Harmonic analysis of the magnetic field of three-phase distributed windings

Naloga diplomskega dela je bila izdelati programsko orodje, ki za različne oblike statorskih lamel električnih motorjev in različna navitja izračuna in analizira porazdelitev magnetnega polja v zračni reži. Porazdelitev magnetnega polja v zračni reži vsebuje prostorske harmonske komponente, ki so posledica različnih tipov navitij, statorske geometrije itd. V nadaljevanju te naloge smo predstavili trifazna porazdeljena navitja, ki so eden od glavnih načinov za ustvarjanje vrtilnega magnetnega polja. Na preprostem primeru dvopolnega magnetnega polja smo prikazali načrtovanje navitja, za katerega smo izračunali tudi magnetno napetost, ki je dober približek magnetnega polja vzdolž zračne reže. Pri tem smo ugotovili, da potek magnetne napetosti precej odstopa od idealnega sinusa, saj je ta sestavljen iz več sinusov z različno frekvenco, ki vplivajo na njeno obliko. Pravimo jim tudi prostorske harmonske komponente, ki povzročajo dodatne motnje pri delovanju motorja in so večinoma nezaželene. Zato smo s pomočjo programskega orodja FEMM za različne tipe navitij in geometrije izračunali porazdelitev magnetnega polja vzdolž zračne reže in s pomočjo diskretne Fourierove transformacije izračunali njen spekter. Cilj naloge je bil prikazati in analizirati pojav višjih harmonskih komponent pri enoplastnem navitju in dvoplastnem navitju s skrajšavo ter različnih statorskih geometrijah. Zaradi velikega števila simuliranih primerov smo v našo analizo vključili le osnovne primere in tiste, ki izstopajo od drugih, in se s tem izognili ponavljajočim rezultatom ter izboljšali preglednost nad rezultati.The task of the thesis work was to create a software tool that would calculate and analyze the distribution of the magnetic field in the air gap for different forms of windings and stator laminations of electric motors. The distribution of the magnetic field in the air gap contains spatial harmonic components resulting from different types of windings, stator geometry, etc. Firstly, the thesis presents three-phase distributed windings, which are one of the main ways to create a rotating magnetic field. In a simple example of a two-pole machine, designing of the winding was demonstrated, for which we also calculated the magnetic voltage, which is a good approximation of the magnetic field distribution along the air gap. It was found that the shape of magnetic voltage deviates significantly from the ideal sine wave, since it is composed of several higher harmonics that affect its shape. They are also called spatial harmonic components, which cause additional engine malfunction and are mostly undesirable. Therefore, we used the FEMM software tool to calculate the magnetic field distribution along the air gap for different types of windings and stator geometries, and then determined the spectrum using a discrete Fourier transform. The aim of the thesis was to demonstrate and analyze the phenomenon of higher harmonic components in different stator geometries, a single-layer winding and a double-layer winding with pitch shortening. Due to a large number of simulated cases, only the basic ones and those that stand out from the others were included in our analysis, thus avoiding repeated results and improving their transparency