battery module equalizer based on state of charge

IEEJ Journal of Industry ApplicationsVol.9 No.5 pp.584–596 DOI: 10.1541/ieejjia.9.584

Paper

Battery Module Equalizer based on State of Charge Observation derivedfrom Overall Voltage Variation

Turmandakh Bat-Orgil∗,∗∗ Student Member, Bayasgalan Dugarjav∗∗ Non-member

Toshihisa Shimizu∗a)Fellow

(Manuscript received Oct. 16, 2019, revised March 9, 2020)

Growth in the electric vehicle industry has resulted in considerable chemical battery waste, which requires specialrecycling processes. The power and recharging capacities of waste batteries are insufficient for the operation of trac-tion motors. However, such batteries can be reused as power sources in residential renewable energy systems becausehousehold energy demands are much lower than those of electric vehicles. To enable this reuse, a battery pack shouldbe equipped with an equalizer. Hence, in this study, we propose a battery module equalizer that adjusts the state ofcharge (SOC) of each battery module to the same point using a generation control circuit (GCC). By strategicallychanging the duty ratio of the GCC while detecting the overall voltage of the entire battery pack, the relative SOCof each battery module can be observed while the battery system is in operation. Although this approach uses onlytwo sensors, it enables SOC observation for the entire battery pack, leading to reduced implementation costs and formfactor. The equalization current is further regulated based on the observed relative SOC. The simulation and experi-mental results demonstrate the rapid equalization capability of the proposed GCC-type equalizer during the dischargingprocess.

Keywords: battery management system, battery equalizer, Generation control circuit (GCC), state of charge (SOC)

1. Introduction

Rechargeable electrochemical battery technology plays animportant role in power applications such as electric vehi-cles (EVs) and renewable energy systems (1)–(3). Since 2001,nickel-metal hybrid (NiMH) batteries have been widely uti-lized as power sources in several commercial hybrid elec-tric vehicles (HEVs), including the Toyota Prius and HondaInsight (4)–(6). However, due to the accumulation of charge–discharge cycles, the condition of NiMH battery pack de-grades dramatically, resulting in reduced capacity and short-ened life expectancy (7). A useful energy storage device is thusconverted into battery chemical waste, requiring a special re-cycling process (8)–(10).

Numbers of EVs have been increasing rapidly in developednations in the last few decades. In addition, developing na-tions also possess large numbers of EVs due to the second-hand purchase of EVs from overseas sellers. For instance,Mongolia, a country that continuously imports a large quan-tity of secondhand HEVs from Japan, possessed more than160,000 HEVs as of the end of 2018. The majority of theseHEVs were early generation Toyota Prius models, launchedin 1997–2009, and were already considerably old. Due to alack of battery recycling facilities, a large number of NiMH

a) Correspondence to: Toshihisa Shimizu. E-mail: [email protected]∗ Tokyo Metropolitan University

Minami-Osawa 1-1, Hachioji, Tokyo 192-0397, Japan∗∗ National University of Mongolia

Ikh surguuliin gudamj-1, 14201 Ulaanbaatar, Mongolia

batteries from these HEVs have caused hazardous chemicalwaste to be released (11) (12). The development of a methodof efficiently recycling and reusing these waste batteries hasthus become an urgent necessity.

The battery pack of the first-generation Toyota Prius gen-erated 273.6 V as a nominal voltage through the series-connection of 38 NiMH modules, each consisting of six 1.2 Vcells. Cells with very similar characteristics were selectedand assembled into one module after strict testing in the man-ufacturing plant. Therefore, the reassembly of usable mod-ules extracted from waste batteries is a common method ofremanufacture (11) (13). The power and recharging capacities ofthe reassembled batteries are insufficient for operating trac-tion motors, but such batteries can be reused as power sourcesin the residential renewable energy systems, which have beenaccepted as a promising method of providing access to elec-tricity in isolated areas in Mongolia (14). This practice is feasi-ble because household energy demands are much lower thanthose of HEVs. To enable this reuse, each module in a re-assembled battery pack must be equalized because these bat-teries have not been historically equipped with battery man-agement systems (BMSs). Although NiMH batteries can beautomatically equalized through an over-charging operation,it is impossible to use this technique to equalize the mod-ules in a reassembled battery pack because the modules withthe worst performance are vulnerable to problems caused byover-charging (15). Moreover, the modules in a reassembledbattery pack may have a large associated degree of capacitydeviation due to the different traction histories. Thus, a higherequalization current is needed to shorten an equalization time

c© 2020 The Institute of Electrical Engineers of Japan. 584

Battery Module Equalizer based on Relative SOC Observation（Turmandakh Bat-Orgil et al.）

as much as possible and to maintain the equalization duringeach charge–discharge cycle. If this is not done, safety issuesmay also be compromised by the modules with the worst per-formance. Therefore, a module equalizer is required in orderfor such batteries to be efficiently reused.

Numerous balancing circuits have been introduced in pre-vious research which can be categorized into three majorgroups according to the technique applied. These includepassive techniques (16)–(19), active techniques (7) (16)–(20), and hybridtechniques that combine passive and active techniques (21).Passive techniques are amongst the simplest and cheapestbalancing techniques available because a simple resistor isused to remove the excess energy present in a high-SOC bat-tery. Nevertheless, the obvious disadvantage associated withthis kind of approach is the high energy loss. Active tech-niques have been widely studied in order to achieve more ef-ficient balancing and typically employ energy interchangingcomponents, such as capacitors, inductors, and transform-ers, as well as power converters for exchanging energy be-tween high- and low-SOC batteries. Moreover, active tech-niques demonstrate better performance than passive tech-niques. However, active techniques incur high implemen-tation costs and require complex balancing control strate-gies (17) (19). Specifically, the observation of SOC in real-timeremains challenging because of the nonlinear characteristicsof batteries and the impossibility of direct measurement withphysical sensors (22).

Several SOC observation approaches have been proposed,and in summary (22)–(26) can be divided into four major groups:look-up table-based approaches, an ampere-hour integral ap-proach, model-based estimation approaches, and data-drivenestimation approaches. In look-up table-based approaches,the static parameters of batteries, such as open circuit volt-age (OCV), terminal voltage, and impedance, are directlymapped to the SOC. Based on measured static parame-ters, the SOC can be obtained using a look-up table for ei-ther OCV-SOC or impedance-SOC. In the ampere-hour in-tegral approach, the initial SOC of a battery is assumed tobe known. Thus, the battery current is measured and in-tegrated. This approach involves no computational com-plexity. However, there are some associated drawbacks, inthat it cannot accurately estimate SOC for long periods andalso involves uncertain initial SOC and current sensor errors,amongst other problems. In model-based SOC estimationapproaches, battery parameters, including terminal voltage,charge–discharge current, and temperature information, aresent to a computing unit. State equations are then used to ex-press a battery model. In order to estimate the internal stateof a battery, multiple nonlinear state estimation strategies andfilters are utilized. A Kalman filter (27) and its enhanced vari-ations (28)–(30), as well as a particle filter (31), are among the typ-ical algorithms used. In data-driven estimation approaches,the complex internal chemical reactions and unknown exter-nal operating conditions of the batteries are not considered.Only an input-output data train is used to estimate SOC.

Regardless of which of the conventional SOC observationtechniques is considered, numerous voltage/current sensorsare required for active balancing. For instance, in the OCVmethod, n number of voltage sensors must be connected inparallel to the batteries if the battery pack contains n batteries.

Furthermore, simple sensors are inaccurate, which can de-grade the equalization performance in active balancing. Toachieve accurate SOC observation, transducers with exten-sive measurement ranges are essential, resulting in high im-plementation cost and enlarged system form factor.

To overcome the aforementioned problems, herein is pro-posed a module equalizer that adjusts the SOC of eachmodule to the same point using a generation control circuit(GCC) (32). By strategically changing the duty ratio of theGCC while detecting the overall voltage of the entire bat-tery pack, the relative SOC of each battery module can beobserved while the battery system is in operation. This ap-proach involves the use of only two sensors, enabling a SOCobservation for the entire battery pack and leading to reduc-tions in the implementation cost and form factor. The simu-lation and experimental results demonstrated an acceleratedequalization capability for the proposed GCC-type equalizerduring the discharging process.

The rest of the paper is arranged in the following order:The operational principle of the proposed equalizer is dis-cussed in Section 2. The relative SOC observation approachbased on overall voltage variation is introduced in Section 3.Simulation and experimental results are provided in Section4 and Section 5, respectively. Finally, Section 6 presents theconclusion of this paper.

2. Operational Principle of the GCC-TypeEqualizer

2.1 Circuit Configuration Figure 1 shows the circuitconfiguration of the GCC-type equalizer for a system incor-porating n battery modules, B1–Bn. Battery module termi-nal voltages are denoted as V1–Vn. The terms S1,1–S(n−1),2

indicate switching devices and L1–Ln−1 are inductor compo-nents. In addition, the capacitors in parallel with the batterymodules are defined as C1–Cn. Each battery module has as-sociated energy interchange paths connected to the upper andthe lower neighboring battery module. Even though all bat-tery modules are connected in series, single buck-boost chop-pers associated with pairs of battery modules can be operated

Fig. 1. Circuit configuration of a GCC-type equalizerincorporating n batteries

585 IEEJ Journal IA, Vol.9, No.5, 2020


Fig. 2. Two-port GCC-type equalizer

individually. It is thus possible to explain the operationalprinciple of the GCC-type equalizer based on that of a two-port equalizer, as shown in Fig. 2. Although OCV and in-ternal resistance of a battery module vary depending on thepresent SOC condition, these parameters can be assumed tobe constants during a specific switching interval. Each bat-tery module in the two-port equalizer can thus be representedby a voltage source and a resistor in series. The OCV, theinternal resistance, the average current, and the average ter-minal voltage of the top battery module B1 are defined as E1,R1, I1, and V1, respectively, and as E2, R2, I2, and V2, re-spectively, for the bottom battery module B2. Hereafter thesections, V1 and I1 are referred to as the top module voltageand top module current, while V2 and I2 are referred to as thebottom module voltage and bottom module current. In addi-tion, another resistor RL is inserted in series with inductor L,to exhibit a loss component.2.2 Operational Principle The switch on the high

side, S1, is controlled by a gating signal with ON duty ratioD, and the switch on the low side, S2, is controlled by thecomplementary gating signal (1 − D). The ratio of the topmodule voltage and the bottom module voltage is determinedas the reverse of the ON duty ratio as follows:

V1 : V2 = (1 − D) : D. · · · · · · · · · · · · · · · · · · · · · · · · · · · · (1)

Individual batteries in a pack are typically unbalanced interms of their SOCs. Figure 3 shows the operating pointsof unbalanced battery modules on a three-dimensional sur-face, where the primary horizontal axis indicates the modulecurrent (discharging state), the secondary horizontal axis in-dicates SOC, and the vertical axis indicates the module termi-nal voltage. Due to internal resistance, the module terminalvoltage drops while in a discharging state and rises while ina charging state. When the SOC of the top battery module,SOC1, is higher than that of the bottom battery module, SOC2

(SOC1 = 1 and SOC2 = 0.5), the OCVs of the two batterymodules, E1 and E2, are non-identical. This is demonstratedon the surface in Fig. 3, where the OCV line is shown in pink.Before operating the equalizer, each battery module is dis-charged by drawing the same current Iout, regardless of theirSOC condition. Corresponding module operating points aredefined as A′ and B′ and their voltages are defined as V1

′ andV2′, respectively. It can be seen that the module terminal volt-

ages stay at different levels. If the discharging process lastsfor many hours, there is a tendency for the bottom batterymodule B2 to be depleted prior to the other battery module.Subsequently, safety may be compromised with a depletedbattery module.

In order to prevent these problems and to maximize avail-able battery capacity, the equalizer starts operating under the

Fig. 3. Operating points of the unbalanced battery mod-ules in the discharging state

condition D = 0.5. The module currents I1 and I2, are differ-ent depending on their SOC condition. The top battery mod-ule B1 is discharged by drawing current I1, which is higherthan the output current Iout. The bottom battery module B2

retains its stored energy due to its current I2 being smallerthan the output current. The difference between I1 and Iout isequivalent to the top module current change factor ΔI1, andthe difference between I2 and Iout is determined by the bot-tom module current change factor ΔI2. Therefore, I1 and I2

can be expressed as:

I1 = Iout + ΔI1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

and

I2 = Iout − ΔI2. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

The module terminal voltages, V1 and V2, are equalizedand the corresponding module operating points are definedas A and B, shown by the blue triangle and red circle mark-ers on the surface in Fig. 3. V1 and V2 can be obtained using:

V1 = E1 − R1 · I1, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (4)

and

V2 = E2 − R2 · I2. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)

By substituting (2) into (4), and (3) into (5), the modulevoltages can be obtained using:

V1 = E1 − R1(Iout + ΔI1) · · · · · · · · · · · · · · · · · · · · · · · · · (6)

and

V2 = E2 − R2(Iout − ΔI2). · · · · · · · · · · · · · · · · · · · · · · · · (7)

In order to identify the module operating points A and B, itis necessary to derive ΔI1 and ΔI2. In order to do this, theswitching operation of the two-port equalizer shown in Fig. 4was analyzed. The top module current can be calculated us-ing:

I1 =1

TS

∫ TS

0i1(t)dt, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (8)



(a) When S1 is in the ON state

(b) When S1 is in the OFF state

Fig. 4. Switching operation of a two-port equalizer

where TS is the switching interval and i1 is the instantaneouscurrent of the top battery module.

The inductor is connected to the top battery module duringthe ON state of S1, and is switched to the bottom battery mod-ule during the OFF state of S1. Therefore, i1 can be expressedas:

i1(t) =

⎧⎪⎪⎨⎪⎪⎩iC1(t) + iL(t) + iout 0 < t < DTs

iC1(t) + iout DTs < t < Ts, · · · · · · (9)

where iC1 indicates the instantaneous current of the top ca-pacitor C1, iL indicates the instantaneous current of the in-ductor L, and iout indicates the instantaneous output current.

By substituting (9) into (8), the top module current can becalculated using:

I1 =1

TS

∫ DTS

0(iC1(t) + iL(t) + iout)dt

+1

TS

∫ TS

DTS

(iC1(t) + iout)dt. · · · · · · · · · · · · · · · · (10)

Under the steady state condition, the average current of thetop capacitor C1 is zero as shown in Eq. (11):

IC1 =1

TS

∫ TS

0iC1(t)dt = 0. · · · · · · · · · · · · · · · · · · · · · (11)

Therefore, (10) can be shortened to:

I1=1

TS

∫ DTS

0(iL(t)+iout)dt+

1TS

∫ TS

DTS

(iout)dt. · · · · · · (12)

Through simplification of (12), I1 can be expressed as:

I1 = Iout + DIL, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13)

where IL is the average inductor current.Using a similar procedure, I2 can also be obtained using:

I2 = Iout − (1 − D)IL. · · · · · · · · · · · · · · · · · · · · · · · · · · · (14)

From equations (13) and (14), it can be seen that both I1

and I2 have dependencies upon the average inductor current.In steady state operation, this can be determined based on thestate space averaging method. According to Kirchhoff’s cir-cuit laws, the circuit equations for the ON state operation ofS1 shown in Fig. 4(a) are:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

ddt

iL(t) = −RL

LiL(t) +

1L

v1(t)

ddt

v2(t) = − 1R2C2

v2(t) +E2 − R2iout

R2C2

ddt

v1(t) = − iL(t)C1− 1

R1C1v1(t) +

E1 − R1iout

R1C1

,

· · · · · · · · · · · · · · · · · · · (15)

where v1 is the instantaneous terminal voltage of the top bat-tery module and v2 is the instantaneous terminal voltage ofthe bottom battery module. The state equations in (15) canbe converted into the following matrix form:

ddt

⎡⎢⎢⎢⎢⎢⎢⎢⎣iL(t)v2(t)v1(t)

⎤⎥⎥⎥⎥⎥⎥⎥⎦ = A1

⎡⎢⎢⎢⎢⎢⎢⎢⎣iL(t)v2(t)v1(t)

⎤⎥⎥⎥⎥⎥⎥⎥⎦ + b1. · · · · · · · · · · · · · · · · · · · · · (16)

The circuit equations for the OFF state operation of S1

shown in Fig. 4(b) are derived using a procedure similar tothat used to derive the ON state equations of S1, and can beexpressed as:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

ddt

iL(t) = −RL

LiL(t) − 1

Lv2(t)

ddt

v2(t) =iL(t)C2− 1

R2C2v2(t) +

E2 − R2iout

R2C2

ddt

v1(t) = − 1R1C1

v1(t) +E1 − R1iout

R1C1

.

· · · · · · · · · · · · · · · · · · · (17)

The corresponding matrix form of (17) can be expressed as:

ddt

⎡⎢⎢⎢⎢⎢⎢⎢⎣iL(t)v2(t)v1(t)

⎤⎥⎥⎥⎥⎥⎥⎥⎦ = A2

⎡⎢⎢⎢⎢⎢⎢⎢⎣iL(t)v2(t)v1(t)

⎤⎥⎥⎥⎥⎥⎥⎥⎦ + b2. · · · · · · · · · · · · · · · · · · · · · (18)

By combining (16) and (18), A and b matrices are derivedusing:

A = DA1 + (1 − D)A2 · · · · · · · · · · · · · · · · · · · · · · · · · · (19)

and

b = Db1 + (1 − D)b2. · · · · · · · · · · · · · · · · · · · · · · · · · · · (20)

Based on A and b, the average inductor current IL, can bederived as:

IL =D(E1 − R1Iout) − (1 − D)(E2 − R2Iout)

RL + D2R1 + (1 − D)2R2, · · · · · (21)

and is determined by the ON duty ratio, D, the output current,Iout, and the difference in battery SOCs. This is a result of theOCVs, E1 and E2, and the internal resistances, R1 and R2,of the battery modules being dependent on the current SOCcondition.

Therefore, the current change factors ΔI1 and ΔI2, are:

ΔI1 = DIL



= DD(E1 − R1Iout) − (1 − D)(E2 − R2Iout)

RL + D2R1 + (1 − D)2R2

· · · · · · · · · · · · · · · · · · · · (22)

and

ΔI2 = (1 − D)IL

= (1 − D)D(E1 − R1Iout) − (1 − D)(E2 − R2Iout)

RL + D2R1 + (1 − D)2R2.

· · · · · · · · · · · · · · · · · · · · (23)

From equations (22) and (23), it is clear that the currentchange factors have dependencies upon the following param-eters: ON duty ratio D, and output current Iout.

The overall voltage of the two battery modules Vout, whichis referred to as the overall voltage in the following sections,can be obtained most simply using:

Vout = V1 + V2. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(24)

By substituting (6) and (7) into (24), the overall voltage canbe expressed as:

Vout = E1 − R1(Iout + ΔI1) + E2 − R2(Iout − ΔI2).

· · · · · · · · · · · · · · · · · · · (25)

2.2.1 Operation with Symmetric Duty Ratio In aspecific case, the battery modules may be in a balanced state.Figure 5 shows the operation of balanced battery modules un-der the condition D = 0.5. Each module current is identicalto the output current Iout under this condition. Moreover, thevoltages of each module are equal, and are equivalent to 0.5Vout. The module operating points, A and B, are coincidentwith the same position, and the current change factors, ΔI1

and ΔI2, are both zero. Figure 6 shows the operation of un-balanced battery modules, wherein the SOC of the bottombattery module is lower than that of the top battery module.A′ and B′ are the operating points at which the equalizer doesnot operate. Once the equalizer operates under the conditionD = 0.5, A′ moves to A, and B′ moves to B. Under this con-dition, the operation line OL, becomes horizontal. Figure 7shows the transitions of the module operating points depend-ing on variations in the output current. When the battery packis discharged by drawing the output current Iout, the top mod-ule current I1, is larger than Iout, and the bottom module cur-rent I2, can be reduced. The corresponding operating pointsare indicated as A and B. When the output current is shiftedfrom Iout to Iout

′, the operating points also transition from Aand B to A′ and B′. I1

′ and I2′ represent the module currents.

Although the top battery module is discharged by drawing acurrent greater than Iout

′, the bottom battery module can becharged. Therefore, B′ is kept at a voltage level that is higherthan the OCV of the bottom battery module, E2, while A′ iskept at a voltage level that is lower than the OCV of the topbattery module, E1. When the entire battery pack is chargedby output current Iout

′′, the bottom module current I2′′, is

much greater than the top module current I1′′. Therefore, it

can be seen that the module operating points are always po-sitioned on the horizontal operation line under the conditionD = 0.5, even if the output current varies. Most importantly,in the discharging state, the battery module with the higherSOC has a larger associated current than the battery modulewith the lower SOC. As a result, the low-SOC module willoperate for a longer time.

Fig. 5. Operation of balanced battery modules under thecondition D = 0.5

Fig. 6. Operation of unbalanced battery modules underthe condition D = 0.5

Fig. 7. Transition of the module operating points withrespect to variations in the output current

2.2.2 Operation with Asymmetric Duty RatioHowever, a constant duty ratio (D = 0.5) yields an in-

adequate equalization performance when the entire batterypack is discharged by drawing a high current. Changingthe duty ratio allows control of the current from each mod-ule, resulting in enhanced performance. The operation of





the unbalanced battery modules under different ON duty ratioconditions is illustrated in Fig. 8 and Fig. 9. Figure 8 showsoperation under the condition D = 0.4. Here, A and B are themodule operating points. Depending on the given duty ratio,the module voltages are proportional to the overall voltage(V1 = 0.6Vout and V2 = 0.4Vout). Under such a condition, thetop module current I1, is lower than the output current Iout

and the bottom module current I2, is higher. Moreover, theoperation line OL shifts in a counterclockwise direction fromthe horizontal position when D is set at a value smaller than0.5.

Figure 9 shows the operation under the reverse condition(D = 0.6). When D is set larger than 0.5, OL turns in a clock-wise direction. Therefore, it can be seen that not only modulecurrent, but also the module voltage portions are contrasted(V1 = 0.4Vout and V2 = 0.6Vout) in such a condition. In re-view, I2 is lower, while I1 is higher than Iout.

3. Relative SOC Observation Approach basedupon Overall Voltage Variation

Figure 10 shows the overall voltage curve of the balancedbattery modules with respect to the ON duty ratio D. Underthe condition D = 0.4, the top module voltage, the bottommodule voltage, and the overall voltage come to A, B, and

Fig. 10. Overall voltage curve of the balanced batterymodules with respect to the ON duty ratio D

Fig. 11. Overall voltage curve of the unbalanced batterymodules with respect to the ON duty ratio D

C, respectively. Under the condition D = 0.6, the top modulevoltage, the bottom module voltage, and the overall voltagecome to A′, B′, and C′, respectively. When SOC1 and SOC2

are equalized, both A and B′, and B and A′ are identical. Thismeans that C and C′ are also identical (C = C′) if the outputcurrent Iout is constant. Therefore, it can be seen that the over-all voltage curve is purely symmetric when the SOCs of thetwo battery modules are equalized. The peak of the overallvoltage curve is located at D = 0.5. Figure 11 shows an ex-ample of the overall voltage curve of the two battery moduleswhen their SOCs are not identical. SOC1 is assumed to behigher than SOC2 in this case. As in Fig. 10, the top modulevoltage, the bottom module voltage, and the overall voltagecome to A, B, and C, respectively, under the condition D =0.4, and come to A′, B′, and C′, respectively, under the con-dition D = 0.6. In this case, C and C′ are not identical (C >C′) and the difference between them can be expressed as:

ΔVout = Vout − V ′out, · · · · · · · · · · · · · · · · · · · · · · · · · · · · (26)

where ΔVout is the overall voltage variation, Vout is the overallvoltage under the condition D = 0.4, and Vout

′ is the overallvoltage under the condition D = 0.6. By contrast, C′ can behigher than C when SOC1 is smaller than SOC2. It can thus



Fig. 12. Complementary control signals with the dutyratio sequence for relative SOC observation

be seen that the overall voltage curve for the unbalanced bat-tery modules is asymmetric for all cases.

Based on this overall voltage variation effect, the differencebetween SOC1 and SOC2 can be observed while the batteryis in operation by strategically changing the duty ratio of theequalizer while detecting the overall voltage. This differenceis referred to as the relative SOC (ΔSOC), and can be ex-pressed as:

ΔSOC = SOC1 − SOC2. · · · · · · · · · · · · · · · · · · · · · · · · (27)

Figure 12 shows complementary control signals with aduty ratio sequence for the relative SOC observation, whereΔD is the duty ratio change variable, TM is the measurementperiod, TF is the full period, TS is the switching interval,and TE is the equalization period. The observation periodincludes four steps. Step I and Step III initialize the batterymodules while Step II and Step IV are dedicated to the overallvoltage measurements. The increased ON duty ratio 0.5+ΔDand the decreased ON duty ratio 0.5 − ΔD determined by theduty ratio change variable, are sent to the equalizer in Step IIand Step IV, respectively. Thus, the overall voltage for steadystate operation is first detected in Step II, and then detected asecond time in Step IV.

In other words, in order to detect whether or not there is aSOC imbalance between the battery modules, it is necessaryto allow a large current to flow through them. This can beachieved by changing the ON duty ratio, D, because the am-plitude of the inductor current, IL, is strongly dependent onthe ON duty ratio. As a result, the module terminal voltagereduces as the voltage drop across the module’s internal re-sistance increases. Therefore, the overall voltage varies whilethe ON duty ratio changes. This can be seen from Eq. (25),where E1, E2, R1, R2, and Iout are constants, whereas ΔI1 andΔI2 are variables. Allowing a large current to flow throughthe battery modules requires a switch and inductor with highcurrent ratings. However, it should be noted that the batterymodule current and/or inductor current is only increased for avery short duration, which does not result in harmful effects,such as a temperature rise in the battery module. This is sobecause the measurement period, TM, is much shorter thanthe equalization period, TE, as shown in Fig. 12.

In Fig. 13, a two-port equalizer with a voltage transducer(VT) and a current transducer (CT) is shown. The VT is used

Fig. 13. Two-port equalizer with CT and VT

Fig. 14. Three-port GCC-type equalizer with CT and VT

Fig. 15. Relative SOC observation timing diagram for athree-port GCC-type equalizer

to detect the overall voltage while the CT is used to measurethe output current. The charging or discharging state of theentire battery pack can be obtained from the measured outputcurrent. Using the detected overall voltages and measuredoutput current, ΔVout can be obtained, and is directly mappedto ΔSOC.

Moreover, it is possible to apply the relative SOC observa-tion approach to a pack composed of a large number of series-connected batteries. This can be done because each chop-per circuit can be operated sequentially from the top positionwhile other choppers are shut down. For instance, a three-port GCC-type equalizer is detailed along with its circuit con-figuration in Fig. 14. Chopper1 (in the green shaded area)works initially with the duty ratio sequence in Fig. 12 to de-tect the relative SOC of B1 and B2. At this time, Chopper2 (inthe orange shaded area) is completely turned off. Chopper1 isthen turned off and Chopper2 is started in order to observe therelative SOC of B2 and B3. Based on this methodology, thetechnique can be applied to a pack comprising many batterymodules.

Figure 15 shows the SOC observation timing for the three-port equalizer, which is determined based on the number ofpairs of battery modules. The observation process thus lastsfor twice the period TM in the case of three battery modulesin series. Figure 16 shows a flowchart of the balancing strat-egy based on relative SOC observation. In total, seven stepsare performed within the balancing algorithm. The overallvoltage and the output current are the input data. In Step 1,the duty ratio sequence is sent to the equalizer. In Step 2,



Fig. 16. Flow chart for module-balancing strategy basedon relative SOC observation

ΔVout is determined based on the detected overall voltages.The charging or discharging state of the entire battery pack isthen obtained in Step 3. Depending on the measured outputcurrent, the relative SOC of the battery modules is estimatedin Step 4. In Step 5, the estimated relative SOC is evaluated.The symmetric or asymmetric duty ratio (D = 0.525 or D =0.475) is applied to the equalizer in Step 6 based on whetherΔSOC is smaller or larger than 0.1. An accelerated balancingaction is performed on detection of a large relative SOC. Ifthere is a very small imbalance between the two battery mod-ules, the balancing controller keeps a symmetric duty ratio.In the final step, the equalizing operation is continued untilthe end of the equalization period, TE.

4. Simulation Results

In the simulation, a battery model provided by PSIM soft-ware was used. Its OCV and internal resistance characteris-tics are shown in Fig. 17 and specifications are listed in Ta-ble 1. The battery capacity was set to 6.5 Ah, and the initialSOCs of the two battery modules were set to SOC1 = 0.5,SOC2 = 1, ensuring an unbalanced condition. The circuit pa-rameters are shown in Table 2.

Due to equalizer operation during the measurement period,not only a small variation but also a high frequency rippleappeared on the overall voltage. This high-amplitude ripplewould degrade the performance of the SOC observation un-less the amplitude was reduced. A moving average filter wasthus used to remove the ripple voltage and the capacitance of

Fig. 17. OCV and internal resistance characteristics ofNiMH battery module containing six cells (6.5 Ah)

Table 1. Specifications of the NiMH battery model

Table 2. Circuit parameters

the capacitor was reduced by as much as possible. The se-lected switching frequency of the equalizer was 10 kHz. Thebattery pack was discharged at a rate of 0.25 C (1.65 A).4.1 Overall Voltage Variation Under the unbalanced

condition SOC1 = 0.5 and SOC2 = 1, the duty ratio sequencefor the relative SOC observation was sent to the equalizer.The duty ratio change variable ΔD and the measurement pe-riod TM, were configured as 0.1 and 200 ms, respectively.

For appropriate detection of the overall voltage, it was nec-essary to wait until the equalizer operated in the steady statecondition, because the overall voltage fluctuated during thetransient state after changing the ON duty ratio. This meantthat the wait time had to be longer than the transient time.

Figure 18 shows the simulated inductor current and over-all voltage waveforms during the measurement period. T tr1

is the transient time in Step II, Twait1 is the wait time in StepII, T tr2 is the transient time in Step IV, and Twait2 is the waittime in Step IV. The filtered value of the overall voltage isshown in purple along with the measured waveform. It canbe seen that a small variation in the overall voltage during themeasurement period could be detected precisely by using thefiltering method.

In this case, the overall voltage Vout′ was obtained from the

interval for the last 5 ms of Step II, which can be expressedas:

V ′out =1

t2 − t1

∫ t2

t1

vout(t)dt, · · · · · · · · · · · · · · · · · · · · · (28)

where t2 is the end time of Step II, and t1 can be calculatedfrom t2 as shown in the following equation:

t1 = t2 − 5 · 10−3. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(29)



Fig. 18. Simulated waveforms of the inductor currentand overall voltage during the measurement period

The overall voltage Vout can be obtained by:

Vout =1

t4 − t3

∫ t4

t3

vout(t)dt, · · · · · · · · · · · · · · · · · · · · · (30)

where t4 is the end time of Step IV, and t3 can be calculatedfrom t4 as shown in the following equation:

t3 = t4 − 5 · 10−3. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(31)

We could observe a difference between Vout′ and Vout, which

verified the asymmetric shape of the overall voltage variationshown in Fig. 11.

In Fig. 18, the average value of the inductor current isshown in yellow and was equal to −1.8 A in Step I and StepIII. In Step II, it increased to 4.31 A as the ON duty ratio,D, was incremented from 0.5 to 0.6. When the ON duty ra-tio was decremented from 0.5 to 0.4 in Step IV, the averagevalue of the inductor current became −8.86 A and the induc-tor ripple current was approximately 3.75 A.4.2 Relative SOC Observation Several unbalanced

conditions were simulated to visualize the relationship be-tween ΔVout and ΔSOC. SOC1 was incremented from 0.1 to0.9, and SOC2 was kept at 0.1. Figure 19 shows the simu-lated curve of the overall voltage variation with respect to thevarying relative SOC. As can be seen in Fig. 19, |ΔVout| wasclose to 0.1 under the balanced condition SOC1 = 0.1 andSOC2 = 0.1. By contrast, |ΔVout| reached its peak value un-der the highly unbalanced condition SOC1 = 0.9 and SOC2 =

0.1. It can thus be seen that a greater voltage difference wasobserved when the relative SOC of the two battery moduleswas higher.4.3 Module Equalization Process The three-port

equalizer shown in Fig. 14 was employed for the moduleequalization operation. The timing diagram is shown inFig. 20. The full period, TF, lasted for 400 s, and 400 ms ofthis was reserved for observation of the relative SOCs. Theremaining interval was dedicated to the equalization opera-tion. Figure 21 shows the simulated SOC variations of thethree battery modules during the discharging process whenthe equalizer was not in operation. The initial SOCs of the

Fig. 19. Simulated curve of the overall voltage variationwith respect to the varying relative SOC

Fig. 20. Timing diagram for the module equalizationoperation

Fig. 21. Simulated SOC variations during the discharg-ing process with the module equalizer not in operation

Fig. 22. Simulated inductor currents and SOC varia-tions during the discharging process with the moduleequalizer in operation under a constant duty ratio

three battery modules were set at 0.5, 1, and 0.7. FromFig. 21, it can be seen that the battery module with the low-est SOC was fully discharged within approximately 120 minprior to the others. Battery modules with higher SOCs werethus unable to discharge their remaining energy, leaving theunusable battery capacities.

Figure 22 shows the simulated inductor currents and SOCvariations during the discharging process when the module



equalizer was operating under a constant duty ratio (D1 = 0.5and D2 = 0.5). Although the battery module with the low-est SOC was depleted within approximately 160 min prior tothe others, the discharging time was extended by more than30 min and the unused battery capacity remaining after dis-charging could be reduced significantly compared to the casewhen the module equalizer was not in operation. However,the usable battery capacity in battery modules, B2 and B3 wasstill reduced. Operation under a constant duty ratio was thusnot optimal.

Owing to the non-linear OCV-SOC characteristics ofNiMH batteries, the differences in the module terminal volt-ages were higher at the beginning and end of the SOC. Asa result, high amplitude inductor currents, iL1 and iL2, wereinduced at the beginning of the equalization process, eventhough the ON duty ratio was kept constant and the degreeof SOC imbalance varied only slightly. This can be seen inFig. 22, where the average values of the inductor currents areshown in yellow and pink.

Figure 23 shows the simulated inductor currents and SOCvariations during the discharging process with the moduleequalizer in operation based on the relative SOC. The rel-ative SOC of each pair of battery modules associated withsingle buck-boost converter was observed using a ΔVout-ΔSOC look-up table. The inductor currents, iL1 and iL2, hadhigh amplitudes at the beginning of the equalization process,which was similar to the case in which the module equal-izer was in operation with a constant duty ratio. The induc-tor currents then decreased gradually as energy was trans-ferred between the battery modules and finally approached0 A as the batteries approached an equalized condition. Anaccelerated equalization between SOC2 and SOC3 was car-ried out within 55 min. Due to the large degree of imbal-ance between SOC1 and SOC2, the equalization required alonger time, even though the equalization speed had been ac-celerated based on the relative SOC observation. However, itwas noted that the SOC of each battery module reached thesame value after 135 min, and that the maximum availableenergy of the entire battery pack was extracted. In addition,

Fig. 23. Simulated inductor currents and SOC varia-tions during the discharging process with the moduleequalizer in operation based on the relative SOC

the accelerated balancing was well executed using the rela-tive SOC observation. When compared to operation under aconstant duty ratio, the equalization performance was signif-icantly improved.

5. Experimental Results

The experimentation was carried out using the same envi-ronment as in the simulation. A DC electronic load (PLZ-205W-Kikusui) was used as the discharging current source.A battery simulator device (2281S-20-6-Keithley), whichsimulated the OCV and internal resistance characteristicsshown in Fig. 17, was used as the battery. A half-bridge plat-form incorporating GaN devices (TDHBG25000P100-KIT,2.5 kW) was used as the equalizer hardware. A digital con-troller (PE-Expert 4) was used to send module equalizingcontrol signals to the hardware switches. Figure 24 showsa photograph of the experimental setup.5.1 Overall Voltage Variation To verify the over-

all voltage variation of the unbalanced battery modules, thesame conditions applied in the simulation (in terms of theSOCs) were considered. The duty ratio sequence for the rel-ative SOC observation was sent to the equalizer hardware.Figure 25 shows the experimental inductor current and over-all voltage waveform during the measurement period, wherethe filtered value of the overall voltage is shown in purple.A moving average filter with the same characteristics as thatused in the simulation was used to precisely detect the smallvariations in the overall voltage.

The transient waveform was slightly different from thesimulation result due to the response delay of the battery sim-ulator. However, the averages of the overall voltage wave-form between t1 and t2 and between t3 and t4, could be an-alyzed based on equations (28) and (30). It was noted thatVout

′ and Vout were non-identical, which matched the simu-lation result.5.2 Relative SOC Observation Several experiments

were conducted in order to verify the simulated curve of the

Fig. 24. Photograph of the experimental setup



Fig. 25. Experimental waveforms of the inductor cur-rent and overall voltage during the measurement period

Fig. 26. Experimental curve of the overall voltage vari-ation with respect to the varying relative SOCs

overall voltage variation. As in the simulation, SOC1 wasincremented from 0.1 to 0.9, and SOC2 was kept at 0.1. Fig-ure 26 shows the experimental curve of the overall voltagevariation with respect to variations in relative SOCs. Al-though the experimental curve resembled the simulated curveshown in Fig. 19, the specific values of the experimentalcurve were different. For instance, |ΔVout|was almost 0 whenthe battery modules were under the balanced condition ofSOC1 = 0.1 and SOC2 = 0.1. Due to the measurement ac-curacy of the voltage sensor (LV 25-P), this difference couldnot be eliminated completely, even though a moving averagefilter was employed.5.3 Module Equalization Process The experiments

demonstrating the module equalization operation were car-ried out under two different conditions. As in the simulation,the initial SOCs of the three battery modules were set at 0.5,0.1, and 0.7. Figure 27 shows the experimental inductor cur-rents and SOC variations of the three battery modules duringthe discharging process while the equalizer was in operationunder a constant duty ratio (D1 = 0.5 and D2 = 0.5). Thiswas similar to the simulation result shown in Fig. 22 in thatthe discharging time was extended by approximately 30 minand the unusable capacity left after discharging could be sig-nificantly reduced.

Figure 28 shows the experimental inductor currents andSOC variations during the discharging process while theequalizer was in operation based on the relative SOC. Asin the simulation, the relative SOC of each pair of battery

Fig. 27. Experimental inductor currents and SOC vari-ation during the discharging process with the moduleequalizer in operation under a constant duty ratio

Fig. 28. Experimental inductor currents and SOC vari-ations during the discharging process with the moduleequalizer in operation based on the relative SOC

modules associated with single buck-boost converter was ob-served using the ΔVout-ΔSOC look-up table. It can be seenthat SOC equalization was successfully achieved and that themaximum capacity was fully discharged at the end of the dis-charging process. However, the module equalization timewas somewhat longer when compared to the simulation re-sults. Power losses in the equalizer hardware may have anegative effect, and this could be the reason for the loweredequalization performance.

6. Conclusions

In this study, a GCC-type module equalizer was proposedthat equalized the SOC of each battery module to the samepoint. By strategically changing the duty ratio while detect-ing the overall voltage, the relative SOC of each battery mod-ule could be observed while the battery system was in oper-ation. As a result, the use of only two sensors could enableSOC observation for the entire battery pack, leading to a re-duction in implementation cost and system form factor. Theequalization current was controlled in accordance with the



observed relative SOC. The simulation and experimental re-sults verified the functionality of the proposed equalizer anddemonstrated its accelerated equalization performance dur-ing the discharging process. The proposed equalizer is alsoappropriate for use with other batteries that possess similarcharacteristics to those used in the study. In addition, the out-put of this study is crucial for the development of battery stor-age systems for developing nations such as Mongolia. Theanalysis of energy losses and temperature dependency willbe conducted in future work.

AcknowledgmentThis work was partially supported by “Higher Engineer-

ing Education Development” Project–Research and Develop-ment for Power Electronics and Industrial Automation (Grantnumber: J14C16).

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Appendix

If a battery module has experienced a certain degree ofdegradation, there is an attendant increase in its internal re-sistance. When a couple of battery modules with differ-ent internal resistances are connected to the module equal-izer, depending on the amplitude of the output current, Iout,the terminal voltage curves may not be parallel as shown inapp. Fig. 1. However, the overall voltage under the conditionD = 0.4, Vout, is still higher than that under the condition D= 0.6, Vout

′, as shown in app. Fig. 2. Based on the differencein these overall voltages, ΔVout, the relative SOC of the bat-

app. Fig. 1. Operation of unbalanced battery moduleswith different internal resistances under the condition D= 0.5



app. Fig. 2. Overall voltage curve of unbalanced batterymodules with different internal resistances with respect tothe ON duty ratio D

tery modules can be observed. The SOC equalization of eachbattery module can then be achieved using the proposed SOCobservation technique.

Turmandakh Bat-Orgil (Student Member) received his B.E. degreein Electronics Engineering and his M.E. degree inRenewable Energy Engineering from the NationalUniversity of Mongolia, Ulaanbaatar, Mongolia, in2015 and 2017, respectively. He is presently work-ing towards his Ph.D. degree in Electrical Engineer-ing at Tokyo Metropolitan University, Tokyo, Japan.In 2017, he became a Faculty Member in the De-partment of Electronics and Communication Engi-neering, National University of Mongolia. His re-

search interests include power electronics-based active battery balancingtechniques, active power-decoupling circuits and distributed power gener-ation technology.

Bayasgalan Dugarjav (Non-member) received his B.S. degree in Me-chanical Engineering from the Mongolian Universityof Science and Technology, Ulaanbaatar, Mongolia,in 2005. He received his M.S. and Ph.D. degreesin Electrical Engineering from the Konkuk Univer-sity, Seoul, Korea, in 2008 and 2012, respectively.From 2010 to 2012, he was a Research Engineer inthe Inverter R&D Center of Seoho Electric Co., Ltd.,Anyang, Korea. In 2014, he joined the Departmentof Electronics and Communication Engineering, Na-

tional University of Mongolia, where he is presently working as an AssociateProfessor. His research interests include distributed power generation tech-nology, power conversion systems for renewable energy sources and electricvehicles.

Toshihisa Shimizu (Fellow) received his B.E., M.E., and Dr.Eng. de-grees all in Electrical Engineering from the TokyoMetropolitan University, Tokyo, Japan, in 1978,1980, and 1991, respectively. He was a VisitingProfessor at the Virginia Power Electronics Center(VPEC), Virginia Polytechnic Institute and State Uni-versity, Blacksburg, VA, USA, in 1998. In 1980,he became a Research Engineer in the Research andDevelopment Department of Fuji Electric Co., Ltd.,Tokyo, Japan. Since 1993, he has been with the De-

partment of Electrical Engineering, Tokyo Metropolitan University, wherehe is presently working as a Full Professor. His current research interestsinclude power converters, high-frequency inverters, photovoltaic power gen-eration systems, EMI in power converters, high power density converter de-sign, and passive components for power converters. He is an Associate Edi-tor of the IEEE Transactions on Power Electronics. He has authored or coau-thored more than 100 journal papers and 120 international conference pro-ceedings and 6 technical books. He also holds ten patents and more than tenpatents pending. Dr. Shimizu has received transaction paper awards from theInstitute of Electrical Engineers of Japan in 1999 and 2010. He was a recip-ient of six best paper awards at International Power Electronics Conference(IPEC2010-ECCE Asia), International Power Electronics and Motion Con-trol Conference (EPE-PEMC2010), ECCE2015-7, and International Confer-ence on Power Electronics (ICPE2019-ECCE Asia), respectively. He is aFellow of the IEEE and IEEJ.


battery module equalizer based on state of charge

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