Second-order Thevenin model

Although the first-order Thevenin model captures the primary electrical behaviour of a battery, practical batteries exhibit multiple electrochemical processes that occur over different time scales. A single RC network cannot accurately represent both fast and slow polarization effects during dynamic operating conditions.

To improve modelling accuracy, the second-order Thevenin model introduces a second resistor-capacitor (RC) network. This additional branch enables the model to represent two independent polarization processes simultaneously, resulting in a more accurate prediction of the battery's transient voltage response.

The second-order model consists of:

• Open Circuit Voltage (OCV)
• Ohmic resistance ($R_0$)
• First RC branch ($R_1$, $C_1$)
• Second RC branch ($R_2$, $C_2$)

The first RC branch models the faster polarization dynamics that occur immediately after a change in current. The second RC branch represents slower electrochemical processes that continue to influence the terminal voltage over a longer period.

Polarization resistance ($R_2$)

The resistance $R_2$ represents the slower polarization effects that are not captured by the first RC branch. It contributes to the gradual voltage recovery observed after charging or discharging pulses.

Polarization capacitance ($C_2$)

The capacitance $C_2$ determines the time constant associated with the second polarization process. Together, $R_2$ and $C_2$ model the slower transient behaviour of the battery.

By combining two RC networks, the second-order Thevenin model provides a significantly better representation of the voltage response of lithium-ion batteries during rapidly changing load conditions while maintaining relatively low computational complexity.

For this reason, the second-order Thevenin model is widely used in Battery Management Systems and forms the battery model adopted throughout this manual.