**1. 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 [1–5] 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 e fficiency and extend the lifetime of battery strings, a battery managemen<sup>t</sup> system (BMS) [10–16] is a key feature which is utilized to monitor the parameters of the battery. Also, BMS plays an important role for managemen<sup>t</sup> 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 situation of over-charging or over-discharging from the battery packs. The last one is about the

balancing technique for each cell. In general, the balancing circuits can be divided into passive or active balancing topologies. The most common passive balancing schemes [19–22] utilize series resistors, series diodes, or Zener diodes to be the voltage dividers which are parallel to each cell for balancing purpose. These passive concepts with simple control methods and smaller size of balancing circuits can achieve a voltage equalizer for each cell during the process; however, the power losses and thermal issues will be the key factors to influence the balancing performance, accuracy, and the lifetime of cells. On the other hand, the active balancing topologies [23–27] can deliver the energy from higher voltage cell to lower one by using the storing elements and switches networks. Some of the active balancing schemes adopted multi-windings of the main transformer to fulfill the balancing performance with better electrical isolation feature, but the number of cells is limited by the windings; therefore, the dimension of the transformer will be increased for purpose of more balanced cells. In facts, these active balancing methods help to increase the e fficiency and the performance during the balancing process, but they spent more time for delivering the energy from the high voltage cell to the low voltage cell. The reason is that if the highest voltage cell begins to charge to the lowest voltage cell, the energy flow has to be delivered through the other cells one by one to the target cell. Thus, the balancing path has a big problem of time wasting. In this paper, the proposed concept is to shorten the balancing time and to make the balanced cell being charged precisely. To recall the active balancing concept mentioned above, the basic concept of active balancing is to deliver the energy from the higher voltage battery to the lower voltage battery to achieve the balancing function for each cell. Nowadays, BMS is a core of many electric applications powered by batteries.

Based on the descriptions aforementioned, the paper proposed a fast charging balancing circuit for LiFePO4 battery pack. In this study, a digital signal processor (DSP) is adopted to implement the algorithm and to be the main controller.

#### **2. Proposed Structure and Operation Mode Analysis**

#### *2.1. 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 e ffectively. 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 di fferential 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.

**Figure 1.** The proposed fast charging balancing circuit for LiFePO4 battery.

#### *2.2. 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 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 VBat1 to VBat8 can be represented as a battery cell in the green dotted block in Figure 1.

2.2.1. The Operation Mode of Balancing Process from the Odd-Numbered Battery to the Even-Numbered Battery

The following analysis is stated for balancing from VBat1 to VBat8. The theoretical waveforms are shown in Figure 2.

**Figure 2.** The theoretical waveforms in balancing process from VBat1 to VBat8.

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 <sup>o</sup>ff. In this mode, the current from VBat1 will charge to Lma through π filter I. In the meantime, the energy from the primary winding Npa can be transferred to the secondary winding Nsa; thus, Db is turned on by the forward bias. The current iNsa begins to charge to VBat8 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 <sup>o</sup>ff, but Sodd\_0, Sodd\_1, Seven\_7, and Seven\_8 are all still turned on. The rest of switch sets are turned <sup>o</sup>ff. 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.

**Figure 4.** Mode II, the battery balancing process from higher VBat1 to lower VBat8.

2.2.2. The Operation Mode of Balancing Process from the Even-Numbered Battery to the Odd-Numbered Battery

The following analysis is stated for balancing from VBat8 to VBat1, and Figure 5 shows the theoretical waveforms during the balancing process.

**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 <sup>o</sup>ff. 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.

**Figure 6.** Mode III, the battery balancing process from higher VBat8 to lower VBat1.

Mode IV-Recycling Mode (t3 < t < t4)

As shown in Figure 7, the bi-directional switch set Sb turns <sup>o</sup>ff, but Sodd\_0, Sodd\_1, Seven\_7, and Seven\_8 are all still turned on. The rest of the switch sets are turned <sup>o</sup>ff. 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 inductor can be released and also recycled to the battery (VBat8) effectively. At the left side of the converter, the energy of VBat1 is provided by π filter I. In this recycling mode, the energy is saved during this interval.

**Figure 7.** Mode II, the battery balancing process from higher VBat8 to lower VBat1.

#### **3. 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.




**Table 2.** Specification of cell, (Company: A123 System LiFePO4 ).

The turns ratio can be derived by the voltage of the charging behavior. Refer to Figure 8, Vin is fed in π filter I, and the voltage across the primary side NPa is also the Vin (assuming the filters and the switches are ideal). At the secondary side, the voltage VNsa across NSa is induced by NPa. During the charging state from Vin to Vo, the condition (VNSa − Vo) > VD has to be satisfactory to turn on the diode Db. Therefore, the charging path can be established as red dotted current.

**Figure 8.** Determine turns ratio by voltage of charging behavior.

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 V*<sup>o</sup>*. 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).

$$(\mathbf{V}\_{\rm in} \times \frac{\mathbf{N}\_{\rm s}}{\mathbf{N}\_{\rm P}} - \mathbf{V}\_{\rm o}) > \mathbf{V}\_{\rm D} \tag{1}$$

$$\mathbf{V}\_{\rm in} \times \left(\frac{\mathbf{N}\_{\rm s}}{\mathbf{N}\_{\rm P}} - 1\right) > \mathbf{V}\_{\rm D} \tag{2}$$

After rearranged (2), the equation (3) can be obtained as below.

$$\frac{\text{N}\_{\text{s}}}{\text{N}\_{\text{P}}} > \frac{\text{V}\_{\text{D}}}{\text{V}\_{\text{in}}} + 1 \tag{3}$$

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.

$$\frac{\text{N}\_{\text{s}}}{\text{N}\_{\text{P}}} > \left[\frac{0.45}{3.3} + 1\right] = 1.14\tag{4}$$

In this study, the actual turns ratio is chosen for 1.2 in this experiment.

#### **4. 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.

**Figure 9.** The structure of fast 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).

$$\mathbf{V\_{avg}} = \frac{\mathbf{V\_{bat1}} + \mathbf{V\_{bat2}} + \dots + \mathbf{V\_{bat8}}}{8} \tag{5}$$

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.

$$\mathbf{V}\_{\text{balance\\_start}} = \mathbf{V}\_{\text{avg}} + \Delta \mathbf{V} \tag{6}$$

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.

**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, V1 = VO. 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.

$$\mathbf{V\_O} = (\frac{\mathbf{R\_2}}{\mathbf{R\_1}}) \times \mathbf{V\_{bat}} \tag{7}$$

**Figure 11.** The detection of battery voltage circuit.

#### **5. 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.

#### *5.1. 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.

**Figure 12.** Experiment of VGS triggering waveforms for turning on the switch network (VGSodd\_0, VGSodd\_1, VGSeven\_7, VGSeven\_8), VGSodd\_0, VGSodd\_1, VGSeven\_7, VGSeven\_8: 10 V/div, Time: 20 μs/div.

When the balancing loop keeps turning on all the time, Sa also turns on (VGSa: high) in the meantime. The converter goes to charging mode when VBat1 charges to VBat8. If Sa turns off (VGSa: 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 VBat1. The following experiments and simulations are shown from Figures 13–16.

**Figure 13.** Experiment of voltage waveforms of Sa (VGSa, VDSa), VGSa, VDSa: 10 V/div, Time: 20 μs/div.

**Figure 14.** Simulation of voltage waveforms of Sa (VGSa, VDSa), VGSa, VDSa: 10 V/div, Time: 20 μs/div.

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.

**Figure 15.** Experiment of current waveforms (iNsb, iNpa), iNsb, iNpa: 500 mA/div, Time: 20 μs/div.

**Figure 16.** Simulation of current waveforms (iNsb, iNpa), iNsb, iNpa: 500 mA/div, Time: 20 μs/div.

#### *5.2. Waveforms for VBat8 Charges to VBat1*

This operation principle is almost the same as the previous section, but the only di fference 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.

**Figure 17.** Experiment of VGS triggering waveforms for the switch network (VGSodd\_0, VGSodd\_1, VGSeven\_7, VGSeven\_8), VGSodd\_0, VGSodd\_1, VGSeven\_7, VGSeven\_8: 10 V/div, Time: 20 μs/div.

After the balancing loop established, Sb turns on in the meantime as well. The converter enters into charging mode when VBat8 charges to VBat1. However, if Sb turns <sup>o</sup>ff, the converter moves to recycling mode and the rest of energy stored in the magnetizing inductor will charge back to VBat8. The experiments and simulations are shown from Figures 18–21.

**Figure 18.** Experiment of voltage waveforms of Sb (VGSb, VDSb), VGSb, VDSb: 10 V/div, Time: 20 μs/div.

**Figure 19.** Simulation of voltage waveforms of Sb (VGSb, VDSb), VGSb, VDSb: 10 V/div, Time: 20 μs/div.

**Figure 20.** Experiment of current waveforms (iNsa, iNpb), iNsa, iNpb: 500 mA/div, Time: 20 μs/div.

**Figure 21.** Simulation of current waveforms (iNsa, iNpb), iNsa, iNpb: 500 mA/div, Time: 20 μs/div.

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).


**Table 3.** Open loop voltage for discharged cells in the test battery string.

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.** Battery's voltage curve during fast charging balancing process.


**Table 4.** Balancing time and energy loss in each interval.

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 e ffectively. Besides, after the balancing process, the maximum di fferential voltage among the balanced cells is 0.018 V.


**Table 5.** Measurement of battery balancing process.

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.

**Table 6.** Comparison of different single V for a complete balancing process.

