ODE-Based Li-ion Charging Model

Battery Charging Dynamics & Degradation Modeling

This project simulates lithium-ion battery charging using a system of coupled ordinary differential equations. We capture state-of-charge (SOC), SEI growth, thermal behaviour, and transient overpotentials under different charging policies such as constant voltage, constant current, and pulsed profiles.

SOC evolution Thermal model SEI growth Custom charging policies

Run Simulation View ODE System

Project Overview

The core of this work is an ODE-based model of a lithium-ion cell under charge. The state vector is:

\[ y(t) = \big[ V(t), I(t), R(t), T(t), \text{SOC}(t), \text{SEI}(t), V_{\text{transient}}(t) \big] \]

Each mechanism (charging, thermal dynamics, SEI formation, and transient RC behavior) contributes a set of differential equations. These are summed into a total derivative \( \frac{dy}{dt} \), which is integrated via a 4th-order Runge–Kutta (RK4) scheme.

Model Structure

Mechanisms

The model is modular: each physical mechanism is implemented in its own class with a get_gradient(y, t, v_source) method returning contributions to \( \frac{dy}{dt} \).

Charging: SOC update based on applied current and nominal capacity.
Thermo: Ohmic heating and cooling toward ambient temperature.
SEI: Growth of the solid–electrolyte interphase, impacting long-term degradation.
Transient (optional): RC dynamics capturing overpotential effects.

Charging Policies

Charging is driven by a set of control policies from charging_policy.py. Each policy exposes a get_voltage(t, y) method that computes the source voltage based on the current state.

Constant Voltage (CV)
Constant Current (CC)
Pulse Charging
Sinusoidal Charging

Visit the Policies & Mechanisms page for details.

Goals of the Project

Compare how different charging policies affect SOC, temperature, and SEI growth.
Visualize transient responses during aggressive or high-frequency charging.
Connect physically meaningful ODEs to observable battery behavior.

Use the Simulation page to interactively explore how different policies influence battery state over time.