Discharge Ratio Optimization of Supercapacitor Storage for Size-Critical Applications

Supercapacitors (SCs) possess properties suitable for meeting power demands over a short duration, typically up to a few minutes. The size of an SC stack is influenced by the discharge ratio, defined as the ratio of minimum and nominal stack voltages. However, existing stack design algorithms present no clear guidelines for optimizing this design parameter to obtain minimal stack size. The discharge ratio is commonly set to an arbitrary value such as 50$\%$, but it has been found that an optimal choice of discharge ratio exists. This paper proposes a size-optimal discharge ratio (SODR) to minimize the size of SC stacks. The proposed SODR, which can be integrated into existing stack design algorithms, is derived analytically from considerations of load demand, power and energy densities, and the discharge efficiency of the stack. Based on the SODR, an iterative sizing algorithm for SC-only and SC/battery hybrid storage is proposed. The proposed sizing strategy is validated in simulation and in experiments on a 1 kW laboratory prototype, achieving up to 40$\%$ reduction in SC stack size compared to existing approaches.