Conclusion
A battery model to represent the behavior under high frequency excitation, e.g. induced by the current ripple of power electronics, has been proposed. It is based on an equivalent circuit that consists of an inductive constant phase element that is approximated by an almost arbitrary number of RL-circuits. In this work, using three RL-circuits has shown good results continuously within a frequency range up to 100 kHz which should suffice for a broad variety of applications. Moreover, a capacitive constant phase element has been added to take mid frequency effects down to 1 Hz into account so that the simulation can remain accurate as the inductive behavior is affected by the capacitive one and vice versa [18]. It is convenient to also model the capacitive CPE with corresponding RC-circuits. To obtain the parameters of the model, electrochemical impedance measurements have been conducted in a frequency range from 1 Hz to 1 MHz. However, the data has been cropped at 100 kHz to achieve higher accuracy in the most important range for a lot of power electronic applications, see Fig. 10 and the middle part of graphic Figure 12. The equivalent circuit has been implemented into MATLAB/Simulink as a block diagram that has been given a battery current with severe ripple, originating from a half bridge DC/DC-converter, to validate its calculated voltage response. The results clearly indicate that the model delivers the anticipated results so that it might be considered to improve commercial battery models in battery energy systems such as electric vehicles or larger scale stationary battery systems, for they all have their battery systems connected to power electronics that induce high frequency ripple. At the present day, it is not yet well known, how the aforementioned current ripple affects the battery performance and especially if there is any severe effects on battery aging. A model like the one that is introduced in this work can play a key role in further investigating battery systems and answer questions that have arisen in this context.