Adiabatic charging and discharging method with minimum energy dissipation for a variable-gap capacitor system

This study considers a method for minimising the energy dissipation when charging a variable-gap capacitor. The authors assume a capacitor coupled with repulsive mechanical potential energy. The potential energy is proportional to 1/dⁿ, where d is the plate distance. With this capacitor model, the authors use the method of Lagrange multipliers to investigate a way to minimise the energy dissipation. When n = 3 (Q = pV² is satisfied in this case), the authors confirm that the conventional equal-step charging does not minimise the energy dissipation. From the viewpoint of the charge transfer per step, conventional constant-charge-transfer charging does not minimise the energy dissipation, but increasing-charge-transfer charging (small charge transfer at the initial step and large charge transfer at the final step) does minimise the energy dissipation. From analyses of the charging and discharging processes, it becomes clear that the ratio of energy dissipations between the conventional and proposed methods approaches 0.89 when the step number increases. This means the proposed method reduces the energy dissipation by 11% compared with the conventional one. A circuit that enables the minimum energy dissipation as discussed above is also described.