Capacitance measurement and parameter estimation method for supercapacitors with variable capacitance

Abstract: Estimating the parameters of capacitance function is important for supercapacitor manufacture and integration. The estimated parameters are useful for fault monitoring and health state identification. Because the capacitance can't be measured directly, indirect measurement model is needed. The capacitance of supercapacitor has relation with voltage or current. The existing methods of supercapacitor parameters estimation have poor performance on variable capacitance and poor adaptability with signal noise. According to the disadvantages of existing methods, a capacitance measurement and parameter estimation method for variable capacitance of supercapacitors was proposed in this paper. This method included two parts: a measurement model; and parameter estimation. The time variable parameter classic model with variable capacitance was used to simulate the time variance character of supercapacitor. Based on this model, a new method was inferred. In this method, the equations based on charge and energy conservation were used to form measuring equation group. Trapezoid formula was applied to solve discrete integral in the equation group. By solving equation groups, the capacitance in every sampling time was measured indirectly. As result, the time series of capacitance were expressed by stack of voltage and current. After bringing the measured voltage and current into the expression of capacitance, the time series of capacitance were obtained. After the capacitances were measured indirectly, the fixed memory least squares method was applied on the time series of capacitance to estimate the parameters of capacitance function. Two simulation experiments based on Matlab were conducted to verify the capacitance measurement and parameter estimation. In these experiments voltage source and load resistance were used to make the supercapacitor charge and discharge randomly. In the first experiment, we used four different functions of the capacitance to test the adaptability of measurement. Comparisons were made between methods, published one in the literature and the ones proposed in this paper. When the capacitance was constant, the average relative error of measurement was 1.51%. The error of reference group was 8.23%. When the capacitance was linear function, the average relative error of measurement was 3.74%. The error of reference group was 36.15%. When the capacitance was quadratic polynomial function, the average relative error of measurement was 11.04%. The error of reference group was 100%. When the capacitance was exponent function, the average relative error of measurement was 26.85%. The error of reference group was 100%. This result showed that the new method was effect under four situations while the reference method was only effect in the situation of that the capacitance was constant and the capacitance was linear function. The second experiment was done with two types of capacitance functions to verify the method under measurement noise. The white Gaussian noise was added into the measured signal to simulate the practical situation. When the capacitance was linear function of current, the average relative errors of measurement were 0.6% and 7%. When the capacitance was quadratic polynomial function of voltage, the average relative errors of measurement were 10.62%, 19.7% and 11.5%. The result showed that the new method was effective under white Gaussian noise. The reference simulation of capacitance measurement based on an existing method was made. The reference method is a computing capacitance method. The result showed that the proposed method had lower error than the reference method. The experiment result supported that the proposed method in this paper was adaptive for different function of capacitance and the method was effect under additive white Gaussian noise on voltage and current signal.