一种新型的高效 低成本的平衡方法在串联电池的应用

A Novel High-Efficiency Compact-Size Low-CostBalancing Method for Series-ConnectedBattery ApplicationsYi-Hsun Hsieh,Tsorng-Juu Liang,Senior Member,IEEE,Shih-Ming(Orion)Chen,Member,IEEE,Wan-Yi Horng,and Yi-Yuan ChungAbstract—This paper proposes a novel balancing method for series-connected batteries applications.The proposed method uses a transformer to couple the energy from charger or discharger to batteries for energy balancing.The proposed method has the ad-vantages of high efficiency,compact size,suitable for any type of switching converter,load-related balancing energy,and extremely simple structure without any active switch for voltage balance func-tion.Three converters,including a CLL converter,an interleaved noninverting buck–boost(BB)converter,and a noninverting BB converter,with voltage balancing function and state-of-charge bal-ancing function are built to verify the feasibility of the proposed balancing methods.Index Terms—Compact size,equalizer,high efficiency,low cost, series-connected batteries,state-of-charge(SOC)balance,voltage balance.I.I NTRODUCTIONR ECHARGEABLE batteries are widely applied in portable devices,electric vehicles,hybrid electric vehicles,energy storage systems,etc.The terminal voltage of a single battery cell is usually low,for example,2V in lead-acid batteries,3.6V in lithium-ion batteries,and3.3V in lithium iron phosphate (LiFePO4)batteries[1].To meet the load voltage requirements, the batteries are usually connected in series[2].Because of the manufacturing variance of cells,series-connected batteries without a proper balancing method suffers serious unbalanced problems,which lead to safety issues,shortened lifetime or decreased usable capacity[3]–[6].As shown in Fig.1,the balancing topologies can be catego-rized as passive and active balancing methods.Shunt resistors are used in passive balancing to absorb redundant energy to prevent overcharge of the cells[7],[8]while the active bal-ancing properly distributes energy of each cells in the battery pack.Active balancing can be further divided into two typesManuscript received November2,2012;revised January19,2013; accepted January24,2013.Date of current version June6,2013.This work was supported by the National Science Council of Taiwan under project NSC101-3113-P-006-024.Recommended for publication by Associate Editor L.Gauchia.The authors are with the Department of Electrical Engineer-ing/Advanced Optoelectronic Technology Center(AOTC),National Cheng Kung University,Tainan701,Taiwan(e-mail:ericsys3152@; tjliang@.tw;orion.chen@;n26004545@mail.ncku. edu.tw;teddybear10059@).T.-J.Liang is the corresponding author.Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TPEL.2013.2246584Fig.1.Battery balancingtopologies.Fig.2.Equalizers with different balancing energy obtaining and distributingprocesses.(a)Multicapacitor.(b)Single capacitor.(c)Multi-inductor BB.(d)Single-inductor BB.(e)Multiwindingflyback.(f)Single-windingflyback.of approaches:to transfer energy between cells and to controlcharging/discharging currents.The major difference betweenthese two active balancing methods is that the former continu-ously provides constant balancing energy and the later adjustsbalancing energy depending on load condition.As a result,thesystem efficiency with a balancing method of transferring en-ergy between cells under light-load condition will be lower.The active balancing methods can be categorized in two re-spects:topological respect and energy-transferring respect.Inenergy transferring point of view,there are two major pro-cesses in active balancing,including balancing energy obtain-ing and balancing energy distributing.Fig.2(a)and(b)showstwo capacitor-based equalizers with the same energy obtainingprocess,using capacitors to transfer the energy,but with dif-ferent energy distributing processes[9]–[11].The equalizer inFig.2(a)obtains balancing energy by shunting capacitor to the 0885-8993/$31.00©2013IEEEFig.3.Proposed balancing methods.(a)Basic.(b)With selecting switched.(c)With one secondary winding pair.high-voltage battery,and distributes the energy to its adjacent one.The equalizer in Fig.2(b)obtains the energy in the same way,yet it distributes the energy to any cell in the battery pack by controlling the selecting switches.Similarly,Fig.2(c)and (d)shows buck–boost equalizers [12],[13]and Fig.2(e)and (f)shows flyback equalizers [14],[15]with the same energy ob-taining process but with different energy distributing processes,respectively.Some papers proposed new energy obtaining meth-ods to increasing the efficiency of equalizer or reducing the size of magnetic components [16],[17],[20],[21],while others pro-posed new algorithms to speed up or gain more accurate of the balancing process [10],[11],[13],[18],[19].Nevertheless,this paper focuses on improving the performances of the balancing energy obtaining process.Categorized by topologies,there are three types of active bal-ancing methods,including capacitor-based [9]–[11],inductor-based [12]–[15],and converter-based topologies [16]–[21].Capacitor-based type has the advantages of a simple structure and simple control method.However,the capacitor-based type performs poorly in obtaining balancing energy because the ca-pacitor is shunted directly to each cell,causing large inrush cur-rent.In addition,capacitor-based type can only achieve voltage balance by distributing balancing energy rather than state-of-charge (SOC)balance.Balance among cells means that all the cells are fully charged or discharged at the same time.If the voltage difference caused by SOC difference is less than volt-age drop on an equivalent series resistor,the voltage may fail to be balanced in the end [20],[22],[23].On the contrary,inductor-based type does not suffer high current stress and can achieve either voltage balance or SOC balance,because the inductor acts as a buffer between two cells and can deliver energy even from low-voltage side to high-voltage side.As a result,it is more energy efficient and can realize more balancing algorithms than capacitor-based type.Moreover,many topologies have been proposed to im-prove the performance over the capacitor-based or inductor-based type balancing methods.Some use resonant technol-ogy to improve balancing efficiency [16],[17].Some accel-erate the balancing speed [18],[19],others increase the utiliza-tion rate of magnetic components [20],[21].These advanced methods are all categorized into converter-based type balancing topologies.Controlling charging/discharging current can be achieved ei-ther by using a multi-input/output converter-based type [24]or by using battery modules [25],[26].A multi-input/output converter-based type is that in which cells are connected in se-ries to form a battery pack,and then the whole battery pack is connected to the converter.On the other hand,battery modules are that each cell is connected to its individual converter,and then the modules are connected in series.Battery module is the most complicated of all balancing methods,because it requires the communication between all modules;however,its balancing performance is the best among others [25],[26].In order to realize the load-related balancing energy and im-prove the performances of balancing energy obtaining,a novel balancing method is proposed.Fig.3(a)shows the basic pro-posed balancing method,where the equalizer obtains the bal-ancing energy from charger or discharger by magnetic coupling and distributes the energy to each cell depending on its terminal voltage to achieve voltage balance.The proposed balancing method has the following advan-tages.It does not suffer from inrush current and is capable of SOC balancing since the coupled energy from charging or dis-charging current can be regarded as a current pared with inductor-based type balancing,the magnetic component acts as a transformer rather than an energy storage device,so the balancing efficiency will be higher and the size will be more compact.Additionally,the proposed method can be ap-plied to any type of switching converter,making it suitable from low-power to high-power applications.Moreover,since the bal-ancing energy is directly related to charging or discharging en-ergy,the balancing energy will be automatically reduced under light-load condition.Most of all,the proposed method does not require any active switch to perform voltage balancing function,and has the least number of active switches compared with other methods while it has to perform SOC balance function.Furthermore,additional switches added to the secondary windings of a balancing transformer,as shown in Fig.3(b),act as selecting switches to achieve SOC balancing algorithm or overcome the mismatching problem of a multiwinding trans-former [24].Fig.3(c)shows the proposed equalizer with only one secondary winding pair needed for a balancing transformer;this scheme can further reduce the size of a transformer yet with the tradeoff of using more switches.HSIEH et al.:NOVEL HIGH-EFFICIENCY COMPACT-SIZE LOW-COST BALANCING METHOD5929Fig.4.Chargers with the proposed equalizer.(a)CLL.(b)IBB.(c)Type A BB.(d)Type B BB.This paper is organized as follows.The operating princi-ples of the proposed equalizer,which is applied to nonover-lapped symmetric-current-waveform(SCW)topologies,over-lapped SCW topologies,and asymmetric-current-waveform (ACW)topologies,are presented in Section II.Section III de-scribes the steady-state analysis of the proposed equalizer.Fi-nally,the experimental results are discussed in Section IV.Three topologies,including a CLL charger,an interleaved noninvert-ing buck–boost(IBB)charger,and a buck–boost(BB)charger, are built to verify the proposed balancing method.II.C HARACTERISTICS AND O PERATING P RINCIPLES OF THEP ROPOSED B ALANCING M ETHODBecause using a transformer to deliver power should deal with a demagnetization problem,the proposed balancing method is suitable for the circuit topologies with SCWs,such as a resonant converter,a push–pull converter,a full-bridge(FB)converter, and an interleaved structure.Moreover,the proposed balancing method can also be applied to ACW topologies,such as a buck converter,a boost converter,and a buck–boost converter.How-ever,the time for the magnetizing inductor to be demagnetized will be insufficient without proper design,which may cause saturation of magnetic components.Fig.4shows the CLL charger,the IBB charger,and the BB charger with the proposed equalizer,and these three topolo-gies will be used as examples to explain the operating princi-ples of the proposed balancing method for nonoverlapped SCW topologies,overlapped SCW topologies,and ACW topologies, respectively.Only the operating principle of the configuration in Fig.3(a)is discussed because the operating principle of the other two is similar to that except there are no currentflows in the nonconnected secondary windings of the balancing transformer T b.The windings in the primary side of T b of the balancing circuit are designed to be connected in series to output diodes;therefore,the balancing energy is proportional to the charging energy.To simplify the circuit analysis of the proposed equalizer, the following assumptions are made:1)All components are ideal,except for the magnetizing inductance of the balancing transformer T b.2)The switching frequency of the charger is much higher than the battery time constant,so the terminal voltage V Bi of each cell,from B1to B m,remains the same, and the voltage of the battery pack,which consists of m cells connected in series,equals to m·V B in one switching period.3) The turn ratios n a and n b of the two secondary windings of the balancing transformer T b for each cell are identical and equal to N sa/N p and N sb/N p.Furthermore,n a and n b are equal to n for nonoverlapped and overlapped SCW topologies.The operating principles of the proposed equalizer are similar to that of the multi-input/output converter-based topologies us-ing a multiwinding transformer and are well discussed in[24]. The main concept is that the higher the terminal voltage of the cell,the lower the balancing current delivered.All the cells are distributed the same amount of current when the whole battery pack reaches voltage balance.Therefore,this paper only illus-trates the operating principles under the condition that all the cell voltages are equal.In addition,the characteristics and operating principles of the CLL converter,the IBB converter,and the BB converter are well discussed in[27]–[29].Therefore,this paper focuses on the operating principles of the balancing circuit.A.Nonoverlapped SCW TopologiesFig.5illustrates typical waveforms of balancing circuit,and Fig.6shows the currentflowing paths of three operating modes for the CLL balancing charger in half-switching period.The three operating modes will be described later,and operating principles of the other half-switching period is similar to the5930IEEE TRANSACTIONS ON POWER ELECTRONICS,VOL.28,NO.12,DECEMBER2013Fig.5.Typical waveforms of the CLL balancing charger.described ones except for the currents areflowing in the opposite direction.Mode I[t0−t1,Fig.6(a)]:During this interval,D1is con-ducting,and the balancing transformer T b couples the energy from the CLL charger to equally charge the battery pack through D1a to D ma.The magnetizing inductor L mfirst releases its en-ergy to the battery pack,and then part of balancing energy is stored in L m after it is demagnetized.This mode ends when i Lm=i p1/n.Mode II[t1−t2,Fig.6(b)]:When i Lm>i p1/n,T b equally charges battery pack through D1b to D mb,and L m starts releas-ing its energy to the battery pack until the main charging current i p1drops to zero.Mode III[t2−t3,Fig.6(c)]:During this interval,D1is OFF,and there is no charging current in the CLL charger.L m releases its energy to the battery pack through D1b to D mb.This mode ends when D2conducts and the symmetric half-switching period will be started.B.Overlapped SCW TopologiesFigs.7and8show the operating waveforms of balancing cir-cuit and the currentflowing paths in half-switching period for the IBB balancing charger,respectively.There are two types of current waveforms of i p1and i p2in the IBB converter,one is under the condition of conducting period of i p1and i p2being shorter than T s/2,and the other is greater than T s/2.The follow-ing analysis is under the condition of conducting timegreater Fig.6.Currentflowing paths of the CLL balancing charger.(a)Mode I.(b) Mode II.(c)Mode III.than T s/2,where the overlapping of i p1and i p2occurs.The other condition will not be discussed because it is mentioned previously.Mode I[t0−t1,Fig.8(a)]:During this interval,D2and D4 are conducting simultaneously,so the overlapping waveforms of i p1and i p2occur.Because i p1and i p2induce the opposite flowing directions of magneticflux in the balancing transformer T b,the effectiveflux in T b equals to theflux induced by i p1−i p2.As a result,the balancing energy is reduced in this situation. The balancing energy induced by i p1−i p2is used to equally charge the battery pack through D1a to D ma;meanwhile,the magnetizing inductor L m releases its energy to the battery pack through the same path.This mode ends when D4is OFF. Mode II[t1−t2,Fig.8(b)]:In this interval,D4is cut off, so T b can deliver the whole balancing energy induced by i p1to the battery pack through D1a to D ma.L m releases its energy to the battery pack through the same path,and then part of the balancing energy is stored in L m after it is demagnetized. This mode ends when D4starts to conduct,and the symmetric half-switching period will be started.C.ACW TopologiesThere are two methods for demagnetizing the balancing trans-former T b,Type A is transferring the demagnetizing energy toHSIEH et al.:NOVEL HIGH-EFFICIENCY COMPACT-SIZE LOW-COST BALANCING METHOD5931Fig.7.Typical waveforms of the IBB balancingcharger.Fig.8.Current flowing paths of the IBB balancing charger.(a)Mode I.(b)Mode II.battery cells,and Type B is transferring the demagnetizing en-ergy to the charger.Fig.9shows the typical waveforms of the BB balancing charger with Type A demagnetization.Three op-erating modes will be explained later,and the current flowing paths of these operating modes are depicted in Fig.10.Fig.9.Typical waveforms of the Type A BB balancing charger.Mode I [t 0−t 1,Fig.10(a)]:During this interval,D 2is con-ducting,and the balancing transformer T b couples balancing energy to equally charge the battery pack through D 1a to D ma ;meanwhile,part of the balancing energy is stored in the magne-tizing inductor L m .Mode II [t 1−t 2,Fig.10(b)]:The current flowing paths are shown in Fig.10(b).In this interval,D 2stops conducting,L m releases its energy to the battery pack through D 1b to D mb .This mode ends when the energy of L m is reset to zero.Mode III [t 2−t 3,Fig.10(c)]:After L m is fully demagne-tized,there is no energy transfer in balancing circuit.This mode ends when D 2conducts again and the next switching period will be started.Figs.11and 12show the typical waveforms and current flow-ing paths of the BB balancing charger with Type B demagneti-zation.The operating modes are similar to Type A demagnetiza-tion except for the demagnetization process.In Mode I [t 0−t 1,Fig.12(a)],T b couples balancing energy form the charger to equally charge the battery pack and L m is magnetized.In Mode III [t 2−t 3,Fig.12(c)],after T b is demagnetized,there is also no energy transfer in balancing circuit.The only difference is the demagnetization process in Mode II [t 1−t 2,Fig.12(b)],which is described as follows.Mode II [t 1−t 2,Fig.12(b)]:During this interval,D 2re-mains conducting.The magnetizing inductor is demagnetized through D 2and Q 2to the whole battery pack.The current of D 2i p flows continuously and the current of Q 2i Q2slightly de-creases.Type B demagnetization uses only half the number of trans-former windings and diodes comparing with Type A.However,the voltage stress across diodes from D 1a to D ma of Type B is5932IEEE TRANSACTIONS ON POWER ELECTRONICS,VOL.28,NO.12,DECEMBER2013Fig.10.Currentflowing paths of the Type A BB balancing charger.(a)Mode I.(b)Mode II.(c)Mode III.m·n a·V B,which is typically much higher than(1+n a/n b)·V B of the voltage stress across diodes of Type A.Besides,when ap-plying the proposed method to the bidirectional converter,Type A still works due to its symmetrical configuration;however,in the discharging process,the balancing transformer T b of Type B becomes a coupled inductor,which acts like aflyback converter and will lose many advantages of using a transformer to transfer energy.III.S TEADY-S TATE A NALYSISThe steady-state analysis includes the charging current cal-culation,the charger design optimization,the transformer de-sign analysis,and the comparison of the normalized core area products.The magnetizing inductance of the balancing trans-former is assumed to be large enough,so it can be neglected in charger current calculation and charger designoptimization.Fig.11.Typical waveforms of the Type B BB balancing charger.A.Charging Current CalculationAssuming the average current of primary windings of the bal-ancing transformer T b is I p,the total balancing current I bal total can be foundI bal total=I pn a.(1) The average balancing current for each cell under voltage balance condition I bal is obtainedI bal=I pm·n a.(2) B.Charger Design OptimizationAssuming the voltage balance is achieved,the voltage across the primary side of balancing the transformer V p can be found as follows:V p=V Bn a.(3) Typically,because balancing current is much smaller than the main charging current,V p is so small that the original circuit can be regarded as unaffected by V p.However,if charger design optimization is necessary and the balancing transformer coupled energy directly from main charging current,as the examples presented in this paper,the equivalent battery pack voltage V eq can be obtained asV eq=m·V B+V p=m+1n a·V B(4) and the converter charging current I p for the desired average charging current I B is derived asI p=I B−I bal.(5) Substituting(2)into(5)yieldsI p=I B1+1/m·na.(6)HSIEH et al.:NOVEL HIGH-EFFICIENCY COMPACT-SIZE LOW-COST BALANCING METHOD5933Fig.12.Currentflowing paths of the Type B BB balancing charger.(a)Mode I.(b)Mode II.(c)Mode III.C.Transformer Design AnalysisThe magnetizing inductance of the balancing transformer should be large enough;otherwise,most of the energy for bal-ance will be stored in it.Though the balancing current wave-forms vary from topology to topology,the following design equation for minimum magnetizing inductance can be obtained by making the currentflowing in magnetizing inductor ten times less than the total balancing current:L m>10·V BI bal total·f s(7)where f s is the switching frequency of the converter. Referring to Fig.9,the demagnetization winding of Type A demagnetization can be designed by applying thevolt–second Fig.13.Two types of primary windings of the balancing transformer.(a)Double primary windings.(b)Single primarywindings.Fig.14.Secondary windings with FB rectifiers.balance principle on the magnetizing inductor L m:t1t0(V Bi)·dt+t2t1−n an b·V Bi·dt=0.(8)From(8),the maximum turn ratio n b max of the demagneti-zation windings can be obtained asn b max=1−DD·n a.(9) The size of the balancing transformer is proportional to the product of maximumflux and the root-mean-square(RMS) value of the currentflowing in the winding.First,the maximumflux of different topologies is calculated next.Theflux stress of SCW topologiesφSCW can be derivedφSCW=1N sa·12·V B·T s2.(10) Theflux stress of ACW topologiesφACW can be derivedφACW=1N sa·V B·(D·T s).(11) Second,the current RMS values of primary and secondary windings are calculated separately.There are two types of pri-mary windings for the balancing transformer to couple the5934IEEE TRANSACTIONS ON POWER ELECTRONICS,VOL.28,NO.12,DECEMBER 2013TABLE IC OMPARISON B ETWEEND IFFERENT T YPES OF THE P ROPOSED B ALANCING METHODSTABLE IIC OMPARISON OF N ORMALIZED C ORE A REA PRODUCTcharger energy as balancing energy for SCW topologies,as shown in Fig.13,one is using double primary windings shown in aforementioned examples,and the other is using a single pri-mary winding if there is pure ac current in the converter such as a resonant converter and an FB converter.The required primary winding copper cross-sectional area under the same total balancing current I bal total and the wire current density J for double primary windings A Cu pd and a single primary winding A Cu ps can be derivedA Cu pd =2·I pd rmsJ =2·k f pd ·n a · I bal total /2 J(12)andA Cu ps =I ps rmsJ =k f ps ·n a ·I bal total J(13)where k f pd and k f ps are form factors,which are defined as the RMS value divided by the average absolute value,for the currents of double primary side and the current of a single primary side,respectively.If the current waveform of primary-side windings of the bal-ancing transformer is half-sinusoidal waveform for double pri-mary windings as shown in Fig.13(a)and is sinusoidal wave-form for single primary winding shown in Fig.13(b),k f pd is equal to 1.57and k f ps is equal to 1.11;therefore,A Cu pd is about 1.41times the size of A Cu ps .In secondary windings,in addition to the center-tapped (CT)rectifier used in the examples,the FB rectifier can also be used for rectifying ac balancing energy coupled from the balancing transformer T b to equally charge the battery pack for SCWTABLE IIIS PECIFICATIONS OF THE PROPOSED B ALANCING C HARGERSTABLE IVC HARGING P ERFORMANCES C OMPARISONOF D IFFERENT C HARGERStopologies as shown in Fig.14.In most cases,the FB recti-fiers are suitable for high-voltage applications such as balancing among battery packs and modularized equalizer [19].HSIEH et al.:NOVEL HIGH-EFFICIENCY COMPACT-SIZE LOW-COST BALANCING METHOD5935Fig.15.Balancing current waveforms.(a)CLL voltage balance.(b)CLL SOC balance.(c)IBB voltage balance.(d)IBB SOC balance.(e)BB voltage balance.(f)BB SOCbalance.Fig.16.Nonoverlapped IBB current waveforms.(a)IBB voltage balance.(b)IBB SOCbalance.Fig.17.Equivalent circuit of balancing circuit taking leakage inductances into consideration.Assuming the form factor of the currents of double primary windings shown in Fig.13(a)is 1.4times than that of the single primary winding shown in Fig.13(b),and the form factor of the currents of the FB rectified secondary windings shown in Fig.14is also 1.4times than that of the CT secondary windings,the comparison of different types of the proposed equalizer is listed in Table I.parison of Normalized Core Area ProductsIn order to compare the performances of using a magnetic component as a transformer with the performances of using it as an inductor or a coupled inductor,the area products of a magnetic component of BB and flyback converters are derived in the Appendix to represent the use of inductor and coupled inductor,respectively.The following shows the magnetic component design equa-tion:A p =A e ·A w = xi =1λx ·I x ,rmsF F ·J ·B max (14)where A p is the core area product,A e is the effective core area,A w is the winding area,x is the number of winding,λx is the flux linkage,I x ,rms is the RMS value of the current of the winding,FF is the fill factor,B max is the maximum flux density,and J is the current density.The lower the value of J and B max ,the higher the efficiency of the magnetic component.However,decreasing the flux and current density to increase the efficiency will cause large mag-netic component size.In order to compare the performance of the magnetic component among different converters,the nor-malized core area product A pN is defined as follow:A pN = xi =1λx ·I x ,rmsP rated /f s(15)where P rated is the rated power of the converter.As a result,one magnetic component with less A pN value will have either higher5936IEEE TRANSACTIONS ON POWER ELECTRONICS,VOL.28,NO.12,DECEMBER2013Fig.18.Terminal voltages and charging currents of each cell during the charging process.(a)CLL without balance.(b)CLL with voltage balance.(c)CLL with SOC balance.(d)IBB without balance.(e)IBB with voltage balance.(f)IBB with SOC balance.(g)BB without balance.(e)BB with voltage balance.(f)BB without SOC balance.efficiency or smaller size compared with others delivering the same power and operating at the same frequency.Based on the formula listed in Table I and the A pN derivation of BB and flyback converters in the Appendix,the comparison of the normalized core area products is made and listed in Table II.The current ripple ratio r is set to 100%and 50%to represent boundary conduction mode and continuous conduction mode in the comparison,respectively.Moreover,the duty ratio of BB and flyback converters as well as ACW topologies is set to 50%to simplify the comparison.According to the normalized core area products listed in Table II,the magnetic components used as a transformer of the proposed equalizers are usually more efficient than ones used as an inductor or coupled inductor.Besides,if the losses of power switches and driver circuit are taken into consideration,the pro-posed equalizer can outperform inductor-based equalizers.Moreover,if the charger or discharger utilizes soft-switching converters such as resonant converters,the soft-switching prop-erty will be inherent in the proposed equalizer.As a result,it does not require any additional component to achieve soft-switchingfunction,which makes it more competitive than other resonant equalizers.IV .E XPERIMENTAL R ESULTSA 400-V CLL charger with the proposed double-primary-winding CT-rectifier equalizer,a 48-V IBB charger with the proposed double-primary-winding CT-rectifier equalizer,and a 48-V BB charger with the proposed Type A-demagnetization equalizer are built to charge four series-connected lead-acid bat-teries (REC50-12,12V ,50Ah,as the rating of electric scooters),labeled as B 1,B 2,B 3,and B 4,with average 0.2-C constant current charge for each cell to verify the proposed balancing method.The main specifications of the three converters are listed in Table III.The turn ratio n a of the balancing transformer is set to 3to produce total balancing current equal to one-third of the charging current.Both the voltage and SOC balancing functions are applied to the three aforementioned charger.Four additional switches,S 1,S 2,S 3,and S 4,for B 1,B 2,B 3,and B 4,respec-tively,are used to realize SOC balancing function,as shown in。