Direct charge transfer between arbitrary lithium polymer cells based on a new control strategy

In this paper, a new control strategy, along with an innovative switching pattern, is proposed for the transfer of charge from one cell to another, whether they are adjacent or nonadjacent, or even to multiple cells simultaneously. Therefore, this strategy improves the efficiency of state of charge balancing, which is critical for lithium polymer (LiPo) batteries. Unlike in previous studies, all these functions are realized with a simple structure that employs standard DC–DC buck‐boost converters, without any additional complexities. By implementing the proposed control strategy, the effects of inaccuracies in the gain of current sensors, as well as multiplicative measurement noises, are reduced. The proposed method is applied to a set of five series LiPo cells, and a comprehensive investigation is conducted to assess both its balancing algorithm and operation. The simulation results illustrate the effective balancing performance and the achievement of the desired charge transfer through the proposed approach. An experimental setup, which includes five LiPo cells with a capacity of 1530 milliampere‐hours (mAh), is used to verify the proposed method. The outcomes demonstrate that the balancing of all cells is accurately performed under different initial conditions, within an acceptable time frame.


| INTRODUCTION
2][3] Lithiumion cells are highly susceptible to overcharging and over-discharging operations. 4These situations can significantly damage the cells or reduce their lifespan. 5o address this issue and optimize energy usage, lithiumion battery packs need to be balanced.In general, balancing a battery pack means equalizing the voltage or state of charge (SoC) of its cells. 6,7Balancing methods are typically classified as passive or active approaches.The passive cell balancing dissipates excess charge from overcharged cells, 8 while the active cell balancing involves transferring charge between the cells. 9One of the active balancing method types is adjacent cell to cell (CTC) balancing. 10These methods merely transfer the charge between two adjacent cells.The most important advantages of these approaches are simplicity in implementation and lower costs.However, an important challenge with these methods is the extended time required for battery balancing, particularly in systems with a large number of cells. 11To improve the efficiency of these methods, direct cell to cell (DCTC) balancing techniques are employed.While they can enhance balancing speed, DCTC techniques become more complex with a large number of transformers and electronic devices. 12In other words, most studies focus on the structure of the balancing circuits. 7In this paper, a new control strategy is proposed that allows active DCTC balancing to be achieved with the same circuit as the adjacent CTC method, without the need for any additional electronic equipment.At first, a literature review is presented as follows.In Qiu and Lu 13 and Dai et al., 14 different methods and topologies for cell balancing systems are presented.Based on the aforementioned references, the well-known buck-boost converter is a straightforward and affordable circuit topology for adjacent CTC charge transfer.The low speed of the adjacent CTC methods leads researchers to design DCTC circuits.For example, in Chen et al., 15 a high-speed DCTC balancing method is proposed using a multiwinding transformer.But, it is with complexity in magnetic design, implementation, and control.In Uno and Yoshino, 16 a modular equalization system by DCTC ability is proposed, but the circuit has many switches with a complex structure.In Pham et al., 17 a highefficiency active DCTC balancing using a switch matrix circuit with a transformer and a resonant converter is presented.However, the circuit has a lot of elements with complexity in design and control.It should be mentioned that the resonant and quasi-resonant DC-DC converters can reduce the electromagnetic interference (EMI) caused by switching devices, and novel soft switching methods are of interest. 18,19A switch matrix DCTC balancing circuit is presented in Habib et al. 20 with a high number of switches.In La and Choi, 21 a DCTC equalizer using a switch matrix single capacitor converter is proposed to improve the performance efficiency compared to the conventional switched-capacitor equalizers.However, the circuit complexity and the requirement for a dual MOSFET package are its disadvantages.To increase the balancing speed, some studies are dedicated to design the any cell to any cell (ACTAC), cell to pack (CTP), and pack to cell (PTC) balancing approaches 10,22 with relative complexity in design and implementation.In Shang et al., 23 an optimized meshstructured switched-capacitor balancing system is proposed, which results in a high-performance and cost-effective structure.However, it necessitates more switches and higher control complexity compared to a standard bidirectional buck-boost circuit for cell balancing.In Zhou et al., 24 a two-mode balancing method using switched-capacitor is proposed, capable of being operated in both DCTC and ACTAC modes with high speed and accuracy.However, it may be confronted with complexity in design and control, and it involves a relatively large number of MOSFETs compared to a typical balancing system using bidirectional buck-boost converters.In Zillo et al., 25 a new topology balancing circuit is proposed for series-connected lithium-ion cells, utilizing a multiport active half-bridge converter and a multiwinding transformer capable of operating in two modes: CTC and PTC.Although the proposed circuit in this work offers lower complexity compared to its relevant structures, it remains more intricate than the conventional buckboost balancing structure and also necessitates the proper design of its magnetic components.In Zhang et al., 26 a novel ACTAC balancing system is proposed for series-connected energy storage cells, utilizing switchedcapacitor equalizers, which leads to balancing improvements.However, it includes a number of MOSFETs twice that of conventional systems based on buck-boost converters.In Wu et al., 27 a mode-varying cell equalizer system is proposed, which combines the advantages of two balancing approaches: CTP and adjacent CTC balancing methods, utilizing interleaved parallel multiple transformers.In Liu et al., 28 a modular balancing circuit with auxiliary windings is proposed that it performs in automatic ACTAC fashion in each module.Nevertheless, its structure is relatively complex and requires proper magnetic design considerations.
Previous studies often attempted to propose complex new structures for direct cell to cell balancing.Moreover, proposing a way to have both advantages of the DCTC and one cell to others is notable.On the other hand, trying to improve the Coulomb counting method as a standard method for estimating the SoC of battery cells results in complicated techniques, algorithms, and calculations such as works in He and colleagues. 29,30In this paper, all the advantages of charge transfer between two arbitrary cells (direct charge transfer) and charge transfer from one cell to the other cells are achieved by using the typical and standard DC-DC buck-boost converter structure without the addition of extra circuit devices.Furthermore, the proposed method can enhance Coulomb counting accuracy by reducing the impact of inaccuracies in current sensor gain parameters and multiplicative measurement noise.LiPo batteries have received relatively little attention in previous studies.In this paper, the main focus is placed on the balancing of LiPo cells.The main contributions of this paper are presented as follows: 1. Direct charge transfer between any two cells, whether they are adjacent or not, utilizing a novel control strategy is possible without the addition of any extra components to the conventional DC-DC buck-boost converter structure.2. Simultaneous charge transfer from one cell to several other cells.3. Reducing the impact of current sensor gain inaccuracy and multiplicative noise of measurement.
A comparison of recent developments in active cell balancing structures is presented in Table 1, where the abbreviations DCTC, ACTAC, PTC, CTP, and CTC, only adjacent cells represent different balancing methods.N represents the number of battery cells and N m is the number of battery modules.This table compares various recent studies based on the number of MOSFETs, magnetic design requirements, and structural and control complexity.Magnetic devices, such as transformers, can increase the size and cost of the balancing system and also require proper design.The complexity of the structures and control systems in these studies is graded as simple, moderate, and complex.Table 1 demonstrates the superior performance of the proposed method, which is further detailed in the following sections.The rest of the paper is organized as follows.In Section 2, the problem hardware layout and circuit structure are presented.Then, the proposed control strategy and the scheme of control system are introduced in Section 3. In Section 4, the simulation results are studied.In Section 5, the proposed method performance is verified through an experimental setup containing five 1530 mAh LiPo cells.Finally, in Section 6, the conclusions are presented.

| HARDWARE LAYOUT
In this section, the hardware structure is introduced and its equipment is described.The circuit structure for five LiPo cells is illustrated in Figure 1.This structure employs one bidirectional buck-boost converter for every two adjacent cells.Therefore, the number of switches is N 2( − 1).Additionally, the number of inductors is equal to the number of buck-boost converters, both of which are N ( − 1).The switches in the balancing circuit shown in Figure 1 are n-channel MOSFETs.Their body diodes can be recognized according to Figure 1.A current sensor is utilized for each cell to measure the SoC of the LiPo cells.The circuit can be used for any number of cells.The proposed control strategy is explained in detail in the next section.

| PROPOSED METHOD
First, in this section, the necessary preparations are explained.Then, the proposed method is precisely described using different scenarios.

| SoC Calculations
SoC is a parameter that determines the amount of charge in a battery cell.In other words, it represents the charge status of a battery cell.The unit of electric charge in SI * is Coulomb.SoC is a unitless variable between 0 and 1 or 0% and 100%.SoC is usually represented by "z" and is defined as follows: where η t ( ) represents the Coulombic efficiency (CE) of the cell.In LiPo cells and, generally, in lithium-ion cells, η t ( ) is approximately equal to 1.This holds true specifically during the higher cycles. 31,32Therefore, in this study, it is assumed that η t ( ) = 1.i t ( ) denotes the current of the cell.It has positive values during charging and negative when discharging.Q is the total capacity of the cell.In Equation (1), Q should be calculated in Ampere-seconds, also known as Coulombs.According to Equation (1), SoC can be calculated as follows: It should be noted that an accurate estimation of the initial SoC and precise calibration of the current sensors are essential for achieving an accurate SoC estimation result.This model-free estimation method is well-known as the "Coulomb counting" method.The most important advantage of this method is its straightforward calculations with easy implementation. 33In the proposed balancing method, the effect of the current sensor gain inaccuracy and multiplicative measurement noise is reduced.

| Control strategy
Generally, one controller between every three adjacent cells is required in the proposed method.Therefore, for a balancing circuit with N cells, where N N 2, ( − 2)  controllers are required.Figure 2 shows the relationship between the cells and the controllers needed.It should be emphasized that in the proposed method, a new control strategy is crucial and the type of controllers is not the primary purpose.In this study, simple PI controllers are used to implement the control system.
Due to an increase in cell currents, simultaneous charge transfer is not possible without a proper switching pattern.These high currents may seriously damage the battery pack.With the proposed switching pattern, charges can transfer from all cells simultaneously in each switching cycle.This switching pattern along with control actions can be used to direct charge transfer from one cell to another arbitrary cell.Without loss of generality, the proposed method can be described by examples in three different scenarios as follows.The key waveforms for these scenarios are depicted in Figure 3.
Scenario 1: Charge transfer from one cell to its adjacent cell In this scenario, the charge transfers to its adjacent cell by turning a related switch on for a time interval.This can be described using an example that shows the charge transfer from cell 5 to cell 4. For this aim, S54 is turned on for a time duration.In this condition, the inductor L 4 is charged through the LiPo cell 5.The duration of this step is from t 0 to t 1 (see Figure 3A).The current of inductor L 4 , i L 4 , by supposing t = 0 0 and i t , is obtained using the following equation: where V C 5 is the voltage of the LiPo cell 5.At . T 1 is the duration that S54 is on, given by the following equation: It should be mentioned that the sign of cell currents can be arbitrarily determined, depending on whether the cell is charging or discharging.For example, if the discharging direction is positive: where in Equation ( 5), i C 5 is the current of LiPo cell 5.
Then, in the second step, S54 is turned off.By turning the switch S54 off, i C 5 will be zero.the body diode of S45 is turned on and the current stored in L 4 is passed through this diode and the LiPo cell 4 starts to charge.In this step, i L 4 is calculated by the following equation: If only the charge transfer from cell 5 to cell 4 is required, the other switches must be off and this scenario will be finished by reaching i C 4 to zero.In this condition, scenario 1 is finished at t t = sce1 .Figure 3A shows the switch and current waveforms for this scenario.

Scenario 2: Direct charge transfer between two nonadjacent cells
It is possible to transfer charge from one cell to a nonadjacent cell using suitable switching actions.Continuing from the prior scenario, by turning S43 on, after turning S54 off, the charge transfers from cell 4 to inductor L 3 , that is, L 3 is charged.The duration of this step is from t 1 to t 2 (see Figure 3B).Then, i L 3 , that is, the current of inductor L 3 is obtained using Equation (7).It is assumed that i t ( ) = 0 where V C 4 is the voltage of the LiPo cell 4. Therefore:     (8)   where in Equation ( 8), i C 4 is the current of LiPo cell 4. At , in which 1 .By turning S43 off At t 2 , LiPo cell 3 is charged.Transferring charge to cell 3 finishes at t 4 .The current of LiPo cell 3, i C 3 is obtained as follows: At t 4 the current of LiPo cell 3 is zero: Scenario 2 is finished by reaching i C 3 to zero. Figure 3B shows the switch and current waveforms for this scenario.According to Figure 3B , the net charge variation of cell 4 is zero.It means that the charge is directly transferred from cell 5 to cell 3.This strategy can be used for any two nonadjacent cells.
Scenario 3: Charge transfer from one cell to several cells simultaneously Continuing from the previous scenarios, the following steps demonstrate how the charge can be transferred from one cell to several cells in a single switching cycle.Firstly, for transferring charge from LiPo cell 3 to LiPo cell 2, S32 is turned on at t 0 .In this step, i C 3 that is equal to the current of inductor L2, i L 2 , is linearly risen up.The duration of this step is from t 0 to t 3 (see Figure 3C).i t where V C 3 is the voltage of the LiPo cell 3.By turning S32 off, i C 3 equals zero at t 3 .The procedure continues by turning S32 off and turning S21 on at t 3 .The duration of this part is from t 3 to t 5 .According to the initial current of L 2 , the current of LiPo cell 2, i C 2 is calculated by Equation ( 12): Simple scheme representing the relation between cells and controllers.
ESMAEILI and NARM where i L 1 , is the current of inductor L 1 .T 3 is the time duration from t 0 to t 3 : , in which T t t = − 4 5 3 .By turning S21 off, the current of inductor L 1 is discharged through the body diode of S12, and LiPo cell 1 is charged.The duration of this mode is from t 5 to t 6 .i L 1 and the current of LiPo cell 1, i C 1 are calculated as follows: This mode is continued until i C 1 reaches zero at t 6 .t 6 is simply calculated by Equation ( 16): Figure 3C shows the aforementioned procedure.If the net charge variation of the middle cells (cell 4, cell 3, and cell 2) is zero, it means that the charge directly transfers from cell 5 to cell 1.This is the basis of the proposed control strategy.The fundamental of the proposed control strategy is direct charge transfer between the cell with maximum SoC and the cell with minimum SoC so that the net transferred charge for the other cells is zero in each switching cycle.According to this scenario, through proper control, the net charge variation in the middle cells is adjustable.For example, referring, to Figure 3C if the following condition is met, it indicates that the charge of cell 5 is distributed to the other cells within a single switching cycle.

| Controller type and its implementation
As mentioned before, the control theory can help to realize a new approach for DCTC charge transferring between arbitrary cells without extra circuit complexity.In this paper, the control strategy is the charge transfer from the cell with maximum SoC to the cell with minimum SoC such that the net charge transferred through the cells between them is zero in each switching cycle.According to Equation (2), the area of "t − i(t)" graph for each cell shows the charge variation of it.Therefore, by setting the area bounded with the current of LiPo cells that are between the cells with maximum and minimum SoC to zero, the net charge is directly transferred from the cell with maximum SoC to the cell with minimum SoC.As can be observed from Figure 3C, if the conditions are satisfied as follows, the net charge is directly transferred from cell 5 to cell 1 in each cycle.
To this aim, three controllers are required for SoC control of LiPo cell 2, LiPo cell 3, and LiPo cell 4. In fact, in a five-cell balancing circuit, a maximum of three controllers may simultaneously perform to control the transferred charge of each cell.Actually, depending on the number of cells that must transfer charge between each other, one, two, or three controllers are triggered to control the charge of the middle cells which are located between the cells with maximum and minimum SoC.Different types of controllers can be used and implemented.Due to the simplicity and appropriate performance of the well-known PI controllers in practice, PI controllers with identical parameters are used to realize the strategy.Figure 4 shows the control scheme for the charge control of LiPo cell 2 in direction of charge transfer from LiPo cell 1 to LiPo cell 3. Without loss of generality, this approach is used in the whole balancing system.
Controller 1 is also used for the charge control of the LiPo cell 2 in the direction of charge transfer from LiPo cell 3 to LiPo cell 1.The integration block refers to the integration of the current in each switching cycle.For direct charge transfer, the reference value must be set to zero. Figure 5 shows the flowchart of the proposed balancing method.In the flowchart, CBS means "cell balancing system."C max and C min represent the cells with the maximum and minimum SoC, respectively.if more than one cells have the maximum or minimum SoC values, it is necessary to determine the cells with minimum distance.This means selecting C max and C min so that the number of cells between them is minimum.SWS shows all switch states that are determined by SW i , and generated by the proposed control scheme.According to the flowchart, the proposed algorithm is started by selecting two cells with maximum and minimum SoCs and minimum distance.If the difference between the SoC of C max and the SoC of C min is greater than 10 −4 the switch states will be updated to i + 1.It should be mentioned that, at the first step i = 0, all switches are set to off, that is, SWS SW = 0 .These steps are repeated until the differences between all the cell SoCs are lower than 10 −4 or 0.01%.SoC values are measured between 0 and 1.But, they can be expressed as percentages.It should be mentioned that the proposed control method enables the charge transfer from one cell to the other cells in one direction, simultaneously by setting the aforementioned areas   A 1 -  A 6 to desired values.
F I G U R E 4 Controller action in direction of charge transfer from LiPo cell 1 to LiPo cell 3.
In this section, the proposed balancing method is simulated by MATLAB/Simulink.The results are presented.Battery cells are simulated using a generic battery model block in MATLAB, with appropriate parameters.The total capacity of each cell is Q = 300 mAh.PI controller gains are set by the proper view of the system and its operating point.Table 2 shows the initial SoC of the cells.It should be noted that the initial charges of the cells can be arbitrary, and these values are only considered for simplicity and shortening the balancing time.Moreover, the MOSFETs and inductors are identical.The values of inductors are equal to 470 μH and the switching frequency is considered 1 kHz.In the first step of the proposed method simulation, it is expected the charge directly transfers from cell 5 with a maximum charge to cell 1 with a minimum charge.Then, by decreasing the SoC difference of the cells 5 and 1-10 −4 , the algorithm selects new two cells to transfer charge directly.This procedure is continued until balancing the battery pack.Figure 6 shows the SoCs of the series five-cell battery pack.The simulation results show the SoCs of the cells converge to each other almost in 24 s.As expected, the balancing algorithm is started by directly transferring charge from cell 5 to cell 1.During this, the charges of the other three cells do not change.
By decreasing the difference between cell 5 and cell 1 SoCs to 0.01%, the algorithm selects the new two cells to equalize their charges.Cell 4 and cell 3 are selected in the second step.As can be seen, in the second step, the maximum SoC belongs to cell 4, and cells 2 and 3 have minimum SoCs.However, the proposed algorithm selects cell 3 because of the nearer distance to cell 4.Moreover, Figure 6 shows the proposed control method and the PI controllers appropriately perform.In all steps, the charge is directly transferred between the cells with maximum and minimum SoCs and the charges of the other cells are fixed.Finally, the whole battery cells are equalized.The final value of SoC for all cells is 89.647%.The mean value of the SoCs for the unbalanced cells is 89.7% and this shows the equalized SoC is not necessarily equal to the mean value of the SoCs.The balancing time depends on certain characteristics of the system.For example, If the cells with high C-rates should be balanced, by using inductors with lower inductance the balancing time will be reduced.Also, according to Equation ( 2), the lower total capacity results in a lower charging and discharging time.In this simulation, the time of balancing is relatively short because of the low total capacity and high C-rate of the cells.Also, the differences between the initial SoC of the cells are assumed to be near to each other.In Figure 7, the key waveforms obtained using simulation are represented for a specific time interval.
Figure 7A shows the current of the cells in the first step of the balancing algorithm, that is, direct charge transfer from cell 5 to cell 1.According to Figure 7A, the charge transfer occurs from cell 5 to cell 1, directly.the switching period T is 0.001 s.According to what is described in Section 3.2, in the simulation test, the current direction in discharging mode is considered positive.Therefore, the positive integration shows the cell discharging and the negative integration shows the cell charging.In each time period, the time integration of i C 5 is positive, and the time integration of i C 1 is negative.Also, the current graphs of i i , , and i C 4 clearly show that in each time period, the time integrations for these currents are zero.Discharging current of cell 5, i C 5 has almost 2 A peak value.This means that in this step, cell 5 is discharged at a 6.6 C-rate.The pulses of S54, S43, S32, and S21, in the first balancing step, that is, when the charge directly transfers from cell 5 to cell 1, are shown in Figure 7B.One of the most important advantages of the proposed method is improving the accuracy of the Coulomb counting method.Current sensor accuracy is dependent on different factors such as manufacturer quality, ambient temperature, the supply voltage of them, and so on.For example, the Hall-effect sensors may encounter scaling factor (gain parameter) errors.The proposed control method is based on measuring the area which is bounded by the sensor outputs and the time axis, that is, the time integration of the sensor outputs.Therefore, in the balancing situations in which the number of cells between the cells that the charge must be directly transferred through them is one or higher, the effect of gain errors and inaccuracies on the SoC variation of these cells (middle cells) are eliminated.This improvement is also true for multiplicative noise on the current sensors.Eventually, this advantage improves the total accuracy of the balancing system.From Figure 7B, the pulses of the switches are produced by three identical PI controllers so that in each time period, the time integration of i i , , and i C 4 is zero.S54 and S43 are not simultaneously on.This is also true for S32 and S21.In the next section, the experimental results are presented.

| EXPERIMENTAL RESULTS
In this section, the experimental results are presented.The experimental setup consists of a battery pack with five identical 1530 mAh lithium-ion polymer cells.The cathode F I G U R E 6 SoC of the cells after 24.5 s for five-cell battery pack balancing.

(A) (B)
F I G U R E 7 Waveforms obtained using simulation: (A) current of the cells for an interval in which the charge directly transfers from cell 5 to cell 1. (B) Pulse of the switches for charge transfer from cell 5 to cell 1.

ESMAEILI and NARM
| 223 material is lithium-cobalt-oxide LiCoO 2 with a solid polymer electrolyte.A double-output variable DC power supply is used.The maximum voltage of each variable output is 30 V/3 A. Waveforms are derived and plotted using a "Hantek-DSO4104C" digital storage oscilloscope.For the implementation of controllers, an Arduino-Due microcontroller is used.Also, to measure the of LiPo cells, 5A ACS712 Hall-effect-based current sensors are used.The value of inductors is equal to 470 μH and the switching frequency is considered 1 kHz.Figure 8 shows the experimental setup.In this section, the initial SoC estimation approach for the LiPo cells is described first.Then, the experimental results of the proposed balancing method are represented for two different initial conditions.

| Initial SoC estimation
As mentioned before, one of the most important challenges in the Coulomb counting method is the initial SoC estimation.There are different methods to estimate the initial SoC.In this paper, the relation between open circuit voltage (OCV) and SoC is used.It is important to obtain this relation accurately.In other words, the SoC is a function of OCV but it is influenced by factors such as the hysteresis phenomenon, the ambient temperature, 34 and the rates of charging and discharging. 31By considering these practical effects and collecting the experimental data, an injective fifth-order polynomial function V z ( ) oc is obtained using curve fitting.

| Results of cell balancing
In this section, the experimental results of the proposed control method for cell balancing are represented.Two different initial conditions are considered for LiPo cells to show the circuit performance in both directions of the charge transfer.Table 3 shows these initial SoC conditions.
As can be found from Table 3, the initial conditions 1 is the same as the initial conditions in Section 4. In initial conditions 2, unlike the initial conditions 1, LiPo cell 1 has the maximum SoC, and LiPo cell 5 has the minimum SoC.At first, the results of initial conditions 1 are shown.Figure 10 displays the SoC of the LiPo cells.These data are collected using Arduino IDE 1.8.13 and plotted using MATLAB.Figure 10 shows that the charge is directly transferred from cell 5 to cell 1 at first, and in this duration, the charges of other LiPo cells do not change.In this step of balancing, three PI controllers are activated.Then, by decreasing the difference between SoC of LiPo cells 5 and 1 to 10 −4 , the proposed algorithm selects the next two cells for balancing.In this step, LiPo cell 4 and LiPo cell 3 are selected to transfer charge between them.In this step, it is not required to control the currents of i i , , and i C 3 .Actually, the charge directly transfers between two adjacent cells.It should be noted although in this step, S54, S32, and S21 are off, and only S43 is on, the charges of three other LiPo cells in this step have a little change.This change is due to errors in current sensor measurements.More precisely, to perform accurate current sensor measurements, in addition to the gain parameter, their bias parameter (i.e., zero current output) may also need to be accurately adjusted.Also, the current sensors need to be calibrated over time.Therefore, in practice, not accurately setting this parameter causes slight changes F I G U R E 9 SoC-OCV plot using curve fitting to estimate the initial SoC of the LiPo cells. in the SoCs.The balancing algorithm is continued until all LiPo cells are equalized.The balancing with these initial conditions starts with a direct transfer from cell 5 to cell 1, then it is continued with direct charge transfer from cell 4 to cell 3, cell 1 to cell 2, cell 5 to cell 3, and so on.The balancing is finished by charge transfer from cell 1 to cell 3.The four steps and the final step are represented as follows.Figure 11 shows the currents of the LiPo cells in the aforementioned steps.It should be mentioned that in the experimental circuit, the current sensors are implemented in such a way that the positive direction of the currents corresponds to the charging direction.According to Figure 11, during the first step of the balancing procedure, the area bounded by the time-current plot is zero for three signals i i , , and i C 4 , which represent the currents of the middle LiPo cells.In the second step, as shown in Figure 11B, the time integration of i C 3 is positive, indicating the charging of LiPo cell 3. Additionally, i C 4 has a negative time integration, indicating the discharge of LiPo cell 4.An important observation arises in this step.Figure 11B clearly depicts that i C 2 is zero, signifying that the current sensor should output zero.However, according to Figure 10 in the second step, the SoC of LiPo cell 2 has a little increase.This is due to the effect of not accurately setting the bias parameter of the current sensor, which was mentioned earlier.For the middle cells, that is, the cells between the cells with maximum and minimum SoC in the balancing procedure, the proposed control method eliminates the effect of not accurately setting the gain parameter of current sensors, as well as multiplicative measurement noise.In the subsequent steps, as evidenced by Figures 11C-E, direct charge transfers from cell 1 to cell 2, from cell 5 to cell 3, and from cell 1 to cell 3 are clearly observed.Finally, Figure 12 shows the switch pulses for the first balancing step.Figure 12 shows appropriate switch pulses so that the adjacent switches are not simultaneously turned on.According to the direction of current sensors in the experimental setup that are positive for cell charging, by turning S32 on, LiPo cell 3 is discharged.Then by turning S43 off, this cell is charged.Now, the results of initial conditions 2 are studied.Figure 13 shows the SoC of the LiPo cells for these conditions.The data are collected using Arduino IDE 1.8.13 and plotted using MATLAB.Figure 13 shows that in the first step, the charge is directly transferred from LiPo cell 1 to LiPo cell 5.In this duration, the SoC of other cells are fixed and do not change.Then, second, the charge is directly transferred between LiPo cells 2 and 5.An important subject is observed in this step.By direct charge transferring from LiPo cell 2 to LiPo cell 5, the SoCs of two cells between them, that is, cell 3 and cell 4 are fixed due to control actions.However, the SoC of LiPo cell 1 slightly changes.In this step, S12 is off and the current of LiPo cell 1 is zero.However, a slight change in SoC is observed due to the inaccurate setting of the bias parameter for the current sensor.The proposed method can improve the accuracy of the balancing system by eliminating the effect of sensor errors in the cells between those that have the maximum and minimum SoCs, provided that they are caused by gain inaccuracies and multiplicative measurement noise.The balancing procedure is continued by direct charge transferring from cell 4 to cell 5, cell 3 to cell 5, and so on.The balancing finishes by direct charge transferring from LiPo cell 2 to LiPo cell 3. Finally, the SoCs of the five LiPo cells are equalized.Figure 14 shows the current of the LiPo cells in the aforementioned steps.Like the previous test, the current sensors are implemented so that the positive direction of the currents is the charging direction and the negative one is the discharging direction.Figure 14 shows that in different steps, the currents of the LiPo cells have expected waveforms.According to Figure 14A, the time integration for the current of LiPo cells 2, 3, and 4 is zero.This states that in each switching cycle, the net charge transferred in these cells is zero.Figure 14B shows the time integration for i C 2 is negative and for i C 3 and i C 4 is zero.This is expected due to direct charge transfer from LiPo cell 2 to LiPo cell 5.In the same way, Figures 14C-E show direct charge transferring from cell 4 to cell 5, cell 3 to cell 5, and cell 2 to cell 3, respectively.Finally, Figure 15 shows the switch pulses the first balancing step by considering initial conditions 2. Figure 15 shows the appropriate pulses generated by three PI controllers.Two sets of adjacent switches, S23 and S34, and S34 and S45, are not turned on simultaneously.i C 3 also represents the correct switching.By turning S34 on, the charge is transferred from LiPo cell 3 and this cell starts to discharge.Also, by turning S23 off, the charge is transferred to LiPo cell 3 and this cell is charged.S45 is turned on with an appropriate duty cycle to facilitate the charge transfer from LiPo cell 4 to LiPo cell 5. To protect the LiPo battery cells, they require to be balanced.In this paper, a new control strategy combined with a novel switching pattern was proposed to establish a DCTC balancing system.The proposed method is capable of transferring charge from one cell to several other cells simultaneously.The circuit had a typical structure with DC-DC bidirectional buck-boost converters.In other words, only the proposed controlling actions and the novel switching pattern result in a DCTC balancing without additional circuit elements.To accomplish this, PI controllers utilized to implement the strategy and control the charge transferred between the cells.It was demonstrated that precise charge transfer into and from the middle cells was achieved, effectively eliminating the impact of gain inaccuracies in current sensors as well as multiplicative noise on them in the middle cells.The simulation results for the balancing system with five series cells demonstrated the appropriate and efficient performance of the proposed method.Finally, an experimental setup was used for the proposed method performance verification.The experimental results represented appropriate DCTC balancing in each switching cycle.To completely eliminate measurement errors, future works may consider the use of model-based SoC estimation methods.In addition, to reduce the effect of EMI and increase the electromagnetic consistency of the balancing method, a study on the use of resonant and quasi-resonant DC-DC buck-boost converters in the proposed balancing method is also a potential topic for future research.

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I G U R E 11 Current of LiPo cells for five steps of the balancing procedure with initial conditions 1, direct charge transfer from (A) cell 5 to cell 1, (B) cell 4 to cell 3, (C) cell 1 to cell 2, (D) cell 5 to cell 3, and (E) cell 1 to cell 3. F I G U R E 12 Switch pulses in direct charge transfer from LiPo cell 5 to LiPo cell 1.F I G U R E 13 Experimental results for SoC of LiPo cells with initial conditions 2.

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I G U R E 14 Current of LiPo cells for five steps of the balancing procedure with initial conditions 2, direct charge transfer from (A) cell 1 to cell 5, (B) cell 2 to cell 5, (C) cell 4 to cell 5, (D) cell 3 to cell 5, and (E) cell 2 to cell 3. F I G U R E 15 Switch pulses in direct charge transfer from LiPo cell 1 to LiPo cell 5.
Comparison between different active balancing methods.
*International system of units.ESMAEILI and NARM | 217 Flowchart of the proposed balancing method.
T A B L E 2 Initial SoC of the cells in simulation.
T A B L E 3 Two different initial conditions for LiPo cells.Experimental results for SoC of LiPo cells with initial conditions 1.