Optimal charging of ultracapacitors during regenerative braking

Finding the optimal charging profile of an ultra-capacitor energy storage system during a regenerative braking event is the focus of this paper. After showing that resistive losses can be high during a high power regeneration event, we formulate the charging problem in an optimal control framework with the objective of maximizing the energy recuperated into the ultracapacitor bank while satisfying braking power demands. We employ Pontryagin's maximum principle to understand the necessary conditions the solution should satisfy and use numerical techniques to find such optimal solution(s). The result should provide more insight into the maximum achievable regeneration efficiency with ultracapacitors under different braking conditions and can also aid in sizing an ultracapacitor energy storage system and the associated power electronics device.