A Fast Charging Balancing Circuit for LiFePO 4 Battery

: In this paper, a fast charging balancing circuit for LiFePO 4 battery is proposed to address the voltage imbalanced problem of a lithium battery string. During the lithium battery string charging process, the occurrence of voltage imbalance will activate the fast balancing mechanism. The proposed balancing circuit is composed of a bi-directional converter and the switch network. The purpose of bi-directional is that the energy can be delivered to the lowest voltage cell for charging mode. On the other hand, the energy stored in the magnetizing inductors of the transformer can be charged back to the higher voltage cell in recycling mode. This novel scheme includes the following features: (1) The odd-numbered and even-numbered cells in the string with the maximum di ﬀ erential voltage will be chosen for balancing process directly. In this topology, there is no need to store and deliver the energy through any intermediate or the extra storing components. That is, the energy loss can be saved to improve the e ﬃ ciency, and the fast balancing technique can be achieved. (2) There is only one converter to complete the energy transfer for voltage balancing process. The concept makes the circuit structure much simpler. (3) The structure has bi-directional power ﬂow and good electrical isolation features. (4) A single chip controller is applied to measure the voltage of each cell to achieve the fast balancing process e ﬀ ectively. At the end of the paper, the practical test of the proposed balancing method on LiFePO 4 battery pack (28.8 V / 2.5 Ah) is veriﬁed and implemented by the experimental results.


Introduction
In recent years, lithium batteries and related techniques have developed and are widely used. The battery industries have experiences and capabilities for mass production of battery packs and modules. Battery packs and modules are composed of several battery cells for high power energy storing applications. However, there is a critical issue about imbalance of electric charge [1][2][3][4][5] within high power battery strings. The issue is caused by the characteristic [6], depth of discharge [7], and aging problem of each cell [8,9]. Based on the reasons above, when the battery string is being charged or discharged, the imbalance of each cell of the battery string becomes more serious. In addition, as the cycle of charging-discharging from the battery string increases, the internal resistance and the capacity of each cell will be varied to shorten the life cycle of battery strings.
In order to increase the efficiency and extend the lifetime of battery strings, a battery management system (BMS) [10][11][12][13][14][15][16] is a key feature which is utilized to monitor the parameters of the battery. Also, BMS plays an important role for management and protection of the battery. The main functions of BMS are monitoring, protection, and balancing parts [17,18]. The monitoring is to sense the relative key parameters from the battery packs, like voltage, current, and temperature. The protection is to avoid

The Proposed Balancing Circuit
As shown in Figure 1, the proposed balancing method utilizes a bi-directional converter [28,29] to balance the voltage of each cell in a battery string. This method helps to deliver the energy from higher-voltage battery to lower-voltage battery directly. In other words, there is no more energy loss during the delivering process, and this technique can also shorten the balancing time effectively. In this study, the forward converter has good isolation feature and simple structure for bi-directional function. The strategy is to balance the voltage between the odd-numbered battery and the even-numbered battery which exist maximum differential voltage in the battery string. The switch network shown in blue dotted block is formed by several couples of MOSFETs with back-to-back connection, and each connection also becomes a bi-directional switch set with two MOSFETs which is connected with the cell. Hence, this connection can provide a bi-directional path to deliver the energy. In addition, each of the bi-directional switches set can avoid the other currents flowing through the cell during the balancing process.

The Operation Mode Analysis
The operation mode can be divided by two different modes. The first one is to balance the voltage from odd-numbered battery to even one. The other mode is to balance the voltage from evennumbered battery to odd one. The operation principle of these two modes will be discusses in detail below. In the following analysis, each battery denoted from VBat1 to VBat8 can be represented as a battery cell in the green dotted block in Figure1.

The Operation Mode of Balancing Process from the Odd-Numbered Battery to the Even-Numbered Battery
The following analysis is stated for balancing from VBat1 to VBat8. The theoretical waveforms are shown in Figure 2. Mode I-Charging Mode (t0 < t < t1) As shown in Figure 3, the bi-directional switch set Sa, Sodd_0, Sodd_1, Seven_7, and Seven_8 are all turned on. The others are all turned off. In this mode, the current from VBat1 will charge to Lma through π filter

The Operation Mode Analysis
The operation mode can be divided by two different modes. The first one is to balance the voltage from odd-numbered battery to even one. The other mode is to balance the voltage from even-numbered battery to odd one. The operation principle of these two modes will be discusses in detail below. In the following analysis, each battery denoted from V Bat1 to V Bat8 can be represented as a battery cell in the green dotted block in Figure 1.

The Operation Mode of Balancing Process from the Odd-Numbered Battery to the Even-Numbered Battery
The following analysis is stated for balancing from V Bat1 to V Bat8 . The theoretical waveforms are shown in Figure 2.

The Operation Mode Analysis
The operation mode can be divided by two different modes. The first one is to balance the voltage from odd-numbered battery to even one. The other mode is to balance the voltage from evennumbered battery to odd one. The operation principle of these two modes will be discusses in detail below. In the following analysis, each battery denoted from VBat1 to VBat8 can be represented as a battery cell in the green dotted block in Figure1.

The Operation Mode of Balancing Process from the Odd-Numbered Battery to the Even-Numbered Battery
The following analysis is stated for balancing from VBat1 to VBat8. The theoretical waveforms are shown in Figure 2.  Mode I-Charging Mode (t0 < t < t1) As shown in Figure 3, the bi-directional switch set Sa, Sodd_0, Sodd_1, Seven_7, and Seven_8 are all turned on. The others are all turned off. In this mode, the current from VBat1 will charge to Lma through π filter Mode I-Charging Mode (t 0 < t < t 1 ) As shown in Figure 3, the bi-directional switch set S a , S odd_0 , S odd_1 , S even_7 , and S even_8 are all turned on. The others are all turned off. In this mode, the current from V Bat1 will charge to L ma through π filter I. In the meantime, the energy from the primary winding N pa can be transferred to the secondary winding N sa ; thus, D b is turned on by the forward bias. The current i Nsa begins to charge to V Bat8 through π filter II. The red dotted current path shows the charging condition.  Figure 3. Mode I, the battery balancing process from higher VBat1 to lower VBat8.
Mode II-Recycling Mode (t1 < t < t2) As shown in Figure 4, the bi-directional switch set Sa turns off, but Sodd_0, Sodd_1, Seven_7, and Seven_8 are all still turned on. The rest of switch sets are turned off. In this interval, the energy stored in Lma, and the current iLma remains continuously. Thus, iLma (shown with green dotted current) will flow through the primary winding Npa to induce a current iNsb from Nsb. The induced current iNsb also flows through π filter I and charge back to VBat1. During this mode, the energy stored in the magnetizing inductor can be released and also recycled to the battery(VBat1) effectively. At the right side of the converter, the energy of VBat8 is provided by π filter II.  Mode II-Recycling Mode (t 1 < t < t 2 ) As shown in Figure 4, the bi-directional switch set S a turns off, but S odd_0 , S odd_1 , S even_7 , and S even_8 are all still turned on. The rest of switch sets are turned off. In this interval, the energy stored in L ma , and the current i Lma remains continuously. Thus, i Lma (shown with green dotted current) will flow through the primary winding N pa to induce a current i Nsb from N sb . The induced current i Nsb also flows through π filter I and charge back to V Bat1 . During this mode, the energy stored in the magnetizing inductor can be released and also recycled to the battery(V Bat1 ) effectively. At the right side of the converter, the energy of V Bat8 is provided by π filter II.  Figure 3. Mode I, the battery balancing process from higher VBat1 to lower VBat8.
Mode II-Recycling Mode (t1 < t < t2) As shown in Figure 4, the bi-directional switch set Sa turns off, but Sodd_0, Sodd_1, Seven_7, and Seven_8 are all still turned on. The rest of switch sets are turned off. In this interval, the energy stored in Lma, and the current iLma remains continuously. Thus, iLma (shown with green dotted current) will flow through the primary winding Npa to induce a current iNsb from Nsb. The induced current iNsb also flows through π filter I and charge back to VBat1. During this mode, the energy stored in the magnetizing inductor can be released and also recycled to the battery(VBat1) effectively. At the right side of the converter, the energy of VBat8 is provided by π filter II.

The Operation Mode of Balancing Process from the Even-Numbered Battery to the Odd-Numbered Battery
The following analysis is stated for balancing from V Bat8 to V Bat1 , and Figure 5 shows the theoretical waveforms during the balancing process. The following analysis is stated for balancing from VBat8 to VBat1, and Figure 5 shows the theoretical waveforms during the balancing process.
Ⅳ t 2 t 3 t 4 Figure 5. The theoretical waveforms in balancing process from VBat8 to VBat1.
Mode III-Charging Mode (t2 < t < t3) As shown in Figure 6, the bi-directional switch set Sb, Sodd_0, Sodd_1, Seven_7, and Seven_8 are all turned on. The others are all turned off. The current from VBat8 will charge to Lmb through π filter II and also deliver the energy from the primary winding Npb to the secondary winding Nsb. In this transferring state, Da is turned on, and iNsb starts to charge to VBat1 through π filter I. The charging path is shown in red-dotted current. Mode Ⅳ-Recycling Mode (t3 < t < t4) As shown in Figure 7, the bi-directional switch set Sb turns off, but Sodd_0, Sodd_1, Seven_7, and Seven_8 are all still turned on. The rest of the switch sets are turned off. In this interval, the energy stored in Lmb, and the current iLmb remains continuously. Thus, iLmb (shown with green dotted current) will flow thru the primary winding Npb to induce a current iNsa from Nsa. The induced current iNsa also flows through π filter II and charge back to VBar8. During this mode, the energy stored in the magnetizing Mode III-Charging Mode (t 2 < t < t 3 ) As shown in Figure 6, the bi-directional switch set S b , S odd_0 , S odd_1 , S even_7 , and S even_8 are all turned on. The others are all turned off. The current from V Bat8 will charge to L mb through π filter II and also deliver the energy from the primary winding N pb to the secondary winding N sb . In this transferring state, D a is turned on, and i Nsb starts to charge to V Bat1 through π filter I. The charging path is shown in red-dotted current. The following analysis is stated for balancing from VBat8 to VBat1, and Figure 5 shows the theoretical waveforms during the balancing process.
Ⅳ t 2 t 3 t 4 Figure 5. The theoretical waveforms in balancing process from VBat8 to VBat1.
Mode III-Charging Mode (t2 < t < t3) As shown in Figure 6, the bi-directional switch set Sb, Sodd_0, Sodd_1, Seven_7, and Seven_8 are all turned on. The others are all turned off. The current from VBat8 will charge to Lmb through π filter II and also deliver the energy from the primary winding Npb to the secondary winding Nsb. In this transferring state, Da is turned on, and iNsb starts to charge to VBat1 through π filter I. The charging path is shown in red-dotted current. Mode Ⅳ-Recycling Mode (t3 < t < t4) As shown in Figure 7, the bi-directional switch set Sb turns off, but Sodd_0, Sodd_1, Seven_7, and Seven_8 are all still turned on. The rest of the switch sets are turned off. In this interval, the energy stored in Lmb, and the current iLmb remains continuously. Thus, iLmb (shown with green dotted current) will flow thru the primary winding Npb to induce a current iNsa from Nsa. The induced current iNsa also flows through π filter II and charge back to VBar8. During this mode, the energy stored in the magnetizing Figure 6. Mode III, the battery balancing process from higher V Bat8 to lower V Bat1 .

Mode IV-Recycling Mode (t 3 < t < t 4 )
As shown in Figure 7, the bi-directional switch set S b turns off, but S odd_0 , S odd_1 , S even_7 , and S even_8 are all still turned on. The rest of the switch sets are turned off. In this interval, the energy stored in L mb , and the current i Lmb remains continuously. Thus, i Lmb (shown with green dotted current) will flow thru the primary winding N pb to induce a current i Nsa from N sa . The induced current i Nsa also flows through π filter II and charge back to V Bar8 . During this mode, the energy stored in the magnetizing inductor can be released and also recycled to the battery (V Bat8 ) effectively. At the left side of the converter, the energy of V Bat1 is provided by π filter I. In this recycling mode, the energy is saved during this interval.

Design Consideration and Specification of Cell
In this part, the design consideration is discussed in detail. Table 1 lists the experiment key parameters (switching frequency, duty cycle, turns ratio, capacitance, and inductance) in this study. In addition, Table 2 is the specification of LiFePO4 battery. These parameters of battery help to design the charger and the related components. At first, the turns ratio (NS/NP) of the transformer has to be determined by using the nominal voltage of cell. In order to simplify the derivation, all the switches are assumed to be ideal. Besides, this application is operated in low voltage, the power switches and the diodes can be selected for low power rating to decrease the cost of the converter.

Design Consideration and Specification of Cell
In this part, the design consideration is discussed in detail. Table 1 lists the experiment key parameters (switching frequency, duty cycle, turns ratio, capacitance, and inductance) in this study. In addition, Table 2 is the specification of LiFePO 4 battery. These parameters of battery help to design the charger and the related components. At first, the turns ratio (N S /N P ) of the transformer has to be determined by using the nominal voltage of cell. In order to simplify the derivation, all the switches are assumed to be ideal. Besides, this application is operated in low voltage, the power switches and the diodes can be selected for low power rating to decrease the cost of the converter.

Model Number ANR26650M1B
Charging Voltage The turns ratio can be derived by the voltage of the charging behavior. Refer to Figure 8, V in is fed in π filter I, and the voltage across the primary side N Pa is also the V in (assuming the filters and the switches are ideal). At the secondary side, the voltage V Nsa across N Sa is induced by N Pa . During the charging state from V in to V o , the condition (V NSa − V o ) > V D has to be satisfactory to turn on the diode D b . Therefore, the charging path can be established as red dotted current. Based on (1), the across voltage on the diode has to be higher than the cut-in bias VD for turning on the diode. That is, the input voltage Vin is definitely higher than Vo. After the battery balancing process ends, Vin will approach to the charging voltage of the battery and also to be identical to Vo In the steady state, Vin = Vo. Thus, the equation (1) can be rewritten which is shown in (2).
In order to obtain the turns ratio from (3), the voltage of Vin is 3.3V, and the forward bias voltage of VD is 0.45 V respectively. Based on these parameters which are substituted into (4), the derived turns ratio is 1.14.
In this study, the actual turns ratio is chosen for 1.2 in this experiment.

Fast Battery Balancing Control Strategy and the Algorithm
The main digital controller utilized in this proposed structure is dsPIC33EP128GM304 from Microchip Technology. The first step of the procedure is to sense the voltage of each battery by the voltage detector circuit and to send the information to the processor with A/D converters. After analyzing from the processor, the battery cell in the string which needs to be activated for balancing will be chosen by the processor. In other words, the related switches (S1, S2, Sodd_0~Sodd_7, and Seven_1~Seven_8) around the imbalanced battery cells will be turned on or off for balancing process. Figure 9 shows the structure of the proposed fast battery charging balancing circuit. Based on (1), the across voltage on the diode has to be higher than the cut-in bias V D for turning on the diode. That is, the input voltage V in is definitely higher than V o . After the battery balancing process ends, V in will approach to the charging voltage of the battery and also to be identical to V o In the steady state, V in = V o . Thus, the equation (1) can be rewritten which is shown in (2).
In order to obtain the turns ratio from (3), the voltage of V in is 3.3V, and the forward bias voltage of V D is 0.45 V respectively. Based on these parameters which are substituted into (4), the derived turns ratio is 1.14.
In this study, the actual turns ratio is chosen for 1.2 in this experiment.

Fast Battery Balancing Control Strategy and the Algorithm
The main digital controller utilized in this proposed structure is dsPIC33EP128GM304 from Microchip Technology. The first step of the procedure is to sense the voltage of each battery by the voltage detector circuit and to send the information to the processor with A/D converters. After analyzing from the processor, the battery cell in the string which needs to be activated for balancing will be chosen by the processor. In other words, the related switches (S 1 , S 2 , S odd_0~Sodd_7 , and S even_1~Seven_8 ) around the imbalanced battery cells will be turned on or off for balancing process. Figure 9 shows the structure of the proposed fast battery charging balancing circuit.  When the battery string is being charged, the digital processor utilizes A/D converters and the voltage detection circuit to detect the battery voltage from VBat1 to VBat8. After detecting the actual battery voltage, the average voltage Vavg can be calculated by the processor, and the formula is shown in (5).
Besides, the start-up voltage Vbalance_start for balancing process is shown in (6), and △Ｖ is the threshold voltage which can be determined by users' demand.
If any of the battery voltage is higher than the preset of Vbalance_start, the proposed balancing mechanism will be activated. Once the battery balancing mechanism enables, these batteries which exist the maximum differential voltage between the odd-numbered and even-numbered will be selected. During the balancing procedure, the digital processor keeps detecting the batteries voltage and refreshing the average voltage. Until the highest battery voltage VH ≤ Vavg or the lowest battery voltage VL ≥ Vavg, the balancing process will be finished. Figure 10 is the flow chart of dynamic battery charging balancing strategy. When the battery string is being charged, the digital processor utilizes A/D converters and the voltage detection circuit to detect the battery voltage from V Bat1 to V Bat8 . After detecting the actual battery voltage, the average voltage V avg can be calculated by the processor, and the formula is shown in (5).
Besides, the start-up voltage V balance_start for balancing process is shown in (6), and V is the threshold voltage which can be determined by users' demand.
If any of the battery voltage is higher than the preset of V balance_start , the proposed balancing mechanism will be activated. Once the battery balancing mechanism enables, these batteries which exist the maximum differential voltage between the odd-numbered and even-numbered will be selected. During the balancing procedure, the digital processor keeps detecting the batteries voltage and refreshing the average voltage. Until the highest battery voltage V H ≤ V avg or the lowest battery voltage V L ≥ V avg , the balancing process will be finished. Figure 10 is the flow chart of dynamic battery charging balancing strategy.  Figure 10. Flow chart of dynamic battery charging balancing strategy.
In the balancing process, the voltage of each cell will be kept detecting and measuring all the time. In order to sense the voltage of each cell precisely, and to avoid the load effect between the cell and the input of the analog to digital converter (ADC), the detection circuit for battery voltage is adopted. From Figure 9, the detection of battery voltage is composed of a differential-voltage operational amplifier (OPA) and a low pass filter (LPF) to achieve the voltage measurement of a cell. The function of LPF is to filter the high frequency noise at the output of OPA. Then, the output of LPF will connect to the ADC's input of the MCU. In facts, the charging voltage of cell, VBat is 3.6 V, but the maximum input voltage of the ADC is 3 V; therefore, the proportion of the resistors around the OPA needs to be considered (R1 = R3, R2 = R4) for full scale voltage as shown in (7). In this circuit, the LPF has no attenuation in low frequency. Thus, V = V . In the meanwhile, the voltage of cell can also be measured by the voltage recorder. The detection of battery voltage circuit is shown in Figure 11. In the balancing process, the voltage of each cell will be kept detecting and measuring all the time. In order to sense the voltage of each cell precisely, and to avoid the load effect between the cell and the input of the analog to digital converter (ADC), the detection circuit for battery voltage is adopted. From Figure 9, the detection of battery voltage is composed of a differential-voltage operational amplifier (OPA) and a low pass filter (LPF) to achieve the voltage measurement of a cell. The function of LPF is to filter the high frequency noise at the output of OPA. Then, the output of LPF will connect to the ADC's input of the MCU. In facts, the charging voltage of cell, V Bat is 3.6 V, but the maximum input voltage of the ADC is 3 V; therefore, the proportion of the resistors around the OPA needs to be considered (R 1 = R 3 , R 2 = R 4 ) for full scale voltage as shown in (7). In this circuit, the LPF has no attenuation in low frequency. Thus, V 1 = V O . In the meanwhile, the voltage of cell can also be measured by the voltage recorder. The detection of battery voltage circuit is shown in Figure 11.

Differential-voltage operational amplifier Low-pass filter
To ADC

To voltage recorder
Detection of battery voltage Figure 11. The detection of battery voltage circuit.

Experimental and Simulation Results
In order to verify the proposed battery charging balancing circuit with the theoretical derivation, Figures 12-16 show the triggering waveforms for building up the balancing loop and the related waveforms when VBat1 charges to VBat8. In the opposite, Figures 17-21 provide the waveforms when VBat8 charges to VBat1. These waveforms are measured and simulated to prove that the balancing process is feasible and implemented.

Waveforms for VBat1 Charges to VBat8
In this section, the simulation results are shown to compare with the experiments. Figure 11 shows the gate signals for turning on Sodd_0, Sodd_1, Seven_7, and Seven_8.

Experimental and Simulation Results
In order to verify the proposed battery charging balancing circuit with the theoretical derivation, Figures 12-16 show the triggering waveforms for building up the balancing loop and the related waveforms when V Bat1 charges to V Bat8 . In the opposite, Figures 17-21 provide the waveforms when V Bat8 charges to V Bat1 . These waveforms are measured and simulated to prove that the balancing process is feasible and implemented.

Waveforms for V Bat1 Charges to V Bat8
In this section, the simulation results are shown to compare with the experiments. Figure 11 shows the gate signals for turning on S odd_0 , S odd_1 , S even_7 , and S even_8 .

Differential-voltage operational amplifier Low-pass filter
To ADC

To voltage recorder
Detection of battery voltage Figure 11. The detection of battery voltage circuit.

Experimental and Simulation Results
In order to verify the proposed battery charging balancing circuit with the theoretical derivation, Figures 12-16 show the triggering waveforms for building up the balancing loop and the related waveforms when VBat1 charges to VBat8. In the opposite, Figures 17-21 provide the waveforms when VBat8 charges to VBat1. These waveforms are measured and simulated to prove that the balancing process is feasible and implemented.

Waveforms for VBat1 Charges to VBat8
In this section, the simulation results are shown to compare with the experiments. Figure 11 shows the gate signals for turning on Sodd_0, Sodd_1, Seven_7, and Seven_8.   When the balancing loop keeps turning on all the time, S a also turns on (V GSa : high) in the meantime. The converter goes to charging mode when V Bat1 charges to V Bat8 . If S a turns off (V GSa : low), the converter goes to recycling mode. In recycling mode, the rest of energy stored in the magnetizing inductor from the previous stage will charge back to V Bat1 . The following experiments and simulations are shown from Figures 13-16. Electronics 2019, 9, x FOR PEER REVIEW 10 of 16

Differential-voltage operational amplifier Low-pass filter
To ADC

To voltage recorder
Detection of battery voltage Figure 11. The detection of battery voltage circuit.

Experimental and Simulation Results
In order to verify the proposed battery charging balancing circuit with the theoretical derivation, Figures 12-16 show the triggering waveforms for building up the balancing loop and the related waveforms when VBat1 charges to VBat8. In the opposite, Figures 17-21 provide the waveforms when VBat8 charges to VBat1. These waveforms are measured and simulated to prove that the balancing process is feasible and implemented.

Waveforms for VBat1 Charges to VBat8
In this section, the simulation results are shown to compare with the experiments. Figure 11 shows the gate signals for turning on Sodd_0, Sodd_1, Seven_7, and Seven_8.     Figures 15 and 16, when the converter is being operated in charging mode, iNpa starts to increases for charging the magnetizing inductor and to deliver the energy to lower voltage cell. Once the converter goes to recycling mode, iNsb is induced by the magnetizing inductor. Thus, the stored energy is charged back to the higher voltage cell through the filter. From these two figures below, the current direction of iNpa is opposite to iNsb. This phenomenon proves that the recycling mode is successful.

Waveforms for VBat8 Charges to VBat1
This operation principle is almost the same as the previous section, but the only difference is that the charging direction is inverse (VBat8 charges to VBat1). The simulation results are shown to compare with the experiments. Figure 17 shows the gate signal for turning on Sodd_0, Sodd_1, Seven_7, and Seven_8 for building up the charging path. In addition, Figures 18-21 present the related waveforms when VBat8 charges to VBat1.   Figures 15 and 16, when the converter is being operated in charging mode, i Npa starts to increases for charging the magnetizing inductor and to deliver the energy to lower voltage cell. Once the converter goes to recycling mode, i Nsb is induced by the magnetizing inductor. Thus, the stored energy is charged back to the higher voltage cell through the filter. From these two figures below, the current direction of i Npa is opposite to i Nsb . This phenomenon proves that the recycling mode is successful. Referred to Figures 15 and 16, when the converter is being operated in charging mode, iNpa starts to increases for charging the magnetizing inductor and to deliver the energy to lower voltage cell. Once the converter goes to recycling mode, iNsb is induced by the magnetizing inductor. Thus, the stored energy is charged back to the higher voltage cell through the filter. From these two figures below, the current direction of iNpa is opposite to iNsb. This phenomenon proves that the recycling mode is successful.

Waveforms for VBat8 Charges to VBat1
This operation principle is almost the same as the previous section, but the only difference is that the charging direction is inverse (VBat8 charges to VBat1). The simulation results are shown to compare with the experiments. Figure 17 shows the gate signal for turning on Sodd_0, Sodd_1, Seven_7, and Seven_8 for building up the charging path. In addition, Figures 18-21 present the related waveforms when VBat8 charges to VBat1.  Referred to Figures 15 and 16, when the converter is being operated in charging mode, iNpa starts to increases for charging the magnetizing inductor and to deliver the energy to lower voltage cell. Once the converter goes to recycling mode, iNsb is induced by the magnetizing inductor. Thus, the stored energy is charged back to the higher voltage cell through the filter. From these two figures below, the current direction of iNpa is opposite to iNsb. This phenomenon proves that the recycling mode is successful.

Waveforms for VBat8 Charges to VBat1
This operation principle is almost the same as the previous section, but the only difference is that the charging direction is inverse (VBat8 charges to VBat1). The simulation results are shown to compare with the experiments. Figure 17 shows the gate signal for turning on Sodd_0, Sodd_1, Seven_7, and Seven_8 for building up the charging path. In addition, Figures 18-21 present the related waveforms when VBat8 charges to VBat1.

Waveforms for V Bat8 Charges to V Bat1
This operation principle is almost the same as the previous section, but the only difference is that the charging direction is inverse (V Bat8 charges to V Bat1 ). The simulation results are shown to compare with the experiments. Figure 17 shows the gate signal for turning on S odd_0 , S odd_1 , S even_7 , and S even_8 for building up the charging path. In addition, Figures 18-21 present the related waveforms when V Bat8 charges to V Bat1 . Referred to Figures 15 and 16, when the converter is being operated in charging mode, iNpa starts to increases for charging the magnetizing inductor and to deliver the energy to lower voltage cell. Once the converter goes to recycling mode, iNsb is induced by the magnetizing inductor. Thus, the stored energy is charged back to the higher voltage cell through the filter. From these two figures below, the current direction of iNpa is opposite to iNsb. This phenomenon proves that the recycling mode is successful.

Waveforms for VBat8 Charges to VBat1
This operation principle is almost the same as the previous section, but the only difference is that the charging direction is inverse (VBat8 charges to VBat1). The simulation results are shown to compare with the experiments. Figure 17 shows the gate signal for turning on Sodd_0, Sodd_1, Seven_7, and Seven_8 for building up the charging path. In addition, Figures 18-21 present the related waveforms when VBat8 charges to VBat1.  To sum up the measurements and simulations above, these results are compared and proved that the proposed fast charging and balancing circuit is feasible.
Before the balancing process starts, each of the battery cells has been discharged for test and experiment. The open loop voltage of each cell is listed in Table 3 from VBat1 to VBat8 individually. When the cell is being charged with 1C current, the △V is set for 0.03 V during the balancing interval I to IV. If the voltage reaches to 3.5 V, the △V is set from 0.03 V to 0.02 V during the balancing interval V to VII. As the battery voltage rises from 3.5 V to 3.6 V at interval V, the main concept of choosing △V is set for lower voltage to make the balancing process much more precise. During the experiments, the voltage and the curve of each cell is measured and drawn by a voltage recorder (model number: midi LOGGER GL800, manufacture: GRAPHTEC). To sum up the measurements and simulations above, these results are compared and proved that the proposed fast charging and balancing circuit is feasible.
Before the balancing process starts, each of the battery cells has been discharged for test and experiment. The open loop voltage of each cell is listed in Table 3 from VBat1 to VBat8 individually. When the cell is being charged with 1C current, the △V is set for 0.03 V during the balancing interval I to IV. If the voltage reaches to 3.5 V, the △V is set from 0.03 V to 0.02 V during the balancing interval V to VII. As the battery voltage rises from 3.5 V to 3.6 V at interval V, the main concept of choosing △V is set for lower voltage to make the balancing process much more precise. During the experiments, the voltage and the curve of each cell is measured and drawn by a voltage recorder (model number: midi LOGGER GL800, manufacture: GRAPHTEC). To sum up the measurements and simulations above, these results are compared and proved that the proposed fast charging and balancing circuit is feasible.
Before the balancing process starts, each of the battery cells has been discharged for test and experiment. The open loop voltage of each cell is listed in Table 3 from VBat1 to VBat8 individually. When the cell is being charged with 1C current, the △V is set for 0.03 V during the balancing interval I to IV. If the voltage reaches to 3.5 V, the △V is set from 0.03 V to 0.02 V during the balancing interval V to VII. As the battery voltage rises from 3.5 V to 3.6 V at interval V, the main concept of choosing △V is set for lower voltage to make the balancing process much more precise. During the experiments, the voltage and the curve of each cell is measured and drawn by a voltage recorder (model number: midi LOGGER GL800, manufacture: GRAPHTEC). To sum up the measurements and simulations above, these results are compared and proved that the proposed fast charging and balancing circuit is feasible.
Before the balancing process starts, each of the battery cells has been discharged for test and experiment. The open loop voltage of each cell is listed in Table 3 from VBat1 to VBat8 individually. When the cell is being charged with 1C current, the △V is set for 0.03 V during the balancing interval I to IV. If the voltage reaches to 3.5 V, the △V is set from 0.03 V to 0.02 V during the balancing interval V to VII. As the battery voltage rises from 3.5 V to 3.6 V at interval V, the main concept of choosing △V is set for lower voltage to make the balancing process much more precise. During the experiments, the voltage and the curve of each cell is measured and drawn by a voltage recorder (model number: midi LOGGER GL800, manufacture: GRAPHTEC). To sum up the measurements and simulations above, these results are compared and proved that the proposed fast charging and balancing circuit is feasible.
Before the balancing process starts, each of the battery cells has been discharged for test and experiment. The open loop voltage of each cell is listed in Table 3 from V Bat1 to V Bat8 individually. When the cell is being charged with 1C current, the V is set for 0.03 V during the balancing interval I to IV. If the voltage reaches to 3.5 V, the V is set from 0.03 V to 0.02 V during the balancing interval V to VII. As the battery voltage rises from 3.5 V to 3.6 V at interval V, the main concept of choosing V is set for lower voltage to make the balancing process much more precise. During the experiments, the voltage and the curve of each cell is measured and drawn by a voltage recorder (model number: midi LOGGER GL800, manufacture: GRAPHTEC). From Figure 22, each of these cells has 7 balancing intervals from interval I to VII. The balancing time and the energy loss of the proposed converter from I to VII are summarized as Table 4. As shown in Table 4, the balancing time becomes shorter when each cell reaches to the charging voltage 3.6 V. Also, the energy loss of the converter gets lower because the balancing process goes to the end.   Figure 22, each of these cells has 7 balancing intervals from interval I to VII. The balancing time and the energy loss of the proposed converter from I to VII are summarized as Table 4. As shown in Table 4, the balancing time becomes shorter when each cell reaches to the charging voltage 3.6 V. Also, the energy loss of the converter gets lower because the balancing process goes to the end.  In Table 5, the measurements and experimental results are listed. The total balancing time is to sum up the time from interval I to VII. To compare with the conventional balancing method, the proposed concept can shorten the balancing time effectively. Besides, after the balancing process, the maximum differential voltage among the balanced cells is 0.018 V.  In Table 5, the measurements and experimental results are listed. The total balancing time is to sum up the time from interval I to VII. To compare with the conventional balancing method, the proposed concept can shorten the balancing time effectively. Besides, after the balancing process, the maximum differential voltage among the balanced cells is 0.018 V.  As mentioned above, V is determined by user's demand and the balancing performance. If the user requires a lower differential voltage among these cells in the battery string, V has to be set lower to achieve the better balancing performance; however, it takes more time for the balancing process. Table 6 gives a comparison of different value of V. In the opposite, a higher V will obtain a worse balancing performance even the balancing time is shorter.

Conclusions
The paper proposes a fast charging balancing circuit for LiFePO 4 battery. The main concept is to give a fast voltage balancing strategy for each cell within a single battery string. In this study, a novel bi-directional forward converter is utilized and connected with the balancing bi-directional switches network to form a bi-directional battery balancing circuit.
The feature of the proposed scheme is to balance the maximum differential voltage between the odd-numbered battery and the even-numbered battery in the battery string directly. In order to verify the proposed structure, a fast battery charging circuit for a string with 8 pieces of cell (3.6 V/2.5 Ah for each cell) is implemented. In addition, the merit of this circuit can also avoid over charging situation during the balancing process.
Referred to the experimental and simulation results in previous section, a faster charging balancing circuit for a battery string is achieved. The advantage of this scheme also improves the precision of each cell after balancing procedure. The future research will keep improving the balancing algorithms for random cells in the battery string. Moreover, the proposed study can save more time during the balancing process. At present, industrial applications, electric vehicles batteries, and higher capacity batteries are always composed of many cells connected in series and parallel; therefore, the characteristics and aging phenomenon of each cell have to be concerned with care. In the near future, a battery management system can be added for the proposed balancing circuit to obtain a high precision and faster battery equalizer for each cell.

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