Abstract
This paper presents a comprehensive approach to improving the equivalent circuit model of lithium-ion batteries for energy storage systems. The proposed method leverages the second-order RC equivalent circuit model and introduces an innovative solution to enhance its accuracy under varying temperatures and discharge rates. By utilizing a Back Propagation (BP) neural network, we predict and compensate for the model terminal voltage errors across a wide range of operating conditions. This approach significantly mitigates the need for repetitive charging and discharging experiments, thus preserving battery cycle life. Experimental and simulation results demonstrate the feasibility of the proposed method, showcasing improved model adaptability and precision. The model is further applied to battery screening, cascade utilization in energy storage systems, and State of Charge (SOC) prediction, thereby offering practical engineering significance for new energy generation battery storage systems.
Keywords: Lithium-ion batteries, equivalent circuit, neural network, small sample data expansion, additional controlled voltage source, energy storage
1. Introduction
Renewable energy sources such as solar and wind power have gained significant attention due to their environmental benefits. However, their inherent intermittency poses challenges for reliable power supply. Energy storage systems, particularly those utilizing lithium-ion batteries, play a crucial role in ensuring grid stability and power balance. Decommissioned or retired batteries can also be repurposed for energy storage, contributing to a circular economy and reducing waste.
Accurate battery modeling is vital for predicting battery behavior, optimizing system performance, and enhancing safety measures. Two primary categories of battery models exist: electrochemical models and equivalent circuit models. Electrochemical models, while precise, are computationally intensive. In contrast, equivalent circuit models, despite their simplicity, can effectively capture battery dynamics and are widely adopted in engineering applications.
This paper focuses on enhancing the second-order RC equivalent circuit model by incorporating an additional controlled voltage source. By leveraging a BP neural network, we dynamically compensate for model errors across different temperatures and discharge rates, thereby improving model accuracy and applicability.
2. Lithium-Ion Battery Modeling Fundamentals
2.1 Types of Battery Models
Battery models can be broadly classified into two categories:
- Electrochemical Models: These models describe the internal electrochemical reactions within the battery, offering high precision but requiring complex computations.
- Equivalent Circuit Models: These models use electrical components such as resistors, capacitors, and voltage sources to mimic battery behavior. They are easier to implement and interpret but may sacrifice some accuracy.
2.2 Second-Order RC Equivalent Circuit Model
The second-order RC equivalent circuit model, illustrated in Figure 1, comprises two RC networks and an open-circuit voltage (OCV) source. This model captures the dynamics of battery polarization effects, including activation polarization (R1, C1) and concentration polarization (R2, C2).
The model’s governing equations are:
fracdU1dt=−fracU1R1C1+fracIC1
fracdU2dt=−fracU2R2C2+fracIC2
Ut=Uoc−U1−U2−R0I
where U1 and U2 are the voltages across the RC networks, Ut is the terminal voltage, I is the battery current, and R0, R1, R2, C1, and C2 are the model parameters.
3. Model Parameter Identification
Accurate parameter identification is crucial for the second-order RC model. This section outlines the methods used to identify the OCV and RC network parameters.
3.1 Open-Circuit Voltage (OCV) Identification
The OCV is a function of the State of Charge (SOC) and can be experimentally determined by performing a full charge-discharge cycle at a controlled temperature. A polynomial fit is then applied to the experimental data to establish the OCV-SOC relationship.
3.2 Resistance and Capacitance Identification
The RC network parameters (R1, C1, R2, C2, and (R_0)) are identified through a combination of charge-discharge experiments and data fitting techniques. A cyclic pulse discharge test is typically employed, where the battery is discharged in short pulses followed by rest periods. The battery’s voltage response during and after each pulse is analyzed to estimate the RC parameters.
4. Enhanced Model with an Additional Controlled Voltage Source
4.1 Motivation
The base second-order RC model’s accuracy can deteriorate under varying operating conditions, particularly at extreme temperatures and high discharge rates. To address this, we propose incorporating an additional controlled voltage source into the model to dynamically compensate for errors.
4.2 Back Propagation (BP) Neural Network
A BP neural network is used to predict the model errors across a wide range of temperatures and discharge rates based on a limited set of experimental data. The neural network architecture comprises an input layer with two nodes (temperature and discharge rate), a hidden layer, and an output layer predicting the voltage error.
4.3 Training and Validation
The neural network is trained using a dataset consisting of measured and simulated terminal voltages across different temperatures (-10°C to 30°C) and discharge rates (0.3C to 1.2C). The neural network’s performance is evaluated by comparing its predictions with the actual voltage errors.
5. Experimental Results and Analysis
5.1 Model Error Analysis
Experimental results show that the base model’s errors increase with lower temperatures and higher discharge rates. By incorporating the BP neural network-based controlled voltage source, the model’s accuracy improves significantly, as evidenced by reduced average and relative errors (see Table 1).
Table 1: Comparison of Model Errors before and after Improvement
| Temperature (°C) | Discharge Rate (C) | Average Error (V) – Before Improvement | Average Error (V) – After Improvement |
|---|---|---|---|
| -10 | 0.3 | -0.30448 | 0.00182 |
| 25 | 0.5 | -0.16265 | -0.00176 |
| 30 | 1.0 | -0.19331 | -0.00237 |
| … | … | … | … |
5.2 Model Adaptability
The enhanced model demonstrates excellent adaptability across different operating conditions. As shown in Figure 2, the model’s predicted terminal voltage closely matches the measured values, indicating its robustness.
6. Applications in Energy Storage Systems
6.1 Battery Screening and Cascade Utilization
The proposed model can be utilized for battery screening and cascade utilization in energy storage systems. By analyzing battery performance data, aged batteries can be effectively sorted for repurposing, maximizing their residual value.
6.2 SOC Prediction and Thermal Management
Accurate SOC prediction is vital for maintaining system stability and optimizing energy usage. The enhanced model, combined with real-time monitoring, enables precise SOC estimation. Furthermore, the model’s internal resistance parameters facilitate thermal management by predicting battery heating and triggering cooling mechanisms when necessary.
6.3 System Performance Assessment
The model can also be employed to assess the overall performance of energy storage systems. By simulating various operating scenarios, system designers can identify potential bottlenecks and optimize component configurations for improved efficiency and reliability.
7. Conclusion
This paper presents a comprehensive approach to improving the second-order RC equivalent circuit model of lithium-ion batteries for energy storage systems. By incorporating an additional controlled voltage source based on a BP neural network, we dynamically compensate for model errors across a wide range of temperatures and discharge rates. Experimental results demonstrate the feasibility and effectiveness of the proposed method, resulting in improved model accuracy and adaptability. The enhanced model finds practical applications in battery screening, cascade utilization, SOC prediction, thermal management, and system performance assessment, offering significant benefits for new energy generation battery storage systems.