Abstract
A model of electric batteries with a variable equivalent capacitance and internal dissipation is established. The control differential equation set of the battery voltage for maximum work output is obtained by using optimal control theory. Analytical solutions for the case with a constant equivalent capacitance are further obtained based on the general results, while numerical solutions in case of variable equivalent capacitance are provided. The optimal load matching and the selection of the discharging time are discussed, and influences of design parameters and boundary conditions on the optimisation performance are also analysed.
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