On the optimization of energy extraction from a supercapacitor under an impulse load

The problem of energy extraction from a supercapacitor (within the given duration $\tau$) under an impulse load has been considered. It has been shown that for each $\tau$ there exists an optimal load value at which the maximum energy will be released. In a simple model of a single $RC$ element the problem can be solved analytically. For more complex models of supercapacitors (such as self-similar ladder $RC$ networks, tree-like RC networks, etc.), numerical simulations have been conducted. The simulations have shown that the sharpness of the maximum decreases with increasing $\tau$ and with the degree of distributiveness of $RC$ network. A computer program has been developed to model impulse loads directly in the time domain for any equivalent supercapacitor circuit. This allows to consider nonlinear systems and avoid the need for complex conversion of impedance $Z(\Omega)$ into the time domain. The developed approach (together with the simulation program) can be directly applied to solving practical problems related to the impulse operation mode of supercapacitors.