Research on SOC of Lithium-ion Power Battery for Vehicles

　　In order to estimate the state of charge (SOC) of lithium-ion power batteries, based on the analysis of factors affecting the SOC value and traditional SOC estimation methods, a new idea is adopted according to the actual situation, that is, the working conditions of the battery are divided into three states: static, recovery, and charge and discharge, and the SOC is estimated for the three states respectively. In the estimation process, the factors affecting the SOC value are dispersed and eliminated. Especially in the charge and discharge state, the dynamic recovery amount of electricity based on the coulomb efficiency factor is used to improve the ampere-hour measurement method, which solves the problem of cumulative error in the ampere-hour measurement method. Experiments have shown that this method improves the accuracy of battery SOC calculation and meets the application requirements of power vehicles.

　　Lithium batteries have been widely used in industries and daily life, and the estimation of battery state of charge (SOC) has become an important part of battery management . However, due to the complex structure of the battery, the battery state of charge is affected by factors such as discharge current, internal battery temperature, self-discharge, and aging, making it difficult to estimate SOC. Currently, the SOC estimation methods include: open circuit voltage method, ampere-hour measurement method, internal resistance method, neural network and Kalman filter method. V. Pop et al. proposed the EMF-SOC model [1-2], which is a relationship model between the battery electromotive force and the state of charge to estimate the SOC. This model is equivalent to the open circuit voltage method. This method is used to estimate the SOC after the battery has been stationary for a long enough time and cannot be used for real-time estimation. Some people also use the ampere-hour measurement method or the Kalman filter method to estimate the SOC. The ampere-hour measurement method has inaccurate estimation due to large current fluctuations or long-term accumulation of measurement errors. The Kalman filter method has great difficulties in establishing an accurate and practical battery dynamic model. For this reason, this paper adopts a new idea to estimate the SOC based on the actual situation of lithium batteries in applications. The working condition of the battery is divided into three states, and the SOC of each state is estimated one by one. In the estimation process, the factors affecting the SOC are eliminated, and the SOC values ​​in the three states are mutually premised, thereby improving the estimation accuracy of the SOC.

　　1. Battery working status and SOC estimation

　　The battery status can be divided into three states according to actual conditions, which are defined here as static, recovery, and charge and discharge. Their relationship is shown in Figure 1.

Figure 1 Battery working status diagram

　　1.1 Static state

　　The static state of the battery refers to the state in which the battery is fully recovered after stopping working. It can be directly transferred to the charge and discharge state from the recovery state. The calculated amount of SOC in this state is used as the initial value of SOC estimation in the charge and discharge state. Since the characteristics of this state are zero current and no polarization phenomenon, its SOC value has a good correspondence with the open circuit voltage, so the open circuit voltage method can be used to directly estimate the SOC value of the battery. The relationship curve between the open circuit voltage and SOC value of the battery is shown in Figure 2.

Figure 2 Relationship between battery open circuit voltage and SOC value

　　In the static state, the battery capacity is mainly affected by the self-discharge phenomenon, which causes the battery power to decrease over time. Estimating the SOC using the correspondence between the open circuit voltage and the SOC value can eliminate the influence of the power loss caused by self-discharge, thereby enabling the SOC value to more accurately reflect the battery status.

　　1.2 Recovery status

　　The recovery state refers to the transition stage from the discharge or charge state to the static state of the battery. Generally, this stage lasts for 8 hours (this value is an empirical value). The calculated SOC in this state is used as the initial value of the SOC estimation in the charge and discharge state. The SOC estimation at this time mainly considers the change in the battery power after the discharge or charge is completed. After entering the recovery state from the discharge or charge state, the battery power will increase with time. The reason for the change is that polarization occurs inside the battery during the discharge or charge process. Part of the power is not used in the actual charge and discharge but slowly accumulates. When the battery stops working, the polarization phenomenon will slowly disappear and the accumulated power will also recover.

　　Estimation of SOC during the recovery phase:

　　(a) If the state enters the recovery state from the discharge state

　　SOCt=SOCd+M×t/(8×Q)×100%

　　Where: SOCt is the state of charge value in the recovery state; SOCd is the state of charge value when the discharge state is terminated; M is the accumulated power during the battery discharge process (can be recovered); t is the time the battery has been in the recovery state; Q is the actual capacity of the battery.

　　(b) If entering the recovery state from the charging state

　　SOCt=SOCc+M×t/(8×Q)×100%

　　Where: SOCt is the state of charge value in the recovery state; SOCc is the state of charge value when the charging state is terminated; M is the accumulated power during the battery charging process (can be recovered); t is the time the battery has been in the recovery state; Q is the actual capacity of the battery.

　　Calculation of M value:

　　(a) Discharge state

　　If η2>η1,

　　Mt+Δt=Mt+I2×Δt×(1-η2)/η2-I1×Δt×(η2-η1)/η1×η2(1)

　　The derivation is as follows:

　　At time t+Δt, the amount of electricity calculated by the ampere-hour measurement method is: I2×Δt;

　　At time t+Δt, the actual amount of electricity discharged by the battery is: I2×Δt/η2;

　　At time t+Δt, the battery loses power: I2×Δt ×(1-η2)/η2;

　　At time t, when I1 is discharged, due to η2>η1, the power loss I1×Δt×（1-η1）/η1 is large, and a small amount of power will be recovered at time t+Δt, and the recovery amount is:

　　I1×Δt×(1-η1)/η1-I1×Δt×(1-η2)/η2

　　That is, I1×Δt×(η2-η1)/η1×η2

　　If η1≥η2, the amount of power lost at time t+Δt is greater, so there is no recovery amount I1×Δt ×（η2-η1）/η1×η2.

　　Mt +Δt=Mt+I2×Δt×(1-η2)/η2 (2).

　　Where: η1, I1 are the discharge Coulomb efficiency and current of the battery at time t, η2, I2 are the discharge Coulomb efficiency and current of the battery at time t + Δt.

　　(b) In the charging state, the charging method is generally constant current and constant voltage, so the changes in coulomb efficiency and current value are more stable than in the discharging state.

　　In the constant current stage, the current is constant, but the battery temperature increases:

　　M t +Δt=Mt+I×Δt × (1+η1-2η2)

　　The derivation of the formula is the same as (1).

　　Where: I is the current value in the constant current stage; η1 and η2 are the charging coulombic efficiencies in the constant current stage, η2>η1, and their difference is caused by temperature. In the constant voltage stage, the current will decrease as the voltage increases.

　　If η2>η1, Mt +Δt=Mt+I2×Δt×(1-η2)-I1×Δt×(η2-η1) The derivation of the formula is the same as (1).

　　If η1≥η2, Mt+Δt=Mt+I2×Δt×（1-η2）, the formula derivation is the same as (2).

　　Where: η1, I1 are the charging coulomb efficiency and current of the battery at time t; η2, I2 are the charging coulomb efficiency and current of the battery at time t + Δt.

　　In the case of charging, the specified current is generally used for charging, and η can be considered to be 1.

　　1.3.1 Improvement of the ampere-hour measurement method.

　　In this state, the ampere-hour measurement method is generally used for SOC estimation, that is, Q=∫IDT. However, since this method does not take into account the coulomb efficiency, the calculation result will have an increasingly large error as time accumulates. Therefore, this paper improves the ampere-hour measurement method by adding the coulomb efficiency factor and the dynamic recovery power part calculated based on it to the SOC estimation during the charging and discharging process, thereby improving the accuracy of the ampere-hour measurement method.

　　1.3.2 Calculation of Coulomb efficiency η

　　The discharge coulombic efficiency is defined as the battery being discharged at a specific current and temperature (which can be arbitrary) at a constant current and temperature until it is fully discharged, and the amount of electricity discharged is compared with the amount of electricity before the battery is discharged.

　　The coulombic efficiency of charging is defined as the battery being charged at a specific current (usually defined) and temperature in an empty state until it reaches the capacity before discharge, and the amount of charge charged is compared with the amount of charge before discharge.

　　Due to the existence of internal resistance and polarization, there will be power loss during the charging and discharging process of the battery, resulting in the power calculated by the ampere-hour method not being able to fully reflect the actual power of the battery during charging and discharging. The coulomb efficiency reflects the difference between the two.

　　The coulombic efficiency under the traditional definition does not take into account the influence of factors such as charge and discharge differences, current size, operating temperature, etc. In order to overcome the shortcomings of the traditional coulombic efficiency, this paper uses neural networks to estimate the coulombic efficiency, because neural networks have the advantages of representing arbitrary nonlinear relationships and learning capabilities, so that more accurate results can be obtained.

　　This paper adopts an adaptive neural network, as shown in Figure 3. Its structure is two nodes in the input layer, current and temperature; the number of nodes in the middle layer depends on the actual situation (this paper uses 19 nodes); and one output layer node η. The reason for using current and temperature as input nodes is that the Coulomb efficiency η is mainly affected by them, especially by the current.

Figure 3 Adaptive neural network model

　　The process of estimating the Coulomb efficiency η using a neural network is: (1) obtaining empirical data through experiments; (2) training the neural network with the obtained empirical data; and (3) applying the trained neural network to estimate η in real time during SOC estimation.

　　Figures 4 and 5 are curves showing the relationship between the charge and discharge coulomb efficiency and the current and temperature. The connecting lines in Figures 4 and 5 represent the curves obtained from the charge and discharge experiments, and “+” represents the result estimated by the neural network.

Figure 4. Relationship between discharge coulomb efficiency, current and temperature

Figure 5 Relationship between charging coulomb efficiency, current and temperature

　　It can be seen from the two figures that the simulation results of the charge and discharge Coulomb efficiency are consistent with the experimental values, indicating that the Coulomb efficiency η can be estimated using neural networks.

　　Finally, lithium batteries will gradually age as the number of charge and discharge times increases, which is manifested by the reduction of the actual capacity of the battery. The actual capacity of the battery can be corrected using the formula: Q=100×Qch/(SOCsf-SOCsi). In the formula: Q represents the actual capacity after correction; SOCsf represents the SOC value at rest before charging, SOCsi represents the SOC value at rest after charging; Qch represents the amount of electricity charged into the battery during charging. Correcting the actual capacity of the battery will further reduce the calculation error of the SOC, making it closer to the actual value.

　　1.3.2 Calculation of Coulomb efficiency η

　　The discharge coulombic efficiency is defined as the battery being discharged at a specific current and temperature (which can be arbitrary) at a constant current and temperature until it is fully discharged, and the amount of electricity discharged is compared with the amount of electricity before the battery is discharged.

　　The coulombic efficiency of charging is defined as the battery being charged at a specific current (usually defined) and temperature in an empty state until it reaches the capacity before discharge, and the amount of charge charged is compared with the amount of charge before discharge.

　　Due to the existence of internal resistance and polarization, there will be power loss during the charging and discharging process of the battery, resulting in the power calculated by the ampere-hour method not being able to fully reflect the actual power of the battery during charging and discharging. The coulomb efficiency reflects the difference between the two.

　　The coulombic efficiency under the traditional definition does not take into account the influence of factors such as charge and discharge differences, current size, operating temperature, etc. In order to overcome the shortcomings of the traditional coulombic efficiency, this paper uses neural networks to estimate the coulombic efficiency, because neural networks have the advantages of representing arbitrary nonlinear relationships and learning capabilities, so that more accurate results can be obtained.

　　This paper adopts an adaptive neural network, as shown in Figure 3. Its structure is two nodes in the input layer, current and temperature; the number of nodes in the middle layer depends on the actual situation (this paper uses 19 nodes); and one output layer node η. The reason for using current and temperature as input nodes is that the Coulomb efficiency η is mainly affected by them, especially by the current.

Figure 3 Adaptive neural network model

　　The process of estimating the Coulomb efficiency η using a neural network is: (1) obtaining empirical data through experiments; (2) training the neural network with the obtained empirical data; and (3) applying the trained neural network to estimate η in real time during SOC estimation.

　　Figures 4 and 5 are curves showing the relationship between the charge and discharge coulomb efficiency and the current and temperature. The connecting lines in Figures 4 and 5 represent the curves obtained from the charge and discharge experiments, and “+” represents the result estimated by the neural network.

Figure 4. Relationship between discharge coulomb efficiency, current and temperature

Figure 5 Relationship between charging coulomb efficiency, current and temperature

　　It can be seen from the two figures that the simulation results of the charge and discharge Coulomb efficiency are consistent with the experimental values, indicating that the Coulomb efficiency η can be estimated using neural networks.

　　Finally, lithium batteries will gradually age as the number of charge and discharge times increases, which is manifested by the reduction of the actual capacity of the battery. The actual capacity of the battery can be corrected using the formula: Q=100×Qch/(SOCsf-SOCsi). In the formula: Q represents the actual capacity after correction; SOCsf represents the SOC value at rest before charging, SOCsi represents the SOC value at rest after charging; Qch represents the amount of electricity charged into the battery during charging. Correcting the actual capacity of the battery will further reduce the calculation error of the SOC, making it closer to the actual value.