1. Introduction
With the rapid development of renewable energy, electrochemical energy storage system (EESS) have become indispensable for balancing energy supply and demand. Among energy storage devices, lithium iron phosphate (LiFePO₄) batteries are widely adopted due to their high energy density, long cycle life, and environmental friendliness. Accurate State of Charge (SOC) estimation is critical for optimizing battery management, enhancing safety, and prolonging the lifespan of lithium iron phosphate battery. Traditional SOC estimation methods, such as periodic or fixed-time estimation, suffer from limited coverage and significant steady-state errors. This study proposes an advanced SOC estimation framework that integrates multi-step observation equations, deep neural networks (DNN), and Open Circuit Voltage (OCV) verification to address these limitations.
2. Methodology
2.1 SOC Compensation Coefficient and Multi-step Observation Equation
Conventional SOC estimation for lithium iron phosphate battery oftens relies on single-point measurements, which fail to account for dynamic operating conditions. To overcome this, we first calculate the SOC compensation coefficient BB, derived from battery health, capacity, temperature, and cycle count:B=∑i=1nθi2−z⋅yθB=i=1∑nθi2−θz⋅y
where:
- θθ: Battery health coefficient
- zz: Temperature factor
- yy: Cycle discharge count
Next, a multi-step observation equation is established to expand the estimation range:[Dj(g)Dk(g)SOC(k)]=[eΔf−δ000e+1Δf−δ0001][Dj(g−1)Dk(g−1)SOC(k−1)]Dj(g)Dk(g)SOC(k)=Δfe−δ000Δfe+1−δ0001Dj(g−1)Dk(g−1)SOC(k−1)
where:
- Dj(g)Dj(g), Dk(g)Dk(g): Polarization voltages
- ΔfΔf: Frequency variation
- δδ: Decay factor
This equation enables real-time tracking of polarization effects and SOC dynamics under varying discharge rates.
2.2 Deep Neural Network Model for SOC Estimation
A DNN-based model is designed to integrate voltage, current, and temperature data for SOC estimation. The model leverages impedance characteristics of lithium iron phosphate battery, where impedance ZZ is expressed as:Z=Re(z)+j⋅Im(z)Z=Re(z)+j⋅Im(z)
- Re(z)Re(z): Real component (resistive losses)
- Im(z)Im(z): Imaginary component (capacitive effects)
The DNN architecture processes time-series data to predict SOC using the following relationship:ξ=(1−ζ2)⋅vξ=(1−ζ2)⋅v
where:
- ξξ: Estimated SOC
- ζζ: Impedance variation feature
- vv: Current differential
The model iteratively refines predictions by minimizing the loss function through backpropagation.
2.3 OCV Verification and Correction
OCV-SOC mapping is employed to correct estimation errors. Temperature and aging effects are compensated using:OCVcorrected=OCVmeasured⋅α(T,η)OCVcorrected=OCVmeasured⋅α(T,η)
where α(T,η)α(T,η) is a compensation factor for temperature TT and aging coefficient ηη. This step ensures robustness against environmental and operational variabilities.
3. Experimental Setup and Results
3.1 Test Configuration
Experiments were conducted under controlled conditions:
- Battery Specifications:
- Rated Capacity: 25 Ah
- Voltage Range: 2.16 V (min) to 4.25 V (max)
- Sampling Frequency: 1.25 Hz
- Ambient Temperature: 25°C
- Test Parameters:ParameterValueOCV6.5 VConstant Discharge Current10–12 AStatic Capacity20–28 AhTemperature Range18–25°C
Pulse discharge tests were performed at 50°C with intervals of 0.1 s, 0.3 s, and 0.5 s. Voltage and current data were collected to evaluate SOC estimation accuracy.
3.2 Performance Metrics
Steady-state SOC estimation errors were calculated using:H=πr+(1−φ⋅1Q)H=πr+(1−φ⋅Q1)
where:
- ππ: Pulse discharge initial value
- φφ: Discharge cycle
- QQ: Convergence speed
Results across four test cycles are summarized below:
| Cycle | SOC Error (0.1 s) | SOC Error (0.3 s) | SOC Error (0.5 s) |
|---|---|---|---|
| 1 | 0.26 | 0.32 | 0.37 |
| 2 | 0.17 | 0.28 | 0.35 |
| 3 | 0.13 | 0.25 | 0.24 |
| 4 | 0.11 | 0.14 | 0.19 |
The proposed method reduced steady-state errors to below 0.4 across all discharge durations, demonstrating superior generalization compared to traditional approaches.
4. Conclusion
This study presents a comprehensive framework for SOC estimation in lithium iron phosphate battery, combining multi-step observation equations, deep learning, and OCV correction. The method effectively addresses nonlinear dynamics, aging, and environmental variability, achieving steady-state errors below 0.4 under diverse discharge conditions. By enhancing the accuracy and reliability of SOC estimation, this work contributes to safer and more efficient management of electrochemical energy storage system. Future research will focus on real-time implementation and scalability for industrial applications.