Reduced order dynamical model for supercapacitors

A novel dynamical model for a single cell electric double-layer capacitor is proposed. The model was derived from a distributed-parameter electrochemical model, first reformulated and then approximated to reduce its order. Finite dimension approximations were obtained by applying finite differences, finite element and differential quadrature semidiscretization methods. The best approach was obtained with differential quadrature and the final result is a linear time invariant dynamical model relating the input current and the output voltage in the supercapacitor. The model has physical meaning, high accuracy, low order and few parameters, is controllable, observable and well suited for control design, dynamical analysis and numerical implementation.