In this paper, we discuss the optimal charging and discharging of supercapacitors to maximize the delivered energy by deploying the fractional and multivariate calculus of variations. We prove mathematically that the constant current is the optimal charging and discharging method under R s -CPE model of supercapacitors. The charging and round-trip efficiencies have been mathematically analyzed for constant current charging and discharging. © 2020 The Electrochemical Society (“ECS”). Published on behalf of ECS by IOP Publishing Limited.
A Study on Fractional Power-Law Applications and Approximations
The frequency response of the fractional-order power-law filter can be approximated by different techniques, which eventually affect the expected performance. Fractional-order control systems introduce many benefits for applications like compensators to achieve robust frequency and additional degrees of freedom in the tuning process. This paper is a comparative study of five of these approximation techniques. The comparison focuses on their magnitude error, phase error, and implementation complexity. The techniques under study are the Carlson, continued fraction expansion (CFE), Padé, Charef, and MATLAB curve-fitting tool approximations. Based on this comparison, the recommended approximation techniques are the curve-fitting MATLAB tool and the continued fraction expansion (CFE). As an application, a low-pass power-law filter is realized on a field-programmable analog array (FPAA) using two techniques, namely the curve-fitting tool and the CFE. The experiment aligns with and validates the numerical results. © 2024 by the authors.
Fractional-Order Equivalent-Circuit Model Identification of Commercial Lithium-Ion Batteries
The precise identification of electrical model parameters of Li-Ion batteries is essential for efficient usage and better prediction of the battery performance. In this work, the model identification performance of two metaheuristic optimization algorithms is compared. The algorithms in comparison are the Marine Predator Algorithm (MPA) and the Partial Reinforcement Optimizer (PRO) to find the optimal model parameter values. Three fractional-order (FO) electrical equivalent circuit models (ECMs) of Li-Ion batteries with different levels of complexity are used to fit the electrochemical impedance spectroscopy (EIS) data operating under different states of charge (SoC) and different operating temperatures. It is found that there is a tradeoff between ECM complexity, identification accuracy, and precision. © 2024 The Electrochemical Society (“ECS”). Published on behalf of ECS by IOP Publishing Limited
Two implementations of fractional-order relaxation oscillators
This work proposes general formulas for designing two different topologies of fractional-order relaxation oscillators
Programmable constant phase element realization with crossbar arrays
Introduction: Constant Phase Elements (CPEs) have been widely used in many applications due to the extra degree of freedom, which offers new responses and behaviors
Comprehensive comparison based on meta-heuristic algorithms for approximation of the fractional-order Laplacian s ? as a weighted sum of first-order high-pass filters
To implement an approximation of the fractional order Laplacian operator s ? as a weighted sum of high pass filter sections, it is essential to extract the cutoff frequencies and filter gains of each section in order to achieve the lowest error possible
Effect of Different Approximation Techniques on Fractional-Order KHN Filter Design
Having an approximate realization of the fractance device is an essential part of fractional-order filter design and implementation
Modeling and analysis of fractional order DC-DC converter
Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated
Fractional calculus definitions, approximations, and engineering applications
The basic idea behind fractional calculus is that it considers derivatives and integrals of non-integer orders giving extra degrees of freedom and tuning knobs for modeling complex and memory dependent systems with compact descriptions
Identifying the Parameters of Cole Impedance Model Using Magnitude Only and Complex Impedance Measurements: A Metaheuristic Optimization Approach
Due to the good correlation between the physiological and pathological conditions of fruits and vegetables and their equivalent Cole impedance model parameters, an accurate and reliable technique for their identification is sought by many researchers since the introduction of the model in early 1940s