A Nonlinear Model Based Analysis and Accurate Design of Ultracapacitor Stack for Energy Storage Systems

Sizing of ultracapacitor (UC) stack is an essential requirement in the design of energy storage systems (ESS), which are widely deployed today in varied power conversion applications. Unlike a linear capacitor that displays constant capacitance characteristics over the operating voltage range, UCs exhibit considerable nonlinearity in the form of voltage-dependent capacitance and display notable variation in characteristics during operation. Analyzing the behavior of the overall UC bank that consists of several stacked nonlinear UC cells and evaluating its effective capacitance is therefore critical. In this paper, an exact-analysis framework is presented for characterizing the nonlinear behavior of the overall UC stack. Closed-form expressions for the UC stack’s effective voltage-dependent capacitance, terminal voltage characteristics, and stored energy are derived as a function of unit cell nonlinear parameters and the number of series-parallel cells, using which the deviations in the UC stack behavior from the linear characteristics are analytically captured. It is shown, owing to the linear model of the UC employed in existing design methods, that the resultant stack will either be (a) over-sized and expensive, or (b) insufficient to meet the ride-through specifications in practice as the inherent nonlinearity is ignored. To address these limitations, an improved UC stack design method is proposed based on the nonlinear UC model, which not only optimizes the size of the UC stack, but also guarantees that the ESS specifications are accurately met. Experimental results on two UC stack hardware prototypes validate the accuracy of the proposed nonlinear analysis and the improved design method for ride-through applications.