Abstract
The accurate estimation of the State of Charge (SOC) of Lithium Iron Phosphate (LFP) batteries is crucial for battery management systems (BMS) to prevent overcharge or overdischarge, thus extending battery lifespan. The relationship between the SOC and Open-Circuit Voltage (OCV) of lithium-ion batteries is a core factor influencing SOC estimation accuracy. This paper proposes an OCV model optimization method to address the low accuracy of the short-duration Low-Current OCV (LO) test. The proposed method utilizes the Douglas-Peucker (DP) algorithm and piecewise linear functions to create an initial OCV model based on LO test data. Subsequently, a Particle Swarm Optimization (PSO) algorithm is employed to optimize the OCV curve by selecting four critical OCV points as variables. The optimized OCV curve significantly improves the absolute average error of terminal voltage estimation by 83.5% under dynamic conditions, and the SOC estimation error using Adaptive Extended Kalman Filter (AEKF) is less than 0.3%. This approach enables accurate OCV curves to be obtained from time-efficient LO tests, reducing testing costs in lithium-ion battery research and applications.
1. Introduction
With the global push towards sustainable energy solutions, electric vehicles (EVs) have gained significant traction in recent years. Lithium-ion batteries, particularly Lithium Iron Phosphate (LFP) batteries, have emerged as a prominent energy storage solution due to their high energy density, long cycle life, and improved safety characteristics compared to other lithium-ion chemistries. However, accurate estimation of the State of Charge (SOC) of these batteries remains a challenge.
The SOC, defined as the remaining capacity of a battery relative to its total capacity, is a crucial parameter for battery management systems (BMS) to ensure efficient and safe operation. Inaccuracies in SOC estimation can lead to premature battery degradation or even catastrophic failure. Since the SOC cannot be measured directly, various estimation methods have been developed, including electrochemical models, black-box models, and equivalent circuit models. Among these, equivalent circuit models, specifically the Thevenin model, have gained popularity due to their simplicity and relatively high accuracy.
The relationship between the Open-Circuit Voltage (OCV) and SOC of lithium-ion batteries plays a pivotal role in SOC estimation accuracy. However, accurate OCV curves are traditionally obtained through time-consuming Open-Circuit Voltage tests (OCV tests), which involve fully discharging and then recharging the battery while measuring the voltage at various SOC levels. Alternatively, the Low-Current OCV (LO) test provides a faster alternative but often yields less accurate results.
This paper proposes an OCV model optimization method that combines the speed of the LO test with the accuracy of traditional OCV tests. By leveraging the DP algorithm, piecewise linear functions, and the PSO algorithm, this method enables the rapid acquisition of high-fidelity OCV curves, significantly reducing testing time and costs.
2. Lithium-Ion Battery Modeling
2.1 Thevenin Model
The Thevenin model is a widely used equivalent circuit model for lithium-ion batteries due to its balance between complexity and accuracy [8]. the Thevenin model comprises an ideal voltage source representing the battery’s OCV, a series resistance (R0), and a parallel RC network simulating the battery’s dynamic response.
The mathematical representation of the Thevenin model is given by:
Ut=UOC−Up−ILR0
Up=−CpRpUp+CpIL
where Ut is the terminal voltage, UOC is the open-circuit voltage, Up is the voltage across the polarization capacitor Cp, Rp is the polarization resistance, IL is the load current, and R0 is the internal resistance.
2.2 OCV-SOC Relationship
The relationship between the OCV and SOC is a nonlinear function that is influenced by battery chemistry, temperature, and aging effects. Accurate knowledge of this relationship is essential for precise SOC estimation.
3. Proposed OCV Model and Optimization Method
3.1 LO Test and Initial OCV Model
The LO test involves discharging the battery at a low current rate (e.g., C/20) while continuously measuring the voltage. While faster than traditional OCV tests, the LO test often yields less accurate OCV-SOC curves due to polarization effects and other dynamic phenomena.
To address this, the proposed method first utilizes the LO test data to construct an initial OCV model using the DP algorithm and piecewise linear functions. The DP algorithm simplifies the OCV curve by removing unnecessary data points while preserving its overall shape, reducing computational complexity.
3.2 OCV Model Optimization using PSO
To further improve the accuracy of the OCV curve, the PSO algorithm is employed to optimize the initial OCV model. The PSO algorithm is a population-based optimization technique that mimics the social behavior of bird flocking and fish schooling . In this context, each particle represents a potential solution to the optimization problem, and the swarm’s movement is guided by the best solutions found so far (both individually and globally).
Four critical OCV points on the initial curve (two endpoints and two inflection points) are selected as variables. A follow-up model is then established for the remaining OCV points, allowing them to vary in response to changes in the four selected variables. The PSO algorithm iteratively adjusts these variables to minimize the Root Mean Square Error (RMSE) between the estimated and measured terminal voltages under dynamic conditions.
The optimization objective function is defined as:
textRMSE=N1k=1∑N(Mk−Ek(θ))2
where Mk is the measured voltage at time step k, Ek(θ) is the estimated voltage based on the current parameter set θ, and N is the total number of data points.
4. Experimental Setup and Data Collection
4.1 Test Battery
The experimental data used in this study were obtained from the Advanced Life Cycle Engineering Center at the University of Maryland. The test battery specifications are summarized in Table 1.
Table 1: Test Battery Specifications
| Parameter | Value |
|---|---|
| Battery Type | Lithium Iron Phosphate |
| Rated Voltage | 3.3 V |
| Rated Capacity | 1.1 Ah |
| Cut-off Voltage | 2.0 V / 3.6 V |
| Maximum Current | 30 A |
| Operating Temp. | 0°C – 50°C |
4.2 Data Collection
The LO test was conducted by fully charging the battery at a constant current and voltage, followed by discharging at C/20 while continuously measuring the voltage. The SOC was calculated using the ampere-hour integration method.
5. Results and Discussion
5.1 Initial OCV Model Construction
The DP algorithm was applied to the LO test data to construct an initial OCV model. the OCV curve obtained from the LO test and the simplified curve generated by the DP algorithm. The maximum error between the measured and simplified OCV points was 43.17 mV, with an absolute average error of 0.903 mV.
5.2 OCV Model Optimization
The PSO algorithm was then employed to optimize the initial OCV model. The optimized OCV curve, along with the reference OCV curve obtained from a traditional OCV test.
Under dynamic conditions (FUDS cycle at 25°C), the terminal voltage estimation error was significantly reduced. As shown in Table 2, the absolute average error and RMSE of the terminal voltage estimation based on the optimized OCV curve were 11.4 mV and 14.7 mV, respectively, representing an 83.5% reduction in absolute average error compared to the initial OCV model.
Table 2: Terminal Voltage Estimation Errors
| OCV Curve | Maximum Error (mV) | Absolute Average Error (mV) | RMSE (mV) |
|---|---|---|---|
| Initial OCV Model | 180.3 | 69.2 | 70.0 |
| Optimized OCV Curve | 166.1 | 11.4 | 14.7 |
| Reference OCV Curve | 465.3 | 16.1 | 19.6 |
5.3 SOC Estimation using AEKF
The Adaptive Extended Kalman Filter (AEKF) was utilized to estimate the SOC based on the optimized OCV curve and Thevenin model. The SOC estimation results under different temperatures (0°C, 25°C, and 50°C) are shown in Table 3.
Table 3: SOC Estimation Errors
| Temperature (°C) | OCV Curve | Maximum Error (%) | Absolute Average Error (%) | RMSE (%) |
|---|---|---|---|---|
| 0 | Optimized OCV Curve | 0.807 | 0.251 | 0.320 |
| Reference OCV Curve | 0.881 | 0.279 | 0.370 | |
| 25 | Optimized OCV Curve | 0.404 | 0.064 | 0.097 |
| Reference OCV Curve | 0.476 | 0.104 | 0.130 | |
| 50 | Optimized OCV Curve | 0.606 | 0.145 | 0.230 |
| Reference OCV Curve | 0.852 | 0.246 | 0.360 |
The SOC estimation errors based on the optimized OCV curve were consistently lower than those based on the reference OCV curve, with maximum errors ranging from 0.404% to 0.807% and absolute average errors below 0.3% across all temperatures.
6. Conclusion
This paper presents an optimization method for the OCV model of Lithium Iron Phosphate batteries based on Low-Current OCV test data. By leveraging the Douglas-Peucker algorithm, piecewise linear functions, and the Particle Swarm Optimization algorithm, the proposed method enables the rapid acquisition of high-fidelity OCV curves with significantly reduced testing time and costs. The optimized OCV curve results in a substantial reduction in terminal voltage estimation errors (83.5% lower absolute average error) and precise SOC estimation (errors below 0.3%) using the Adaptive Extended Kalman Filter. This work demonstrates the feasibility and effectiveness of the proposed method for improving SOC estimation in lithium-ion batteries, particularly for applications requiring rapid and accurate battery state assessment.