As the emergency power supply for a simulation substation, lead-acid batteries have a work pattern featuring non-continuous operation, which leads to capacity regeneration. However, the accurate estimation of battery state of charge (SOC), a measurement of the amount of energy available in a battery, remains a hard nut to crack because of the non-stationarity and randomness of battery capacity change. This paper has proposed a comprehensive method for lead-acid battery SOC estimation, which may aid in maintaining a reasonable charging schedule in a simulation substation and improving battery’s durability. Based on the battery work pattern, an improved Ampere-hour method is used to calculate the SOC during constant current and constant voltage (CC/CV) charging and discharging. In addition, the combined Particle Swarm Optimization (PSO) and Least Squares Support Vector Machine (LSSVM) model is used to estimate the SOC during non-CC discharging. Experimental results show that this method is workable in online SOC estimation of working batteries in a simulation substaion, with the maximum relative error standing at only 2.1% during the non-training period, indicating a high precision and wide applicability.

As the hub of the power grid, substations are responsible for power supply for different regions, which makes training on substation operation and maintenance crucial. By combining the transformed primary equipment and a simulation platform, we can create a simulation substation for trainees. The DC power supply system is an important part of a simulation substation, as it powers relay protection devices, switch control devices, simulation operation equipment, etc. [

Since the French physicist Gaston Plante invented the world’s first rechargeable battery based on lead-acid chemistry in 1859, the lead-acid battery has been gaining momentum and applied in more and more scenarios due to its high safety, low cost, stable operation and long service life [

So far, there has been a lot of in-depth research in the field of SOC estimation at home and abroad. Wang et al. [

Lead-acid batteries in the DC system of a simulation substation are charged/discharged in either CC model or non-CC model. CC means that the working current of the lead-acid battery changes slightly in a continuous period of time. Non-CC means that the working current of the lead-acid battery is always changing at a fast rate and in a high amplitude [

There are many factors that affect the durability of batteries, such as the SOC window and temperature control etc. The most important one is the SOC window of the battery cell. The SOC window refers to the reasonable upper and lower bound of the SOC during charging and discharging. The SOC window range is 30%–70% [

The calculation formula based on the Ampere-hour method is as follows:

where

Due to the limitation of the Ampere-hour method [

In China, the standard temperature for the rated capacity of a lead-acid battery is generally 25°C. When the temperature changes, the available battery capacity will have a certain difference from the rated capacity. At present, the common compensation coefficient formula is:

where

where

The rated battery capacity refers to the amount of electricity discharged from the battery to the cut-off voltage at a current of 0.05 C (20-h discharge rate). When the working current of the battery is greater than 0.05 C, the total energy released at the discharge cut-off voltage is less than the rated capacity [

MATLAB is used to fit the curve of

Without considering the temperature, we can obtain the following equation from

where

The battery charging usually has three stages: CC charging, CV charging and floating charging.

The CC model is used firstly, so that the battery voltage can reach a certain amplitude as soon as possible. When the battery voltage reaches a certain voltage value, the CV model should take over, as continued CC charging will lead to water electrolysis (produce hydrogen and oxygen gases and elevate the battery temperature), instead of improving the charging efficiency. At this time, the charging voltage remains unchanged, but the charging current starts to taper off. In the process of CV charging, the magnitude of the current is similar to the MAS theoretical curve, as shown in

where

where

The least square method of MATLAB is used to fit the curve:

where

The charging process is also affected by temperature. The charging voltage needs to decrease by 4 mV (2 V battery) for every 1°C rise in temperature (based on the standard temperature of 25°C); the charging voltage needs to increase by 4 mV (2 V battery) for every 1°C drop in temperature [

where

Therefore, the calculation formula of SOC during charging is:

where

Non-CC discharging refers to a process where the discharge current will change with the increase or decrease of the battery load in actual use [

The LSSVM method can obtain the optimal result when the linear target is interfered with by Gaussian noise, so it is often used to fit the numerical points in the plane [

In the sample sets

Assume the regression function in the case of nonlinearity is:

where

where

To solve the above optimization problem, the Lagrange multiplier method is used:

where

Derivate

According to

where

Then the following regression estimation function can be obtained:

where

The Kernel Function affects the estimation accuracy of LSSVM to a great extent. The Kernel Functions of LSSVM are generally Radial Basis Kernel Function (RBF), Linear Kernel Function (LKF), and Polynomial Kernel Function (PKF) and so on [

where

PSO is used to optimize the parameters of Kernel Function in order to avoid error caused by experience and random selection. PSO is to find the optimal solution by iteration from the perspective of a random solution where fitness is used to measure the quality of the optimal solution. It can find the global optimal solution by following the current optimal value [

In this algorithm, the following formula is used for iteration:

where

The weight parameter

where

Internal resistance is an important parameter for battery SOC estimation. In this paper, a 6 V, 4,500 mAH battery is discharged in stages with different currents. The internal resistance of the battery is measured by the Kelvin detection method. The excitation signal input and the voltage measurement are realized by two different wires, respectively, as shown in

Three kernel functions are used to estimate the SOC, and the results are compared in order to ensure the accuracy of model estimation. The evaluation indexes of the regression algorithm are generally Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and R-Squared. The LSSVM estimation results of different kernel functions are compared based on these three indexes.

Kernel functions | RMSE | MAE | R-squared |
---|---|---|---|

Poly | 1.4446 | 1.0766 | 0.9925 |

Lin | 0.9869 | 0.7623 | 0.9966 |

RBF | 0.4855 | 0.3936 | 0.9992 |

According to the evaluation indexes in

It can be seen from the relationship between the OCV and the capacity of the battery, when the same capacity is discharged on the basis of different remaining capacities, the OCV drops at different rates. In addition, different discharge rates lead to different voltage drop rates. There could be a voltage recovery when the discharge current switches from high to low. At this time, the internal temperature of the battery will decrease, thereby reducing the energy loss. There is a close correspondence between a battery’s working voltage and its OCV, so for non-CC discharging, the terminal voltage difference and the discharge time in the current fluctuation period are used as the input of the estimation algorithm.

Based on the comprehensive analysis of various influencing factors of the battery, this paper proposes a PSO-LSSVM model for SOC estimation during non-CC discharging based on four indicators: battery internal resistance, terminal voltage difference, temperature, and discharge time. The internal resistance is obtained by the self-built four-terminal Kelvin testing equipment. Current, terminal voltage, temperature and other parameters are detected by Neware’s high-performance battery detection equipment. The experimental environment is shown in

The curve of discharge current variation is shown in

Voltage differences between several time intervals (5, 10, and 20 min) are calculated. This is to ensure there are one or more current changes in each time interval, thus making the training data closer to the real data. The battery discharging experiment has generated a total of 1,140 groups of non-repetitive data in different time periods, and the time interval between every two groups is 10 s. After an out-of-order arrangement, the first 1,000 groups are selected as the training data and the rest as the validation data.

The accuracy of the estimated value is determined by the penalty factor

As the backup power supply for the DC system in a simulation substation, lead-acid batteries feature non-continuity in operation. However, the accurate SOC estimation remains a challenge due to the non-stationarity and randomness of battery capacity change. This paper proposes a comprehensive method for battery SOC estimation, which may aid in maintaining a reasonable charging schedule in a simulation substation and improving battery’s durability. Based on the different working conditions of a battery, taking into account factors such as the terminal voltage, internal resistance, temperature and discharge time of the battery, different estimation methods are selected to improve the accuracy of SOC estimation. An improved Ampere-hour method is used to calculate the battery SOC during CC/CV charging and discharging. A PSO algorithm is employed to optimize the kernel function parameters, and a combined PSO-LSSVM algorithm is introduced to estimate the battery SOC, with the maximum relative error being 2.1%, which is significantly less than that obtained by conventional kernel function parameters. The PSO-LSSVM algorithm automatically discovers the data rules during online data collection and accurately estimates the SOC change during non-CC discharging, solving the problem of low estimation accuracy obtained by the improved Ampere-hour method.

The authors are grateful for the financial support provided by State Grid Jiangsu Electric Power Co., Ltd.