Remaining discharge-time prediction for batteries using the Lambert function

Abstract

The prediction of the remaining discharge-time in real-time is an important Battery Management System indicator in many engineering applications. It is the time in which the battery satisfies the load demanded until the voltage reaches its admissible lower limit. It is often obtained by the difference between the current and final charge scaled by a constant discharge current. The final charge can be obtained using a simple battery model like a pure integrator which leads to a simple but inaccurate solution. A more precise estimation is obtained by running models that take into account the Rate Capacity Effect but they are time consuming. In this paper we propose to use the Lambert function for an accurate and fast prediction of the remaining discharge-time using a simple electrochemical model. We demonstrate that the errors in the prediction are similar to that obtained by running the well known electrical circuit. In order to illustrate the method, experimental parameter identification and remaining discharge-time predictions are carried out using a commercial Lithium-ion battery type.