Generally, two different ECM fitting strategies are followed. Effective models can be devised, where the dominant processes for the impedance response are macroscopically represented by suitable equivalent circuit elements. This approach facilitates direct fitting of the data, and the obtained ECM may be used as the basis for a digital twin of a battery. Residuals are reduced by increasing the number of circuit elements, but this does not necessarily improve the physical meaning of the fit and may lead to over-fitting.