Active Battery Voltage Equalization Based on Chain-Loop Comparison Strategy

Abstract

This paper describes active battery balancing based on a bidirectional buck converter, a flyback converter, and battery cells by using the proposed chain-loop comparison strategy. The role of the bidirectional buck converter is to charge/discharge the battery pack. During the charging period, the converter is in buck mode, and its output is controlled by constant current/voltage; during the discharging period, the converter is in boost mode, and its output is controlled by constant voltage. The role of the flyback converter is voltage equalization of the battery pack, and its output is controlled by constant current. A chain-loop comparison strategy is used to control battery voltage equalization. In this work, three equalization modes, namely, charging balance, discharging balance, and static balance, were considered. The voltage difference between the maximum and minimum is 0.007 V after a balancing time of 19.75 min, 0.005 V after a balancing time of 24 min, and 0.007 V after a balancing time of 20 min for charging balance, discharging balance, and static balance, respectively.

1. Introduction

A single lithium battery cell is not sufficient to meet the demand of modern appliances due to the increase in human demand for electricity and the different power specifications required by products. To solve this problem, cells are connected in series to increase the voltage and in parallel to increase the capacity to form a pack to meet the system specifications. It is generally recognized that each battery cell has different features [1,2,3,4], such as capacity, impedance, self-discharge rate, and aging, thereby making voltage imbalance between the battery cells occur when the batteries are in operation. If a battery pack continues to be used in an imbalanced condition, the battery cells will be overcharged/discharged, the battery life will be shortened, and in severe cases, the battery pack will explode [3,4]. Therefore, it is necessary to use a battery balancing circuit in order to allow the battery pack to operate safely for a long period of time. Battery balancing circuits are divided into two groups [5,6,7,8,9,10,11,12,13,14,15], passive balancing and active balancing, as shown in Figure 1.

In the case of passive balancing, as shown in Figure 1, the method of Reference [16] is to put a resistor on each battery cell, through which the higher-voltage battery cell is depleted until it matches and balances the voltage of other battery cells. The approach of Reference [17] improves on Reference [16] by adding a switch to prevent the resistor from continuously consuming, which requires the battery cell voltage to be detected, and the corresponding switch is turned on if the battery cell voltage is higher. Energy is consumed in the resistors in both methods mentioned above, and hence heat is generated in the resistors. Therefore, these methods waste energy, but they have the advantages of simple structure and low cost.

Active balancing, as shown in Figure 1, is mainly for energy recycling and is more efficient than passive balancing, but the structure of this method is complicated, and the cost is higher. Active balancing can be analyzed from the circuit and the battery perspectives.

As shown in Figure 1, circuits can be divided into three types: capacitor, inductor, and converter. Capacitors [18,19,20,21,22,23] are used as energy storage elements between the battery cells by switching the control to form a loop to achieve energy transfer. An advantage of this method is that the volume of a capacitor is smaller than that of a magnetic component. However, the balance current is determined by the difference in voltage between the battery cells, so the cells are inevitably balanced by slow speed and inrush current. The inductor type [24,25,26,27,28] involves the inductive energy transfer from the battery cells or the battery pack to the battery cells or the battery pack, and this method is characterized by its ability to provide a larger balance current and significantly shorten the balance time. Therefore, compared to the capacitive method, the balancing time is relatively short, but the size of the magnetic component is larger. In addition, when using a multi-winding transformer, the complexity of the transformer design increases, and the need to ensure that each winding has the same characteristics makes the entire system more complex and bulky. Common circuit topologies are usually employed, such as the Cuk converter [29], flyback converter [30,31,32], buck–boost converter [33], and forward converter [34]. This method has more freedom to allow the battery to equalize the voltage, so the balancing effect is better than that of other methods, but the structure is more complicated compared to passive balancing.

As shown in Figure 1, batteries can be divided into three modes, i.e., cell-to-cell (C2C), cell-to-pack (C2P), and pack-to-cell (P2C), and these modes should be combined with active balancing to achieve battery balancing along with a capacitor, inductor, or converter.

The C2C mode uses the higher-voltage cell to transfer energy to the lower-voltage cell through the capacitor, inductor, or converter to achieve battery voltage equalization. This structure requires the addition of multiple sets of switches to connect the battery cells, thereby increasing the losses caused by the switches. However, the control is simpler, and the circuits are often modularized, which is known as individual cell equalization (ICE). Reference [29] reports the use of a battery equalization module for voltage balancing. This module combines the neighboring cells plus the Cuk converter to achieve C2C battery voltage equalization. The balancing speed of the neighboring cells in this structure is faster than those of other structures, and this is because of the converter across the battery cell. However, if voltage balancing is required for distant cells, the balancing speed will be slower because the energy needs to be transferred through other cells. Consequently, in order to improve the method of [29], References [35,36] divided the battery voltage equalization module into cell modules and a module composed of cell modules for battery balancing. In their method, the balancing speed is faster, but the circuit is more complicated, and the number of required components is significantly higher. Reference [37] combines the buck–boost converter and the switched-capacitor converter. In addition, the inductor is changed to a coupled inductor. If the imbalanced cells are far away from each other, the energy will be transferred through the coupled inductor and the switched capacitor, so the balancing speed is faster. Reference [38] combines a switched-capacitor converter and an external LC resonant circuit. The switched-capacitor converter is used for battery balancing when the maximum voltage difference between the cells is large, while the LC resonant circuit is used for battery balancing when the maximum voltage difference between the cells is small. By doing so, the disadvantage of capacitive balancing is solved; however, if the voltage difference is too small, the balancing speed will be slowed down.

The cell-to-pack mode utilizes the higher-voltage cell to transfer energy to the battery pack through a capacitor, inductor, or converter to achieve battery voltage equalization, while in the case of the P2C mode, this is achieved by utilizing a battery pack to transfer energy to the lower-voltage cell through a capacitor, inductor, or converter. Both approaches have more regulation methods than the cell-to-cell mode, allowing multiple cells to be equalized at the same time. However, because of the connection to the battery pack, the parts are subjected to higher voltage stresses. Reference [39] proposes the division of the batteries into modules for balancing, and each module corresponds to a winding for voltage equalization, so the number of transformers can be reduced. In the P2C mode, an area with an even or odd number of cells can be utilized to perform voltage equalization, so if the same module has two cells with lower voltage, the voltage balancing takes more time. In order to connect each cell, the required number of switches is much higher, and a bidirectional switch must be used to increase the conduction loss and switching loss.

Reference [40] uses a bidirectional non-isolated DC–DC converter for the battery voltage equalization of the P2C and C2P modes, and the circuit behavior can be classified into the buck mode or the boost mode. Due to the use of a non-isolated converter, the main circuit’s mode of judgment is based on the last battery cell, so it needs to withstand continuous charging and discharging, which affect the battery life. Reference [41] reports charge balancing where the main structure is a buck-derived converter, which is combined with a charger and a voltage equalizer. The inductor of the buck converter of the charger is replaced with a multi-winding transformer, and the transformer output is connected to its corresponding battery cell for battery balancing, so there is no need for additional active switching and control. However, accurate control over the balancing current cannot be achieved. Reference [42] adopts two flyback converters for battery voltage equalization. The corresponding operating principle is to first magnetize one of the coupled inductors of the high-voltage battery cell, and when this coupled inductor is demagnetized, the rechargeable battery pack magnetizes the other coupled inductor at the same time, and when the other coupled inductor is demagnetized, the low-voltage battery cell is recharged. Although this topology is simple and easy to control, which helps to reduce the cost of the battery balancing system, it has the disadvantage of additional losses due to the need for additional switches and diodes. Reference [43] outlines a combination of a power supply and voltage equalizer so that the number of power supplies can be reduced. Although this circuit is mainly based on a bidirectional flyback converter, this structure only has discharge balancing. Its modes are divided into the cell-to-load (C2L) mode and the battery C2C mode, and the efficiency of the converter needs to be especially considered because the voltage equalizer of this structure is related to the main power stage. In addition, in the battery C2C mode, the converter passes through two converters, so there is a larger loss. Reference [44] details a simple fault-tolerant control (FTC) technique based on online vector calculation and a constraint mechanism to balance DC voltage for a single-phase cascaded H-bridge multilevel converter (CHBMC).

2. System Configuration

A battery voltage equalizer with a bidirectional buck converter and a flyback converter for charging balance, discharging balance, and static balance is presented herein. The system configuration is shown in Figure 2. A Cyclone III EP3CE144C8N FPGA is used to control the proposed circuit system. This bidirectional buck converter is a battery charger, and its control mode is set to a constant current/constant voltage (CC/CV) to charge the battery during charging. In addition, this circuit has a bidirectional function, so it can discharge the battery and supply power to the load, and its control mode is set to a constant voltage (CV). The primary side of the flyback converter is connected to the low-voltage side of the bidirectional buck converter and the battery pack, and the secondary side of the flyback converter is connected to each corresponding battery cell. A voltage-chasing method, called chain-loop comparison, is proposed for battery voltage equalization. This method involves detection of the voltage of each battery cell and determining whether the corresponding flyback converter is activated or not by comparing each battery cell based on the chain loop. In addition, OPA1 is used as a difference amplifier with filters to sense the voltage across R_siL to obtain the current I_iL flowing through the bidirectional buck converter, whereas OPA2 to OPA5 are used as difference amplifiers without any filters to sense the battery voltages V_{b1_s}, V_{b2_s}, V_{b3_s}, and V_{b4_s}. The voltages V_buck and V_boost of the bidirectional buck converter are sensed by the voltage divider, and the currents I_ob1, I_ob2, I_ob3, and I_ob4 of the secondary-side DC currents of the flyback converters are sensed by the hall current sensors. These sensed voltages mentioned above are sent to the FPGA to generate gate driving signals for the switches.

3. Operating Principle of the Battery Voltage Equalizer

In order to facilitate the analysis, Figure 2 was converted into a block diagram as shown in Figure 3. Prior to explaining the operating principle, the associated symbols in Figure 3 are defined first. Since four series of three parallel lithium batteries are used in this design, the voltage balance is composed of four flyback converters and four series of lithium batteries. In the equalizer presented in this paper, the total current flowing into the flyback converter is I_{in_bT}; the primary-side currents are I_{in_b1}, I_{in_b2}, I_{in_b3}, and I_{in_b4}; and the secondary-side currents are I_{o_b1}, I_{o_b2}, I_{o_b3}, and I_{o_b4} and are maintained at 2 A during the operation of the flyback converters. The battery cells flow through the currents I_{b1_T}, I_{b2_T}, I_{b3_T}, and I_{b4_T}, and the current through the battery pack is I_pack.

Table 1. Possible cases of the operating principles for four flyback converters.

	Flyback_1	Flyback_2	Flyback_3	Flyback_4
Case 1	0	0	0	0
Case 2	0	0	0	1
Case 3	0	0	1	0
Case 4	0	0	1	1
Case 5	0	1	0	0
Case 6	0	1	0	1
Case 7	0	1	1	0
Case 8	0	1	1	1
Case 9	1	0	0	0
Case 10	1	0	0	1
Case 11	1	0	1	0
Case 12	1	0	1	1
Case 13	1	1	0	0
Case 14	1	1	0	1
Case 15	1	1	1	0

shows the possible cases of the operating principles for four flyback converters based on the voltage-chasing method, where 1 means the flyback converter is in operation, and 0 means the flyback converter is not in operation.

3.1. Charging Balance

Figure 4 shows the schematic diagram of the charging balance. In this state, the bidirectional buck converter provides a stable current source I_{o_buck} to supply energy to the flyback converter and the battery pack, so the final current I_pack through the battery pack can be obtained as shown in (1). The total input current I_{in_bT} of the flyback converters is shown in (2), and the current flowing through each battery is shown in (3) to (6):

$$I_{pack}=I_{o\_buck}-I_{in\_bT}$$

(1)

$$I_{in\_bT}=I_{in\_b1}+I_{in\_b2}+I_{in\_b3}+I_{in\_b4}$$

(2)

$$I_{b1\_T}=I_{pack}+I_{o\_b1}$$

(3)

$$I_{b2\_T}=I_{pack}+I_{o\_b2}$$

(4)

$$I_{b3\_T}=I_{pack}+I_{o\_b3}$$

(5)

$$I_{b4\_T}=I_{pack}+I_{o\_b4}$$

(6)

If the battery voltage is V_b4 > V_b3 > V_b2 > V_b1, using the proposed chain-loop comparison method, we can determine that V_b4 > V_b3, implying that Flyback_3 is on and Flyback_4 is off; V_b3 > V_b2, implying that Flyback_2 is on and Flyback_3 is off; V_b2 > V_b1, implying that Flyback_1 is on and Flyback_2 is off; and V_b4 > V_b1, implying that flyback_1 is on and Flyback_4 is off.

By summarizing the above, it can be seen that Flyback_1, Flyback_2, and Flyback_3 are on, but Flyback_4 is off, as shown in Figure 5, which corresponds to case 15 in Table 1. Equations (2) and (6) can be rewritten as (7) and (8), respectively, while Equations (1) and (3)–(5) remain unchanged. Since three flyback converters are on, the stabilized current source I_{o_buck} provides part of the current to the flyback converter I_{in_bT}, which reduces battery pack current I_pack, thereby slowing the charge speed of the battery with the highest voltage V_b4. In addition, the batteries with the voltages V_b3, V_b2, and V_b1 are charged by the battery peak current I_pack plus the stable current of 2 A provided by the individual flyback converters, thus increasing the charging speed so that the battery voltage of V_b3, V_b2, and V_b1 can catch up with that of V_b4 to achieve the purpose of charging balance:

$$I_{in\_bT}=I_{in\_b1}+I_{in\_b2}+I_{in\_b3}$$

(7)

$$I_{b4\_T}=I_{pack}$$

(8)

When the battery is balanced in case 1, as shown in Figure 6, Flyback_1, Flyback_2, Flyback_3, and Flyback_4 are turned off, and the associated equation is (9):

$$I_{o\_buck}=I_{pack}=I_{b1\_T}=I_{b2\_T}=I_{b3\_T}=I_{b4\_T}$$

(9)

3.2. Discharging Balance

Figure 7 shows the schematic diagram of the discharging balance. In this state, the battery pack has to provide energy to the bidirectional buck converter and provide energy to the flyback converter so that we can determine the final current I_pack through the battery pack as shown in (10). The total input current of the flyback converters, I_{in_bT}, is shown in (2), and the current flowing through each battery is shown in (11) to (14):

$$I_{pack}=I_{in\_boost}+I_{in\_bT}$$

(10)

$$I_{b1\_T}=I_{pack}-I_{o\_b1}$$

(11)

$$I_{b2\_T}=I_{pack}-I_{o\_b2}$$

(12)

$$I_{b3\_T}=I_{pack}-I_{o\_b3}$$

(13)

$$I_{b4\_T}=I_{pack}-I_{o\_b4}$$

(14)

If the battery voltage is V_b4 < V_b3 < V_b2 < V_b1, using the proposed chain-loop comparison method, we can determine that V_b4 < V_b3, implying that Flyback_4 is on and Flyback_3 is off; V_b3 < V_b2, implying that Flyback_3 is on and Flyback_2 is off; V_b2 < V_b1, implying that Flyback_2 is on and Flyback_1 is off; and V_b4 < V_b1, implying that Flyback_4 is on and Flyback_1 is off. By summarizing the above, it can be seen that Flyback_2, Flyback_3, and Flyback_4 are off, but Flyback_1 is on as shown in Figure 8, which corresponds to case 8 in Table 1. Here, Equations (2) and (11) can be rewritten as (15) and (16), respectively, while Equations (10) and (12)–(14) remain unchanged. Since three flyback converters are on, the battery pack provides part of the current to the flyback converter I_{in_bT} and also provides part of the current to the bidirectional buck converter I_{in_boost}, in which the batteries with lower voltages V_b2, V_b3, and V_b4 can be made up by the stable current of 2 A provided by the individual flyback converters. Thus, the current provided by these batteries is reduced, and the battery with the highest voltage V_b1 discharges more current so as to achieve the purpose of discharging balance:

$$I_{in\_bT}=I_{in\_b2}+I_{in\_b3}+I_{in\_b4}$$

(15)

$$I_{b1\_T}=I_{pack}$$

(16)

When the battery is balanced in case 1, as shown in Figure 9, Flyback_1, Flyback_2, Flyback_3, and Flyback_4 are turned off, and the associated equation is shown in (17):

$$I_{in\_boost}=I_{pack}=I_{b1\_T}=I_{b2\_T}=I_{b3\_T}=I_{b4\_T}$$

(17)

3.3. Static Balance

Figure 10 shows the schematic diagram of static balancing, which is performed when there is no load or power supply and the batteries have uneven voltages. In this state, the battery pack has to provide energy to the flyback converter, so the current I_pack through the battery pack can be obtained as shown in (18), where the total current of the flyback converters I_{in_bT} is shown in (2), and the current flowing through each battery is shown in (11) to (14).

$$I_{pack}=I_{in\_bT}$$

(18)

If the battery voltage is V_b3 > V_b1 > V_b4 > V_b2, using the proposed chain-loop comparison method, we can determine that V_b4 < V_b3, implying that Flyback_4 is on and Flyback_3 is off; V_b3 > V_b2, implying that Flyback_2 is on and Flyback_3 is off; V_b2 < V_b1, implying that Flyback_2 is on and Flyback_1 is off; V_b4 > V_b1, implying that Flyback_1 is on and Flyback_4 is off; V_b2 < V_b1, implying that Flyback_2 is on and Flyback_1 is off; and V_b4 > V_b1, implying that Flyback_1 is on and Flyback_4 is off. By summarizing the above, we can see that Flyback_2 and Flyback_4 are on, but Flyback_1 and Flyback_3 are off, as shown in Figure 11, which corresponds to case 6 in Table 1. Here, Equations (2), (11) and (13) can be rewritten as (19), (16), and (20), respectively, while Equations (12) and (14) remain unchanged. Since two flyback converters are on, the battery pack provides part of the current to the flyback converter I_{in_bT}, where the batteries with the lower-voltage cells V_b2 and V_b4 can be made up by the stable current of 2 A provided by the individual flyback converters. Therefore, the current discharged by these batteries is reduced, and the batteries with the voltages V_b1 and V_b3 discharge more current so as to achieve a static balance:

$$I_{in\_bT}=I_{in\_b2}+I_{in\_b4}$$

(19)

$$I_{b3\_T}=I_{pack}$$

(20)

When the battery is balanced in case 1, as shown in Figure 12, Flyback_1, Flyback_2, Flyback_3, and Flyback_4 are turned off, and the associated equation is (21):

$$I_{pack}=I_{b1\_T}=I_{b2\_T}=I_{b3\_T}=I_{b4\_T}=0$$

(21)

4. Design Considerations

Table 2. Specifications of bidirectional buck converter in buck mode.

Mode	Constant Current	Constant Voltage
Operation Mode	CCM	CCM
Input Voltage (Vin_buck)	48 V	48 V
Output Voltage (Vo_buck)	12~16.8 V	16.8 V
Output Current (Io_buck)	10 A	0.35~10 A
Output Power (Po_buck)	120~168 W	5.88~168 W

,

Table 3. Specifications for bidirectional buck converter in boost mode.

Mode	Constant Voltage
Operation Mode	CCM
Input Voltage (Vin_boost)	12~16.8 V
Output Voltage (Vo_boost)	48 V
Output Current (Io_boost)	0.5~3.5 A
Output Power (Po_boost)	24~168 W
Switching Frequency (fs1)	150 kHz

,

Table 4. Flyback converter specifications.

Mode	Constant Current
Operation Mode	DCM
Input Voltage (Vin_b)	12~16.8 V
Output Voltage (Vo_b)	3~4.19 V
Output Current (Io_b)	2 A
Output Power (Po_boost)	6~8.38 W
Turns Ratio (Np_b/Ns_b)	4
Switching Frequency (fs1)	65 kHz

and

Table 5. Battery cell specifications.

Model	NCR18650GA
Charge	3300 mAh
Nominal Voltage	3.6 V
Full Charge Voltage	4.2 V
Discharge Cut-Off Voltage	2.5 V
Battery Pack	4 Series, 3 Parallel (=12 pcs)
Battery Pack Voltage	12~16.8 V

are the specifications for converters and battery cells.

4.1. Circuit Parameter Design

This subsection will describe the circuit parameter design in detail, including the inductance, magnetizing inductance, and capacitance.

4.1.1. Inductance Design for Bidirectional Buck Converter

In the design of the inductor, the buck mode was chosen. The boundary output current was set to 2 A. When the output current is lower than this current, the inductor current i_L becomes a negative value. The input voltage V_{in_buck} is 48 V, and the output voltage V_{o_buck} is 16.8 V, so the corresponding duty cycle D_buck is 0.35. Therefore, the value of the inductor is 18.2 μH:

$$\begin{gathered} L={\displaystyle \frac{(V_{in\_buck}-V_{o\_buck})D_{buck}}{2\times I_{o\_buck}\times f_{s1}}}={\displaystyle \frac{V_{o\_buck}(1-D_{buck})}{2\times I_{o\_buck}\times f_{s1}}} \\ ={\displaystyle \frac{(48-16.8)\times 0.35}{2\times 2\times 150\mathrm{k}}}={\displaystyle \frac{16.8\times (1-0.35)}{2\times 2\times 150\mathrm{k}}}=18.2\mathsf{\mu }\mathrm{H} \end{gathered}$$

(22)

In order to ensure that the inductor current i_L of 2 A or more is free from negative current over the entire operating range, an inductance of 23 μH was selected.

4.1.2. Output Capacitance Design for the Bidirectional Buck Converter

The designs of the output capacitances for the buck and boost modes are detailed in the following.

Output Capacitance C_buck in Buck Mode

Figure 13 shows the key waveforms for calculating the capacitance in buck mode of the bidirectional buck converter. According to the Ampere-second balance, the average current flowing into the capacitor in one cycle in steady state is zero, so the values of ∆Q₊ and |∆Q₋| are equal and can be expressed as (23), where ∆V_{o_buck} is the output voltage ripple in buck mode:

$$\Delta Q_{+}=C_{buck}\times \Delta V_{o\_buck}={\displaystyle \frac{1}{2}}\times \left({\displaystyle \frac{1}{2}}\Delta i_L\right)\times \left({\displaystyle \frac{1}{2}}{T}_{s1}\right)={\displaystyle \frac{1}{8}}\Delta i_L\times T_{s1}$$

(23)

Since ∆i_L is the peak-to-peak value of the inductor current, Equation (23) can be rewritten as (24):

$${\displaystyle \frac{\Delta V_{o\_buck}}{V_{o\_buck}}}={\displaystyle \frac{1-D_{buck}}{8\times C_{buck}\times L\times {f^2}_{s1}}}$$

(24)

Assuming that the output voltage ripple is less than 1%,

$${\displaystyle \frac{\Delta V_{o\_buck}}{V_{o\_buck}}}\le 0.01$$

(25)

Substituting (25) into (24) and rearranging this result with associated values yields

$$C_{buck}\ge {\displaystyle \frac{1-D_{buck}}{0.08\times L\times {f^2}_{s1}}}={\displaystyle \frac{1-\frac{12}{48}}{0.08\times 23\mathsf{\mu }\times {\left(150\mathrm{k}\right)}^2}}=18.12\mathsf{\mu }\mathrm{F}$$

(26)

Finally, by considering the effect of frequency on the capacitance, the actual value should be chosen to be higher than the calculated value, so a 220 µF/50 V electrolytic capacitor was selected.

Output Capacitance C_buck in Boost Mode

Figure 14 shows the key waveforms for calculating the capacitance in boost mode of the bidirectional buck converter. The average current flowing into the capacitor in one cycle in steady state is zero, so the values of ∆Q₊ and |∆Q₋| are identical and can be expressed as (27), where ∆V_{o_boost} is the output voltage ripple in boost mode.

$$\Delta Q_{+}=C_{boost}\times \Delta V_{o{\_}_{boost}}=I_{o\_boost}\times D_{boost}\times T_{s1}$$

(27)

Rearranging (27) yields

$${\displaystyle \frac{\Delta V_{o\_boost}}{V_{o\_boost}}}={\displaystyle \frac{D_{boost}}{C_{boost}\times R_{o\_boost}\times f_{s1}}}$$

(28)

Assuming that the output voltage ripple is less than 1%,

$${\displaystyle \frac{\Delta V_{o\_boost}}{V_{o\_boost}}}\le 0.01$$

(29)

Substituting (29) into (28) and rearranging this result with associated values yields

$$\begin{gathered} C_{boost}\ge {\displaystyle \frac{D_{boost}}{0.01\times R_{o\_boost}\times f_{s1}}}={\displaystyle \frac{1-\frac{V_{in\_boost}}{V_{o\_boost}}}{0.01\times R_{o\_boost}\times f_{s1}}} \\ ={\displaystyle \frac{\left(1-\frac{12}{48}\right)}{0.01\times \frac{48}{3.5}\times 150\mathrm{k}}}=36.46\mathsf{\mu }\mathrm{F} \end{gathered}$$

(30)

Finally, by considering the effect of frequency on the capacitance, the actual value should be chosen to be higher than the calculated value, so a 220 µF/100 V electrolytic capacitor was selected.

4.1.3. Magnetizing Inductance Design for Flyback Converter

In order to ensure that the circuit can be maintained in DCM, the sum of the magnetizing time ratio D_x1 and the demagnetization time ratio D_x2 of the magnetizing inductance L_{m_b} was set to 0.85, i.e.,

$$D_{\mathit{max}}=D_{x1}+D_{x2}=0.85$$

(31)

From the voltage conversion ratio M_b in (32), the demagnetization time ratio D_x2 can be rewritten as

$$M_b={\displaystyle \frac{V_{o\_b}}{V_{in\_b}}}={\displaystyle \frac{D_{x1}}{D_{x2}}}\times {\displaystyle \frac{N_{s\_b}}{N_{p\_b}}}$$

(32)

$$D_{x2}=D_{x1}\times {\displaystyle \frac{V_{in\_b}}{V_{o\_b}}}\times {\displaystyle \frac{N_{s\_b}}{N_{p\_b}}}$$

(33)

Substituting (33) into (31) yields

$$D_{x1}={\displaystyle \frac{D_{\mathit{max}}}{1+\frac{V_{in\_b}}{V_{o\_b}}\times \frac{N_{s\_b}}{N_{p\_b}}}}$$

(34)

From (31) and (34), the equations of D_x1 and D_x2 can be obtained as

$$D_{x1}={\displaystyle \frac{D_{\mathit{max}}}{1+\frac{V_{in\_b}}{V_{o\_b}}\times \frac{N_{s\_b}}{N_{p\_b}}}}$$

(34)

$$D_{x2}=D_{\mathit{max}}-{\displaystyle \frac{D_{\mathit{max}}}{1+\frac{V_{in\_b}}{V_{o\_b}}\times \frac{N_{s\_b}}{N_{p\_b}}}}$$

(35)

By substituting (34) and (35) into (36), the output current I_{o_b} can be obtained as

$$I_{o\_b}={\displaystyle \frac{1}{2}}\times {\displaystyle \frac{V_{in\_b}{D}_{x1}{T}_{s2}}{L_{m\_b}}}\times {\displaystyle \frac{N_{p\_b}}{N_{s\_b}}}\times D_{x2}={\displaystyle \frac{V_{o\_b}}{R_{o\_b}}}$$

(36)

$$I_{o\_b}={\displaystyle \frac{1}{2}}\times {\displaystyle \frac{V_{in\_b}{T}_{s2}}{L_{m\_b}}}\times {\displaystyle \frac{D_{\mathit{max}}}{1+\frac{V_{in\_b}}{V_{o\_b}}\times \frac{N_{s\_b}}{N_{p\_b}}}}\times {\displaystyle \frac{N_{p\_b}}{N_{s\_b}}}\times \left(D_{\mathit{max}}-{\displaystyle \frac{D_{\mathit{max}}}{1+\frac{V_{in\_b}}{V_{o\_b}}\times \frac{N_{s\_b}}{N_{p\_b}}}}\right)$$

(37)

Since the converter is operated in DCM, Equation (37) can be rewritten as (38), and then the value of D_max in (31), the output current I_{o_b} of 2 A, the turns ratio N_{p_b}/N_{s_b} of 4, and the maximal and minimal output and input voltages in Table 4 are substituted into the Equation (38) to draw the curves of relationship between L_{m_b} and V_{o_b}. This is shown in Figure 15, with the dotted line as the minimum input voltage V_{in_b_min} for each battery and the solid line as the maximum input voltage V_{in_b_max}. From this figure, the minimum magnetizing inductance can be found to be 33.37 µH, and the actual magnetizing inductance was chosen to be 29 µH to ensure that the converter can be operated in DCM.

$$L_{m\_b}={\displaystyle \frac{1}{2}}\times {\displaystyle \frac{V_{in\_b}{T}_{s2}}{I_{o\_b}}}\times {\displaystyle \frac{D_{\mathit{max}}}{1+\frac{V_{in\_b}}{V_{o\_b}}\times \frac{N_{s\_b}}{N_{p\_b}}}}\times {\displaystyle \frac{N_{p\_b}}{N_{s\_b}}}\times \left(D_{\mathit{max}}-{\displaystyle \frac{D_{\mathit{max}}}{1+\frac{V_{in\_b}}{V_{o\_b}}\times \frac{N_{s\_b}}{N_{p\_b}}}}\right)$$

(38)

4.1.4. Output Capacitance Design for Flyback Converter

Figure 16 shows the illustrated waveforms of the output capacitor of the flyback converter. Firstly, the related value of x should be calculated, and Equation (39) can be written by using the similar triangle, where I_{sd_s_peak} is the peak current on the switch S_{b_p}, and ∆i_{sd_s_peak} is the peak-to-peak current on the switch S_{b_p}:

$$\begin{array}{l}{\displaystyle \frac{I_{sd\_s\_peak}-I_{o\_b}}{I_{o\_b}}}={\displaystyle \frac{x}{D_{x2}-x}}\\ x={\displaystyle \frac{\left(I_{sd\_s\_peak}-I_{o\_b}\right)D_{x2}}{\Delta i_{sd\_s\_peak}}}\end{array}$$

(39)

According to the Ampere-second balance, the average current flowing into the capacitor in one cycle in steady state is zero, so the values of ∆Q₊ and |∆Q₋| are equal, and ∆Q₊ can be expressed as (40), where ∆V_{o_b} is the output voltage ripple of the flyback converter.

$$\begin{gathered} \Delta Q_{+}=C_{o\_b}\times \Delta V_{o\_b} \\ ={\displaystyle \frac{1}{2}}\times \left(I_{sd\_s\_peak}-I_{o\_b}\right)\times {\displaystyle \frac{\left(I_{sd\_s\_peak}-I_{o\_b}\right)D_{x2}{T}_{s2}}{I_{sd\_s\_peak}}} \end{gathered}$$

(40)

By assuming that the output voltage ripple is less than 1%, it can be found that

$${\displaystyle \frac{\Delta V_{o\_b}}{V_{o\_b}}}\le 0.01$$

(41)

By substituting (41) into (40), (42) can be obtained, and the associated values are substituted into (42) and plotted in Figure 17, from which the highest output capacitance can be found to be 659.42 µF:

$$C_{o\_b}\ge {\displaystyle \frac{\frac{1}{2}\times \left(I_{sd\_s\_peak}-I_{o\_b}\right)\times \frac{\left(I_{sd\_s\_peak}-I_{o\_b}\right)D_{x2}{T}_{s2}}{I_{sd\_s\_peak}}}{0.01V_{o\_b}}}$$

(42)

Finally, by considering the effect of frequency on the capacitance, the actual value was chosen to be higher than the calculated value, so a 1500 µF/50 V electrolytic capacitor was selected.

5. Control Considerations

In control strategies for converters in different modes, a field-programmable gate array (FPGA) is used as a digital controller; the chip used is a Cyclone III EP3CE144C8N, and the required functions inside the FPGA are described by the hardware description language (HDL).

5.1. Control Strategies for Converters in Different Modes

Figure 18 shows the control strategy of the bidirectional buck converter in buck mode, which consists of two analog-to-digital converters (ADCs) to sample signals V_buck and I_iL shown in Figure 2, two PI controllers, a constant current and constant voltage multiplexer (CC/CV MUX), a pulse-width-modulated (PWM) generator, and two blanking time generators. This control strategy is mainly for CC/CV control. The voltage and current feedback signals V_buck and I_iL shown in Figure 18 are converted into digital data by the ADCs, and after this, the digital commands Ref1 and Ref2 are subtracted from the corresponding digital data to generate the error values, which are then sent to the PI controllers to create the required control force. These control forces are sent to the CC/CV to determine the control authority and finally sent to the PWM generator to yield the required gate driving signals to drive the switches.

Figure 19 shows the control strategy of the bidirectional buck converter in boost mode, which is composed of an ADC, a PI controller, a PWM generator, and two blanking time generators. This control strategy is mainly for CV control. The feedback signal V_boost of the voltage shown in Figure 19 is converted into digital data by the ADC, and then the digital command Ref3 is subtracted from the digital data to generate the error value, which is sent to the PI controller to generate the required control force and finally sent to the PWM generator to yield the required gate driving signal to drive the switch.

Figure 20 shows the control strategy of the four flyback converters, which consist of four ADCs, four PI controllers, and four PWM generators. This control strategy is mainly for CV control. The four feedback signals I_{o_b1}, I_{o_b2}, I_{o_b3}, and I_{o_b4} in Figure 20 are converted to digital data by individual ADCs, and then the corresponding digital commands Ref1, Ref2, Ref3, and Ref4 are subtracted from these digital data to generate the error values, which are sent to individual PI controllers to generate the required control forces and then sent to the PWM generators to yield the required duty cycles. Finally, these duty cycles perform an AND logic operation with the signals C_trlb1, C_trlb2, C_trlb3, and C_trlb4 created from chain-loop comparison so as to obtain the gate driving signals to drive the switches.

5.2. Chain-Loop Comparison Signals

Figure 20 shows the control strategy of the flyback converters, where the chain-loop comparison signals C_trlb1, C_trlb2, C_trlb3, and C_trlb4 are used to decide whether to activate the flyback converter corresponding to each battery for battery balancing. Figure 21 shows the flowchart of the chain-loop comparison strategy, and Figure 22 shows the operation diagram of the chain-loop comparison strategy. From Figure 22, it can be seen that there are two comparison values for each battery: C_{trlb1_1} and C_{trlb1_2}, C_{trlb2_1} and C_{trlb2_2}, C_{trlb3_1} and C_{trlb3_2}, and C_{trlb4_1} and C_{trlb4_2} for the first, second, third, and fourth batteries, respectively. After chain-loop comparison, these two pieces of data are aggregated by an OR logic operation to obtain the chain-loop comparison signals of each of the four batteries, namely, C_trlb1, C_trlb2, C_trlb3, and C_trlb4.

6. Experimental Results

In this section, some experimental waveforms and measurements are shown below.

6.1. Experimental Results for Charging Balance

Figure 23 shows the experimental results for charging balance, in which the initial values of the batteries are 3.507 V for V_b4, 3.397 V for V_b3, 3.25 V for V_b2, and 3.092 V for V_b1. It can be found that at this time the voltage difference between the maximum and minimum is 0.415 V, and after the proposed chain-loop comparison for battery balancing, the voltages of the four batteries after 19.75 min are 4.0 V for V_b4, 3.997 V for V_b3, 3.995 V for V_b2, and 3.993 V for V_b1. After battery balancing, the voltage difference is 0.007 V, and the four battery voltages converge to 3.99 V.

6.2. Experimental Results for Discharging Balance

Figure 24 shows the experimental results for discharge balancing, in which the initial values of the batteries are 3.985 V for V_b4, 3.839 V for V_b3, 3.803 V for V_b2, and 3.566 V for V_b1. It can be found that the voltage difference between the maximum and minimum at this time is 0.419 V, and after battery balancing through the proposed chain-loop comparison, the voltages of the four batteries after 24 min are 3.338 V for V_b4, 3.336 V for V_b3, 3.334 V for V_b2, and 3.333 V for V_b1. After battery balancing, the battery voltage difference is 0.005 V, and the four battery voltages converge to 3.335 V.

6.3. Experimental Results for Static Balance

Figure 25 shows the experimental results for static balance, in which the initial values of the batteries are 3.756 V for V_b4, 3.716 V for V_b3, 3.357 V for V_b2, and 3.249 V for V_b1. It can be found that the voltage difference between the maximum and minimum at this time is 0.507 V. After the proposed chain-loop comparison, the voltages of the four batteries after 20 min are 3.482 V for V_b4, 3.479 V for V_b3, 3.477 V for V_b2, and 3.475 V for V_b1. After battery balancing, the voltage difference between the maximum and minimum is 0.007 V, and the four battery voltages converge to 3.478 V.

6.4. Experimental Waveforms of Converters

In this subsection, some measured waveforms related to the converters are shown.

Figure 26 and Figure 27 show that the closed-loop control allows the bidirectional buck converter in buck mode to be controlled at a constant current and a constant voltage, respectively. Figure 28 shows that the closed-loop control allows the bidirectional buck converter in boost mode to be controlled at a constant voltage. Figure 29 shows that the voltage across the primary-side switch S_{b_p}, called v_{ds_p}, and the voltage across the secondary-side switch S_{b_s}, called v_{ds_s}, allow the flyback converter to be operated in DCM. This is because when the magnetizing inductance L_{m_b} is fully demagnetized, it resonates with the equivalent output capacitance of the switch S_{b_p}, which generates oscillations and maps them to the secondary side. Figure 30 shows that the closed-loop control allows the flyback converter to be controlled at a constant current.

6.5. Converter Efficiency Measurement

In this subsection, the efficiency measurement methods are shown in Figure 31, Figure 32, Figure 33 and Figure 34 for the different conditions of the main power stages. As shown in each figure, the digital meters are used to measure the input voltage, output voltage, and the voltage of the current-detecting resistor (Shunt) to obtain the input and output currents, which can be used to obtain the input power and output power, while the required load is regulated by a DC electronic load. Finally, the resulting input and output powers are used to calculate the efficiency of the actual circuit operation. Figure 35 shows the efficiency curve of the bidirectional buck converter in buck mode at a constant current. Figure 36 shows the efficiency curve of the bidirectional buck converter in buck mode at a constant voltage. Figure 37 shows the efficiency curve of the bidirectional buck converter in boost mode at a constant voltage. Figure 38 shows the efficiency curve of the flyback converter at a constant current.

Figure 35 shows the efficiency curve of the bidirectional buck converter in buck mode at a constant current of 10 A. In Figure 35, the efficiency is above 94.25% and can be up to 95.82%. Figure 36 shows the efficiency curve of the bidirectional buck converter in buck mode at a constant voltage of 16.8 V. In Figure 36, as the output current decreases, the efficiency also decreases; the efficiency is above 92.51% and can be up to 96.67%. Figure 37 shows the efficiency curve of the bidirectional buck converter in boost mode at a constant voltage of 48 V. Figure 38 shows the efficiency curve of the bidirectional buck converter in boost mode at a constant voltage of 48 V. Comparing the two curves in Figure 38 with the input voltages of 16.8 V and 14.4 V, it can be seen that the efficiency decreases due to the increase in the input current because of the low input voltage, and the efficiency of the bidirectional buck converter is above 92.23% and can be up to 95.79%. Figure 38 shows the efficiency curve of the flyback converter at a constant current of 2 A. In Figure 38, due to the low output voltage range, the efficiency increases slightly when the output voltage is gradually increased, and the efficiency is above 88.54% and can be up to 90.25%.

7. Literature Comparison

The flyback converter was adopted as the circuit of the battery voltage equalizer in this study, and a comparison between our results and relevant studies in the literature was conducted.

Regarding charging balance, as shown in

Table 6. Comparison of charging balance.

		[42]	Proposed
Before Balancing	Vb_max_before	3.774 V	3.507 V
	Vb_min_before	3.464 V	3.092 V
	∆Vb_before	0.31 V	0.415 V
After Balancing	Vb_max_after	3.871 V	4.0 V
	Vb_min_after	3.823 V	3.993 V
	∆Vb_after	0.048 V	0.007 V
	Balancing time	140 min	19.7 min

, the initial maximum and minimum battery voltages in [42] are 3.774 V and 3.464 V, respectively, with a battery voltage difference of 0.31 V, and the final maximum and minimum battery voltages are 3.871 V and 3.823 V, respectively, with the voltage difference between the maximum and minimum of 0.048 V after 140 min. The initial maximum and minimum battery voltages for the proposed control strategy are 3.507 V and 3.092 V, respectively, with the voltage difference between the maximum and minimum of 0.415 V, and the final maximum and minimum battery voltages proposed are 4.0 V and 3.993 V, respectively, with the voltage difference between the maximum and minimum of 0.007 V after 19.75 min. Therefore, from the comparison between the two, it can be seen that the proposed strategy has a higher initial battery voltage difference, shorter balancing time, and a smaller final battery voltage difference.

Regarding discharge balance, as shown in

Table 7. Comparison of discharging balance.

		[42]	[43]	Proposed
Before Balancing	Vb_max_before	4.027 V	4.1 V	3.985 V
	Vb_min_before	3.693 V	3.99 V	3.566 V
	∆Vb_before	0.334 V	0.11 V	0.419 V
After Balancing	Vb_max_after	3.543 V	3.99 V (Balanced Voltage)	3.338 V
	Vb_min_after	3.494 V		3.333 V
	∆Vb_after	0.049 V	None	0.005 V
	Balancing time	140 min	41.67 min	24 min

, the initial maximum and minimum battery voltages in [42] are 4.027 V and 3.693 V, respectively, with the voltage difference between the maximum and minimum of 0.334 V. After 140 min, the final maximum and minimum battery voltages are 3.543 V and 3.494 V, respectively, with the voltage difference between the maximum and minimum of 0.049 V. The initial maximum and minimum battery voltages in [43] are 4.1 V and 3.99 V, respectively, with the voltage difference between the maximum and minimum of 0.11 V. Since this paper does not provide the detailed battery voltages, it is only known that the battery voltages are balanced at 3.99 V after 41.67 min. The initial maximum and minimum battery voltages for the proposed control strategy are 3.985 V and 3.566 V, respectively, with the voltage difference between the maximum and minimum of 0.419 V. After 24 min, the final maximum and minimum battery voltages are 3.338 V and 3.333 V, respectively, with the voltage difference between the maximum and minimum of 0.005 V. Therefore, from the comparison between the three, it can be seen that the proposed strategy has a higher initial battery voltage difference, shorter balancing time, and a smaller final battery voltage difference.

Regarding static balance, as shown in

Table 8. Comparison of static balance.

		[39] Case 1	[39] Case 2	[43]	Proposed
Before Balancing	Vb_max_before	3.846 V	3.86 V	4.08 V	3.756 V
	Vb_min_before	3.79 V	3.8 V	3.98 V	3.249 V
	∆Vb_before	0.056 V	0.06 V	0.1 V	0.507 V
After Balancing	Vb_max_after	3.84 V (Balanced Voltage)	3.84 V (Balanced Voltage)	4.04 V (Balanced Voltage)	3.482 V
	Vb_min_after				3.475 V
	∆Vb_after	None	None	None	0.007 V
	Balancing time	30 min	55 min	33.33 min	20 min

, the initial maximum and minimum values of the battery voltages in case 1 of [39] are 3.846 V and 3.79 V, respectively, with the voltage difference between the maximum and minimum of 0.056 V. Since this paper does not provide the detailed battery voltages, it is only known that the battery voltages are balanced at 3.84 V after 30 min. The initial maximum and minimum values of the battery voltages in case 2 of [39] are 3.86 V and 3.8 V, respectively, with the voltage difference between the maximum and minimum of 0.06 V. Since this paper does not provide the detailed battery voltages, it is only known the battery voltages are balanced at 3.84 V after 55 min. The initial maximum and minimum battery voltages are 3.756 V and 3.249 V, respectively, with the voltage difference between the maximum and minimum of 0.056 V. Since this paper does not provide the detailed battery voltages, it is only known that the final battery voltages are balanced at 4.04 V after 33.33 min. The initial maximum and minimum battery voltages for the proposed control strategy are 3.756 V and 3.249 V, respectively, with the voltage difference between the maximum and minimum of 0.507 V. After 20 min, the final maximum and minimum final battery voltages are 3.482 V and 3.475 V, respectively, with the voltage difference between the maximum and minimum of 0.007 V. Therefore, from the comparison between the three, it can be seen that the proposed control strategy has a higher initial battery voltage difference, shorter balancing time, and a smaller final battery voltage difference.

8. Conclusions

The chain-loop comparison strategy for battery voltage equalization based on the bidirectional buck converter and the flyback converter is presented. There are three modes, namely, charging balance, discharging balance, and static balance. The experimental results show that all three modes have the effect of battery voltage balancing. The voltage difference between the maximum and minimum is 0.007 V after a balancing time of 19.75 min, 0.005 V after a balancing time of 24 min, and 0.007 V after a balancing time of 20 min for charging balance, discharging balance, and static balance, respectively. The efficiency of the bidirectional buck converter is above 92.51% and up to 96.67% over the entire operating range, whereas the efficiency of the flyback converter is above 88.54% and up to 90.2% in this range. Accordingly, the effectiveness of the proposed chain-loop comparison strategy for active battery voltage balance can be verified by experiments and comparisons.