The state of charge (SOC) of the battery describes the amount of remaining battery power and is one of the most important parameters during battery use. Since the SOC is affected by factors such as charge and discharge rate, temperature, self-discharge, and aging, the battery exhibits a high degree of nonlinearity during use, which brings great difficulty to accurately estimate the SOC. So far, although new SOC estimation methods continue to emerge, the problem of accurate estimation of the SOC of electric vehicle power batteries has not been completely solved. In addition, all electric vehicles use battery packs, and how to define the SOC of battery packs with poor consistency is still a topic. A commonly used method in actual use is to treat the battery pack as a single battery cell. In order to ensure the safety of the battery, the SOC of the worst battery cell is often used to define the SOC of the battery pack.

At present, the commonly used methods include discharge test method, ampere-hour measurement method, open circuit voltage method, load voltage method, internal resistance method, neural network method, and Kalman filter method. The following will briefly introduce each method one by one.

**1. Discharge test method**The discharge test method is the most reliable SOC estimation method. The battery is continuously discharged with a constant current to the terminal voltage, and the product of the discharge current and the time is the remaining capacity of the battery. The discharge test method is often used in the laboratory and is suitable for all batteries, but it has two significant disadvantages: it takes a lot of time; the work on the battery is forced to be interrupted. The discharge test method is not suitable for electric vehicles in motion and can be used for the maintenance of electric vehicle batteries.

**2. Ampere-hour measurement**Ampere-hour measurement is the most commonly used SOC estimation method. If the initial state of charge and discharge is SOC

_{0}, the SOC of the current state can be calculated by the formula.

SOC=SCO

_{0}-(1/C

_{N})∫

^{t}

_{0}ηIdr

In the formula, C

_{N}is the rated capacity; I is the battery current; η is the charge-discharge efficiency.

There are three main problems in the application of the ampere-hour measurement method: the method itself cannot give the initial SOC of the battery; inaccurate current measurement will cause SOC calculation errors, which will accumulate for a long time, and the error will become larger and larger; the charging and discharging efficiency of the battery must be considered. The current measurement problem can be solved by using high performance current sensors, but the cost will increase. To solve the problem of battery charge and discharge efficiency, an empirical formula for battery charge and discharge efficiency should be established through a large number of experiments in advance. Ampere-hour metering can be applied to all electric vehicle batteries. Ampere-hour metering is a simple and reliable SOC estimation method if the current measurement is accurate and there is enough data to estimate the starting state.

**3. Open circuit voltage method**The open circuit voltage of the battery is numerically close to the battery electromotive force. The electromotive force of lead-acid batteries is a function of the electrolyte concentration, and the electrolyte density decreases proportionally with the discharge of the battery, so the open circuit voltage can be used to estimate the SOC more accurately. The relationship between the open circuit voltage and SOC of NiMH and Li-ion batteries is not as linear as that of lead-acid batteries, but the corresponding relationship can also estimate SOC. Especially in the early and final stages of charging, the effect is better.

The obvious disadvantage of the open circuit voltage method is that it requires the battery to stand for a long time to achieve voltage stability, and it takes several hours for the battery state to recover from operation to stability, which makes the measurement difficult, and how to determine the standing time is also a problem, so this method is used alone Only suitable for electric vehicles in parked state. Because the open-circuit voltage method has a good effect on SOC estimation at the beginning and end of charging, it is often used in combination with the ampere-hour measurement method.

**4. Load voltage method**At the moment when the battery starts to discharge, the voltage of the battery rapidly changes from the open-circuit voltage state to the load voltage state. When the battery load current remains unchanged, the variation of the load voltage with SOC is similar to the variation of the open-circuit voltage with SOC. Figure 1 shows the relationship between DOD (depth of discharge)-discharge current-battery voltage of a 100A·h nickel-metal hydride battery pack. When the battery is discharging, the SOC estimation value can be obtained according to the discharge voltage and current look-up table.

The advantage of the load voltage method is that it can estimate the SOC of the battery pack in real time, and it has a better effect in constant current discharge. In practical applications, the violently fluctuating battery voltage brings difficulties to the application of the load voltage method. The load voltage method is rarely applied to real vehicles, but is often used as a criterion for battery charge and discharge cut-off.

**5. Internal resistance method**The internal resistance of the battery is divided into the AC impedance (Impedance) and the DC internal resistance (Resistance). Both AC impedance and DC internal resistance are closely related to SOC. The AC impedance of the battery is the transfer function between the battery voltage and the current. It is a complex variable that represents the resistance of the battery to the AC power. It should be measured with an AC impedance meter. The AC impedance of the battery is greatly affected by temperature, and there is controversy about whether the AC impedance measurement is performed in the open circuit state after the battery is stationary or during the charging and discharging process, so it is rarely used in real vehicles.

The DC internal resistance represents the resistance of the battery to DC, which is equal to the ratio of the battery voltage change to the current change in the same short period of time. In the actual measurement, the battery is charged or discharged with constant current from the open-circuit state, and the difference between the load voltage and the open-circuit voltage at the same time divided by the current value is the DC internal resistance. Experiments show that in the later stage of discharge, the DC internal anode of the lead-acid battery increases significantly, which can be used to estimate the battery SOC: the change law of the DC internal resistance of the nickel-metal hydride battery and the lithium-ion battery is different from that of the lead-acid battery, and it is less used.

The size of the DC internal resistance is affected by the calculation time period. If the time period is shorter than 10ms, only the ohmic resistance can be detected. If the time period is long, the internal resistance will become complicated. It is difficult to accurately measure the internal resistance of a battery cell, which is the disadvantage of the DC internal resistance method. The internal resistance method is suitable for the estimation of battery SOC in the later stage of discharge, and can be used in combination with the ampere-hour measurement method.

**6. Neural network method**The battery is a highly nonlinear system, and it is difficult to establish an accurate mathematical model for its charging and discharging process. Neural network has nonlinear basic characteristics, parallel structure and learning ability, and can give corresponding output for external excitation, so it can simulate the dynamic characteristics of battery to estimate SOC.

A three-layer typical neural network is often used to estimate the battery SOC. The number of neurons in the input and output layers is determined by actual needs and is generally a linear function. The number of neurons in the middle layer depends on the complexity of the problem and the accuracy of the analysis. Commonly used input variables for estimating battery SOC include battery voltage, current, temperature, internal resistance, accumulated discharge power, and ambient temperature. Whether the selection of the input variables of the neural network is appropriate, and whether the number of variables is appropriate, directly affects the accuracy of the model and the amount of calculation. The neural network method is suitable for all kinds of batteries. The disadvantage is that it requires a large amount of reference data for training, and the estimation error is greatly affected by the training data and the training method.

**7. Kalman filter method**The core idea of Kalman filter theory is to make the optimal estimation of the state of the dynamic system in the sense of minimum variance. Applied to battery SOC estimation, the battery is regarded as a power system, and SOC is an internal state of the system. The general mathematical form of the battery model is:

State equation x

_{k+1}=A

_{k}x

_{k}+B

_{k}μ

_{k}+ω

_{k}=f(x

_{k}·μ

_{k})+ω

_{k}

Observation equation y

_{k}=C

_{k}x

_{k}+υ

_{k}=g(x

_{k}·μ

_{k})+υ

_{k}

The input vector u

_{k}of the system usually contains variables such as battery current, battery temperature, remaining battery capacity and internal resistance, the output y

_{k}of the system is usually the working voltage of the battery, and the battery SOC is included in the state quantity x

_{k}of the system. Both f(x

_{k}, u

_{k}) and g(xk, uk) are nonlinear equations determined by the battery model and are linearized during the calculation. The core of the estimation SOC algorithm is a set of recursive equations including the SOC estimation value and the covariance matrix reflecting the estimation error. The covariance matrix is used to give the estimate error bounds. The formula below is the basis for describing SOC as an internal state in the battery model equation of state.

SOC

_{k+1}=SOC

_{k}-[η(i

_{k})i

_{k}△t/C]

The research on the estimation of battery SOC by Kalman filter has only started in recent years. This method is suitable for all kinds of batteries. Compared with other methods, it is especially suitable for the estimation of SOC of hybrid electric vehicle battery with severe current fluctuation. It not only gives the estimated value of SOC, but also gives the estimation error of SOC. It has high requirements on battery model accuracy and computing power.