells are divided into two sides, B11 and B12 are on the left side, and B13 and B14 are on theright side. According to the position where the target battery and the source battery are located,the battery balancing topology proposed in this paper contains three in-group balancing modes andone between-group balancing mode.

1.1. MODE 1: In-Group Flyback Mode

If the target battery and the source battery are on different sides of the battery group, the energy istransferred between the batteries by the Flyback operation. Assuming that B11 is the source battery andB13 is the target battery, at time t1, Q111 and Q112 are turned on, Q113 and all other MOSFETs are turnedoff. The energy is transferred from battery B11 to transformer L11 for storage. In [t1, t2], the dischargecurrent is calculated as Equation (1), and the current flow direction is shown in Figure 3a. At time t2,Q111, Q112 and Q113 are turned off; Q131 and Q132 are turned on. Most of the energy in L11 is releasedto the Battery B13. At this time, the current flowing through the inductor L13 is located and can becalculated according to the superposition theorem, in Equation (3), iB13(t2) represents the initial valueof the current at time t2, the relationship between iB13(t2) and the current value iB11(t2) of the primarywinding at time t2 is shown in Equation (2). The voltage across the winding L13 is clamped to voltageVB13 by the battery cell, so iB13(t) gradually decreases with time, Equation (3) expresses this decayprocess. Due to the leakage inductance of L11, the current cannot be entirely transferred to the otherside when Q111 and Q112 are turned off. At the time of [t2, t3], the charge current of B13 is calculated asEquation (3). Eventually, the energy is transferred from B11 to B12. The MOSFET switching state of thewhole process is shown in Figure 4a:

iB11(t) =VB11

L11(t− t1) (1)

iB13(t2) = iB11(t2) (2)

iB13(t) = iB13(t2) −VB13

L13(t− t2) (3)


In the schematic diagram of in-group equalization in each group, taking four cells as an example, the cells are divided into two sides, B11 and B12 are on the left side, and B13 and B14 are on the right side. According to the position where the target battery and the source battery are located, the battery balancing topology proposed in this paper contains three in-group balancing modes and one between-group balancing mode.

1.1. MODE 1: In-Group Flyback Mode

If the target battery and the source battery are on different sides of the battery group, the energy is transferred between the batteries by the Flyback operation. Assuming that B11 is the source battery and B13 is the target battery, at time t1, Q111 and Q112 are turned on, Q113 and all other MOSFETs are turned off. The energy is transferred from battery B11 to transformer L11 for storage. In [t1, t2], the discharge current is calculated as Equation (1), and the current flow direction is shown in Figure 3a. At time t2, Q111, Q112 and Q113 are turned off; Q131 and Q132 are turned on. Most of the energy in L11 is released to the Battery B13. At this time, the current flowing through the inductor L13 is located and can be calculated according to the superposition theorem, in Equation (3), 213 ( )Bi t represents the

initial value of the current at time 2t , the relationship between 213 ( )Bi t and the current value 211( )Bi t

of the primary winding at time 2t is shown in Equation (2). The voltage across the winding 13L is

clamped to voltage 13BV by the battery cell, so 13( )Bi t gradually decreases with time, Equation (3) expresses this decay process. Due to the leakage inductance of L11, the current cannot be entirely transferred to the other side when Q111 and Q112 are turned off. At the time of [t2, t3], the charge current of B13 is calculated as Equation (3). Eventually, the energy is transferred from B11 to B12. The MOSFET switching state of the whole process is shown in Figure 4a:

( ) ( )= −11

11 111

BB

Vi t t t

L (1)

( ) ( )=13 112 2B Bi t i t (2)

( ) ( ) ( )= − −13

13 13 2 213

BB B

Vi t i t t t

L (3)

B12

B11

B13

B14Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R31

Q133L13

Q141 Q142

R41

Q143L14

R21

B12

B11

B13

B14Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R31

Q133L13

Q141 Q142

R41

Q143L14

R21

(a) (b)

B12

B11

B13

B14Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R31

Q133L13

Q141 Q142

R41

Q143L14

R21

(c)

Figure 3. Three in-group-pack equalization circuit modes: (a) MODE 1; (b) MODE 2; and (c) MODE 3.

Figure 3. Three in-group-pack equalization circuit modes: (a) MODE 1; (b) MODE 2; and (c) MODE 3.

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Q111

Q112

Q113

Q131

Q132

t1 t2 t3

Q111

Q112

Q113

Q121

Q122

t1 t2 t3 (a) (b)

Figure 4. Control signal: (a) MODE 1; and (b) MODE 2.

1.2. MODE 2: In-Group Forward Mode

If the target battery and the source battery are on the same side and the voltage difference is larger than 150 mV, the energy is transferred between batteries by the forward operation. We assumed that B11 is the source cell and B12 is the target cell. At time t1, Q111, Q112, Q121, and Q122 are all turned on, and the energy of the cell B11 is directly transmitted to B12 through the transformer. At time [t1, t2], the current is calculated as Equation (4), and the current flow direction is shown in Figure 3b. At the time t2, the switches Q111, Q112, Q121, and Q122 are turned off, the energy transfer is finished. In the [t1, t2], the maximum current value can be calculated as Equation (4). The R represents the equivalent impedance of the entire loop:

−= 11 12B B

loop

V VI

R (4)

Finally, the energy transformation from the source battery to the target battery is realized, and the MOSFET control signal for the entire process is shown in Figure 4b.

1.3. MODE 3: In-Group Passive Balancing Mode

If the target battery and the source battery are in the same group, and the batteries do not satisfy the condition that the voltage difference is large enough, active equalization is not suitable. In this case, the topology adopts the passive equalization, which is very suitable for the equalization with the batteries with small inconsistencies. Take B11 as an example: Q113 is turned on and other MOSFETs are turned off. As shown in Figure 3c. At this time, the on-resistance of the MOSFET is ignored, and the current can be calculated according to (4). The passive equalization of other battery cells is the same as the above process. Eventually, the excess energy is dissipated in the form of heat:

( ) BB

Vi t =

R11

1111

(5)

1.4. MODE 4: Between-Group Bidirectional Flyback Mode

If there is a difference between the battery groups, the topology adopts a between-group mode. The triggering condition of the mode is the maximum voltage difference larger than 80 mV. The bidirectional flyback active balancing circuit transfers energy from the higher-power battery group to the entire power supply system by controlling the switch of the MOSFET, or vice versa. This paper uses the balancing between two battery groups as an example to explain the working principle of the between-group balancing. As shown in Figure 5a, assuming that the battery group where B11 is in higher energy state, the battery group where B11 is located serves as the primary side of the Flyback transformer, and the power supply system serves as the secondary side of the Flyback converter. Q13, Q14, and Q11, Q12 are turned on or off by complementary pulse-width modulation (PWM) driving

Figure 4. Control signal: (a) MODE 1; and (b) MODE 2.

1.2. MODE 2: In-Group Forward Mode

If the target battery and the source battery are on the same side and the voltage difference is largerthan 150 mV, the energy is transferred between batteries by the forward operation. We assumed thatB11 is the source cell and B12 is the target cell. At time t1, Q111, Q112, Q121, and Q122 are all turned on,and the energy of the cell B11 is directly transmitted to B12 through the transformer. At time [t1, t2],the current is calculated as Equation (4), and the current flow direction is shown in Figure 3b. At thetime t2, the switches Q111, Q112, Q121, and Q122 are turned off, the energy transfer is finished. In the [t1,t2], the maximum current value can be calculated as Equation (4). The R represents the equivalentimpedance of the entire loop:

Iloop =VB11 −VB12

R(4)

Finally, the energy transformation from the source battery to the target battery is realized, and theMOSFET control signal for the entire process is shown in Figure 4b.

1.3. MODE 3: In-Group Passive Balancing Mode

If the target battery and the source battery are in the same group, and the batteries do not satisfythe condition that the voltage difference is large enough, active equalization is not suitable. In thiscase, the topology adopts the passive equalization, which is very suitable for the equalization with thebatteries with small inconsistencies. Take B11 as an example: Q113 is turned on and other MOSFETs areturned off. As shown in Figure 3c. At this time, the on-resistance of the MOSFET is ignored, and thecurrent can be calculated according to (4). The passive equalization of other battery cells is the same asthe above process. Eventually, the excess energy is dissipated in the form of heat:

iB11(t) =VB11

R11(5)

1.4. MODE 4: Between-Group Bidirectional Flyback Mode

If there is a difference between the battery groups, the topology adopts a between-groupmode. The triggering condition of the mode is the maximum voltage difference larger than 80 mV.The bidirectional flyback active balancing circuit transfers energy from the higher-power battery groupto the entire power supply system by controlling the switch of the MOSFET, or vice versa. This paperuses the balancing between two battery groups as an example to explain the working principle of thebetween-group balancing. As shown in Figure 5a, assuming that the battery group where B11 is inhigher energy state, the battery group where B11 is located serves as the primary side of the Flybacktransformer, and the power supply system serves as the secondary side of the Flyback converter.Q13, Q14, and Q11, Q12 are turned on or off by complementary pulse-width modulation (PWM) drivingsignals, respectively. At this time, the battery group charges the whole power supply system throughthe flyback converter. The current flow is shown in Figure 5a: the converter works in DCM mode,

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the duty cycle is set to 45%, and according to the transformer transformation ratio it is 1:m, with mbeing number of bottom groups, where m = 2 when Q13 and Q14 are turned on, battery pack G1 chargeswinding L2, Vg1 is the voltage value of G1. The peak value of the primary charging current Ipri_pk iscalculated according to Equation (6). Then, the average current value Ipri_aver is obtained by Equation (7).After that, Q13 and Q14 are turned off, and Q11 and Q12 are turned on. At this time, the secondarywinding discharges to the entire top layer group, and the initial value of the secondary current is itspeak value. Its value is represented by Equation (8), and the average value of the secondary windingcurrent is represented by Equation (9):

Ipri_pk =Vg1Ton

L2(6)

Lpri_aver =12

TonIpri_pk =Vg1T2

on

2L2(7)

Isec_pk =12

Ipri_pk (8)

Isec_aver =12

To f f Isec_pk =12

To f f ∗12

Ipri_pk =Vg1TonTo f f

4L2(9)Electronics 2020, 9, x FOR PEER REVIEW 7 of 23

B12

B11 Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R13

Q133L13

Q141 Q142

R14

Q143L14

R12

B22

B21 Q211 Q212

Q221 Q222

R21

Q213

Q223

L21

L22

Q231 Q232

R23

Q233L23

Q241 Q242

R24

Q243L24

R22

Q11 Q12 Q13 Q14L1

L2

B23

B24

B13

B14

Q21 Q22 Q23 Q24L3

L4

G1

G2

(a)

B12

B11 Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R13

Q133L13

Q141 Q142

R14

Q143L14

R12

B22

B21 Q211 Q212

Q221 Q222

R21

Q213

Q223

L21

L22

Q231 Q232

R23

Q233L23

Q241 Q242

R24

Q243L24

R22

Q11 Q12 Q13 Q14L1

L2

B23

B24

B13

B14

Q21 Q22 Q23 Q24L3

L4

G1

G2

(b)

Figure 5. Schematic diagram of the bidirectional flyback converter in inter-pack, (a) Energy transfers from the group G1 to the top layer group, (b) Energy transfers from the top layer group to group G1.

2. Performance Evaluation

In order to evaluate the balancing performance of the proposed topology, we compared the proposed topology and the adjacent batteries balancing topology (as shown in Figure 6) [17] (position). In the rest of this section, we specifically analyze the equalization efficiency. We assume that there are n cells in the battery group, and the equalization efficiency of each sub-equalizer is 𝜂.

B12

B11

B14

B13

B22

B21

B24

B23

Figure 6. The adjacent batteries’ balancing topology.

Figure 5. Schematic diagram of the bidirectional flyback converter in inter-pack, (a) Energy transfersfrom the group G1 to the top layer group, (b) Energy transfers from the top layer group to group G1.

In another case, when the energy of the battery group in the entire power supply system is lowerthan the average level, by controlling the corresponding MOSFET to be turned on and off, the energyof the entire power supply system can be transferred to the lower power battery group. Assuming thatthe power level of B11 at this time is lower than the average level, the bidirectional flyback converter isconfigured as a buck converter to charge it. At this time, L1 in Figure 5a is the primary-side transformerwinding, and (Q13,Q14), (Q11,Q12) are turned on or off by the complementary PWM drive, respectively.The whole power supply sysem is charged to the battery group with a lower energy level, and the

Electronics 2020, 9, 1744 7 of 21

current flow is shown in Figure 5b, that when Q11 and Q12 are turned on, L1 is charged, Vtotal is thevoltage of the top battery group, and its expression is Equation (11). At this time, the top group sideis the primary side of the transformer, the peak charging current of the primary side is calculatedaccording to Equation (12). Then, the average current value is obtained by Equation (13). After Q11,Q12 are turned off, Q13, Q14 are turned on, the secondary winding discharges to the battery groupG1. The initial value of the secondary current at this time is the peak value, which is expressed byEquation (14), and the average current value is expressed by Equation (15).

Ipri_pk =VtotalTon

L1(10)

Vtotal = Vg1 + Vg2 (11)

Ipri_pk =(Vg1 + Vg2)Ton

L1(12)

Ipri_aver =12

TonIpri_pk = (Vg1+Vg2

2L1)T2

on (13)

Isec_pk = 2Ipri_pk (14)

Isec_aver =12

To f f Isec_pk =VtotalTo f f Ton

L1= (

Vg1+Vg2

L1)To f f Ton (15)


In order to evaluate the balancing performance of the proposed topology, we compared theproposed topology and the adjacent batteries balancing topology (as shown in Figure 6) [17] (position).In the rest of this section, we specifically analyze the equalization efficiency. We assume that there aren cells in the battery group, and the equalization efficiency of each sub-equalizer is η.


B12

B11 Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R13

Q133L13

Q141 Q142

R14

Q143L14

R12

B22

B21 Q211 Q212

Q221 Q222

R21

Q213

Q223

L21

L22

Q231 Q232

R23

Q233L23

Q241 Q242

R24

Q243L24

R22

Q11 Q12 Q13 Q14L1

L2

B23

B24

B13

B14

Q21 Q22 Q23 Q24L3

L4

G1

G2

(a)

B12

B11 Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R13

Q133L13

Q141 Q142

R14

Q143L14

R12

B22

B21 Q211 Q212

Q221 Q222

R21

Q213

Q223

L21

L22

Q231 Q232

R23

Q233L23

Q241 Q242

R24

Q243L24

R22

Q11 Q12 Q13 Q14L1

L2

B23

B24

B13

B14

Q21 Q22 Q23 Q24L3

L4

G1

G2

(b)



In order to evaluate the balancing performance of the proposed topology, we compared the proposed topology and the adjacent batteries balancing topology (as shown in Figure 6) [17] (position). In the rest of this section, we specifically analyze the equalization efficiency. We assume that there are n cells in the battery group, and the equalization efficiency of each sub-equalizer is 𝜂.

B12

B11

B14

B13

B22

B21

B24

B23



2.1. The Adjacent Batteries Balancing Topology

In the adjacent batteries’ balancing topology, there are n − 1 kinds of unbalanced state (x1, x2, x3,. . . , xn−1), corresponding to the n − 1 balancing efficiency (η1, η2, η3, . . . , ηn−1). The distribution ofthe balancing efficiency is shown in Figure 6. Assuming that the state of charge (SOC) of the cells inthe battery group is arbitrary, there is a total of n·(n − 1) balancing states, and the average balancingefficiency of the entire system depends on the current unbalanced state of the system. Assuming thatthe balancing efficiency value η(i) is determined by the given unbalance state xi. The probability

Electronics 2020, 9, 1744 8 of 21

of (x = xi) is calculated as Equation (16). The expected value of the balancing effect of the adjacentbatteries’ balancing topology is calculated as Equation (17):

P(x = xi) =2(n− i)n(n− r)

(16)

E(η) =n−1∑i=1

η(i)P(x = xi) =n−1∑i=1

ηi 2(n−i)n(n−1)

=2η(1−η)(1−ηn−1)(n−1)+ηn−1(1−η)(2n−3)−η(1−ηn−1)

(n−1)(2n−3)(1−η)2

(17)

2.2. The Proposed Topology

For the topology proposed in this paper, the efficiency of the balancing between the battery cellsis assumed to be η. Then, there is only active balancing in the in-group balancing, and the efficiency isη. Therefore, the expected balancing efficiency of the proposed topology is calculated as Equation (18):

E(η) =n−1∑i=1

xiP(x = xi) = η (18)

Once the equalization circuit is built up, the efficiency η is a constant. This paper assumesη = 0.9. The expectation curve is shown in Figure 7. The blue curve is the adjacent batteries’ balancingtopology, and the orange curve is the topology proposed in this paper. If n < 3, the adjacent cells’balancing topology is more efficient. If n = 3, the efficiency of the two topologies is approximatelyequal. However, if n > 3, the efficiency of the proposed topology in this paper is obviously higher.As the number of batteries increases, the topology performance proposed in this paper is more obvious.Since lithium battery groups usually have a large number of batteries in series under actual conditions,the topology proposed in this paper has great advantages in performance. According to the aboveanalysis, the proposed topology can directly transmit energy and the adjacent batteries’ balancingtopology can only be transmitted between the adjacent batteries, so it can be seen that the topology ofthis paper has a faster speed. Tables 1 and 2 show the performance comparison between the solutionproposed in this paper and other common solutions.


2.1. The Adjacent Batteries Balancing Topology

In the adjacent batteries’ balancing topology, there are n − 1 kinds of unbalanced state (𝑥 , 𝑥 , 𝑥 , …, 𝑥 ), corresponding to the n − 1 balancing efficiency (𝜂 , 𝜂 , 𝜂 , …, 𝜂 ). The distribution of the balancing efficiency is shown in Figure 6. Assuming that the state of charge (SOC) of the cells in the battery group is arbitrary, there is a total of n·(n − 1) balancing states, and the average balancing efficiency of the entire system depends on the current unbalanced state of the system. Assuming that the balancing efficiency value 𝜂(i) is determined by the given unbalance state 𝑥 . The probability of (𝑥 = 𝑥 ) is calculated as Equation (16). The expected value of the balancing effect of the adjacent batteries’ balancing topology is calculated as Equation (17):

( ) ( )( )

2i

n-iP x=x =

n n-r (16)

( ) ( ) ( ) ( )( )

( )( )( ) ( )( ) ( )( )( )( )

= =

-1 -1

1 1

-1 -1 -1

2

21

2 1 1 1 1 2 3 1

1 2 3 1

n ni

ii i

n n n

n-iE η = η i P x=x = η

n n-

η -η -η n- +η -η n- -η -η=

n- n- -η

(17)

2.2. The Proposed Topology

For the topology proposed in this paper, the efficiency of the balancing between the battery cells is assumed to be η . Then, there is only active balancing in the in-group balancing, and the efficiency is η . Therefore, the expected balancing efficiency of the proposed topology is calculated as Equation (18):

( )η η=

-

( )n 1

i ii 1

E = x P x=x = (18)

Once the equalization circuit is built up, the efficiency η is a constant. This paper assumes η = 0.9. The expectation curve is shown in Figure 7. The blue curve is the adjacent batteries’ balancing topology, and the orange curve is the topology proposed in this paper. If n < 3, the adjacent cells’ balancing topology is more efficient. If n = 3, the efficiency of the two topologies is approximately equal. However, if n > 3, the efficiency of the proposed topology in this paper is obviously higher. As the number of batteries increases, the topology performance proposed in this paper is more obvious. Since lithium battery groups usually have a large number of batteries in series under actual conditions, the topology proposed in this paper has great advantages in performance. According to the above analysis, the proposed topology can directly transmit energy and the adjacent batteries’ balancing topology can only be transmitted between the adjacent batteries, so it can be seen that the topology of this paper has a faster speed. Table 1 and Table 2 show the performance comparison between the solution proposed in this paper and other common solutions.

2 3 4 5 6 7 8 9 10

0.70

0.75

0.80

0.85

0.90 Adjacent balancing topologyProposed topology

E(η)

n Figure 7. The efficiency curve. Figure 7. The efficiency curve.

Table 1. Component quantity comparison.

Method Switch Resistor Capacitor Inductor Transformer Diode

Single-trans. 2n + 1 - - - 1 1Multi-trans. 2n - - - n nMulti-layer 2n + 4m - - - n + m -Capacitor 2n - n − 1 - - -Inductor 4n - - 1 - 4nPassive n n - - - -

Proposed method 3n + 4m n - - 2m -

Electronics 2020, 9, 1744 9 of 21

Table 2. Perfomence comparsion.

Method Speed Efficiency Condition Complexity Cost Suitable String

Single-trans. Medium Medium Ch/disch Complex Medium MediumMulti-trans. Medium High Ch/disch Simple Medium LongMulti-layer Quick Medium Ch/disch Medium High Very longCapacitor Very slow Very high Ch/disch Simple Low MediumInductor Quick Very high Ch/disch Simple low MediumPassive Very slow - Charge Very simple Very Low Long

Proposed method Very quick Very high Ch/disch Medium Medium Very long

3. Simulation

MATLAB 2018b/Simulink was used to validate the topology proposed in this paper. This paperwill verify the in-group and between-group balancing separately.

The intra-in-group balancing circuit was built by the components in the Simscape library inSimulink. The battery model parameters used in the simulation are used the parameters of ternarylithium battery, they are set as shown in Table 3. The circuit is shown in Figure 8, PWM_G1_1,PWM_G1_2, PWM_G1_3, and PWM_G1_4 are the driving signals of the bidirectional switch respectively,and each signal is a 100 kHz PWM waveform, Each bidirectional switch applies different drivewaveforms according to different working modes, When the circuit works in the flyback equilibriummode, the phase difference of the switching drive waveforms of the two cells for energy transfer is180, When in the forward equilibrium mode, the switching drive waveforms of the two cells forenergy transfer are the same in phase. PASSIVE_G1, PASSIVE_G2, PASSIVE_G3, PASSIVE_G4 arecontrol switches for passive equalization discharge resistance respectively, The switch is opened whenoperating the cell that needs to be discharged.

Table 3. The battery model parameters for simulation.

Battery Model Type Lithium-Ion

Nom-Voltage 3.7 VRated capacity 2.8 Ah

Internal resistance 30 mΩNom-voltage capacity 2.3 AhFully charged voltage 4.1 V


Table 1. Component quantity comparison.

Method Switch Resistor Capacitor Inductor Transformer Diode Single-trans. 2n + 1 - - - 1 1 Multi-trans. 2n - - - n n Multi-layer 2n + 4m - - - n + m - Capacitor 2n - n − 1 - - - Inductor 4n - - 1 - 4n Passive n n - - - -

Proposed method 3n + 4m n - - 2m -

Table 2. Perfomence comparsion.

Method Speed Efficiency Condition Complexity Cost Suitable String Single-trans. Medium Medium Ch/disch Complex Medium Medium Multi-trans. Medium High Ch/disch Simple Medium Long Multi-layer Quick Medium Ch/disch Medium High Very long Capacitor Very slow Very high Ch/disch Simple Low Medium Inductor Quick Very high Ch/disch Simple low Medium Passive Very slow - Charge Very simple Very Low Long

Proposed method Very quick Very high Ch/disch Medium Medium Very long

3. Simulation

MATLAB 2018b/Simulink was used to validate the topology proposed in this paper. This paper will verify the in-group and between-group balancing separately.

The intra-in-group balancing circuit was built by the components in the Simscape library in Simulink. The battery model parameters used in the simulation are used the parameters of ternary lithium battery, they are set as shown in Table 3. The circuit is shown in Figure 8, PWM_G1_1, PWM_G1_2, PWM_G1_3, and PWM_G1_4 are the driving signals of the bidirectional switch respectively, and each signal is a 100 kHz PWM waveform, Each bidirectional switch applies different drive waveforms according to different working modes, When the circuit works in the flyback equilibrium mode, the phase difference of the switching drive waveforms of the two cells for energy transfer is 180°, When in the forward equilibrium mode, the switching drive waveforms of the two cells for energy transfer are the same in phase. PASSIVE_G1, PASSIVE_G2, PASSIVE_G3, PASSIVE_G4 are control switches for passive equalization discharge resistance respectively, The switch is opened when operating the cell that needs to be discharged.

gm

DS

+

_

m

+

_

m

gm

DS1+

1

2+

2

+3

3

+4

4gm

DS

gm

DS

+

_

m+

_

m

g m

D S

g m

D S

g m

D S

g m

D S

B1

B2B3

B4

[PWM_G1_3]

[PWM_G1_4]

[PWM_G1_1]

[PWM_G1_2]

g mD S

g mD S

gmDS

gmDS

[PASSIVE_G1]

[PASSIVE_G2]

[PASSIVE_G4]

[PASSIVE_G3]

R13

R14

R12

R13

Figure 8. The simulation circuit diagram of in-group equalization.

Figure 8. The simulation circuit diagram of in-group equalization.

(1) In the simulation, MODE 1 is first verified. The condition that the balanced topology works inMODE 1 is that the highest and lowest battery cells are on different sides of the battery group. B1 is thesource battery in the balancing process, and B3 is the target battery. The initial SOCs of B1 and B3 are

Electronics 2020, 9, 1744 10 of 21

set to 99% and 30%, respectively. At this time, the gate drive waveforms of the corresponding MOSFETin the balancing circuits of B1 and B3 were shown in Figure 9. It can be seen that the phase differencebetween the two was 180, so the PWM signals were complementary. The circuit worked in the in-groupFlyback Mode. The current and voltage waveforms on the bidirectional switch are shown in Figure 10:the working frequency was 100 kHz, the rated output power was set to 4.5 W, the efficiency was set to85%, the duty cycle was set to 45%, the calculation process of the primary magnetizing inductanceand leakage inductance were as processed in Equation (19), the transformer leakage inductance wasestimated to be 5% of the magnetizing inductance, and the copper loss resistance of the primarywinding was set to 25 m·Ω.

Pin = Poη = 4.5 W

0.85 ≈ 5.3 W

Iaver =Pin

Vmin= 5.3 W

3.7 V ≈ 1.43 AIpri_pk =

Iaver0.5 D = 1.43 A

0.5∗0.45 ≈ 6.36 ALpri =

VinTonIpk

=3.7 V∗10 µs∗0.45

6.36 A ≈ 2.62 µH

Lleakage = Lpri ∗ 0.05 = 2.62 µH ∗ 0.05 ≈ 0.131 µH

(19)

Electronics 2020, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/electronics

B12

B11 Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R13

Q133L13

Q141 Q142

R14

Q143L14

R12

B22

B21 Q211 Q212

Q221 Q222

R21

Q213

Q223

L21

L22

Q231 Q232

R23

Q233L23

Q241 Q242

R24

Q243L24

R22

Q11 Q12 Q13 Q14L1

L2

B23

B24

B13

B14

Q21 Q22 Q23 Q24L3

L4

G1

G2

(a)

B12

B11 Q111 Q112

Q121 Q122

R11

Q113

Q123

L11

L12

Q131 Q132

R13

Q133L13

Q141 Q142

R14

Q143L14

R12

B22

B21 Q211 Q212

Q221 Q222

R21

Q213

Q223

L21

L22

Q231 Q232

R23

Q233L23

Q241 Q242

R24

Q243L24

R22

Q11 Q12 Q13 Q14L1

L2

B23

B24

B13

B14

Q21 Q22 Q23 Q24L3

L4

G1

G2

(b)


0.1

0.2

0.3

0.4

0.5

0

0.7

0.8

0.9

1

0.6

0.2

0.4

0.6

0.8

1

0

1.2

PWM

G1-

1(V

)PW

M G

1-3(

V)

PWM G1-3

PWM G1-1

Time(millisecond)

T = 10usDuty cycle = 45%


1.23 1.24 1.25 1.26 1.27 1.28

1.23 1.24 1.25 1.26 1.27 1.28

Figure 9. The waveform of PWM_G1_1 and PWM_G1_3 in MODE 1.

Figure 9. The waveform of PWM_G1_1 and PWM_G1_3 in MODE 1.Electronics 2020, 9, x FOR PEER REVIEW 2 of 5

B3 S

witc

h C

urre

nt(A

)B3

Sw

itch

Vol

tage

(V)

B1 S

witc

h C

urre

nt(A

)B1

Sw

itch

Vol

tage

(V)

6

4

2

0

6

4

2

0

6

4

2

0

6

4

2

0

B3 Switch Voltage

B3 Switch Current

B1 Switch Current

B1 Switch Voltage

Time(millisecond)





1.23 1.24 1.25 1.26 1.27 1.28 1.29

1.23 1.24 1.25 1.26 1.27 1.28 1.29

1.23 1.24 1.25 1.26 1.27 1.28 1.29

1.23 1.24 1.25 1.26 1.27 1.28 1.29

Figure 10. The current and voltage waveform of MODE 1.

0.2

0.4

0.6

0.8

0

1

0.2

0.4

0.6

0.8

0

1

PWM

G1-

1(V

)PW

M G

1-2(

V)

PWM G1-1

PWM G1-2

Time(millisecond)



5.51 5.52 5.53 5.54 5.55

5.51 5.52 5.53 5.54 5.55

5.56

5.56

Figure 12. The driver waveform of PWM_G1_1 and PWM_G1_2 in MODE 2.


Electronics 2020, 9, 1744 11 of 21

According to the simulation results in Figure 11, it is clear that the equilibrium time is 731.7 s.By Equation (20), the balancing efficiency of this equalization is about 82.1%. The simulation resultsshow that the topology proposed in this paper can realize the balancing mode of MODE 1, and thebalancing efficiency and equalization speed meet the expectation:

P =SOCB1_end + SOCB3_end

SOCB1_be f ore + SOCB3_be f ore(20)


B3 S

witc

h C

urre

nt(A

)B3

Sw

itch

Vol

tage

(V)

B1 S

witc

h C

urre

nt(A

)B1

Sw

itch

Vol

tage

(V)

0.123 0.124 0.125 0.126 0.127 0.128 0.129

0.123 0.124 0.125 0.126 0.127 0.128 0.129

0.123 0.124 0.125 0.126 0.127 0.128 0.129

0.123 0.124 0.125 0.126 0.127 0.128 0.129

6

4

2

0

6

4

2

0

6

4

2

0

6

4

2

0

B3 Switch Voltage

B3 Switch Current

B1 Switch Current

B1 Switch Voltage

Time(second)





×1e-2

×1e-2

×1e-2

×1e-2


According to the simulation results in Figure 11, it is clear that the equilibrium time is 731.7 s. By Equation (20), the balancing efficiency of this equalization is about 82.1%. The simulation results show that the topology proposed in this paper can realize the balancing mode of MODE 1, and the balancing efficiency and equalization speed meet the expectation:

1 _ 3 _

1 _ 3 _

= B end B end

B before B before

SOC SOCP

SOC SOC++

(20)

B1B3

30

40

50

60

70

80

90

100

Cel

l SO

C

Time(second)

<SOC(%)>,<SOC(%)>

0 100 200 300 400 500 600 700 800 900 1000

Time = 731.7sCell B1 SOC = 53.24%

Time = 731.7sCell B3 SOC = 52.83%

Figure 11. The state of charge (SOC) curve during balancing in MODE 1.

(2) In order to verify the MODE 2, B1 was chosen as the source battery, and B2 as the target battery. B1 and B2 are in the same side of the battery group. The initial SOC of B1 was set to 99%, and the initial SOC of B2 was set to 30%. At this time, the gate drive waveforms of the corresponding MOSFET in the balancing circuits of B1 and B2 are shown in Figure 12. It can be seen that the phase difference between the two is 0°, so that they are in-phase PWMs. The circuit works in the In-groupForward Mode. The current and voltage waveforms on the bidirectional switch at this time are shown in Figure 13. MODE 2 requires that the battery voltage difference exceeds the threshold, so at this time, the equalization time is completed at 1006.3 s by Figure 14. After balancing, the SOCs of B1

Figure 11. The state of charge (SOC) curve during balancing in MODE 1.

(2) In order to verify the MODE 2, B1 was chosen as the source battery, and B2 as the target battery.B1 and B2 are in the same side of the battery group. The initial SOC of B1 was set to 99%, and theinitial SOC of B2 was set to 30%. At this time, the gate drive waveforms of the corresponding MOSFETin the balancing circuits of B1 and B2 are shown in Figure 12. It can be seen that the phase differencebetween the two is 0, so that they are in-phase PWMs. The circuit works in the In-groupForwardMode. The current and voltage waveforms on the bidirectional switch at this time are shown inFigure 13. MODE 2 requires that the battery voltage difference exceeds the threshold, so at this time,the equalization time is completed at 1006.3 s by Figure 14. After balancing, the SOCs of B1 and B2 are61.45% and 61.67%, respectively. Compared with the in-group flyback mode, it takes a longer time.The balancing efficiency of this calculation is 95.4% according to Equation (21):

P =SOCB1_end + SOCB2_end

SOCB1_be f ore + SOCB2_be f ore(21)


B3 S

witc

h C

urre

nt(A

)B3

Sw

itch

Vol

tage

(V)

B1 S

witc

h C

urre

nt(A

)B1

Sw

itch

Vol

tage

(V)

6

4

2

0

6

4

2

0

6

4

2

0

6

4

2

0

B3 Switch Voltage

B3 Switch Current

B1 Switch Current

B1 Switch Voltage

Time(millisecond)





1.23 1.24 1.25 1.26 1.27 1.28 1.29

1.23 1.24 1.25 1.26 1.27 1.28 1.29

1.23 1.24 1.25 1.26 1.27 1.28 1.29

1.23 1.24 1.25 1.26 1.27 1.28 1.29


0.2

0.4

0.6

0.8

0

1

0.2

0.4

0.6

0.8

0

1

PWM

G1-

1(V

)PW

M G

1-2(

V)

PWM G1-1

PWM G1-2

Time(millisecond)



5.51 5.52 5.53 5.54 5.55

5.51 5.52 5.53 5.54 5.55

5.56

5.56

Figure 12. The driver waveform of PWM_G1_1 and PWM_G1_2 in MODE 2. Figure 12. The driver waveform of PWM_G1_1 and PWM_G1_2 in MODE 2.

Electronics 2020, 9, 1744 12 of 21Electronics 2020, 9, x FOR PEER REVIEW 3 of 5

00.1

0.2

0.30.4

00.5

1.52

2.5

1

33.5

00.1

0.30.40.5

0.2

0.60.70.8

0.51

22.5

3

1.5

3.5

Time(millisecond)

B2 S

witc

h C

urre

nt(A

)B2

Sw

itch

Vol

tage

(V)

B1 S

wit

ch C

urre

nt(A

)B1

Sw

itch

Vol

tage

(V)

B2 Switch Voltage

B2 Switch Current

B1 Switch Current

B1 Switch VoltageT = 10usDuty cycle = 45%




5.51 5.52 5.53 5.54 5.55


Prim

ary

PWM

(V)

Seco

ndar

y PW

M(V

)

115.2 115.21 115.22 115.23

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Time(millisecond)

Primary PWM

Secondary PWM

115.2 115.21 115.22 115.23



Figure 17. Driving waveform of the bidirectional switch.

Figure 13. The current and voltage waveform of MODE 2.Electronics 2020, 9, x FOR PEER REVIEW 13 of 23

30

40

50

60

70

80

90

100

Cel

l SO

C

Time(second)

<SOC(%)>,<SOC(%)>

0 500 1000 1500

B1B2

Time = 1006.3sCell B1 SOC = 61.67%

Time = 1006.3sCell B2 SOC = 61.45%

Figure 14. The SOC curve during balancing in MODE 2.

(3) This paper then verified MODE 3, in the in-group passive balancing mode. This mode requires that the SOC difference between the battery cells is less than 150 mV. The SOCs of four batteries are set to 80.4%, 80.2%, 80%, and 78.2%, respectively. At this time, the corresponding battery voltages are 3.465, 3.463, 3.459, and 3.443 V, and the maximum voltage difference is 22 mV, which exceeds the threshold of passive equalization. The SOCs at the final termination are 78.19%, 78.21%, 78.23%, and 78.18%, respectively. The entire balancing process takes 531.3 s. The SOC change curve in the process is shown in Figure 15.

B1B2B3B4

78

78.5

79

79.5

80

80.5

100 200 300 400 500 600 7000Time(second)

Cel

l SO

C

<SOC(%)>,<SOC(%)>,<SOC(%)>,<SOC(%)>

Time = 531.3sCell B1 SOC = 78.23%

Time = 480.8sCell B2 SOC = 78.19%

Time = 439.2sCell B3 SOC = 78.21%


(4) MODE 4 is the between-group bidirectional flyback mode. In Figure 16, taking the power supply system composed of four battery groups as an example, the energy exchange between the entire power supply system and one of the battery groups is used to achieve a balanced effect.


(3) This paper then verified MODE 3, in the in-group passive balancing mode. This mode requiresthat the SOC difference between the battery cells is less than 150 mV. The SOCs of four batteries areset to 80.4%, 80.2%, 80%, and 78.2%, respectively. At this time, the corresponding battery voltagesare 3.465, 3.463, 3.459, and 3.443 V, and the maximum voltage difference is 22 mV, which exceedsthe threshold of passive equalization. The SOCs at the final termination are 78.19%, 78.21%, 78.23%,and 78.18%, respectively. The entire balancing process takes 531.3 s. The SOC change curve in theprocess is shown in Figure 15.

(4) MODE 4 is the between-group bidirectional flyback mode. In Figure 16, taking the powersupply system composed of four battery groups as an example, the energy exchange between theentire power supply system and one of the battery groups is used to achieve a balanced effect.

The between-group balancing should wait until the end of in-group balancing. Each battery groupin the power supply system is equivalent to a large-capacity battery cell. Because the battery group isconnected in series, the capacity of the equivalent battery group is equal to the sum of the capacities of

Electronics 2020, 9, 1744 13 of 21

all the batteries in it, and the voltage of an equivalent battery group is equal to the sum of the voltageof all the series batteries in it. G1, G2, G3, and G4 are used to represent four battery groups in the powersupply system, each of which has a rated voltage of 13.2 V.


30

40

50

60

70

80

90

100

Cel

l SO

C

Time(second)

<SOC(%)>,<SOC(%)>

0 500 1000 1500

B1B2

Time = 1006.3sCell B1 SOC = 61.67%

Time = 1006.3sCell B2 SOC = 61.45%


(3) This paper then verified MODE 3, in the in-group passive balancing mode. This mode requires that the SOC difference between the battery cells is less than 150 mV. The SOCs of four batteries are set to 80.4%, 80.2%, 80%, and 78.2%, respectively. At this time, the corresponding battery voltages are 3.465, 3.463, 3.459, and 3.443 V, and the maximum voltage difference is 22 mV, which exceeds the threshold of passive equalization. The SOCs at the final termination are 78.19%, 78.21%, 78.23%, and 78.18%, respectively. The entire balancing process takes 531.3 s. The SOC change curve in the process is shown in Figure 15.

B1B2B3B4

78

78.5

79

79.5

80

80.5

100 200 300 400 500 600 7000Time(second)

Cel

l SO

C

<SOC(%)>,<SOC(%)>,<SOC(%)>,<SOC(%)>

Time = 531.3sCell B1 SOC = 78.23%

Time = 480.8sCell B2 SOC = 78.19%

Time = 439.2sCell B3 SOC = 78.21%


(4) MODE 4 is the between-group bidirectional flyback mode. In Figure 16, taking the power supply system composed of four battery groups as an example, the energy exchange between the entire power supply system and one of the battery groups is used to achieve a balanced effect.

Figure 15. The SOC curve during balancing in MODE 3.Electronics 2020, 9, x FOR PEER REVIEW 14 of 23

Q11 Q12 Q13 Q14L1

L2

Q21 Q22 Q23 Q24L3

L4

Q31 Q32 Q43 Q44L5

L6

Q41 Q42 Q43 Q44L7

L8

G1

G2

G3

G4

Figure 16. Bidirectional flyback topology for the between-group equalization.

The between-group balancing should wait until the end of in-group balancing. Each battery group in the power supply system is equivalent to a large-capacity battery cell. Because the battery group is connected in series, the capacity of the equivalent battery group is equal to the sum of the capacities of all the batteries in it, and the voltage of an equivalent battery group is equal to the sum of the voltage of all the series batteries in it. G1, G2, G3, and G4 are used to represent four battery groups in the power supply system, each of which has a rated voltage of 13.2 V.

The between-group balancing proposed in this paper adopts different control strategies for two different situations. First, the average voltage value of the four battery groups is obtained, and the number of battery groups that are lower than the average value and higher than the average value are obtained through comparison. If the number of battery groups higher than the average value is greater, the entire power supply system is used to charge the battery groups that are lower than the average value. On the other hand, a higher-voltage battery group is used to charge the entire power supply system to achieve balance. The termination conditions of the two equalization methods are set such that the absolute value of the difference between the voltage values of all battery groups and the average voltage of the entire power supply system is less than 180 mV. The top-level active equalization simulation is carried out using the circuit diagram shown in Figure 8, which only needs to reasonably set and modify the voltage of the battery, and one bottom-layer group is composed of four cells, its nominal voltage being =g nomV V_ 3.7 . The nominal voltage of the entire top layer group

is = =total g nomV V V_4 59.2 , the top group side is defined as the primary side, the turn ratio is set to

4:1, the output power of the flyback converter between groups is set to 40 W. The efficiency is calculated at 85%, the switching frequency is set to 100 kHz, the leakage inductance of the primary winding is estimated as 5% of the magnetizing inductance, the calculation process of the transformer parameters are expressed as Equation (22). The following will verify this mode:

η

μ μ

μ μ

= = ≈

= = ≈

= = ≈

= = ≈

= = ≈

oin

inaver

averpri pk

in onpri

pk

leakage pri

P WP W

P WI AV V

I AI A D

V T V sL HI A

L L H H

min

_

40 470.85

47 0.859.2

0.8 3.60.5 0.5 * 0.45

59.2 * 10 * 0.45 743.6

* 0.05 74 * 0.05 3.7

(22)

Figure 16. Bidirectional flyback topology for the between-group equalization.

The between-group balancing proposed in this paper adopts different control strategies for twodifferent situations. First, the average voltage value of the four battery groups is obtained, and thenumber of battery groups that are lower than the average value and higher than the average valueare obtained through comparison. If the number of battery groups higher than the average value isgreater, the entire power supply system is used to charge the battery groups that are lower than theaverage value. On the other hand, a higher-voltage battery group is used to charge the entire powersupply system to achieve balance. The termination conditions of the two equalization methods areset such that the absolute value of the difference between the voltage values of all battery groupsand the average voltage of the entire power supply system is less than 180 mV. The top-level activeequalization simulation is carried out using the circuit diagram shown in Figure 8, which only needs toreasonably set and modify the voltage of the battery, and one bottom-layer group is composed of fourcells, its nominal voltage being Vg_nom = 3.7 V. The nominal voltage of the entire top layer group is

Electronics 2020, 9, 1744 14 of 21

Vtotal = 4Vg_nom = 59.2 V, the top group side is defined as the primary side, the turn ratio is set to 4:1,the output power of the flyback converter between groups is set to 40 W. The efficiency is calculatedat 85%, the switching frequency is set to 100 kHz, the leakage inductance of the primary winding isestimated as 5% of the magnetizing inductance, the calculation process of the transformer parametersare expressed as Equation (22). The following will verify this mode:

Pin =Po

η=

40 W0.85

≈ 47 W

Iaver =Pin

Vmin=

47 W59.2 V

≈ 0.8 A

Ipri_pk =Iaver

0.5 D=

0.8 A0.5 ∗ 0.45

≈ 3.6 A

Lpri =VinTon

Ipk=

59.2 V ∗ 10 µs ∗ 0.453.6 A

≈ 74 µH

Lleakage = Lpri ∗ 0.05 = 74 µH ∗ 0.05 ≈ 3.7 µH

(22)

(a) CASE 1: The entire power supply system charges a single battery group.

Considering the practical application, the experiment uses the voltage of the battery group as thevariable of the between-group balancing. The initial voltages of G1, G2, G3 and G4 are set to 14.345 V,14.320 V, 13.961 V and 14.292 V, respectively. At this time, the average voltage of the entire powersupply system is 14.230 V, and an equalization strategy for charging the battery group G3 by the entirepower supply system should be adopted.

At this time, Q31, Q32, Q43, and Q44, shown in Figure 17, are controlled by two complementaryPWMs, respectively, and the circuit with the same structure as Q31 and Q32 is hereinafter referred to asa bidirectional switch. The turns ratio of the transformer is selected as 4:1. Since the secondary groupis charged for the primary group at this time, the side where Q31 and Q32 are located can be definedas the primary side. Correspondingly, the side where Q43 and Q44 are located is the secondary side.At this time, the driving waveform of the bidirectional switch corresponding to the primary side andthe secondary side is shown in Figure 17, The primary side bidirectional switch is composed of Q31 andQ32 in Figure 16, and the secondary side switch is composed of Q43 and Q44, and the correspondingvoltage and current waveforms of bidirectional switch are shown in Figure 18. The battery group SOCchange curve during the equalization process is shown in Figure 19. After balancing, the voltages ofG1, G2, G3, and G4 are set to 14.213 V, 14.243 V, 14.251 V and 14.260 V, respectively. The entire processtakes 877.8 s. The equalization efficiency can be calculated according to Equation (23).

η =Po

Pin=

U2ndrmsI2ndrmsU1strmsI1strms

(23)

U1strms is the effective value of the voltage on the primary side, and I1strms is the effective valueof the current on the primary side. U2strms is the effective value of the voltage on the secondary side,and I2strms is the effective value of the current on the secondary side. The above four quantities arecalculated as Equation (24).

U1strms =

√1T

∫ T0 u2

1st(t)dt

I1strms =

√1T

∫ T0 i21st(t)dt

U2ndrms =

√1T

∫ T0 u2

2nd(t)dt

I2ndrms =

√1T

∫ T0 i22nd(t)dt

(24)

After calculation, the equilibrium efficiency is η ≈ 87.3%.

Electronics 2020, 9, 1744 15 of 21


00.1

0.2

0.30.4

00.5

1.52

2.5

1

33.5

00.1

0.30.40.5

0.2

0.60.70.8

0.51

22.5

3

1.5

3.5

Time(millisecond)

B2 S

witc

h C

urre

nt(A

)B2

Sw

itch

Vol

tage

(V)

B1 S

wit

ch C

urre

nt(A

)B1

Sw

itch

Vol

tage

(V)

B2 Switch Voltage

B2 Switch Current

B1 Switch Current

B1 Switch VoltageT = 10usDuty cycle = 45%




5.51 5.52 5.53 5.54 5.55


Prim

ary

PWM

(V)

Seco

ndar

y PW

M(V

)

115.2 115.21 115.22 115.23

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Time(millisecond)

Primary PWM

Secondary PWM

115.2 115.21 115.22 115.23



Figure 17. Driving waveform of the bidirectional switch. Figure 17. Driving waveform of the bidirectional switch.


Time(millisecond)

0

0.5

1

1.5

2

0

2

4

6

0

50

100

0

10

20

30

Prim

ary

Cur

rent

(A)

Seco

ndar

y Cu

rren

t(A

)Pr

imar

y M

OS

Vol

tage

(V)

Seco

ndar

y M

OS

Volta

ge(V

)

Secondary MOS Voltage

Primary MOS Voltage

Secondary Current

Primary Current

115.2 115.21 115.22 115.23





115.2 115.21 115.22 115.23

115.2 115.21 115.22 115.23

115.2 115.21 115.22 115.23

Figure 18. Voltage and current waveforms of the bidirectional switch.

0.1

0.2

0.3

0.4

0.5

0

0.7

0.8

0.9

1

0.6

0.2

0.4

0

0.8

1

0.6

Primary PWM

Secondary PWM

Prim

ary

PWM

(V)

Seco

ndar

y PW

M(V

)

Time(millisecond)48.35 48.36 48.37 48.38 48.39

48.35 48.36 48.37 48.38 48.39




Figure 18. Voltage and current waveforms of the bidirectional switch.Electronics 2020, 9, x FOR PEER REVIEW 17 of 23

100 200 300 400 500 600 700 800Time(second)

Cel

l Gro

up V

olta

ge(V

)

13.6

13.7

13.8

13.9

14

14.1

14.2

14.3

Group1Group2Group3Group4

Figure 19. The SOC curve of CASE 1 during balancing in MODE 4.

(b) CASE 2: One battery group charges the entire power supply system.

In the power supply system, the initial voltages of G1, G2, G3, and G4 are set to 14.253 V, 14.275 V, 15.191 V, and 14.287 V, respectively. At this time, the battery group G3 with the highest voltage should be used to charge the entire power supply system. Q31, Q32, Q43, and Q44 shown in Figure 20 are controlled by two complementary PWMs, respectively. Since the entire power supply system is charged for the battery group at this time, Q31 and Q32 are located in the primary side, and Q44 is on the secondary side. At this time, the driving voltage waveforms of the primary side and secondary side MOS driving voltages are shown in Figure 20, and the voltage and current waveforms are shown in Figure 21. The battery group voltage change curve is shown in Figure 22. After the balancing is completed, the voltages of G1, G2, G3, and G4 are 14.260 V, 14.284 V, 14.262 V, and 14.293 V, respectively. The entire process takes 803.8 s. According to Equations (20) and (21), the equilibrium efficiency is 83.4%η ≈ .

0.1

0.2

0.3

0.4

0.5

0

0.7

0.8

0.9

1

0.6

0.2

0.4

0

0.8

1

0.6

Primary PWM

Secondary PWM

Prim

ary

PW

M(V

)Se

cond

ary

PWM

(V)

Time(second)48.305 48.306 48.307 48.308 48.309

48.305 48.306 48.307 48.308 48.309



×1e-2

×1e-2



Electronics 2020, 9, 1744 16 of 21

(b) CASE 2: One battery group charges the entire power supply system.

In the power supply system, the initial voltages of G1, G2, G3, and G4 are set to 14.253 V, 14.275 V,15.191 V, and 14.287 V, respectively. At this time, the battery group G3 with the highest voltage should beused to charge the entire power supply system. Q31, Q32, Q43, and Q44 shown in Figure 20 are controlledby two complementary PWMs, respectively. Since the entire power supply system is charged for thebattery group at this time, Q31 and Q32 are located in the primary side, and Q44 is on the secondary side.At this time, the driving voltage waveforms of the primary side and secondary side MOS driving voltagesare shown in Figure 20, and the voltage and current waveforms are shown in Figure 21. The batterygroup voltage change curve is shown in Figure 22. After the balancing is completed, the voltages of G1,G2, G3, and G4 are 14.260 V, 14.284 V, 14.262 V, and 14.293 V, respectively. The entire process takes 803.8 s.According to Equations (20) and (21), the equilibrium efficiency is η ≈ 83.4%.


Time(millisecond)

0

0.5

1

1.5

2

0

2

4

6

0

50

100

0

10

20

30

Prim

ary

Cur

rent

(A)

Seco

ndar

y Cu

rren

t(A

)Pr

imar

y M

OS

Vol

tage

(V)

Seco

ndar

y M

OS

Volta

ge(V

)

Secondary MOS Voltage

Primary MOS Voltage

Secondary Current

Primary Current

115.2 115.21 115.22 115.23





115.2 115.21 115.22 115.23

115.2 115.21 115.22 115.23

115.2 115.21 115.22 115.23


0.1

0.2

0.3

0.4

0.5

0

0.7

0.8

0.9

1

0.6

0.2

0.4

0

0.8

1

0.6

Primary PWM

Secondary PWM

Prim

ary

PWM

(V)

Seco

ndar

y PW

M(V

)

Time(millisecond)48.35 48.36 48.37 48.38 48.39

48.35 48.36 48.37 48.38 48.39



Figure 20. Driving waveform of the bidirectional switch. Figure 20. Driving waveform of the bidirectional switch.


-10

0

10

20

30

Prim

ary

Vol

tage

(V)

100

50

0Seco

ndA

ry V

olta

ge(V

)Pr

imar

y C

urre

nt(A

)Se

cond

ary

Cur

rent

(A)

0

2

4

6

0

0.5

1

1.5

2

Primary Voltage

Secondary Voltage

Primary Current

Secondary Current

Time(millisecond)





48.35 48.36 48.37 48.38 48.39

48.35 48.36 48.37 48.38 48.39

48.35 48.36 48.37 48.38 48.39

48.35 48.36 48.37 48.38 48.39



Electronics 2020, 9, 1744 17 of 21


48.305 48.31 48.315 48.32 48.325 48.33 48.335 48.34 48.345

48.305 48.31 48.315 48.32 48.325 48.33 48.335 48.34 48.345

48.305 48.31 48.315 48.32 48.325 48.33 48.335 48.34 48.345

48.305 48.31 48.315 48.32 48.325 48.33 48.335 48.34 48.345-10

0

10

20

30

Prim

ary

Vol

tage

(V)

100

50

0Seco

ndA

ry V

olta

ge(V

)Pr

imar

y C

urre

nt(A

)Se

cond

ary

Cur

rent

(A)

0

2

4

6

0

0.5

1

1.5

2

Primary Voltage

Secondary Voltage

Primary Current

Secondary Current

Time(second)





×1e-2

×1e-2

×1e-2

×1e-2 Figure 21. Voltage and current waveforms of the bidirectional switch.

100 200 300 400 500 600 700 800

14.2

14.4

14.6

14.8

15

15.2

Group1Group2Group3Group4

Cel

l Gro

up V

olta

ge(V

)

Time(second) Figure 22. The SOC curve of CASE 2 during balancing in MODE 4.

4. Experimental Verification

In this section, the simulation verification of the entire battery equalization system is completed, which proved the feasibility of the scheme. Based on the scheme, we produced a physical circuit system. The transformer used is a planar transformer with a small volume, and the coil is made of a multilayer printed circuit board (PCB). The multilayer PCB increases the apparent power of the transformer. The actual battery balance system consists of three STM32 series microcontrollers as the control core, the microcontroller models are STM32F103C8T6, STM32F030C8T6, STM32F407ZET6, respectively. The three balancing control boards communicate with each other through the CAN bus version 2.0B. The feasibility of the scheme is further verified by the physical circuit system, the battery parameters, key switching devices and transformer parameters, which are listed in Tables 4 and 5, the calculation process of the theoretical value has been deduced in the previous chapter, so it is only listed here. The prototype is shown in Figure 23.


4. Experimental Verification

In this section, the simulation verification of the entire battery equalization system is completed,which proved the feasibility of the scheme. Based on the scheme, we produced a physical circuitsystem. The transformer used is a planar transformer with a small volume, and the coil is made ofa multilayer printed circuit board (PCB). The multilayer PCB increases the apparent power of thetransformer. The actual battery balance system consists of three STM32 series microcontrollers as thecontrol core, the microcontroller models are STM32F103C8T6, STM32F030C8T6, STM32F407ZET6,respectively. The three balancing control boards communicate with each other through the CAN busversion 2.0B. The feasibility of the scheme is further verified by the physical circuit system, the batteryparameters, key switching devices and transformer parameters, which are listed in Tables 4 and 5,the calculation process of the theoretical value has been deduced in the previous chapter, so it is onlylisted here. The prototype is shown in Figure 23.

Table 4. Intra-group parameters.

Circuit Parameters Description

Battery cell type Ternary polymer lithium batteryBattery cell rated parameters 3.7 V/2.8 Ah

Switching frequency 100 kHzIntra-group turn ratio 4:1

Intra-group transformer core EE55Duty cycle 45%

Intra-group topology power 40 WIntra-group topology magnetizing inductance 73.7 uH

Intra-group topology leakage inductance 4.3 uHIntra-group power switches IRF640

Table 5. Inter-group parameters.

Circuit Parameters Description

Switching frequency 100 kHzInter-group turn ratio 1:1:1:1

Inter-group Transformer core EE32Duty cycle 45%

Inter-group topology power 4.5 WInter-group topology magnetizing inductance 3.54 uH

Inter-group topology leakage inductance 0.24 uHInter-group power switches DMN2300UFD

Electronics 2020, 9, 1744 18 of 21


Group balancing board

Battery characteristic meter

Passive balancing board

Cell balancing board

Oscilloscope

Battery Group

Figure 23. Overall effect diagram of the prototype.

Table 4. Intra-group parameters.

Circuit Parameters Description Battery cell type Ternary polymer lithium battery

Battery cell rated parameters 3.7 V/2.8 Ah Switching frequency 100 kHz

Intra-group turn ratio 4:1 Intra-group transformer core EE55

Duty cycle 45% Intra-group topology power 40 W

Intra-group topology magnetizing inductance 73.7 uH Intra-group topology leakage inductance 4.3 uH

Intra-group power switches IRF640

Table 5. Inter-group parameters.

Circuit Parameters Description Switching frequency 100 kHz

Inter-group turn ratio 1:1:1:1 Inter-group Transformer core EE32

Duty cycle 45% Inter-group topology power 4.5 W

Inter-group topology magnetizing inductance 3.54 uH Inter-group topology leakage inductance 0.24 uH

Inter-group power switches DMN2300UFD

As shown in Figure 24a–c, the experimental equilibrium data of MODE 1, MODE 2 and MODE 3 are obtained, which are basically consistent with the simulation results in Figures 11, 14 and 15, respectively. Experimental results show that the proposed hybrid equalization strategy is effective.

Figure 23. Overall effect diagram of the prototype.

As shown in Figure 24a–c, the experimental equilibrium data of MODE 1, MODE 2 and MODE3 are obtained, which are basically consistent with the simulation results in Figures 11, 14 and 15,respectively. Experimental results show that the proposed hybrid equalization strategy is effective.Electronics 2020, 9, x FOR PEER REVIEW 20 of 23

100 200 300 400 500 600 700 8000

0

SOC/%

t/s

25

50

75

100 B1

B3

200 400 600 800 1000 1200 1400 16000

0

SOC/%

t/s

25

50

75

100

B1

B2

(a) (b)

78

SOC/%

78.5

80

80.5

81

100 200 300 400 500 600 700 8000 t/s

B1

B2B3

B4

(c)

Figure 24. The SOC curve during balancing by experiments: (a) in MODE 1; (b) in MODE 2; and (c) in MODE 3.

As shown in Figure 25a,b, the experimental equilibrium data of CASE 1 and CASE 2 in MODE 4 are obtained, respectively, which are basically consistent with the simulation results in Figures 19 and 22, respectively. Experiments further verify the effectiveness of the proposed hybrid equalization strategy.

13.6

Group Voltage/V

13.8

14

14.2

14.4

100 200 300 400 500 600 700 8000 t/s

G1G2

G3

G4

14.2

Group Voltage/V

14.4

14.6

14.8

15

100 200 300 400 500 600 700 8000 t/s

15.2

G1

G2 G4

G3

(a) (b)

Figure 25. The SOC curve during balancing in MODE 4 by experiments: (a) CASE 1; and (b) CASE 2.

The following is an analysis of the balance process between the battery strings of other lengths. Taking a battery string composed of 20 cells as an example, the imbalance state is shown in Table 6.

Table 6. Battery imbalance condition.

Voltage(V) Group Cell1(V) Cell2(V) Cell3(V) Cell4(V) 14.732 G1 3.533 3.725 3.612 3.862 14.553 G2 3.682 3.564 3.665 3.642 15.364 G3 3.847 3.835 3.840 3.842 15.286 G4 3.832 3.645 3.992 3.817 14.952 G5 3.812 3.746 3.802 3.592

Figure 24. The SOCcurve during balancing byexperiments: (a) in MODE1; (b) in MODE2; and(c) in MODE3.

As shown in Figure 25a,b, the experimental equilibrium data of CASE 1 and CASE 2 in MODE 4 areobtained, respectively, which are basically consistent with the simulation results in Figures 19 and 22,respectively. Experiments further verify the effectiveness of the proposed hybrid equalization strategy.


100 200 300 400 500 600 700 8000

0

SOC/%

t/s

25

50

75

100 B1

B3

200 400 600 800 1000 1200 1400 16000

0

SOC/%

t/s

25

50

75

100

B1

B2

(a) (b)

78

SOC/%

78.5

80

80.5

81

100 200 300 400 500 600 700 8000 t/s

B1

B2B3

B4

(c)

Figure 24. The SOC curve during balancing by experiments: (a) in MODE 1; (b) in MODE 2; and (c) in MODE 3.

As shown in Figure 25a,b, the experimental equilibrium data of CASE 1 and CASE 2 in MODE 4 are obtained, respectively, which are basically consistent with the simulation results in Figures 19 and 22, respectively. Experiments further verify the effectiveness of the proposed hybrid equalization strategy.

13.6

Group Voltage/V

13.8

14

14.2

14.4

100 200 300 400 500 600 700 8000 t/s

G1G2

G3

G4

14.2

Group Voltage/V

14.4

14.6

14.8

15

100 200 300 400 500 600 700 8000 t/s

15.2

G1

G2 G4

G3

(a) (b)


The following is an analysis of the balance process between the battery strings of other lengths. Taking a battery string composed of 20 cells as an example, the imbalance state is shown in Table 6.


Voltage(V) Group Cell1(V) Cell2(V) Cell3(V) Cell4(V) 14.732 G1 3.533 3.725 3.612 3.862 14.553 G2 3.682 3.564 3.665 3.642 15.364 G3 3.847 3.835 3.840 3.842 15.286 G4 3.832 3.645 3.992 3.817 14.952 G5 3.812 3.746 3.802 3.592


Electronics 2020, 9, 1744 19 of 21

The following is an analysis of the balance process between the battery strings of other lengths.Taking a battery string composed of 20 cells as an example, the imbalance state is shown in Table 6.


Voltage(V) Group Cell1(V) Cell2(V) Cell3(V) Cell4(V)

14.732 G1 3.533 3.725 3.612 3.86214.553 G2 3.682 3.564 3.665 3.64215.364 G3 3.847 3.835 3.840 3.84215.286 G4 3.832 3.645 3.992 3.81714.952 G5 3.812 3.746 3.802 3.592

The unbalance conditions introduced above include unbalance within groups and unbalancebetween groups. The overall balance process is shown in Figure 26.


The unbalance conditions introduced above include unbalance within groups and unbalance between groups. The overall balance process is shown in Figure 26.

Start

Collect all cell voltages

Solve the bottom-layer group voltage

The voltage difference between groups>50mV?

Turn on balance between top-level groups

The cell voltage difference in the group is >15mV?

Perform passive balance

Y

N

The cell voltage difference in the group is <25mV?

Perform active balance within the group


N

Y

Y

N

Y

N

All equilibrium ends

Figure 26. Long string battery pack balancing process.

According to the process shown in Figure 26 above, after the execution is completed, the gap between the batteries can be reduced to within the threshold range. This proves that the topology mentioned in the article has the ability to balance longer battery strings. As shown in Figure 27, different colors represent different battery packs; the batteries imbalance condition is shown in Table 6, according to the control strategy in this article, and this is the balancing process of five battery groups, a total of 20 battery cells.

3.5

3.6

3.7

3.8

3.9

200 400 600 800 10000

G1G2G3G4

Time/s

Voltage/V

G5

Figure 27. The balancing process of five battery groups.

5. Conclusions

In order to solve the problem of the inconsistent battery cell of the lithium battery group more effectively, this paper proposes a novel topology for hybrid lithium-ion battery cell balancing, and introduced the structure and working principle of the topology. We verify it by MATLAB 2018b /Simulink, and made an actual circuit system based on this topology. The experimental results show


According to the process shown in Figure 26 above, after the execution is completed, the gapbetween the batteries can be reduced to within the threshold range. This proves that the topologymentioned in the article has the ability to balance longer battery strings. As shown in Figure 27,different colors represent different battery packs; the batteries imbalance condition is shown in Table 6,according to the control strategy in this article, and this is the balancing process of five battery groups,a total of 20 battery cells.


The unbalance conditions introduced above include unbalance within groups and unbalance between groups. The overall balance process is shown in Figure 26.

Start

Collect all cell voltages

Solve the bottom-layer group voltage

The voltage difference between groups>50mV?

Turn on balance between top-level groups

The cell voltage difference in the group is >15mV?

Perform passive balance

Y

N


Perform active balance within the group


N

Y

Y

N

Y

N

All equilibrium ends


According to the process shown in Figure 26 above, after the execution is completed, the gap between the batteries can be reduced to within the threshold range. This proves that the topology mentioned in the article has the ability to balance longer battery strings. As shown in Figure 27, different colors represent different battery packs; the batteries imbalance condition is shown in Table 6, according to the control strategy in this article, and this is the balancing process of five battery groups, a total of 20 battery cells.

3.5

3.6

3.7

3.8

3.9

200 400 600 800 10000

G1G2G3G4

Time/s

Voltage/V

G5


5. Conclusions

In order to solve the problem of the inconsistent battery cell of the lithium battery group more effectively, this paper proposes a novel topology for hybrid lithium-ion battery cell balancing, and introduced the structure and working principle of the topology. We verify it by MATLAB 2018b /Simulink, and made an actual circuit system based on this topology. The experimental results show


Electronics 2020, 9, 1744 20 of 21

5. Conclusions

In order to solve the problem of the inconsistent battery cell of the lithium battery groupmore effectively, this paper proposes a novel topology for hybrid lithium-ion battery cell balancing,and introduced the structure and working principle of the topology. We verify it by MATLAB 2018b/Simulink, and made an actual circuit system based on this topology. The experimental results showthat the topology proposed in this paper has high equalization efficiency and fast equalization speedin the experiment. The experimental results confirm that the proposed hybrid equilibrium scheme hasa certain improvement in the equilibrium speed compared with the full active equilibrium scheme.It used the passive equilibrium scheme to reduce the waiting time of the final stage of equilibrium,and it has a higher practical application value. The proposed topology achieved an excellent result,the proposed scheme has been verified by the simulation and experiment, but the top-layer equilibriumtopology only realizes the energy exchange between the top-level group and any bottom-layer group,This topology can theoretically realize energy exchange between any bottom layer group, but moreswitches will pass through energy transmission, which leads to increased control logic complexity andswitching loss will increase. This part of the function needs to be optimized in subsequent work.

Author Contributions: Conceptualization, M.G. and H.L. (Huipin Lin); methodology, H.L. (Huipin Lin). and Z.D.;software, Z.D.; validation, Z.D., J.Q. and H.L. (Hao Lan); formal analysis, J.Q.; investigation, H.L. (Huipin Lin);resources, M.G.; data curation, J.Q.; writing—original draft preparation, W.Z.; writing—review and editing, H.L.(Hao Lan); project administration, Q.W. and Z.D.; funding acquisition, M.G. All authors have read and agreed tothe published version of the manuscript.

Funding: This research was funded by National Natural Science Foundation Project of China (grant number61671194) and the Open Fund of Zhejiang Provincial Key Lab of Equipment Electronics (2019E10009).

Conflicts of Interest: The authors declare no conflict of interest.

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an active and passive hybrid battery equalization strategy

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