Optimal charging of fractional-order circuits with Cuckoo search

A M AbdelAty; Mohammed E Fouda; Menna T M M Elbarawy; A G Radwan

doi:10.1016/j.jare.2020.11.014

Optimal charging of fractional-order circuits with Cuckoo search

J Adv Res. 2020 Dec 3:32:119-131. doi: 10.1016/j.jare.2020.11.014. eCollection 2021 Sep.

Authors

A M AbdelAty¹, Mohammed E Fouda^{2

3}, Menna T M M Elbarawy¹, A G Radwan^{2

4}

Affiliations

¹ Engineering Mathematics and Physics Dept., Faculty of Engineering, Fayoum University, Egypt.
² Engineering Mathematics and Physics Dept., Faculty of Engineering, Cairo University, Egypt.
³ Electrical Engineering and Computer Science Dept., University of California Irvine, Irvine, USA.
⁴ Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt.

Abstract

Introduction: Optimal charging of RC circuits is a well-studied problem in the integer-order domain due to its importance from economic and system temperature hazards perspectives. However, the fractional-order counterpart of this problem requires investigation.

Objectives: This study aims to find approximate solutions of the most energy-efficient input charging function in fractional-order RC circuits.

Methods: This paper uses a meta-heuristic optimization technique called Cuckoo search optimizer to attain the maximum charging efficiency of three common fractional-order RC circuits. An analytical expression of the fractional capacitor voltage is suggested such that it satisfies the boundary conditions of the optimal charging problem. The problem is formulated as a fractional-order calculus of variations problem with compositional functional. The numerical solutions are obtained with the meta-heuristic optimization algorithm's help to avoid the complexities of the analytical approach.

Results: he efficiency surfaces and input voltage charging curves are discussed for fractional-order in the range $0.5 < α \leq 1$ .

Conclusion: The optimized charging function can approximate the optimal charging curve using at most 4 terms. The charging time and the resistive parameters have the most dominant effect on charging efficiency at constant fractional-order $α$ .

Keywords: Cuckoo search optimizer; Fractional capacitor charging; Fractional-order circuits; Optimal charging.