Order Reduction and Analysis of a Simplified Electrochemical Model for Electric Double-Layer Capacitors

A simplified electrochemical model of infinite order for electric double-layer capacitors is approximated through spatial semidiscretization. A family of reduced order models which are linear and time invariant, easy to analyze and implement, have few parameters and physical meaning is obtained. Three typical discretization methods are compared in time and frequency domains: finite difference, finite element and differential quadrature. In addition, two criteria to select the order of approximations are explored, one based on bandwidth and one on residue analysis. Differential quadrature based on polynomials proves to be the most accurate approximation, whereas the residue analysis criterion leads to lower order models. Finally, sufficient conditions to assure controllability and observability of the resulting lumped models are stated with the assumption of certain symmetry properties on the discretization matrices.