Optimal charging of fractional-order circuits with Cuckoo search

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≤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

• Fractional capacitor charging
• Fractional-order circuits
• Optimal charging
• Cuckoo search optimizer