Research on serial lithium‐ion battery alternating discharge equalization control systems

To improve the discharge equalization efficiency of the battery and prevent the occurrence of overdischarge, in this paper, the 18,650 ternary lithium battery is taken as the object of investigation, and an alternating equalization control system for the discharge process of serial cells is proposed. The system implements the alternating discharge of serial cells by switching on and off, using state of charge (SOC) as the equalization variable, and eventually completes the equalization control of the entire battery pack. Discharge simulations were performed in Matlab/Simulink for faulty and normal operating conditions of the battery pack, respectively. The findings indicate that even in the presence of a malfunction, the battery pack can continue to operate continuously for a while; in contrast, under ideal circumstances, the battery pack is capable of maintaining SOC balance throughout the discharge process. Eventually, five batteries are used to construct the experimental platform for the alternating equalization system. The battery pack can still perform selective discharge under fault conditions until the battery pack reaches the discharge cutoff condition. Under normal conditions, the maximum SOC difference of all five batteries can stabilize at about 1%. The experimental results show that the proposed equalization control system can achieve the equalization of battery discharge and prolong the discharge time, and can prevent the occurrence of battery over discharge.


| INTRODUCTION
Due to the current global energy scarcity and ecological deterioration, lithium-ion batteries have become popular in various fields due to their high energy density, reliability, low self-discharge rate, and long lifespan.However, as the voltage of each single unit of the lithium-ion battery is not high enough, they need to be connected in series to meet high voltage requirements. 1owever, inconsistencies among the individual units resulting from varying manufacturing processes and repeated charging and discharging can lead to a "barrel effect."This effect can reduce the lifespan of individual units and even cause combustion or explosion, making battery equalization technology essential for increasing battery capacity, reducing inconsistency between individual units, and extending lifespan. 2ithium-ion batteries are widely used in new energy vehicles and other equipment, where they are usually connected in series or in parallel to form battery packs to meet the power demand.The design of the equalization system for series battery packs is crucial, as it must balance cost and equilibrium efficiency. 3Shang et al. proposed a mesh-structured switched-capacitor equalizer to reduce the size and cost of the equalization structure, based on the existing switched-capacitor equalizer. 4Wang et al. proposed a balanced topology consisting of dual-active half bridges, which requires half the number of switches compared with traditional dual-active bridges.And the use of coreless transformers to provide isolation and energy transfer reduces the cost of energy redistribution balance. 5Habib and coworkers proposed a series of energy storage devices based on a single LC (inductance, capacitance) energy converter, namely, battery, super/ultracapacitor string voltage balancing circuit.It transfers the excess energy directly from the higher cell to the lower cell in the string.This active balancing circuit has high efficiency, fast balancing speed, small size, low cost, and maximum energy recovery. 6,7Van Nguyen and Vinh proposed a design of energy balance circuit for two adjacent lithium-ion battery cells in the cell string based on the modifying of the bidirectional CuK converter principle.This design overcomes the energy loss problem of traditional Cuk equalization circuits that require multilevel direct current (DC) power to turn on metal-oxidesemiconductor field-effect transistors and energy balance circuit components. 8Other researchers have proposed equalization topologies based on multiwinding transformers, such as Wang et al. designed an improved Buck-Boost equalization circuit to reduce the inconsistency of series lithium-ion batteries.Series connected batteries can form a circular energy circuit, improving the equalization speed and facilitating modularization. 9Furthermore, Li et al. have proposed an equalization topology that can achieve the functions of positive and negative converters simultaneously, allowing for independent balancing of different single units in the battery pack, which reduces costs and simplifies control engineering. 10Shang et al. proposed an optimization scheme of a coupled half-bridge converter with multiple winding transformers based on the traditional transformer, which makes the transformer winding halved and also realizes the automatic equalization between single cells. 11Ding et al. based on the Buck-Boost converter circuit, used a power inductor to transfer energy between battery cells, which accomplished a more efficient battery pack equalization without adding extra equipment. 12Li et al. based on the DC-DC converter proposed an active equalization topology circuit, which allows the entire battery pack to charge the lowest energy single cell, improving the speed and flexibility of equalization. 13or higher equalization efficiency, distributed equalization is widely used.Gao et al. divided the battery pack into two layers and combined active and passive equalization, with intergroup equalization at the top layer and intragroup equalization at the bottom layer. 14Cui and Zhang used a coaxial multiwinding DC-DC converter for intermodule energy transfer in the top layer and a capacitor-resistor for equalization purposes in the bottom layer. 15Tavakoli et al. proposed a new modular structure that connects two batteries in series using a bridging module, in which the bridging module is connected in series with three windings of a transformer, compared with other This structure allows for more predictable system operation and analysis than other similar approaches. 16Ouyang et al. established a hierarchical optimization method with the objective of balancing time, temperature rise, and operating constraints for the control problem of hierarchical equilibrium of lithium batteries. 17any other scholars have proposed more efficient equalization strategies and estimation methods for state of charge (SOC) value.Diao et al. developed an equalization strategy to maximize the remaining available energy of the battery pack by combining the influence of the remaining available energy of the battery pack on the equalization of the battery pack. 18The lithium-ion battery pack is a nonlinear system, and many scholars have applied PID algorithms, fuzzy control algorithms, and particle swarm algorithms, which can provide more stable control of complex systems, to the equalization strategy of the battery, which has been effective in reducing the equalization time of the system to improve the stability of the control. 9,19-21Gao et al. aiming at the problem that the network construction of the existing state of health (SOH) estimation method is too simple, a new lithium-ion battery SOH evaluation hybrid framework hierarchical feature coupled module long-shortterm memory composed of two cascade modules is proposed. 22Cai et al. combining the characteristics of attention mechanism and domain adaptive neural network, a method for multiple fault detection of series battery packs based on domain adaptive neural network is proposed. 23 Dong et al. propose an internal cascaded neuromorphic computing system via memristor circuits for electric vehicle (EV) SOC estimation. 24ifferent equalization topologies, each with a unique specialty function, can be categorized into passive and active equalization based on how excess energy is handled during the equalization process. 25Passive equalization is straightforward and quick to operate, but because of its inefficient equalization, energy is not fully utilized and may be wasted. 1,26Active equalization is more energy efficient than passive equalization because it uses active electronic components to transmit energy between battery units, but its complicated construction and control scheme prevent it from being applied widely. 27To address these issues, this paper proposes an alternating equalization control system that connects a power switch with a single cell in series and parallel to form an equalization topology and its corresponding discharge control strategy.During the discharge process, the single cell that does not meet the discharge conditions is disconnected by the power switch, and the spare equalization battery is connected to discharge, achieving discharge equalization of the battery pack.
The paper is organized as follows, Section 2 introduces the alternating equalization control system, including the short-circuit equalization topology and its discharge strategy.In Section 3, the dual polarization (DP) model is established and battery SOC values are estimated based on the extended Kalman filter (EKF) algorithm.In Section 4, discharge simulation and experiments are conducted for the equalization system under normal and fault conditions, respectively.Finally, Section 5 presents the conclusions based on the simulation and experiments of the above equalization system.

| Topology for short-circuit equalization
Although the existing equalization topology structures can improve the utilization of battery energy, however, passive equalization has high losses and low energy utilization.Traditional active equalization topology structures have complex control systems and cannot achieve simple and effective improvement of the driving range of EVs.This article proposes an equalization topology structure based on individual battery cells and power switches, namely, a short-circuit equalization topology structure, as shown in Figure 1.
The topology for short-circuit equalization consists of n + 1 batteries and 2n + 2 power switches, where S 1 , S 2 , …, S n+1 are connection switches and S n+2 , …, S 2n+2 are short-circuit switches.The matching connection switches and short-circuit switches of the same battery are mutually exclusive.The short-circuit equalization topology, which has a high energy usage rate, a straightforward structure, and scalability, comprises two power switches and one battery in each of its modules.
The short-circuit equalization topology with n = 4, that is, a total of five batteries in the battery pack, is chosen as an example, where four batteries are charged and discharged in series and the other one battery is used as the equalization battery.

| Equilibrium judgment threshold
This paper selected the SOC of the battery as the equalization variable, but does not use the traditional comparison of the difference between the SOC value of each battery and the average value SOC with the equalization threshold, because the equalization time will be prolonged when the difference between the SOC values in the battery pack is large, and it may lead to the failure to equalize the battery with a large difference.Therefore, in this paper, the maximum difference of SOC of all cells φ is chosen to compare with the threshold δ, and the difference of SOC of all cells is controlled within δ, that is, In the formula, φ is the maximum difference value of SOC in the battery pack, SOC j is the highest value of SOC | 4689 in the battery pack, and SOC j is the lowest value of SOC in the battery pack.The battery pack is then subjected to various equalization control procedures depending on the magnitude of the lower φ and δ values.In this study, the equalization judgment threshold δ is set at 1%.

| Discharge equalization strategy
It is the discharge equalization control approach, as seen in Figure 2.This equalization control strategy includes fault diagnosis and equalization control judgment of the battery pack, and its specific implementation steps are as follows: (

| SOC ESTIMATION BASED ON EKF
In this paper, a SOC-based battery equalization system is proposed, and a DP model consisting of two resistorcapacitor (RC) networks in series is selected to model and analyze the 18,650 Li-ion battery and estimate its SOC.

| DP battery model
The DP model, that is, the DP model is composed of a voltage source U oc , two polarization capacitors C p1 and C p2 , two polarization resistors R p1 and R p2 , and a battery equivalent internal resistance R Ω , as shown in Figure 3.
The parallel structure of C p1 and C p2 can simulate the process of slow change of voltage at the battery terminal, and R Ω can simulate the process of step change of voltage at the battery terminal.According to the DP model, the following equation can be derived: (2) In the formula, U oc is the battery open-circuit voltage (OCV), U i is the battery operating voltage, R Ω is the equivalent internal resistance of the battery, I is the current flowing through the battery, U p1 and U p2 are the voltages on capacitor C p1 and capacitor C p2 , respectively, and I p1 and I p2 are the currents flowing through capacitors C p1 and C p2 , respectively.
According to the hybrid pulse power performance test proposed in the "FreedomCAR Battery Test Manual," the voltage curve obtained by the hybrid pulse power characterization (HPPC) experiment of the battery circuit model parameter measurement is shown in Figure 4.
The DP model parameters at different SOC values can be obtained by fitting the HPPC voltage curve, as shown in Table 1.
Finally, the operating voltage of the DP model is simulated and verified under 1 C DC discharge conditions and 1 C, 1/3 C intermittent discharge conditions, and the display results are shown in Figure 5.
From Figure 5, IT can be seen that the model values of the voltage are basically consistent with the experimental values, with an average error of 1.19% between the two.Therefore, the battery model can meet the accuracy requirements of the electrical model.

| SOC estimation
Since the battery model is a nonlinear dynamic system, and the underlying Kalman filter algorithm is only for linear dynamic systems, the SOC estimation applicable to nonlinear dynamic systems is adopted in this paper.
According to the DP model, taking U p1 and U p2 as the state variables, I as the input variable and U i as the output variable, the state equation and observation equation of the battery can be obtained: In the formula, t Δ is the current sampling interval and U k OCV(SOC( )) is the OCV value corresponding to the  SOC value of the battery at moment K.According to the EKF algorithm for SOC value estimation, the system input variable is u I = k k , the system output variable is z U = k ik ( ) , and the state variable is T , then its linear equation is obtained according to Equations ( 8) and (9).
The validity of the SOC estimation based on the EKF algorithm is verified according to the above equation, and the simulation results are compared with the experimental results, and the comparison results and errors are shown in Figures 6 and 7.
As shown in Figures 6 and 7, the battery SOC estimation based on EKF calculations can control the error to about 3% for both DC discharge and intermittent discharge conditions.According to GB/T 38661-2020 EV battery management system technical conditions, the SOC estimation error should be within 5%, the estimated results meet the standards and can also provide relatively accurate equalization variables for the later equalization control.

| Simulation analysis
The actual capacity of the 18,650 battery selected in this paper is 3 Ah, and the LC discharge rate, that is, 3 A current, is selected until two or more individual batteries with SOC values below 10% are discharged and stopped.In this paper, five batteries are selected as an example to simulate the fault conditions and normal conditions of the alternating equalization system.

| Fault condition simulation
(1) The entire battery pack stops discharging if the SOC value of two or more batteries in the battery pack falls below 10%.The battery is in a fault state if the initial SOC value of two or more batteries is lower than 10%; if it falls below 10% during the discharge process, it is a discharge cut-off condition.The battery pack is in a failure state with the initial SOC values of the five batteries set to 95%, 90%, 85%, 8%, and 5%, respectively.Figure 8 displays the results of the discharge simulation.
As shown in Figure 8, the SOC values of all five batteries are fixed, indicating that the battery pack is in a faulty state, and the entire battery pack stops discharging and an alarm signal is issued.
(2) The initial SOC value of one battery in the battery pack is below 10%, this battery does not meet the discharge conditions and is disconnected from the circuit.The other four batteries continue to discharge in series until one more single battery SOC value is below 10% and the whole battery pack stops discharging.This case is also a fault state, the battery pack always only four batteries works normally, which can simulate the discharge situation of the battery pack without joining the equalization control strategy.The initial SOC values of the five batteries are set to 95%, 90%, 85%, 80%, and 5%, respectively, and the discharge simulation results are shown in Figure 9.
As shown in Figure 9, batteries 1-4 have been in the discharged state; while battery 5 has been in the disconnected state.During the discharge process, although the φ of batteries 1-5 is greater than 1%, the SOC value of battery 5 is 5%, which is lower than 10% and does not meet the discharge continue to discharge conditions.Therefore, only batteries 1-4 can be connected in series to form a battery pack to discharge, until the SOC value of battery 4 is 9.42% when the entire battery pack stops discharging.The simulation results show that although the equalization control of the battery pack cannot be achieved in this case, the system can still ensure that the other batteries continue to work.
F I G U R E 8 Simulation results when the SOC value of two batteries is lower than 10%.SOC, state of charge.
F I G U R E 9 Simulation results when the SOC value of one cell is below 10%.SOC, state of charge.

| Normal condition simulation
When the initial SOC values of all cells in the battery pack are greater than 10%, different control schemes need to be implemented by judging the magnitude of the φ value and the threshold δ value.
(1) When φ value is less than the threshold value δ, batteries 1-4 are discharged in series, and battery 5 is disconnected.That is, the conduction switches S1, S2, S3, S4, and S10, that is, discharging batteries B1, B2, B3, and B4 in series.(2) When the value of φ is greater than or equal to the threshold value δ, the equalization control strategy is shown in Table 2.
On the basis of the above equalization control strategy, two kinds of operating conditions are simulated for the brand new battery pack and the depreciated battery pack, respectively, that is, all battery SOC values are 100%, and the battery pack individual SOC values are 5% difference state.
① The initial SOC values of all batteries are 100%, and their discharge equalization simulation results are shown in Figure 10.
As shown in Figure 10, during the discharge process, the five cells have been alternately reorganized to form a battery pack consisting of four cells for discharge, and the φ values have been kept at about 1%, with a maximum of 1.556%.At the end of the discharge, the SOC values of the five cells were 9.77%, 9.40%, 9.62%, 9.42%, and 10.56%, and the φ value reached 1.16%, which exceeded the threshold value δ.This is because the delay time set in the simulation is too long and the discharge current is too large, resulting in a large change in the SOC value at each alternate reorganization.The φ value can be further reduced by shortening the delay time and decreasing the discharge current.
② The battery pack single SOC 5% difference state, that is, the initial SOC values of the five batteries are 95%, 90%, 85%, 80%, and 75%, respectively.Their discharge equalization simulation results are shown in Figure 11.
As shown in Figure 11, during the discharge process, the value of φ continuously shrinks from 20% to 1% and fluctuates above and below its 1%, with a maximum of 1.556%.At the end of the discharge, the SOC values of the five cells were 9.82%, 9.90%, 9.42%, 9.70%, and 10.81%, with a φ value of 1.39%, which was 18.61% smaller compared with the initial 20%, significantly reducing the intercell inconsistency.

| Experiment analysis
A charge and discharge tester, a host charge and discharge tester, and a thermostat are among the test tools utilized in the experiment.The battery pack is charged and discharged using the charge/discharge tester; the host computer monitors and maintains the charging and discharging data; and the thermostat replicates the battery pack's operating temperature.The STC12C5A60S2 series microcontroller, relay, Hall current measuring module, voltage acquisition chip ADS1115, 18,650 Li-ion battery, power supply, host computer, and connecting harness make up the alternating equalization control system.In Figure 12, the precise hardware architecture is displayed.According to the corresponding discharge equalization strategies above, the experimental results are shown in Figure 13.
As shown in Figure 13, the SOC values of batteries 1-5 are unchanged.Only three batteries in the battery pack have initial SOC values greater than 10%, which cannot meet the requirement of the normal power supply of the battery pack.The experimental results are the same as the simulation results in Figure 8, indicating that the system is able to achieve the battery pack stop discharge function in this state.
(2) The SOC values of one battery were below 10% state.
The initial SOC values of the five batteries were 95.9%, 91.3%, 87.5%, 80.5%, and 6.1%, and the experimental results are shown in Figure 14 based on the discharge control strategy above: As shown in Figure 14, the SOC values of batteries 1-4 decreased linearly, indicating that batteries 1-4 were in a discharged state until the end of discharge; the SOC value of battery 5 remained unchanged, indicating that battery 5 was always disconnected.the SOC value of battery 5 was 6.1%, which was lower than 10% and did not meet the discharge condition.The experimental results are the same as the simulation results above, indicating that when one battery fails, the battery pack is still able to ensure that the other individual batteries work in series, although the pack fails to equalize.

| Normal condition experiments
(1) All cells SOC values were in 100% condition and the initial SOC values of the five cells were 100%, 100%, 99.9%, 100%, and 99.8%, respectively, the results of their discharge experiments are shown in Figure 15.
As shown in Figure 15, the SOC values of the five cells showed an intermittent decreasing trend, indicating that the cells were alternately reorganized to form a battery pack consisting of four cells until the end of discharge.During the discharge process, the φ value was kept at around 1%, with a maximum of 1.27%; at the end of the discharge, the SOC values of the five cells were 9.90%, 9.95%, 10.11%, 9.99%, and 11.11%, respectively, and the φ values were 1.21%.The experimental results are consistent with the simulation results, and both show that the alternating equalization control system proposed in this paper can maintain the equalization state of the battery pack during the discharge process.
(2) The SOC 5% difference state of the cells, the initial SOC values of the five cells were 93.55%, 89.87%, 85.33%, 80.00%, and 76.59%, respectively, and the results of the discharge experiments are shown in Figure 16.
As shown in Figure 16, at points a, b, c, and d, cells 4, 3, 2, and 1 start to alternate recombination discharges in turn.Thus in the partial magnification diagram, cell 1 is in a constant state of discharge, reaching equilibrium at approximately 1500 s.After point d the five cells are discharged in alternating regroups to maintain their equilibrium state.At the end of the discharge, the SOC values of the five cells are 10.25%, 9.93%, 9.99%, 10.05%, and 11.17%, respectively, with a φ value of 1.24%.The experimental results are consistent with the simulation results, indicating that the system is able to equalize the battery pack during the discharge process.
E)," "very good (VG)," "good (G)," and "poor (P)" to evaluate the equalization speed of each equalizer.Energy efficiency is measured by the power conversion efficiency within a balanced cycle.All three equalizers use 2n switches, indicating consistent losses at the switch.An improved Buck-Boost equalizer, 9 although EN is smaller than The MSSCE, 4 loses some energy due to the need for a resistor to demagnetize the inductor during its balancing process, and the energy consumed is proportional to the square of the current.Therefore, its EE is smaller than The MSSCE. 4 The equalizer proposed in this article can perform active balancing without the use of energy storage components, and the loss only occurs at each switch, with an energy efficiency greater than 90%.
The MSSCE 4 is based on complex control strategies, although its energy efficiency is also as high as 90%.Due to the lack of energy storage components, the equalizer proposed in this article has a smaller size and lower cost compared with it.In terms of equalization speed, the average equalization path of the equalizers proposed in Wang B et al. 9 and Shang et al. 4 will increase with the increase of the number of batteries, and the average equalization path is negatively correlated due to the equalization speed.The equalizer proposed in this article, regardless of any imbalance situation, only has the equalization path of short-circuiting the unbalanced battery and connecting it to the balanced battery, so the equalization speed is more advantageous.

| CONCLUSION
In this paper, a short-circuit equalization circuit based on 18,650 ternary lithium-ion batteries and its control strategy are proposed, and an equalization control system is constructed.The equilibrium control of lithium-ion battery is studied by simulation analysis and experimental verification.The main conclusions are as follows: (1) A DP battery model was developed, based on which the EKF algorithm was used to estimate the SOC value of the cell.In Matlab, the EKF algorithm was simulated to estimate the SOC value of the cell under 1 C DC discharge and 1/3 C intermittent discharge conditions, and the estimation error was around 3%. (2) The alternating equalization control system is presented and the discharge simulation is performed in Matlab/Simulink.Four states were simulated: two cells with SOC below 10%, one cell with SOC below 10%, all cells with 100% SOC, and 5% difference in cell SOC.The first two states are fault conditions, in which one battery SOC value is below 10%, but still able to keep the battery pack discharged; the last two states are normal operation, at the end of the discharge, the SOC difference is 1.16% and 1.39%, respectively.(3) Discharge experiments were carried out on battery packs under fault and normal operating conditions, respectively.Under normal operation, the difference in SOC at the end of discharge was less than 1.27%, demonstrating the effectiveness of the system's discharge equalization control.In the case of a cell with a SOC value below 10% or close to 10%, the system was still able to control the discharge of the battery pack, demonstrating the feasibility of the system.

FF
I G U R E 3 Li-ion battery dual polarization model.I G U R E 4 HPPC voltage curve.(A) HPPC voltage curve of the whole discharge process and (B) HPPC voltage curve of SOC = 90%.HPPC, hybrid pulse power characterization.

F I R E 5
DP model accuracy comparison chart.(A) 1 C DC discharge condition and (B) 1 C, 1/3 C intermittent discharge conditions.DC, direct current; DP, dual polarization.

F 7
I G U R E 6 1 C Simulation results under DC discharge conditions.(A) Simulation and experiment comparison and (B) simulation and experimental errors.DC, direct current.Simulation results under 1 C, 1/3 C intermittent discharge conditions.(A) Simulation and experiment comparison and (B) simulation and experimental errors.

F
I G U R E 12 Alternating equalization control system.F I G U R E 13 Discharge equalization experiment of two cells with SOC value below 10% state.SOC, state of charge.
1) When the SOC value of one battery in the battery pack is lower than 10%, it is a battery pack failure or battery pack power shortage.If the number of batteries with SOC value lower than 10% is greater than or equal to 2, the battery pack stops discharging; if there is only one battery with SOC value lower than 10%, disconnect this battery and discharge the other four batteries in series.At this time, the disconnected battery, because it is not connected to the circuit, has a discharge rate of 0; the other batteries are discharged in series and therefore maintain the same discharge rate.In this case, the working condition of the whole battery pack can be reflected by different fault indicators.(2)When the SOC values of all batteries in the battery pack are greater than or equal to 10%, the battery pack is in normal operating condition.If φ is greater than or equal to the threshold δ, the balancing battery replaces the battery with the lowest SOC value and discharges to form a new battery pack.If φ is less than the threshold δ, the first n batteries are discharged in series.
T A B L E 1 Identification of DP model parameters at different SOC values.
15Discharge equalization experiment with all five cells at 100% SOC.SOC, state of charge.
Abbreviations: E, excel; EE, energy efficiency; EN, element number; G, good; MSSCE, mesh-structured switched-capacitor equalizer; P, poor; SN, switch number; VG, very good.F I G U R E 14 Discharge equalization experiment with one cell with SOC below 10%.SOC, state of charge.

Table 3
compares the proposed equalizer with other active equalizers in the literature for series battery packs with similar structures in terms of switch number (SN), energy storage element number (EN), energy efficiency (EE), and equalization speed (ES).Assuming the battery pack has n units connected in series.The equalization speed is mainly determined by the equalization current and average equalization path.This article uses "excel