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Method of identification of equivalent parameters of the fractional-order transformer

Jakubowska-Ciszek Agnieszka, Walczak Janusz

Poznan University of Technology Academic Journals. Electrical Engineering

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2019

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No. 97

169--180

EN

The paper presents a method for identifying the parameters Lβ1, β1, Lβ2, β2, Mγ, γ of a fractional-order transformer. This method is based on the measurement of the phase resonance frequency in a few systems containing: the investigated fractional-order transformer and two standard capacitors. The dependencies allowing the determination of the fractional-order transformer parameters have been given, on the basis of the described measurements. The obtained results are illustrated by an example.

2

Analysis of parallel resonance RLCα circuit with supercapacitor

Walczak J., Jakubowska A.

Computer Applications in Electrical Engineering

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2014

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Vol. 12

30--37

EN

The paper describes the results of analysis on the resonance phenomenon in a parallel RLCα circuit with supercapacitor modeled as a fractional-order capacitance. A complex, more accurate fractional-order model has been taken into analysis. Formulas for frequency characteristics and resonance conditions have been derived and presented by simulation studies of the concerned fractional-order system.

3

Rezonans w równoległym obwodzie reaktancyjnym ułamkowego rzędu

Walczak J., Jakubowska A.

Prace Naukowe Politechniki Śląskiej. Elektryka

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2013

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z. 2-3

41--50

PL

Artykuł dotyczy analizy zjawiska rezonansu fazy w prostym równoległym obwodzie RLβCα, zawierającym rzeczywistą cewkę i kondensator(np. superkondesator), modelowane jako elementy ułamkowego rzędu. W artykule przyjęto proste modele matematyczne rzędu ułamkowego i wyprowadzono zależności na admitancję zastępczą analizowanego obwodu. Z ogólnego warunku rezonansu fazy wyprowadzono zależności, opisujące częstotliwość rezonansową i przeanalizowano różne przypadki parametrówαi β, mogące wystąpić w obwodzie. Uzyskane wyniki zilustrowano przykładem i wyciągnięto wnioski z przeprowadzonej analizy.

EN

The article analyzes phase resonance phenomenon in a simple parallel RLβCα circuit consisting of a real coil and a capacitor(eg. supercapacitor), modelled as fractional –order elements. Simple fractional –order models have been assumed and relations for equivalent admittance of the concerned circuit have been derived. From the general phase resonance condition, relations describing resonance frequency have been derived too. Various cases of parameters α and β occuring in the circuit have been analyzed. Obtained results have been illustrated by an example and some conclusions from the analysis have been drawn.

4

Analiza zjawisk rezonansowych w szeregowym obwodzie RLC z superkondensatorem

Jakubowska A., Walczak J.

Pomiary Automatyka Kontrola

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2013

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R. 59, nr 10

1105--1108

PL

Artykuł dotyczy analizy warunków zajścia zjawiska rezonansu fazowego i amplitudowego dla szeregowego obwodu RLC z superkondensatorem. Zachowanie superkondensatorów różni się od klasycznych kondensatorów, dlatego ich modele matematyczne są bardziej skomplikowane, wykorzystują m.in. rachunek różniczkowo-całkowy ułamkowego rzędu. Do analizy i symulacji wybrano model oparty o bieguny i zera ułamkowego rzędu. Dobierając odpowiednio parametry obwodu rezonansowego R, L , RS i C można uzyskać w obwodzie rezonans fazowy i amplitudowy.

EN

The phase and magnitude resonance phenomenon in a series RLC circuit with classic reactive components: the inductance L and the capacitance C is widely known in the circuit theory and thoroughly described. The subject of the paper is an analysis of phase resonance conditions in a series RLC circuit with supercapacitor. Supercapacitors differ from classic dielectric capacitors by the construction, behavior and their applications, described in Section 1. There have been created several kinds of mathematical and circuit models (Section 2). Among them, fractional order models demonstrate the best fit to the frequency characteristics as well as dynamic processes occurring in supercapacitors [3], [4] and [10]. The model based on fractional poles and zeros, defined by formulas (2) and (3), was chosen for analysis. The relations for the circuit impedance (10-13) and resonance frequency (14) were derived. They are illustrated in Figs. 2-11. The formula for resonance frequency is a transcendental equation, therefore it is possible to solve it for the investigated system only numerically. The resonance frequency in the examined series RLC circuit whose model is based on fractional poles and zeros depends on five parameters. The results were compared with those obtained from the analysis conducted in paper [6],where frez depends on only three parameters. A more precise supercapacitor model enables more insightful analysis of phase and magnitude resonance phenomenon.