Fractional-order Modelling and Parameter Identification of Electrical Coils

Abstract

The accurate modelling of an electrical coil over a wide range of frequency is the keystone for a precise modelling of an electrical machine. As a consequence of copper losses, eddy-current losses and hysteresis losses; electrical coils with conductive ferromagnetic core show different behaviour from that of an ideal coil. Throughout this paper, dynamic modelling and performance analysis of conventional as well as fractional-order models of an electrical coil with an interchangeable core are achieved. Measurement results are acquired through an integration between Matlab and the high-speed measurement system LTT24. In order to assess the accuracy of these models, simulation results are compared with experimental results whereas unknown parameters are identified through an optimization process that is based on the method of least squares. It is known that the parameters of fractional-order model (Lα, α, Cβ, β) can not be measured directly. Therefore, the paper proposes a possibility based on system analysis to derive these parameters (indirect measurement) from the parameters of the classical model. A frequency band beyond the self-resonant frequency of the electrical coil is explored, thus the parasitic capacitance between coils windings must be considered as an important part of the equivalent circuit. The dependency of model parameters on frequency due to skin-effect is also examined.

Design and analysis of a speed controller for fractional‐order‐modeled voltage‐source‐inverter‐fed induction motor drive

“…The unknown FO-VSI-IM initial reference model is nothing but the identified IO-VSI-IM transfer function model given in (21). The identification method is carried out to identify the FOTF model with the polynomial coefficients and exponent limits as c lim ¼ ½À500; 500e lim ¼ ½10 À8 ;1.…”

“…Some of the recent FO modeling studies in the existing literature such as conical water tank system, 14 wind turbines, 15 DC-DC converters, 16 thermal systems, 17 3-D RC network studies, 18 electroencephalographic (EEG) recorder systems, 19 voltage source converter, 20 modeling of coils, 21,22 RL and RC circuits, 23 three-phase voltage source PWM rectifier, 24 and PMSM speed servo system 25 are carried out. However, the non-linearities like core loss resistance and mutual inductance present in the IM makes the FO modeling study is somewhat complicated.…”

Modeling and Analysis of Caputo–Fabrizio Definition-Based Fractional-Order Boost Converter with Inductive Loads

“…In practical applications, the subordinate circuits carried are mostly capacitive or inductive loads, such as inductor coils, inductor filters, and capacitor couplers. Their electrical characteristics can also be described by fractional-order models [49][50][51][52][53][54][55]. Similar to integer-order models, considering loads with energy storage characteristics during mathematical modeling can transform the model from a fractional-order model with two state variables to a fractional-order model with three state variables, which can provide a more comprehensive description of the system characteristics of circuits.…”

Regional Controllability and Minimum Energy Control of Delayed Caputo Fractional-Order Linear Systems

“…Since its beginnings, fractional calculus has attracted many great mathematicians, who directly or indirectly contributed to its development [2]. Today, many researchers consider fractional calculus an important tool for solving different problems in various fields, e.g., physics, thermodynamics, chemistry, biology, classical and quantum mechanics, viscoelasticity, finance, engineering, signal and image processing, and automatics and control [3][4][5].…”