This work presents an improved pulse-fitting method for the parameter extraction of equivalent circuit models from pulse tests using an evolutionary algorithm (Differential evolution). The focal point of the work is the improvement of existing battery modelling by utilizing global instead of local optimization for the pulse-fitting, and the usage of high-order models. The n-RC model is hereby series-connected with RL (parallel connection of inductance and resistance) to describe the inductive behaviour. The pulse tests have been performed over the entire SOC in 2%-steps, including a full charge and discharge process. The results conclude that precise modelling requires the identification of fast to considerably slow processes. To capture especially fast processes, an extended high-order equivalent circuit model is introduced to evaluate pulse tests with a sampling rate of 100 kHz necessary to describe the high frequency capacitive and inductive behaviour. To verify the results, the estimated parameters from pulse-fitting are used to evaluate the impedance spectrum of the cell and compared to an electrochemical impedance spectroscopy. The results are consistent and the approach has been verified for three battery types: two NMC with a graphite anode and one NMC-cell with a graphite-silicon anode.