🔋 Battery SOC Estimation using Equivalent Circuit Models, EKF, and Embedded Implementation

📌 Overview

This project presents a model-based approach for estimating the State of Charge (SOC) of a lithium-ion battery using:

• A first-order equivalent circuit model (1RC)

• A 1-state Extended Kalman Filter (EKF) for baseline SOC estimation

• A 2-state EKF with states:

  • SOC
  • V_RC

• A lightweight embedded-oriented implementation

• A C-based firmware-style implementation

• Python vs C validation of the estimator

The project demonstrates a complete workflow from battery simulation to embedded-friendly implementation and estimator improvement.

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🎯 Objective

• Simulate battery voltage and current behavior under dynamic load conditions
• Estimate SOC using model-based methods
• Compare true SOC and estimated SOC
• Improve estimation accuracy by extending the EKF state model
• Develop an embedded-oriented implementation
• Translate the estimator into C for firmware-oriented deployment
• Validate the C implementation against the Python reference

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⚙️ Methodology

1. Battery Modeling

• First-order RC equivalent circuit model
• Nonlinear OCV-SOC relationship
• Terminal voltage model:

V_terminal = OCV(SOC) - I*R0 - V_RC

2. Python Simulation

• Time-domain current profile
• Terminal voltage response
• SOC propagation using current integration

3. 1-State EKF

The initial EKF formulation estimated only:

• SOC

This provided a baseline estimator and enabled:

• Q/R tuning
• sensitivity analysis
• embedded-oriented reformulation

4. EKF Tuning

Different Q/R combinations were evaluated to improve robustness under noisy voltage measurements.

Best tuning result from the 1-state EKF stage:

• Q = 1e-6
• R = 1e-2

5. 2-State EKF

The EKF was extended to estimate:

• SOC
• V_RC

This reduced the mismatch between the estimator and the battery simulation model and significantly improved estimation accuracy.

6. Embedded-Oriented Implementation

• Step-based estimator update
• Lightweight structure for real-time use
• Reduced computational complexity

7. C Firmware-Style Implementation

• Struct-based estimator state
• EKF logic implemented in C
• 2-state EKF replay using simulation-generated data

8. Validation

• Python EKF output compared with C EKF output
• Matching results confirm correct translation of the estimator logic

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📊 Example Results

🔹 Current Profile

🔹 Voltage Response

🔹 2-State EKF SOC Comparison

🔹 2-State EKF V_RC Comparison

🔹 2-State EKF SOC Error

🔹 Python vs C Validation (SOC)

🔹 Python vs C Validation (V_RC)

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✅ 2-State EKF Improvement

To improve estimation accuracy, the EKF was extended from a 1-state formulation to a 2-state model:

• SOC
• V_RC

This improved consistency between the estimator and the battery simulation model.

Performance

• MAE: 0.000477
• RMSE: 0.000597

This result shows a clear improvement over the simpler 1-state EKF approach.

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✅ Python vs C Validation for 2-State EKF

The 2-state EKF was implemented both in Python and in firmware-style C.

SOC Error Validation

V_RC Error Validation

Validation Metrics

• SOC MAE: 0.00046861
• SOC RMSE: 0.00058532
• V_RC MAE: 0.00035691
• V_RC RMSE: 0.00044748

These results confirm that the C implementation closely matches the Python 2-state EKF reference.

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📁 Project Structure

battery-soc-estimation/
│
├── src/
│   ├── main.py
│   ├── ekf_soc.py
│   ├── embedded_soc_step.py
│   ├── test_embedded_soc.py
│   └── compare_results.py
│
├── c_version/
│   ├── ekf_soc.h
│   ├── ekf_soc.c
│   └── main.c
│
├── data/
├── results/
├── figures/
│
├── README.md
└── requirements.txt

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▶️ How to Run

Python Version

Install dependencies:

pip install numpy matplotlib pandas

Run the main simulation:

python src/main.py

Run embedded-oriented simulation:

python src/test_embedded_soc.py

Run Python vs C comparison:

python src/compare_results.py

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C Version

Compile:

gcc main.c ekf_soc.c -o ekf_test -lm

Run:

./ekf_test

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📈 Output

The project generates:

• Current profile plot
• Voltage response plot
• Noisy voltage measurement plot
• 2-state EKF SOC comparison
• 2-state EKF V_RC comparison
• 2-state EKF SOC error plot
• Python vs C validation plots
• CSV output files for further analysis

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✅ Validation Summary

The C implementation was validated against the Python 2-state EKF reference implementation.

The final comparison showed that the C implementation closely matches the Python output, confirming that the estimator logic was correctly translated into a firmware-style implementation.

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🚀 Features

• Physics-based battery modeling
• 1-state EKF baseline estimator
• Q/R tuning workflow
• 2-state EKF with improved model fidelity
• Embedded-oriented algorithm design
• C firmware-style implementation
• Python vs C validation

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🔧 Future Work

• Port the 2-state EKF to MCU-specific real-time deployment
• Include temperature effects
• Improve the battery model further (e.g. 2RC model)
• Validate with real battery datasets
• Deploy on STM32 / Arduino
• Explore fixed-point implementation for embedded targets

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🧠 Key Takeaway

This project demonstrates how model-based battery estimation can be developed in Python, improved through EKF state augmentation, adapted for embedded-oriented execution, translated into C, and validated across implementations.

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👤 Author

Hossein Electronics Engineer