Equivalent Circuit Model

An equivalent circuit model (ECM) is a phenomenological model widely used in industry to simulate the voltage response for subsequent Battery Management System control and state estimation.

By conducting experiments to measure the battery voltage at various SoCs and temperatures it is possible to develop an ECM that relates the applied current and the voltage. 

first order equivalent circuit model
A first order Equivalent Circuit Model describing the terminal voltage (Vl) of a battery to a given applied current (I). U(z) is the OCV vs SoC look-up-table and the losses are modelled via resistor and capacitor elements that change with SoC (z) and temperature (T).

Battery Cell Modelling

The primary reason why one is interested in having a model of a battery is it allows us to make informed decisions, optimise or control a battery to deliver on its intended applications. For instance, we may be interested in knowing how different material choices, electrode compositions or cell packaging, will influence the electrochemical and thermal performance of the cell, a model can serve this purpose.