Modeling of transformer characteristics using fractional order transfer functions

Kamath, Aishwarya; Gandhi, J.R; Bohra, A.S; Goel, A.; Patil, Deepika; Kulkarni, Onkar Vitthal; Chandle, J. O.

doi:10.1109/icca.2009.5410191

Cited by 6 publications

(4 citation statements)

References 4 publications

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“…For this article, the original application coded in the Matlab ® environment was utilized to compute the non-integer order differential equation system. The non-integer order derivatives were evaluated numerically by discretization using the Grünwald-Letnikov definition (10), which describes the α-order derivative of a function x at a time t m = m•h.…”

Section: Simulation and Measurement Resultsmentioning

confidence: 99%

“…Therefore, half-order modelling has been proposed to better describe the behaviour of electrical machines susceptible to the presence of induced currents in some of their conductive parts. Previous works have introduced such modelling in mechanical engineering for car suspension modelling [1], in electrochemical engineering for modelling of batteries [2], fuel cells [3], capacitors [4], supercapacitors [5] and ultracapacitors [6], as well as in electrical engineering for modelling of induction machines [7], synchronous machines [8,9] or transformers [10]. Classically, equivalent circuits of electrical device models are enhanced by adding ladder elements with constant parameters, usually R, L or C (resistance, inductance and capacitance, respectively) [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator

et al. 2020

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This article presents a comparison between integer and non-integer order modelling of a synchronous generator, in the frequency domain as well as in the time domain. The classical integer order model was compared to one containing half-order systems. The half-order systems are represented in a Park d-q axis equivalent circuit as impedances modelled by half-order transmittances. Using a direct method based on the approximation of the half-order derivatives by the Grünwald–Letnikov definition, a state-space equation system was solved. For both models, a computational program written in Matlab® software was used. For the purpose of time domain simulation, the machine models were connected to an electric load composed of an RL circuit. To validate and compare both models, simulation results of a three-phase short-circuit and a no-load voltage recovery were compared with corresponding measurements performed on a solid salient-pole synchronous generator of 125 kVA.

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Section: Simulation and Measurement Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator

et al. 2020

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“…It considers complex systems involving impedance modeling, quantum mechanics, and memristor systems as fractional-order system has an unlimited memory [8]. The fractional transfer function determined from the response of the system closely features the original response [9,10]. In fact, fractional calculus helps to improve accuracy in control engineering and better portrays dynamic behavior [11].…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Impedance Identification for Inductors

2022

Progr. Fract. Differ. Appl.

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The accuracy of a model is required to represent the integrated device in any electrical system for quality assurance. This article intends to measure the accurate and realistic impedance of the inductor, called pseudo-inductance. For this purpose, we have applied fractional-order modeling and a simple scheme to estimate the impedance value of the inductor (or inductive coils). Also, the approach does not require any high-end measurement device like the impedance meter. The complexity of the fractional-order derivative for identification purpose is simplified using the block-pulse-operational-matrix. The complexity of the fractional-order derivative for identification purpose is simplified using the block-pulse operational matrix to approximate the time response behaviour in terms of the inductor model's parameters. The study goes on to highlight the importance of fractional derivative and its interpretation in terms of the phase difference. The proposed model can be used to accurately model any inductor based on its time response data. The purpose of the study is validated through the experimental results.

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“…In recent years, fractional calculus has become more and more popular due to its unique advantages, including applications in filters, image processing, control systems, split-resistance components, super-capacitors and so on. In a certain range, the applicability and accuracy of the fractional-order model are greatly improved compared with the integerorder model, and there have been many research results in modeling of the winding equipment such as transformers and overhead lines (Liang et al, 2017;Liang and Gao, 2016;Kamath et al, 2009). There are many methods for solving fractional differential equations, including numerical methods and analytical methods.…”

Section: Introductionmentioning

confidence: 99%

Fractional calculus-based analysis of soil electrical properties

Liang

Yang

2019

COMPEL

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Purpose This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at high frequencies exhibits a fractional effect. In addition, for the fractional-order formulation, this paper aims to provide a more accurate numerical algorithm for solving the fractional differential equations. Design/methodology/approach This paper analyzes the frequency-dependence of soil electrical properties based on fractional calculus theory. A collocation method based on the Puiseux series is proposed to solve fractional differential equations. Findings The algorithm proposed in this paper can be used to solve fractional differential equations of arbitrary order, especially for 0.5th-order equations, obtaining accurate numerical solutions. Calculating the impact response of the grounding electrode based on the fractional calculus theory can obtain a more accurate result. Originality/value This paper proposes an algorithm for solving fractional differential equations of arbitrary order, especially for 0.5th-order equations. Using fractional calculus theory to analyze the frequency-dependent effect of soil electrical properties, provides a new idea for ground-related transient calculation.

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Modeling of transformer characteristics using fractional order transfer functions

Cited by 6 publications

References 4 publications

Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator

Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator

Fractional-Order Impedance Identification for Inductors

Fractional calculus-based analysis of soil electrical properties

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