Analytical Formulation for Power, Energy, and Efficiency Measurement of Ultracapacitor Using Fractional Calculus

Reliability of any electrical system heavily depends on the accuracy of the model used for representing the integrated device components. The design of renewable power sources and energy management systems using ultracapacitor demands adoption of precise mathematical representation of ultracapacitor dynamics. An appropriate model of ultracapacitor not only allows an accurate assessment of its charge/discharge characteristics but also provides a precise estimation of energy storage and power delivery capabilities. However, due to the lack in the usability of data/information provided by the manufacturer, conventional calculus-based ultracapacitor modeling and energy estimation approach often leads to its inaccurate and inefficient utility. In this regard, this paper has focused on fractional calculus-based analytical formulation for power, energy, and efficiency measurement of ultracapacitor and has deployed an upgraded model of the ultracapacitor, which in turn provides a better estimation of its energy efficiency. The work presented in this paper has been supported by extensive experimentation with the ultracapacitor under different input excitations, considering the dependence of energy storage (state of energy) and power delivery capacity of ultracapacitor on the charge/discharge profile. Furthermore, the hybrid optimization-based analysis recommends the requirement and challenges for the design and development of optimal charging/discharging of ultracapacitors for achieving higher energy efficiency.