Modelling of synchronous motor with concentrated windings and interior permanent magnets

Rad se bavi dvoosnim magnetskim nelinearnim dinamičkim modelom sinkronoga motora s unutarnjim permanentni magnetima (SMUPM) i koncentriranim namotom. Model je napisan u smjeru vektora ulančanoga toka permanentnoga magneta. Rad uključuje cjelovitu matematičku analizu modela. Počinje opisivanjem električnih i mehaničkih jednadžbi trofaznoga motora. Magnetski nelinearna svojstva željezne jezgre u ravnotežnim jednadžbama opisuju se karakteristikama ulančanih tokova faznih namota koji ovise o položaju rotora i strujama svih trofaznih namota. Izvorni trofazni model transformira se u dvoosni model orijentiran u osi ulančanoga toka permanentnoga magneta transformacijom trofaznog u rotirajući dvoosni sustav. Slijedom toga, magnetno nelinearna svojstva željezne jezgre postaju funkcija položaja rotora i dvije struje. Prva struja leži u smjeru vektora ulančanoga toka permanentnoga magneta (d osi), dok je druga struja ortogonalna na prvu (q osi). Ravnotežne jednadžbe uključuju magnetske tokove i njihove derivacije. Potonji se mogu izraziti u smislu produkta parcijalnih derivacija od ulančanih tokova i odgovarajućih varijabli s vremenskim derivacijama. Magnetski nelinearni dinamički model SMUPM neupotrebljiv je dok se ne odrede magnetno nelinearna svojstava i njihove parcijalne derivacije. Te magnetno nelinearne karakteristike predstavljaju varijabilne parametre izvedenoga modela i određene su metodom konačnih elemenata (MKE). Karakteristike su podijeljene u dvije skupine. U dinamičkom modelu su po prvi puta dodani gubitci u željeznoj jezgri, koji su izračunati MKE_om za cijelo radno područje rada SMUPM_a. S time se poboljšava preciznost simulacijskih izračuna i bolje slaganje simulacijskih izračuna s mjerenjima na realnom motoru. Podrobno su objašnjene eksperimentalne i numeričke metode za određivanje opisanih karakteristika. Magnetski nelinearni dinamički model PMSM-a uključuje efekte zasićenosti magnetskoga materijala, utora statora, geometrije motora i svojstava permanentnih magneta određenih magnetno nelinearnim karakteristikama ulančanoga toka. Rad također opisuje realizaciju magnetskoga nelinearnoga modela SMUPM_a u programu MatLAB/Simulink, što omogućuje izvršavanje simulacijskih izračuna. Rezultati dobiveni simulacijom uspoređuju se s onima dobivenim mjerenjima i analizom metode konačnih elemenata.The thesis deals with the two-axis magnetically nonlinear dynamic model of the permanent magnet synchronous motor (PMSM). The model is written in the orientation of the permanent magnet flux linkage vector. The thesis incorporates the complete mathematical derivation of the model. It starts by describing the electrical and mechanical balances of the three-phase motor in the form of equations. The magnetically nonlinear properties of the iron core in the balance equations are described with characteristics of phase-winding flux linkages, which depend on the rotor position and currents of all the three phase windings. The original three-phase model is transformed into the two-axis permanent magnet flux linkage oriented model with help of the three-to-two phase transformation and the rotational transformation. Consequently, the magnetically nonlinear characteristics of the iron core become a function of the rotor position and two currents. The first current lies in the direction of the permanent magnet flux linkage vector (d axis), while the other current is orthogonal to the first one (q axis). The balance equations incorporate flux linkages and their derivatives. The latter can be expressed in terms of products of partial derivatives of flux linkages respecting the adequate variable with time derivatives of these variables. The magnetically nonlinear dynamic model of the PMSM is unusable until the magnetically nonlinear characteristics and their partial derivatives are determined. These magnetically nonlinear characteristics represent variable parameters of the derived model and can be determined experimentally or by finite element method. The characteristics are divided into two groups. The first group represents characteristics of flux linkages, which are caused by the permanent magnet excitation. The second group represents characteristics of flux linkages, which are caused by the stator currents. Experimental and numerical methods for determination of the described characteristics are explained in detail. The magnetically nonlinear dynamic model of the PMSM incorporates effects of magnetic material saturation, cross-coupling, stator slotting, motor geometry and properties of permanent magnets by the adequately determined magnetically nonlinear characteristics of flux linkages. The thesis also describes the realization of magnetically nonlinear dynamic model of the PMSM in program Matlab/Simulink, which enables the execution of simulations. The results obtained by simulations are compared with those obtained by measurements and finite element analysis