Time domain simulations of constant phase elements using IIR filter
ABSTRACT: Time domain simulations of electrochemical systems like batteries or super capacitors are important for example in electric vehicles or stationary uninteruptable power supplies. Time domain simulations for example are used for predicting the behavior. For time domain simulations adequate online simulation models and methods are required that sufficiently precise describe the underlying physical mechanisms and require only short computation time and small memory. In the frequency domain a lot of well matching impedance models have been developed to describe them. Many of these impedance models models contain constant phase elements that are difficult for direct time domain simulations. In control theory methods are available for the time domain simulation of systems showing constant phase element behavior. In this work these methods are adopted and applied for battery simulation. The transfer function of a constant phase element first is approximated by an ordinary differential equation. Second the battery voltage is simulated using digital filters. Simulation results for a 18650 lithium ion battery during 1000s show a maximum relative voltage deviation of less than 1%. Because of the small resource requirements the method is well suitable for online predictions in battery management systems.