Research into an Efficient Energy Equalizer for Lithium-Ion ... - MDPI

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Research into an Efficient Energy Equalizer for Lithium-Ion Battery Packs Hongrui Liu, Bo Li, Yixuan Guo, Chunfeng Du, Shilong Chen * and Sizhao Lu Faculty of Electric Power Engineering, Kunming University of Science and Technology, Kunming 650500, China; [email protected] (H.L.); [email protected] (B.L.); [email protected] (Y.G.); [email protected] (C.D.); [email protected] (S.L.) * Correspondence: [email protected]; Tel.: +86-138-8863-9305 Received: 7 November 2018; Accepted: 1 December 2018; Published: 5 December 2018







Abstract: An efficient multi-mode energy equalizer for lithium-ion battery packs is proposed and energy balance strategies are studied in this paper. The energy balance strategies include the selection of the controlled object in the battery’s different working states and the current form of the controlled object. During the energy balancing process, the strongest single cell or the weakest single cell is selected as the controlled object according to the different working states of the battery, and the balanced current of the controlled object is continuous. Therefore, the energy equalizer proposed in this paper has a fast balancing speed, an improved balancing effect, and an excellent balancing reliability. According to the energy equalizer, the relevant experimental platform was built, and balance experiments in the battery’s different working states using a battery pack composed of four serially-connected lithium iron phosphate batteries were completed. Finally, the experimental results proved the effectiveness of the energy equalizer. Keywords: equalizer; energy balance strategies; lithium iron phosphate batteries; balance experiment

1. Introduction Lithium-ion batteries are favored by the electric vehicle market because of their high energy density, long cycle life, and the fact that they have no memory effect [1,2]. The nominal voltage of single cell is between 3.2 V and 3.7 V. A large number of lithium-ion batteries need to be connected in series to meet the voltage requirements [3–5]. However, due to differences in the working environment and the performance of each single cell, their energy is inconsistent, as shown in Figure 1. In the charging process, the single cell with the highest energy becomes full first, and in the discharging process, the single cell with the lowest energy is emptied first. With the increase of charging and discharging times, the charging and discharging capacity of the battery pack will get smaller and smaller. In addition, over-charging and over-discharging are not allowed in each single cell to prevent battery life reduction, however, this creates a risk of explosion when the single cell is over-charged [4]. Therefore, effective balance measures must be taken to solve the problem of energy inconsistencies between single cells and to prolong the life and improve the charging and discharging capacity of the battery pack.

Energies 2018, 11, 3414; doi:10.3390/en11123414

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Figure Figure 1. 1. Schematic Schematic diagram diagram of of the the charge charge and and discharge dischargeprocess. process.

The cancan be divided intointo energy consumption balance and the non-energy Theexisting existingbalance balancemethods methods be divided energy consumption balance and the nonconsumption balance methods. The energy consumption balance method is simpler, it depends energy consumption balance methods. The energy consumption balance methodbut is simpler, butonit energy consumption to achieve balance. The non-energy consumption balance includes the inductance depends on energy consumption to achieve balance. The non-energy consumption balance includes balance [2–10], balance the capacitance balance [11], the inductance-capacitance balance [12–14], and [12– the the inductance [2–10], the capacitance balance [11], the inductance-capacitance balance transformer balance [15,16]. balance The battery pack has different states, including the charging 14], and the transformer [15,16]. Thethree battery packworking has three different working states, state, the discharging state and the static state. Each working state has its own characteristics, a including the charging state, the discharging state and the static state. Each working state has itsand own balance method and may anot be suitable for the three working states simultaneously. The existing characteristics, balance method may notdifferent be suitable for the three different working states balance methods focus more on how to achieve the balanced result, while the different working simultaneously. The existing balance methods focus more on how to achieve the balanced result, states batteryworking and the rapidity securityand of the thesecurity different states while of thethe different states of and the battery thebalance rapidityfor and of working the balance for are the often ignored. different working states are often ignored. In In this this paper, paper, an an energy energyequalizer equalizer for for lithium-ion lithium-ion batteries batteries is is studied studied in in terms terms of of the the balanced balanced speed, the controllability of the balanced energy, the realization of the balance circuit, and speed, the controllability of the balanced energy, the realization of the balance circuit, and the the security security of of the the balanced balanced system. system. According According to to each each working working state state of of the the battery, battery, different different balancing balancing strategies strategies are are developed developed to to realize realize aa multi-mode multi-mode energy energy equalizer equalizer that that is is suitable suitable for for each each working working state state of of the the battery battery simultaneously. simultaneously. The The equalizer equalizer suggested suggested by by this this paper paper can can rapidly rapidly control control the the energy energy rising rising rate rate of of the the strongest strongest single single cell cell in in the the charging charging state, state, and and can can rapidly rapidly control control the the energy energy declining declining rate rate of the weakest single cell in the discharging state. of the weakest single cell in the discharging state. 2. 2. Balance Balance Strategy Strategy 2.1. Relationship between Balanced Control Object and Battery Working State 2.1. Relationship between Balanced Control Object and Battery Working State The strongest/weakest single cell limits the charging/discharging capacity of the battery pack in The strongest/weakest single cell limits the charging/discharging capacity of the battery pack in the battery charging/discharging state. The strongest single cell or the weakest single cell was selected the battery charging/discharging state. The strongest single cell or the weakest single cell was selected as the balanced control object under the same charging current and stop charging conditions, and the as the balanced control object under the same charging current and stop charging conditions, and the state of charge (SOC) curves of three lithium-ion battery cells are shown in Figure 2. Compared with state of charge (SOC) curves of three lithium-ion battery cells are shown in Figure 2. Compared with Figure 2b, the charging time in Figure 2a is extended by t12 , that is, the charging capacity of the battery Figure 2b, the charging time in Figure 2a is extended by t12, that is, the charging capacity of the battery pack increased when the strongest cell was selected as the balanced control object. The charging pack increased when the strongest cell was selected as the balanced control object. The charging capacity of the battery pack represents its ability to absorb energy; the more energy it can absorb, the capacity of the battery pack represents its ability to absorb energy; the more energy it can absorb, the stronger the charging capacity. stronger the charging capacity.

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SOC1 SOC1

SOC1 SOC1

t1 t1

t12 t2 t12 t2

t1 t1

Figure 2. State of charge (SOC) curves in the battery charging state, where the (a) strongest and (b) Figure 2. 2.cell State charge(SOC) (SOC) curves battery charging state, where (a) strongest Figure State ofofcharge curves in in thethe battery charging state, where the the (a) strongest and and (b) weakest is the controlled object. (b) weakest cell is the controlled object. weakest cell is the controlled object.

The strongest single cell or the weakest single cell was selected as the balanced control object The strongest strongest single single cell cell or or the the weakest weakest single single cell cell was was selected selected as the the balanced balanced control control object object The under the same discharging current and stop discharging conditions,asand the SOC curves of three under the same discharging current and stop discharging conditions, and the SOC curves of three under the same discharging and stop 3. discharging and curves oftime three lithium-ion battery cells are current shown in Figure Comparedconditions, with Figure 3a,the theSOC discharging of lithium-ion battery battery cells cells are are shown shown in in Figure Figure 3. 3. Compared Compared with with Figure Figure 3a, 3a, the the discharging discharging time time of of lithium-ion Figure 3b was extended by t12, that is, the discharging capacity of the battery pack increased when Figure 3b 3b was was extended extended by by tt12 that is, the the discharging discharging capacity capacity of the the battery battery pack pack increased increased when when 12, ,that Figure the weakest cell was selected as the is, balanced control object. Theofdischarging capacity of the battery the weakest weakest cell cell was was selected selected as as the the balanced balanced control control object. The The discharging discharging capacity capacity of the the battery battery the pack represents its ability to release energy; the moreobject. energy that can be released, theofstronger the pack represents its ability to release energy; the more energy that can be released, the stronger the pack represents its ability to release energy; the more energy that can be released, the stronger the discharging capacity. discharging capacity. capacity. discharging

SOC2 SOC2

SOC 2 SOC 2

t1 t1

t1 t12 t2 t1 t12 t2

Figure 3. Energy Energychange changediagram diagramininthethe battery discharging state where strongest battery discharging state where thethe (a) (a) strongest andand (b) Figure 3. Energy change diagram in the battery discharging state where the (a) strongest and (b) (b) weakest is the controlled object. weakest cellcell is the controlled object. weakest cell is the controlled object.

Assuming that series, and initial SOC SOC Assuming that aa battery battery pack pack is is composed composed of of n n single single battery battery cells cells in in aa series, and its its initial value, maximum SOC value, SOC are as Assuming that a battery packminimum is composed n single battery cells represented in a series, and its initial SOC max ,, 0଴,, SOC value, maximum SOC value, and and minimum SOCofvalue value are respectively respectively represented as SOC ܱܵ‫ܥ‬ ܱܵ‫ܥ‬ ୫ୟ୶ and SOC , their expressions can be represented by the following equations: value, maximum SOC value, and minimum SOC value are respectively represented as ܱܵ‫ܥ‬ , ܱܵ‫ܥ‬ min ଴ ୫ୟ୶ , and ܱܵ‫ܥ‬୫୧୬ , their expressions can be represented by the following equations: and ܱܵ‫ܥ‬୫୧୬ , their expressions can be represented by the following equations:   = {1SOC , · · · SOC } SOC , SOC = {0SOC  0SOC 1 , SOC 2 ,2SOCn } n SOC0SOC , SOC ,  SOC = {SOC (1) =1 max{2SOC1 , SOC 2 , · · · SOCn } = SOCx n}  max{ SOC1 , SOC2 , SOCn } = SOCx =max (1)  max SOC SOC = min SOC , SOC , · · · SOC = SOC { } n y 1 SOC =min max{SOC , SOC ,2 SOC } = SOC (1)

SOCmax = min{SOC1, SOC 2, SOC n} = SOC x SOC min = min{SOC 1, SOC 2, SOC n} = SOC y The average balance current is Ib and time is t2 , assuming that the SOC value min 1 the balance 2 n y 

The averageisbalance is ‫ܫ‬௕ and the balance thethe SOC value of of Cell-x/Cell-y still thecurrent maximum/minimum at thetime end is of ‫ݐ‬the balance. that When SOC value ଶ , assuming The average balance current is ‫ܫ‬ and the balance time is ‫ݐ‬ , assuming that the SOC value of ௕ ଶ Cell-x/Cell-y is still the maximum/minimum at the end of the balance. When the SOC value of the of the battery pack reaches SOCA/SOCB, the charging/discharging ends. When no balance Cell-x/Cell-y still the maximum/minimum at the end of theends. balance. When the SOCmeasures value of the battery pack is reaches SOCA/SOCB, the charging/discharging When no balance are battery pack reaches SOCA/SOCB, the charging/discharging ends. When no balance measures are

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taken, the charging/discharging capacity of the battery pack can be expressed by the following equations Energies 2018, 11, 3414 4 of 11

C c = ( SOCA − SOC max ) × n × C (2) by  measures are taken, the charging/discharging capacity of the battery pack can be expressed C d = ( SOC min − SOCB ) × n × C the following equations

(

where C is the rated capacity of a Csingle battery − cell. SOCmax ) × n × C c = ( SOCA (2) When the balance measure in Figure 2a/Figure is adopted, the charging/discharging capacity Cd = (SOC − SOCB )×n×C min 3b of the battery pack can be expressed by the following equations:

where C is the rated capacity of a single battery cell. When the balancemeasure in Figure 2a/Figure 3b is tadopted, the charging/discharging capacity Ib × b ( SOC )] × n × C C = [ SOCAby− the max − equations: cbexpressed of the battery pack can be following  C (3)  (

I b × tb tb C = [( Ccb = [SOCA (SOC − Ib × ) −max SOC + − SOCB × nC× C C) ×)]n× min db C Ib ×tb  Cdb = [(SOCmin +

C

) − SOCB) × n × C

(3)

Obviously, ‫ܥ‬௖௕ is bigger than ‫ܥ‬௖ , and ‫ܥ‬ௗ௕ is bigger than ‫ܥ‬ௗ . Obviously, Ccb is bigger than Cc , and Cdb is bigger than Cd .

2.2. 2.2. Energy EnergyTransfer Transfer Forms Forms The The balanced balanced energy energy should should be be transmitted transmittedcontinuously continuouslythroughout throughoutthe thebalanced balancedperiod, period,T.T. Continuous balanced energy is conducive to the fast and effective transfer of energy, thus Continuous balanced energy is conducive to the fast and effective transfer of energy, thus rapidly rapidly improving the charging and discharging capacity of the battery pack and the balanced speed. As improving the charging and discharging capacity of the battery pack and the balanced speed. As shown shown in Figure 4b, if energy (E) transferred under the energy discontinuous mode is equal to the in Figure 4b, if energy (E) transferred under the energy discontinuous mode is equal to the energy energy transferred under the continuous at thetime same time the amount of energy transferred transferred under the continuous mode atmode the same (T), the(T), amount of energy transferred should should be increased in the intermittent energy intermittent otherthe words, thevalue current value is increased. be increased in the energy mode. Inmode. other In words, current is increased. Although Although energy discontinuous mode can the same balanced result inmode continuous mode the energythe discontinuous mode can achieve the achieve same balanced result in continuous by increasing by increasing the current value, a larger current will increase the burden of the balance circuit, the current value, a larger current will increase the burden of the balance circuit, the capacity of the the capacity of theswitch corresponding switch device,problem and theofsecurity problem equalizerTherefore, will be corresponding device, and the security the equalizer will of be the introduced. introduced. Therefore,energy continuous balanced energy is more conducive to the realization of balance. continuous balanced is more conducive to the realization of balance.

Figure 4. Energy transfer forms: (a) continuous mode, and (b) discontinuous mode. Figure 4. Energy transfer forms: (a) continuous mode, and (b) discontinuous mode.

2.3. Balance Strategies 2.3. Balance Strategies In order to improve the charging/discharging capacity and the balanced speed of the battery pack In order to improve charging/discharging capacityfrom andthe thecontrolled balanced object speed and of the quickly and effectively, thethe balance strategies were studied thebattery energy pack quickly and effectively, the balance strategies were studied from the controlled object and the transfer forms under the different working states of the battery in this paper. In the battery charging energy transfer forms under the different working states of the battery in this paper. In the battery state, the strongest battery cell was selected as the balanced control object to be discharged. Conversely, charging state,discharging the strongest battery cell was battery selectedcell as the control object tocontrol be discharged. in the battery state, the weakest wasbalanced selected as the balanced object to Conversely, in the battery discharging state, the weakest battery cell was selected as the balanced be charged, while in the battery static state, the strongest or the weakest battery cell was selected as the control object to be charged, in the or battery static the strongest or the the battery, weakestthe battery cell balanced control object to bewhile discharged charged. Instate, all working states of balanced was selected as the balanced control object to be discharged or charged. In all working states of the energy was continuous and controllable. battery, the balanced energy was continuous and controllable. 3. The Circuit Topology and Principle of the Equalizer 3.1. Circuit Topology of the Equalizer Based on the above balance strategies, the circuit topology of the equalizer was constructed in this paper as shown in Figure 5. The circuit topology of the equalizer is composed of a bidirectional power switch matrix and a balanced main circuit. The bidirectional power switch matrix consist of 2*n

3. The Circuit Topology and Principle of the Equalizer 3.1. Circuit Topology of the Equalizer Based on the above balance strategies, the circuit topology of the equalizer was constructed in Energies 2018, 11, 3414 5 of 11 this paper as shown in Figure 5. The circuit topology of the equalizer is composed of a bidirectional power switch matrix and a balanced main circuit. The bidirectional power switch matrix consist of 2*n bidirectional switch namely k11 and to k1n and k21 to k2n, which can be bidirectional controllable bidirectional switch units,units, namely k11 to k1n k21 to k2n, which can be controllable bidirectional switches relays. main The balanced main circuit consists(L), of an (L), twoswitches, master switches or relays. Theor balanced circuit consists of an inductor twoinductor master control control and M2, and(E) a voltage (E) that is battery obtainedpack fromthrough the battery pack M1 andswitches, M2, and M1 a voltage source that it issource obtained fromitthe a DC/DC through DC/DC and wasthe adjustable. When the two master switches arepulse-width controlled convertora and wasconvertor adjustable. When two master control switches arecontrol controlled by the by the pulse-width (PWM) the signal separately, balanced main circuit is equivalent to modulation (PWM)modulation signal separately, balanced mainthe circuit is equivalent to two completely two completely different chopper circuits. Regardless of the type of chopper circuit,Lthe inductor is different chopper circuits. Regardless of the type of chopper circuit, the inductor is always in Lthe always in the loop as the controlled objectthus in balance thus the balanced energy of the controlled same loop as same the controlled object in balance the balanced energy of the controlled object can object can be continuous. Therefore, the balance-controlled objectbyisthe selected by the power bidirectional be continuous. Therefore, the balance-controlled object is selected bidirectional switch power matrix, and the continuousbidirectional controllable balanced bidirectional balanced energy realized by matrix,switch and the continuous controllable energy is realized byisthe balanced the balanced main circuit. main circuit.

Figure Figure 5. 5. The The topology topology of of the the equalizer. equalizer.

3.2. Principle Principle of of Balance Balance 3.2. In the the battery battery charging charging state, state, the the strongest strongest battery battery cell cell or or several several adjacent adjacent cells cells of of aa battery battery pack pack In are selected as the balanced control object through the switch matrix, meanwhile the PWM signal is are selected as the balanced control object through the switch matrix, meanwhile the PWM signal is performed on the master control switch M1, then the balanced energy is transferred from the control performed on the master control switch M1, then the balanced energy is transferred from the control object to to the the voltage voltage source source E. E. As As shown shown in in Figure Figure 6a, 6a, when when the the M1 M1 is is turned turned on, on, the the energy energy of of the the object control object is transferred to the inductor L and the energy flow direction is shown by the solid line control object is transferred to the inductor L and the energy flow direction is shown by the solid line arrow. When When the the M1 M1 is is turned turned off, off, the the energy energy stored stored in in the the L L is is transferred transferred to to the the voltage voltage source source E E via via arrow. the antiparallel diode D2 of the M2, and the energy flow direction is shown by the dotted line arrow. the antiparallel diode D2 of the M2, and the energy flow direction is shown by the dotted line arrow. In the the battery battery discharging discharging state, state, the the weakest weakest battery battery cell cell or or several several adjacent adjacent cells cells of of aa battery battery pack pack In are selected selected as as the the balanced balanced control control object object through through the the switch switch matrix, matrix, meanwhile, meanwhile, the the PWM PWM signal signal is is are performed on the master control switch M2, then the balanced energy is transferred from the voltage performed on the master control switch M2, then the balanced energy is transferred from the voltage source E E to to the the control control object. object. As As shown shown in in Figure Figure 6b, 6b, when when the the M2 M2 is is turned turned on, on, the the energy energy flow flow source direction is is shown shown by by the the solid solid line line arrow. arrow. When When the the M2 M2 is is turned turned off, off, the the energy energy stored stored in in the the L L is is direction transferred to the control object via the antiparallel diode D1 of the M1, and the energy flow direction is shown by the dotted line arrow. In the battery static state, there are two kinds of balance strategies that can be adopted, and the strongest battery cell/s is/are balanced to be discharged as shown in Figure 6a, or the weakest battery cell/s is/are balanced to be charged as shown in Figure 6b. However, in order to improve the charging

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transferred to the control object via the antiparallel diode D1 of the M1, and the energy flow direction is shown by the dotted line arrow. In the battery static state, there are two kinds of balance strategies that can be adopted, and the Energies 2018, 11, 3414 6 of 11 strongest battery cell/s is/are balanced to be discharged as shown in Figure 6a, or the weakest battery cell/s is/are balanced to be charged as shown in Figure 6b. However, in order to improve the charging and discharging capacity of the battery pack, the former strategy is adopted in the battery static state that happens before the battery charging, and the latter strategy is adopted in the battery static that battery discharging. discharging. happens before or during the battery

Figure thethe equalizer: (a) (a) the the balance in theinbattery charging state, and (b)and the balance Figure 6. 6. The Theprinciple principleofof equalizer: balance the battery charging state, (b) the in the battery discharging state. balance in the battery discharging state.

3.3. Characteristics of the Equalizer 3.3. Characteristics of the Equalizer First, the working state of the battery is considered by the equalizer, and the different balance First, the working state of the battery is considered by the equalizer, and the different balance strategies are proposed for the three working states of the battery. Second, the control object is selected strategies are proposed for the three working states of the battery. Second, the control object is according to the principle of decreasing the energy changing rate of the balanced battery, which can selected according to the principle of decreasing the energy changing rate of the balanced battery, not only effectively improve the charging and discharging capacity of the battery pack, but is also which can not only effectively improve the charging and discharging capacity of the battery pack, conducive to using the battery healthily. Third, the continuous balanced energy is realized, that is, but is also conducive to using the battery healthily. Third, the continuous balanced energy is realized, the balanced energy emitted and absorbed by the balanced battery is always continuous. Therefore, that is, the balanced energy emitted and absorbed by the balanced battery is always continuous. a new topology circuit for a multi-mode energy equalizer was constructed for this paper. The above Therefore, a new topology circuit for a multi-mode energy equalizer was constructed for this paper. three points are also the characteristics of the equalizer proposed in this paper that are different from The above three points are also the characteristics of the equalizer proposed in this paper that are existing equalizers. different from existing equalizers. As shown in Figure 5, when the PWM signal is applied to M1, the continuous energy is transferred As shown in Figure 5, when the PWM signal is applied to M1, the continuous energy is from the balanced battery on the left to the voltage source E on the right, and when the PWM signal is transferred from the balanced battery on the left to the voltage source E on the right, and when the applied to M2, the continuous energy is transferred from the voltage source to the balanced battery on PWM signal is applied to M2, the continuous energy is transferred from the voltage source to the the left. In the battery charging state, the strongest battery cell or several adjacent cells of a battery balanced battery on the left. In the battery charging state, the strongest battery cell or several adjacent pack is/are selected to be discharged, and in the battery discharging state, the weakest battery cell cells of a battery pack is/are selected to be discharged, and in the battery discharging state, the or several adjacent cells of a battery pack is/are selected to be charged. In the battery static state, weakest battery cell or several adjacent cells of a battery pack is/are selected to be charged. In the the strongest or weakest battery cell/s of a battery pack is/are selected to be discharged/charged. battery static state, the strongest or weakest battery cell/s of a battery pack is/are selected to be discharged/charged. 4. Balance Experiment

4. Balance Experiment 4.1. Experimental Platform In this paper, the balance experiments carried out under the three battery working states were 4.1. Experimental Platform carried out for a battery pack composed of four serially connected lithium iron phosphate battery cells. In thisvoltage paper, of thethe balance experiments the threewas battery working states were The rated battery cell was 3.2carried V, andout the under rated capacity 21 Ah. The battery was carried out for a battery pack composed of four serially connected lithium iron phosphate battery charged or discharged through the charging/discharging instrument in the laboratory, as shown in cells. The voltage the battery cell was 3.2 V,included and the rated capacityequalizer, was 21 Ah. The battery Figure 7, inrated addition, theofexperimental platform also the batteries, voltage source, ◦ was charged or discharged through the charging/discharging instrument in the laboratory, as current sensor, and the oscilloscope, and the laboratory temperature was about 25 C. Amongshown them, in Figure in addition, the of experimental platform also included batteries, equalizer, voltage the master7,control switches the equalizer were MOSFETs with the a low on-resistance of IRF3205, source, and the oscilloscope, and the temperature was about 25current °C. Among and thecurrent internalsensor, resistance of the master switch waslaboratory 8 mΩ. The charging/discharging was them, the master control switches of the equalizer were MOSFETs with a low on-resistance of 10 A, which was provided by the charging/discharging instrument. The charging balance experiment IRF3205, and the internal resistance of the master switch was 8 mΩ. The charging/discharging current was stopped until the SOC value of the battery pack reached 70%, and the discharging experiment was stopped until the SOC value of the battery pack dropped to 10%.

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was was 10 10 A, A, which which was was provided provided by by the the charging/discharging charging/discharging instrument. instrument. The The charging charging balance balance experiment was stopped until the SOC value of the battery pack reached 70%, and the discharging experiment was Energies 2018, 11, 3414stopped until the SOC value of the battery pack reached 70%, and the discharging 7 of 11 experiment experiment was was stopped stopped until until the the SOC SOC value value of of the the battery battery pack pack dropped dropped to to 10%. 10%.

charging/discharging charging/discharging instrument instrument

Oscilloscope Oscilloscope

Driving Driving power power

Lithium Lithium iron iron phosphate phosphate battery battery Equalizer Equalizer

Adjustable Adjustable voltage voltage source source

Figure Experimental platform. Figure 7. 7. Experimental platform.

4.2. Balance Experiments Experiments in the Battery Static and the Charging 4.2. State 4.2. Balance Balance Experiments in in the the Battery Battery Static Static and and the the Charging Charging State State values of Cell1, Cell2,Cell2, Cell3 Cell3 and 9.3%, 20%, 20%,20%, and 30%, The initial SOC values of and Cell4 were 9.3%, 20%, and The initial initialSOC SOC values of Cell1, Cell1, Cell2, Cell3Cell4 andwere Cell4 were 9.3%, 20%, 20%,respectively, and 30%, 30%, and the switching frequency of the switch M1 was 20 kHz. The balance experiment in the battery static respectively, and the switching frequency of the switch M1 was 20 kHz. The balance experiment in respectively, and the switching frequency of the switch M1 was 20 kHz. The balance experiment in state was carried out first, and the static time was 1800 s. In the static balance, the battery Cell4 was the the battery battery static static state state was was carried carried out out first, first, and and the the static static time time was was 1800 1800 s. s. In In the the static static balance, balance, the the selected as the control object to be discharged, the ratio of the switch M1of was andwas the battery was selected as control object be discharged, the switch battery Cell4 Cell4 was selected as the the control object to to beduty discharged, the duty duty ratio ratio of the58.85%, switch M1 M1 was average balanced current was about 2.09 A. The balanced current waveform of the battery Cell4 and 58.85%, 58.85%, and and the the average average balanced balanced current current was was about about 2.09 2.09 A. A. The The balanced balanced current current waveform waveform of of the the the PWM waveform the switch M1 are shown in Figure battery Cell4 and PWM waveform of switch M1 battery Cell4 and the theof PWM waveform of the the switch M1 are are8.shown shown in in Figure Figure 8. 8.

8. The Thebalanced balanced current and pulse-width modulation (PWM) waveforms the battery Figure current and pulse-width modulation (PWM) waveforms in static Figure 8. 8. The balanced current and pulse-width modulation (PWM) waveforms in the theinbattery battery static static state. state. state.

After in in thethe battery charging state waswas carried out, out, and After the static balance, the balance experiment battery charging state carried After the the static staticbalance, balance,the thebalance balanceexperiment experiment in the battery charging state was carried out, the charging current was 10 A. In the charging balance, the battery Cell4 was selected to be balanced and and the the charging charging current current was was 10 10 A. A. In In the the charging charging balance, balance, the the battery battery Cell4 Cell4 was was selected selected to to be be and the average balanced current was about 2.02 A. The balanced current waveform and the PWM balanced and the average balanced current was about 2.02 A. The balanced current waveform and balanced and the average balanced current was about 2.02 A. The balanced current waveform and waveform are shownare in Figure the shown the PWM PWM waveform waveform are shown9.in in Figure Figure 9. 9. After 1800 s, the batteries Cell2, Cell3 and Cell4 had the same energy, so the three cells were selected as the balanced control object to discharge, the duty ratio of the switch M1 was 10.9%, and the average balanced current was about 2.06 A. The balanced current waveform of the control object and the PWM waveform of the switch M1 are shown in Figure 10. The balanced experiment was stopped until the SOC value of the battery pack reached 70%, the balanced time was 5760 s, and the SOC values of each battery cell were 65%, 70%, 70%, and 70.2%, respectively, at the end of the balanced experiment. The SOC curves during the experiment of the static and the charging state are shown in Figure 11.

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Figure 9. The balanced current and PWM waveforms in the battery charging state.

After 1800 s, the batteries Cell2, Cell3 and Cell4 had the same energy, so the three cells were selected as the balanced control object to discharge, the duty ratio of the switch M1 was 10.9%, and the average balanced current was about 2.06 A. The balanced current waveform of the control object and the PWM waveform of the switch M1 are shown in Figure 10. The balanced experiment was stopped until the SOC value of the battery pack reached 70%, the balanced time was 5760 s, and the SOC values of each battery cell were 65%, 70%, 70%, and 70.2%, respectively, at the end of the balanced experiment. The SOC curves during the experiment of the static and the charging state are shown in Figure 11.9. The Figure The balanced balanced current current and PWM waveforms in the battery charging state. After 1800 s, the batteries Cell2, Cell3 and Cell4 had the same energy, so the three cells were selected as the balanced control object to discharge, the duty ratio of the switch M1 was 10.9%, and the average balanced current was about 2.06 A. The balanced current waveform of the control object and the PWM waveform of the switch M1 are shown in Figure 10. The balanced experiment was stopped until the SOC value of the battery pack reached 70%, the balanced time was 5760 s, and the SOC values of each battery cell were 65%, 70%, 70%, and 70.2%, respectively, at the end of the balanced experiment. The SOC curves during the experiment of the static and the charging state are shown in Figure 11.

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Figure Figure 10. The The balanced balanced current current and PWM waveforms in the battery charging state.

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Figure 10. The balanced current and PWM waveforms in the battery charging state.

Figure 11. SOC curves in the battery static and charging state. Figure 11. SOC curves in the battery static and charging state.

4.3. Balance Experiments in the Battery Static and Discharging State After the charging experiment, the static balance experiment of 1800 s was carried out. During the experiment, the weakest battery Cell1 was balanced and the average current was about 2 A. The

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Figure 11. SOC curves in the battery static and charging state.

Balance Experiments Experiments in the Battery Static and Discharging State 4.3. Balance After the charging experiment, experiment, the static balance experiment experiment of of 1800 s was carried out. During After the experiment, the weakest battery Cell1 was balanced and the average current about 2 A. the experiment, the weakest battery Cell1 was balanced and the average current was was about 2 A. The The balanced charging current waveform ofbattery the battery the PWM waveform of switch the switch balanced charging current waveform of the Cell1Cell1 and and the PWM waveform of the M2 M2 shown are shown in Figure are in Figure 12. 12.

Figure 12. 12. The The balanced balanced current current and and PWM waveforms. Figure

The SOC SOC values values of of each each battery battery cell cell were were 70%, 70%, 70%, 70%, 70%, 70%, and and 70.2%, 70.2%, respectively, respectively, at at the the end end of of The the static balanced experiment, and the SOC values of the four battery cells became more consistent. the static balanced experiment, and the SOC values of the four battery cells became more consistent. The discharging discharging experiment experiment without without the the balance balance was was then then carried carried out out until until the the SOC SOC value value of of the the The battery pack pack dropped dropped to to 10%, 10%, and and the the discharging discharging current current in in the the experiment experiment was was aa constant constant current current battery of 10 A. The experiment time was 6120 s, the SOC values of each battery cell were 9.5%, 9.5%, 9.5%, of 10 A. The experiment time was 6120 s, the SOC values of each battery cell were 9.5%, 9.5%, 9.5%, Energies 2018,respectively, 11, x FOR PEER 10 of 11 and 9.7%, respectively, at the and 9.7%, atREVIEW the end end of of the the experiment, experiment, and and the the SOC SOC curves curves are are shown shown in in Figure Figure13. 13.

Figure 13. SOC curves curves in in the the battery battery static Figure 13. SOC static and and discharging discharging state. state.

5. Analysis of the Experimental Results 5. Analysis of the Experimental Results In this paper, the different balanced strategies are adopted respectively under the three different In this paper, the different balanced strategies are adopted respectively under the three different working states of the battery, the strongest battery cell/s is/are the control object to be discharged working states of the battery, the strongest battery cell/s is/are the control object to be discharged in in the battery charging state, and the weakest battery cell/s is/are the control object to be charged the battery charging state, and the weakest battery cell/s is/are the control object to be charged in the in the battery discharging state. Therefore, the charging/discharging capacity of the battery pack battery discharging state. Therefore, the charging/discharging capacity of the battery pack will be effectively and quickly improved, which will also increase the balance speed of the equalizer. The balance current is continuous and controllable, as shown in Figures 8–10 and 12. The balance energy of the balanced control object can be transferred stably and continuously, therefore, the security of the equalizer is higher and the balanced speed will be faster.

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will be effectively and quickly improved, which will also increase the balance speed of the equalizer. The balance current is continuous and controllable, as shown in Figures 8–10 and 12. The balance energy of the balanced control object can be transferred stably and continuously, therefore, the security of the equalizer is higher and the balanced speed will be faster. The results of the charging balance experiment, the discharging balance experiment, and the static balance experiment were set out in this paper. The initial SOC values of the four serially-connected battery cells were 9.3%, 20%, 20%, and 30%, respectively, and the SOC values were changed to 9.5%, 9.5%, 9.5%, and 9.7%, respectively, after the balance experiments in this paper. The average value of the balanced current from the balance experiments was about 2 A, and the maximum energy difference between single battery cells was reduced from 20.7% to 0.2% after one charging/discharging cycle balance experiment and a static balance experiment of 3600 s. In practice, both the number of single battery cells in the series and the degree of energy inconsistency between them will affect the balance speed and the balance time. If the number of single battery cells is larger and the degree of the energy inconsistency between them is more serious, multiple balanced charging/discharging cycles will be needed to make the energy between single battery cells consistent. In addition, the value of the balance current can be adjusted according to the degree of energy inconsistency between battery cells, and the higher the balance current value, the faster the balance speed, or the fewer cycles of balanced charging/discharging will be needed. 6. Conclusions The energy balance strategies were studied in terms of the balanced control object and the balanced energy transferred forms based on three different working states of the battery in this paper. In order to improve the charging and discharging capacity of the battery pack and increase the balance speed, the following requirements were set for the equalizer: First, the balance energy should be continuous and controllable; second, the strongest battery cell or cells of the battery pack were selected as the control object to be balanced in the battery charging state, and the weakest battery cell or cells were selected as the control object to be balanced in the battery discharging state. This study described in this paper constructed an equalizer and topology circuit satisfying the above requirements, built a balance experiment platform, and completed the balance experiments. Different balance strategies were proposed for the three working states of the battery, and the balance energy was continuous and controllable, resulting in a fast balance speed. In addition, as the balance energy was continuous and stable and the energy changing rate of the balanced battery always decreased, even a larger balance current will not affect the service life of the battery. Author Contributions: H.L. proposed the main idea of this paper. C.D. and S.C. completed the paper writing. B.L., Y.G., and S.L. set up the experimental platform and completed the balanced experiments of the paper. Funding: This research received no external funding. Acknowledgments: The research is supported in part by National Science Foundation of China (Grant Nos. 51707088 and 51607081). Conflicts of Interest: The authors declare no conflicts of interest.

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