First-order Thevenin model

The first-order Thevenin model is one of the simplest Equivalent Circuit Models used to represent the electrical behaviour of a rechargeable battery. It combines an ideal voltage source with resistive and capacitive elements to reproduce both the instantaneous and transient voltage response observed during battery operation.

The model consists of four main components:

• Open Circuit Voltage (OCV)
• Ohmic resistance ($R_0$)
• Polarization resistance ($R_1$)
• Polarization capacitance ($C_1$)

Figure 4.2: First-Order Thevenin Model

Open Circuit Voltage (OCV)

The Open Circuit Voltage represents the equilibrium voltage of the battery when no current is flowing. It depends primarily on the battery's State of Charge and serves as the main voltage source in the model.

During battery operation, the OCV changes as the amount of stored charge changes. The relationship between OCV and SoC is obtained experimentally through Open Circuit Voltage characterization.

Ohmic resistance ($R_0$)

The resistance $R_0$ represents the instantaneous voltage loss caused by the internal resistance of the battery. This resistance includes contributions from the electrode materials, electrolyte, current collectors, and electrical connections.

Whenever current flows through the battery, an immediate voltage drop occurs according to Ohm's law. This effect is represented by $R_0$.

Polarization resistance ($R_1$)

The resistance $R_1$ represents the slower voltage losses associated with electrochemical polarization inside the battery.

Unlike the instantaneous voltage drop produced by $R_0$, the polarization voltage changes gradually as the battery responds to changes in current.

Polarization capacitance ($C_1$)

The capacitance $C_1$ stores electrical charge within the RC network and determines how quickly the polarization voltage changes over time.

Together, $R_1$ and $C_1$ form a first-order RC network that models the transient voltage behaviour of the battery following a change in load current.

The first-order Thevenin model provides a good representation of battery behaviour under many operating conditions. However, practical batteries often exhibit multiple polarization processes with different response times that cannot be accurately represented by a single RC network.