The Effective Capacitance of a Constant Phase Element with Resistors in Series

The power of energy storage devices is characterized by capacitance and the internal resistance. The capacitance is measured on an assumption that the charges are stored at the electrode interface and the electric double layer behaves like an ideal capacitor. However, in most cases, the electric double layer is not ideal so a constant phase element (CPE) is used instead of a capacitor to describe the practical observations. Nevertheless, another problem with the use of the CPE is that CPE does not give capacitance directly. Fortunately, a few methods were suggested to evaluate the effective capacitance in the literature. However, those methods may not be suitable for supercapacitors which are modeled as an equivalent circuit of a CPE and resistor connected in series because the time constant of the equivalent circuit is not clearly studied. In this report, in order to study the time constant of the CPE and find its equivalent capacitor, AC and DC methods are utilized in a complementary manner. As a result, the time constants in the AC and DC domains are compared with digital simulation and a proper equation is presented to calculate the effective capacitance of a supercapacitor, which is extended to an electrochemical system where faradaic and ohmic processes are accompanied by imperfect charge accumulation process.