Parameter determination for the battery equivalent circuit model using a numerical integro-differential method 2020-01-1179
The battery equivalent circuit model (ECM) consisting of an open circuit voltage (OCV) source and a resistor in series with multiple resistor-capacitor (RC) elements is widely used in system simulation. It can predict both instantaneous and transient voltage response to a dynamic current. The accuracy of the model results relies on the values of the RC parameters prescribed in the ECM. One of the solutions for determining the RC parameters is curve-fitting the measurement data of the battery voltage in the relaxation period corresponding to a charge or discharge current pulse. Since the equation for describing the voltage contains multiple exponential decays, the least-square (LS) algorithm such as the Levevberg-Marquadt (LM) algorithm is sensitive to the initial guesses of the parameters given in the equation. A previous approach that reformulates the nonlinear equation into a linear one converts the nonlinear problem to a linear one, by which good performance of the LS algorithm has been achieved. However, it is restricted to the application of the ECM with two RC elements because the linear equation obtained becomes too complicated to be useful for the ECM with more than two RC elements.
In this work, a numerical integro-differential method is applied to the nonlinear problem arisen from the ECM with more than two RC elements. As a result, a linear equation instead of the original nonlinear one is obtained and used for the description of the ECM. Numerical examples demonstrate that the LM algorithm applied to the linear equation shows no sensitivity to the initial conditions and good accuracy of identification results of multiple RC elements can be achieved.