Modeling battery efficiency with parallel branches

Most contemporary battery models are series-models based on electrochemical principles. Describing the charge/discharge efficiency of a battery is a complex issue and of major importance in the design of control systems in future cars (combined 42 V and 14 V systems). Not only does battery efficiency strongly depend on current levels, it also varies greatly with frequency. In this paper a parallel equivalent model is introduced to get a good grip on this matter. A general description of efficiency as a function of frequency, current level and initial voltage is presented. The parallel model regards the battery as a system with multiple parallel buffers and yields a different perspective on the energy distribution and distribution of losses in a battery. Furthermore, dynamic behavior is easily explained. Depending on the spectral load and required accuracy, it is possible to simplify the parallel model. Identification techniques for both linear and nonlinear model identification are presented. It appears that the nonlinear parallel model is not capable of modeling the battery for the full frequency range. However, the identification techniques can be modified to apply to other model structures as well.