Extended Thevenin model is described by the following system of differential equations:

Where $I$ is the input current, $U_t$ is the terminal voltage, $U_{oc}$ is the Cell open-circuit voltage (a function of SoC), $R_0$ is the Cell internal resistance, and $R_{1,2}$, $C_{1,2}$, and $U_{1,2}$ model the Cell diffusion voltage.

Extended Thevenin model can be used in the following algorithms:

- Estimating State of Charge with an adaptive extended H-infinity filter
- Estimating State of Charge with Kalman Filter
- Stochastic estimator of cell parameters based on an electrical cell model
- Estimator of cell parameters based on particle swarm optimisation

See also:

[1] Digital twin for battery systems: Cloud BMS with online SoC and SoH estimation