Design Considerations of Ultracapacitor Stack for Optimal Sizing of Energy Storage Systems in Contingency Applications

Ultracapacitors (UCs) today are playing an increasing role in the energy storage systems (ESSs) of several power conversion applications. In this article, a design method for optimal sizing of a UC stack is proposed, which minimizes the overall cost of the ESS. The problem is cast with normalized cost parameters of the ESS subsystem, using which the discharge ratio of the stack is optimized for the given ESS specifications. An iterative design algorithm is proposed which systematically engineers the stack parameters of unit cell capacitance, the number of series cells and parallel strings along with the initial and final stack voltage levels that meet the specified ESS requirements while also supplying the equivalent series resistance (ESR) loss. The iterative sizing process also factors in the maximum power transfer constraint imposed by the ESR to guarantee stable operation of the cost-optimal design even as the stack voltage varies during discharge. The design considerations, optimization framework, ESR effects, and the proposed sizing algorithm are synthesized in a generalized formulation in order to capture the variations in cost and subsystem parameter values that typically vary based on scaling requirements as well as the UC and power converter technology. Experimental results on a 4 kWmin UC stack validate the proposed cost-optimal design algorithm and the ESR induced voltage collapse.