SOH represents the ability of a current battery to store electric energy compared with that of a new battery. With the increase in service time, the internal resistance of the battery increases, and the maximum usable capacity decreases. Therefore, capacity and internal resistance parameters are often used to define battery SOH in the industry.

According to the definition in terms of capacity, the SOH can be expressed as

where C_rated is the nominal capacity, and C_curr is the present maximum available capacity, which can be measured by discharging the battery at a fixed current (usually 0.1 C_rated) and air temperature (usually 20 °C to 30 °C). According to the definition in terms of resistance, the SOH can be expressed as $$\mathrm{SOH}=\frac{{\mathrm{R}}_{\mathrm{EOL}{}_{}-{\mathrm{R}}_{\mathrm{curr}{}_{}\frac{{\mathrm{R}}_{\mathrm{EOL}{}_{}-{\mathrm{R}}_{\mathrm{new}{}_{}\frac{}{}\times 100\%}}}{}}}}{}$$ where R_new represents the initial internal resistance of the new battery, R_curr represents the actual internal resistance under the current cycle and R_EOL represents the internal resistance at the end of the battery life [30]^[1]. Another parameter used to describe the state of a battery is the SOC, which is defined as $$\mathrm{SOC}=\frac{{\mathrm{C}}_{\mathrm{remain}{}_{}\frac{{\mathrm{C}}_{\mathrm{curr}{}_{}\frac{}{}\times 100\% }}{}}}{}$$ where C_remain is the remaining capacity of the battery. According to Formulas (2) and (4), SOC and SOH are closely linked through C_curr. Therefore, the accurate estimation of SOH must be related to SOC. According to the IEEE 1188-2005 standard, when the actual capacity of a VRLA is less than 80% of the rated capacity, that is, the SOH is less than 80%, the battery must be maintained or replaced [31]^[2].

2. SOH Estimation Methods

At present, battery SOH estimation methods include the experimental method, the model method, the data-driven method and the fusion method. In this study, the different SOH estimation methods are classified into four different categories: experimentally based, model-based, data-driven and fusion methods. Figure 21 shows the classification of the different SOH estimation methods.

2.1. Experimentally Based Methods

Experimental methods are usually carried out in the laboratory because they require specific equipment and are time-consuming. Experimental methods estimate the SOH by collecting data and measurements that can be used to understand and evaluate the battery aging behavior. The experimental methods usually require less computation and are easy to implement. Therefore, these methods are among the earliest methods used to estimate the SOH of VRLA batteries [23]^[3].

2.1.1. Ampere-Hour Counting Method

The ampere-hour counting method is one of the classical methods to estimate the battery SOH [32]^[4]. The common procedure of this method is to measure the present maximum capacity of the battery. In order to measure the current maximum capacity of the battery, the battery is first fully charged and then fully discharged; the current of the battery is then recorded. Then, the maximum capacity of the battery can be calculated by integrating the discharge current. $${\mathrm{C}}_{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}{}_{}={\displaystyle {\int }_{{\mathrm{t}}_1{{\mathrm{t}}_2{}_{}^{}\mathrm{I}\mathrm{d}\mathrm{t}{\displaystyle }}_{}^{}}^{}}}$$ where I is the discharging current, and t₁ and t₂ are the starting and ending times of the discharge process, respectively. The initial maximum capacity of a battery (C_initial) is usually provided by the manufacturer (referred to as nominal capacity); then, the SOH is determined using Equation (5). The ampere-hour counting method is easy to implement under experimental conditions, and its estimation result is usually regarded as the true value of SOH, which can be used to verify the accuracy of other SOH estimation methods. At present, in power plants and substations, the ampere-hour discharge method is used to check the SOH of the battery pack every 1–2 years. When maintenance staff find a failed battery, they should replace it immediately to maintain the battery in good working condition. The ampere-hour counting method has some disadvantages. For example, it takes too long to test for the battery to be fully charged and discharged, so it is not suitable for online SOH estimation. The full discharge test is also harmful to the battery because deep discharge shortens the service life of the battery [33]^[5].

2.1.2. Open-Circuit Voltage Method

The open-circuit voltage (OCV) of the battery has long been known to have a functional relationship with the battery SOH. If the open-circuit voltage of the battery is measured, the battery SOH can be estimated [34]^[6]. James H. Aylor et al. [35]^[7] proposed a new technology for estimating battery SOH. The technique employs coulometric measurement under loading conditions and open-circuit voltage under no-load conditions in order to predict the change of the battery SOH. This technique was developed to enhance the accuracy and to reduce the required rest period of open-circuit voltage measurement. Mchrnoosh Shahriari [36]^[8] presented an online method for the estimation of the state of health (SOH) of VRLA batteries based on the state of charge (SOC) of the battery. The SOC is estimated using an extended Kalman filter and a neural network model of the battery. Then, the SOH is estimated online based on the relationship between the SOC and the battery open-circuit voltage using fuzzy logic and the recursive least squares method. Experimental results show good estimation of the SOH of VRLA batteries. The open-circuit voltage of the battery cannot be directly detected in the floating charge mode. In order to accurately measure the open-circuit voltage of the battery, it is necessary to keep the battery offline for a long time to reach a stable state. In addition, in order to improve the estimation accuracy of the open-circuit voltage method, it needs to be used in combination with other methods.

2.1.3. Resistance/Impedance Method

The internal resistance of the battery is considered an important index of SOH because it is seriously affected by the degradation of battery performance. When the SOH of the battery decreases, the internal resistance increases. With the increase in internal resistance, the SOH of the battery decreases. Considering the strong correlation between internal resistance and SOH, internal resistance is regarded as a good tool to estimate SOH [37]^[9]. The two main methods used to evaluate battery SOH are the internal resistance method and the electrochemical impedance method [38]^[10]. The internal resistance method usually establishes the corresponding relationship between the internal resistance and SOH and then evaluates the battery SOH according to internal resistance. To measure the internal resistance, a sudden current change (ΔI) is exerted on the battery, and the consequent voltage change (ΔU) is measured. The internal resistance can be calculated as R = ΔU/ΔI. The next step is to perform a regression analysis of the resistance/impedance and SOH. Finally, using the regression function, The SOH of the batteries is estimated [23]^[3]. The internal resistance method only needs to obtain the voltage and current, making it suitable application in online estimation of battery SOH. Generally, the internal resistance of the battery has a certain relationship with SOC and SOH, and maintenance personnel can use these relationships to monitor the battery status in real time [39]^[11]. However, due to the uncertainty of the relationship between internal resistance and SOC, the error of SOH estimation is slightly larger [40]^[12]. In addition, when the capacity of a lead-acid battery is greater than 60%, the internal resistance changes slightly. Therefore, the internal resistance method is only used to roughly judge the battery SOH. EIS is a kind of electrochemical measurement method whereby a low-amplitude sine wave voltage (or current) disturbance signal is imposed on the battery. EIS has no effect on the internal state of the battery and provides more rich information on electrode process dynamics and electrode interface structure details than other conventional electrochemical methods. Based on the circuit model, the relationship between the EIS curve and SOH can be established to accurately analyze the SOH of the battery. However, EIS measurement requires sophisticated and professional test equipment, which has high requirements for the test environment. As the circuit model itself is a technical difficulty, the process of EIS measurement and SOH calculation is relatively complex, which leads to the time-consuming and high cost of the impact method to estimate SOH. Therefore, a simpler and more general method for obtaining EIS parameters online requires further research.

2.1.4. Coup de Fouet Method

After being fully charged, the battery is discharged with a constant current. In the first few minutes, the discharge voltage reaches the peak voltage and then rises to the discharge platform voltage [41,42,43]^[13][14][15]. This phenomenon is referred to as coup de fouet (Figure 32). Several studies have applied the “coup de fouet” phenomenon to estimation of battery SOH. Phillip E. Pascoe et al. [44]^[16] found that the valley voltage and peak voltage in the coup de fouet phenomenon are linearly related to the actual available capacity of the battery; therefore, the SOH can be estimated according to the peak voltage and the platform voltage. A series of experimental studies revealed that the discharge rate and temperature have effects on the peak voltage and the platform voltage. Yuan et al. [45]^[17] assumed that the peak voltage and plateau voltage would be impacted under different discharge conditions (temperature and discharge rate). According to the coup de fouet phenomenon of the battery, the SOH is taken as the output variable, with the peak voltage, plateau voltage, discharge rate and temperature as input variables; accordingly, a battery SOH estimation model based on a BP neural network was built. The results show that the model based on a BP (backpropagation) neural network can effectively predict battery SOH. Due to the short discharge time during the test, the current working state of the battery is not be affected, and SOH can be estimated online. Compared with the traditional discharge test method, the coup de fouet method is more convenient and efficient and is very suitable for online detection of battery SOH as a backup power supply.

2.2. Model-Based Methods

Model-based methods use indirect measurement methods to predict the SOH of the battery. Empirical models, electrochemical models and equivalent circuit models can be applied.

2.3. Data-Driven Methods

With the rapid development of big data and machine learning technology, data-driven technology has broken through the shackles of complex nonlinear systems that are difficult to model and has become the main research direction of battery health. Data-driven methods include artificial neural networks, support vector machines and Gaussian process regression. The general flow of the data-driven prediction method is shown in Figure 6 [59] ^[18]. First, a large amount of battery information (such as voltage, current, temperature and impedance) is collected, which may come from past historical data or real-time data. Secondly, the battery degradation characteristics are extracted. The third step is to train a machine learning model to showing the relationship between the extracted characteristics and the SOH of the battery. Finally, once the machine learning model is determined, it is applied to evaluate the battery SOH.

2.4. Fusion Methods

In recent years, model fusion technology has received extensive attention from many researchers. The idea of the fusion method is to integrate multiple models, including experimental methods, model-based methods and data-driven methods, to give full play to their respective advantages and achieve accurate, reliable and robust battery health state estimation. Fusion-based methods usually include different model-based mutual integration, the merging of model methods and data-driven methods and the convergence of different data-driven methods. Zhong et al. [71]^[19] proposed SOH estimation based on a fusion model for lead-acid batteries used in substations. Two models were established to estimate the SOH of a VRLA battery. The first model evaluates the relationship between the average resistance and SOH. The other model assesses the decline rate of battery voltage and SOH. According to the proportion of the influence of the nuclear discharge and floating charge state on SOH, a fusion model was established to estimate the SOH of a lead-acid battery in a substation. An accelerated life test was used to verify the proposed arithmetic, and the experimental results showed that the arithmetic was accurate and reliable and can realize real-time estimation the SOH of lead-acid batteries used in substations. Therefore, timely detection of poor SOH can greatly improve the safety and reliability of the battery pack. The fusion estimation method overcomes the shortcomings of the single-model method or data-driven method, such as low prediction accuracy, poor reliability or misjudgment. It is an important method for battery SOH estimation in the future and has good application prospects.