Battery dynamic behaviour

The terminal voltage of a battery does not change instantaneously with current. Instead, it exhibits a dynamic response resulting from internal electrochemical processes. Understanding this behaviour is essential for developing mathematical models that accurately represent battery performance.

When a load current is suddenly applied, the battery voltage experiences an immediate drop caused by the internal ohmic resistance. This is followed by a gradual decrease in voltage as electrochemical polarization develops within the battery.

Similarly, when the current is removed, the terminal voltage does not immediately return to its Open Circuit Voltage. Instead, the voltage gradually recovers as the polarization effects dissipate over time. This recovery process is commonly referred to as voltage relaxation.

The dynamic response of a battery can therefore be divided into three regions:

• Instantaneous response caused by the internal ohmic resistance.
• Transient response caused by electrochemical polarization.
• Steady-state response represented by the Open Circuit Voltage.

The resistor-capacitor (RC) branches in the Thevenin model reproduce these transient voltage variations by introducing time-dependent voltage components. A first-order model represents a single polarization process, while a second-order model captures both fast and slow polarization dynamics, resulting in a more accurate representation of practical battery behaviour.

Before the parameters of the Thevenin model can be determined, the electrical characteristics of the battery must be measured experimentally. This process is known as battery characterization and provides the data required to identify the model parameters described in the next chapter.