Parameter Determination for the Battery Equivalent Circuit Model Using a Numerical Integro-Differential Method

The battery equivalent circuit model consisting of an open circuit voltage (OCV) source and a resistor in series with parallel resistor-capacitor (RC) elements is widely used in system-level simulation. The accuracy of the transient I-V characteristics of the battery model strongly relies on the values of the RC parameters prescribed in the circuit. One of the solutions for determining RC parameters is curve-fitting the measurement data of the battery voltage in the relaxation period obtained from a charge or discharge current pulse test. Since the equation used for curve-fitting can be expressed as the sum of multiple exponential functions which are nonlinear with respect to the RC parameters, the nonlinear least-square (LS) algorithm shows poor performance or even fails due to its sensitiveness to initial guesses of the solutions.

One approach that makes use of the unique feature of the sum of two exponentials reformulates the nonlinear voltage equation to a linear one and calculates out the RC parameters using the linear LS algorithm. However, the approach cannot be applied to the model with more than two RC elements. In this work, an integro-differential method is applied to the nonlinear problem arisen from curve-fitting the RC parameters. As a result, the nonlinear equation containing the sum of multiple exponential functions can be linearized. An application example demonstrates that the LS algorithm applied to the resulting linear equation shows no sensitivity to the initial conditions and good accuracy can be achieved.