A methodology for analysis and solving of nonlinear magnetic problems with hysteresis in time domain

[S. B. Divac]

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Cilj ove doktorske disertacije je da predstavi metodologiju za analizu i rešavanje nelinearnih magnetskih problema sa histerezisom u vremenskom domenu. Predložena metodologija, pod nazivom Harmonic Interpolation Method (HIM), zasnovana je na interpolaciji amplituda i faza harmonika dobijenih harmonijskom analizom ograničenog broja merenih rezultata. Njenom primenom se omogućava rešavanje problema bez primene složenih histerezisnih modela ili zamenskih šema veza. Primenjena je na torusno jezgro od feromagnetskog lima i ferita N87. Razmatana su dva pristupa: primena HIM-a u svom osnovnom obliku i u kombinaciji sa Bertotijevom Statističkom teorijom gubitaka. Predložena metodologija je primenjena na: simulaciju vremenskog oblika jačine magnetskog polja na merenoj frekvenciji i za amplitudu magnetske indukcije od interesa, simulaciju dinamičkih histerezisnih petlji za amplitudu, frekvenciju i oblik magnetske indukcije od interesa, rešavanje dinamičkog (naizmeničnog) električnog kola sa nelinearnim histerezisnim kalemom u vremenskom domenu, simulaciju ukupne trenutne snage magnećenja i njenih komponenti, određivanje vremenski promenljivih parametara paralelne RL zamenske šeme i druge probleme. Pored detaljnog opisa predložene metodologije i njenih primena na razmatrane probleme, u okviru disertacije mogu se pronaći eksperimentalni rezultati, detalji o merno-akvizicionom sistemu korišćenom za njihovo prikupljanje, princip razlaganja trenutne snage magnećenja na svoje komponente, rezultati simulacija upoređeni sa merenjima ili rezultatima drugih autora, kao i njihova adekvatna analiza.

The aim of this doctoral dissertation is to present a methodology for analysis and solving of nonlinear magnetic problems with hysteresis in time domain. The proposed methodology is based on interpolation of amplitudes and phases of harmonics from harmonic analysis of limited number of measured waveforms. It is named Harmonic Interpolation Method (HIM). It allows for solutions to be found without the use of complicated hysteresis models or equivalent circuits. It has been used to solve problems regarding toroidal sample of electrical steel either as a standalone procedure or in combination with Bertotti’s Statistical Theory of Losses (STL). It has also been applied to the N87 ferrite toroidal core. Some of the considered problems are: simulation of magnetic field strength waveform at measurement frequency and for the magnetic flux density amplitude of interest, simulation of dynamic hysteresis loops for frequency, shape and amplitude of magnetic flux density of interest, solving of a dynamic electric circuit with nonlinear hysteretic inductor, decomposition of instantaneous magnetising power, simulation of instantaneous magnetising power waveform and its components, calculation of time-varying parameters for parallel RL equivalent circuit and others. Details regarding the measurement setup, results and data acquisition system are also presented. Simulation results have been verified using measurements or the results of other authors. The dissertation also includes the appropriate analysis and discussion of all of the obtained results.

HIM, harmonic interpolation method, harmonijska analiza, interpolacija, STL, simulacija, magnetsko polje, snaga magnećenja, vremenski domen.

HIM, harmonic interpolation method, harmonic analysis, interpolation, simulation, STL, magnetic field strength waveform, instantaneous magnetising power, time domain.

537.623:621.317.35

Magnetna polja, simulacije

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