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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.

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Obtaining precise reducer order battery models is a key component in designing lithium-ion battery management systems. In general, with conventional order reduction techniques, low order is followed by low accuracy. To overcome such limitation, this paper presents a frequency-based constructive method to obtain broad-band low-order approximations of the solid-phase lithium-ion diffusion submodel, the core of the reference pseudo-two-dimensional electrochemical model of lithium-ion cells. The proposed method is a combination of an improvement on the residue grouping technique and of standard balancing and truncation/residualization methods borrowed from control systems theory. As main result, dramatic order reductions from 3000th to 5th-order with minimum accuracy losses are obtained. Taking a well-known case-study of a lithium-ion battery model, it is shown that 5th-order models offer approximations with maximum absolute errors of 0.5%, for characteristic times up to 9.54 × 10 4 s . The proposed method will help to obtain accurate real-time estimations of surface concentration and state of charge of lithium-ion batteries.

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