🔋 BMS State of Charge (SoC) Estimator via EKF

This project implements an Extended Kalman Filter (EKF) to estimate the State of Charge (SoC) of a Lithium-Ion battery. It simulates a realistic Battery Management System (BMS) environment, demonstrating how to compensate for sensor noise and voltage relaxation dynamics using sensor fusion.

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🧠 Overview

Accurate SoC estimation is critical for Electric Vehicle (EV) safety and range prediction. Simple voltage reading is insufficient due to the flat OCV curve of Li-Ion cells and internal resistance drops during acceleration.

This project solves this by:

1. Modeling the battery physics using a Thevenin Equivalent Circuit (1st Order).
2. Simulating real-world driving cycles (UDDS-like current pulses, discharge, regeneration).
3. Applying an EKF to fuse current integration (Coulomb Counting) with voltage feedback, correcting initialization errors and sensor noise.

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⚙️ Mathematical Modeling

1. State Space Model (Process)

The system state evolves according to:

$$ x_{k+1} = \begin{bmatrix} 1 & 0 \\ 0 & e^{-\Delta t / \tau} \end{bmatrix} x_k + \begin{bmatrix} -\frac{\Delta t}{Q_n} \\ R_1(1 - e^{-\Delta t / \tau}) \end{bmatrix} I_k $$

Where the state vector $x$ contains:

• $x[0] = SoC$ (State of Charge)
• $x[1] = V_{c1}$ (Polarization Voltage across the RC pair)

2. Observation Model (Measurement)

The measured terminal voltage $y_k$ is non-linear relative to the SoC:

$$y_k = OCV(SoC_k) - V_{c1, k} - I_k R_0$$

The EKF linearizes the $OCV(SoC)$ curve at each time step to compute the Kalman Gain ($K$), allowing the system to "lock" onto the true SoC even with high sensor noise (Gaussian white noise).

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🧩 Folder Structure

📂 BMS-SoC-Estimator
├── data/
│   └── drive_cycle.csv
├── images/
├── notebooks/
├── src/
│   ├── battery_model.py
│   ├── ekf.py
│   └── utils.py
├── tests/
├── validation/
│   └── validate_model.m
├── main.py
└── requirements.txt

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🚀 How to Use

1. Installation

git clone https://github.com/VoIkmer/BMS-SoC-Estimator.git
cd BMS-SoC-Estimator
pip install -r requirements.txt

2. Generate Data (Optional)

python generate_data.py

3. Run the Simulation

python main.py

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📊 Results

EKF Convergence Test

The filter successfully converges from an incorrect initial estimate:

• Real SoC: 80% (0.8)
• EKF initial guess: 50% (0.5)

Figure: Full simulation showing the EKF (Red) correcting the initial error and tracking the Real SoC (Green) despite current fluctuations.

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🛠️ Tech Stack

Component Technology Description

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Core Logic Python 3.12 EKF implementation Math Engine NumPy Matrices and Jacobians Visualization Matplotlib Plotting Validation MATLAB Cross-check implementation

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❓ FAQ (Frequently Asked Questions)

1. Why use an Extended Kalman Filter (EKF) instead of simple Coulomb Counting?

Coulomb Counting (current integration) is precise in the short term but suffers from drift—small sensor errors accumulate over time, leading to huge inaccuracies after hours of operation. The EKF fuses this integration with voltage measurements to "correct" the SoC estimate in real-time, preventing drift even if the initial guess is wrong.

Figure: Comparison showing Coulomb Counting (Blue) failing to correct an initial error, while EKF (Red) converges to the True SoC (Green).

2. Why not just measure the battery voltage to determine SoC?

Lithium-Ion batteries have a very flat OCV (Open Circuit Voltage) curve between 20% and 80% charge. A voltage change of just 0.01V could represent a 10% difference in charge. Additionally, under load, the terminal voltage drops due to internal resistance ($R_0$). The EKF enables us to estimate SoC accurately even inside this "flat region" and under heavy load.

Figure: Example of a flat OCV curve.

3. Is this code ready for an embedded microcontroller (e.g., STM32, ESP32)?

This Python project serves as a Model-in-the-Loop (MIL) validation. For embedded deployment, the matrix operations (currently handled by NumPy) would need to be ported to C/C++ using a library like CMSIS-DSP or Eigen. However, the logic and the State-Space matrices remain exactly the same.

4. How did you validate the physics model?

The model was cross-validated using a MATLAB script (available in the validation/ folder). The outputs from both Python and MATLAB were compared, yielding a Mean Squared Error (MSE) lower than $10^{-4}$, confirming that the discrete-time implementation of the differential equations is mathematically sound.

Figure: Overlay of Python implementation vs MATLAB reference. The curves are indistinguishable, validating the math engine.

5. Why do we see voltage recovery when the current stops?

This is the relaxation effect caused by the polarization of Lithium ions. It is modeled in this project by the RC parallel branch ($R_1, C_1$) in the Thevenin circuit. The EKF uses this recovery curve to refine its internal estimation of the battery's true chemical state.

Figure: The OCV curve of a Li-Ion battery. Note the flat region where voltage barely changes despite huge capacity variation.

🧑‍💻 Author

Carlos Eduardo
Electrical Engineering Student — UFBA

• Email: cguimaraesbarbosa03@gmail.com
• GitHub: VoIkmer
• LinkedIn: carl0sedu

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📚 License

Licensed under the MIT License.