Optimized OCV Modeling for Accurate SOC Estimation in Lithium Iron Phosphate Batteries

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Accurate estimation of the state of charge (SOC) in lithium iron phosphate batteries relies heavily on the relationship between SOC and open-circuit voltage (OCV). This study presents a novel OCV modeling and optimization method to address challenges in low-current OCV (LO) testing, enabling high-precision SOC estimation while minimizing testing costs.

Lithium Iron Phosphate Battery Structure

1. Battery Modeling and OCV Characterization

The Thevenin equivalent circuit model effectively captures the dynamic behavior of lithium iron phosphate batteries:

$$
\begin{cases}
U_p = -\frac{U_p}{C_p R_p} + \frac{I_L}{C_p} \\
U_t = U_{OC} – U_p – I_L R_0
\end{cases}
$$

Discrete-time implementation enables real-time SOC estimation:

$$
\begin{cases}
U_{p,k} = U_{p,k-1}e^{-\frac{\Delta T}{C_p R_p}} + I_{L,k-1}R_p\left(1 – e^{-\frac{\Delta T}{C_p R_p}}\right) \\
U_{t,k} = U_{OC,k} – U_{p,k} – I_{L,k}R_0
\end{cases}
$$

2. Advanced OCV Modeling Methodology

The proposed OCV modeling framework combines Douglas-Peucker algorithm with piecewise linear functions:

$$
V = V_i + \frac{(V_{i+1} – V_i)(S – S_i)}{S_{i+1} – S_i}, \quad S_i < S < S_{i+1}
$$

Table 1. Key Parameters of Lithium Iron Phosphate Battery
Parameter Value
Nominal Voltage 3.3 V
Capacity 1.1 Ah
Voltage Range 2.0-3.6 V

3. Particle Swarm Optimization Framework

The optimization process employs four critical OCV points as variables:

$$
\theta = [OCV_1, OCV_2, OCV_3, OCV_4, R_0, R_p, C_p]
$$

Objective function minimizes terminal voltage estimation errors:

$$
RMSE = \sqrt{\frac{1}{N}\sum_{k=1}^N (M_k – E_k(\theta))^2}
$$

Table 2. OCV Optimization Results at 25°C
Parameter Initial Optimized
OCV₁ (0% SOC) 1.9997 V 2.0000 V
OCV₂ (9.88% SOC) 3.1776 V 3.2441 V
R₀ 0.164 Ω 0.159 Ω

4. Adaptive Extended Kalman Filter Implementation

The AEKF algorithm enhances SOC estimation robustness:

$$
\begin{cases}
x_k^- = A_k x_{k-1}^+ + B_k u_k \\
P_k^- = A_k P_{k-1} A_k^T + Q_k \\
K_k = P_k^- C_k^T (C_k P_k^- C_k^T + R_k)^{-1}
\end{cases}
$$

Table 3. SOC Estimation Performance Comparison
Temperature Method Max Error RMSE
25°C Conventional 0.476% 0.130%
Optimized 0.404% 0.097%
50°C Conventional 0.852% 0.360%
Optimized 0.606% 0.230%

5. Key Advantages for Lithium Iron Phosphate Batteries

The proposed method demonstrates significant improvements:

  • 83.5% reduction in terminal voltage estimation error
  • Sub-0.3% absolute SOC estimation error across temperatures
  • 79% reduction in OCV modeling RMSE

This methodology enables rapid acquisition of high-precision OCV characteristics for lithium iron phosphate batteries while significantly reducing testing time and resource requirements. The optimized models maintain exceptional performance across various operating conditions, making them particularly suitable for electric vehicle applications where battery management system efficiency is critical.

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