Methodology to Obtain the Voltage-Dependent Parameters of a Fourth-Order Supercapacitor Model With the Transient Response to Current Pulses

In order to design power circuits including supercapacitors, a model that responds as closely as possible to results in actual tests, in both fast and slow transients, is required. The network of the parallel RC branches model is widely used to justify the electrical behavior of supercapacitors. In that model, in order to achieve a good fitting between simulation and actual transient responses, the interdependence among the parameters, as well as their voltage dependence, must be considered. This study presents a method to deduce the parameters of the RC network model through the transient response of the supercapacitor including theirs voltage dependence. The methodology considers that the electrical charge provided to the device in the current pulses is not only injected in the fastest branch, but also is simultaneously distributed toward the slower branches. A set of tests have been carried out through the whole voltage range of the device in such a way that in each one the parameters can be considered constant. Then, with the obtained series of values for each parameter, their voltage dependence has been deduced through linear regression. Practical results of a fourth-order model with voltage-dependent parameters are presented and compared with simulations.