595 KB0 KB201320252025Banković, BojanFilipović, FilipKostić, VojkanMitrović, NebojšaPetronijević, MilutinStojiljković, Anđelaletnik:18številka:issue 3str. 145-159ISSN:1855-5748COBISSID_HOST:265057795URN:URN:NBN:SI:doc-1PVMIYLIenFakulteta za energetikoUniversity of Maribor, University of Maribor PressJournal of energy technologyClarke transformationClarkejeva transformacijacoordinate transformationsizobraževanje s področja močnostne elektronikekoordinatne transformacijekrmiljenje motorjevmotor controlPark transformationParkova transformacijapower electronics educationreference frame theoryteorija referenčnih sistemovSystematic derivation of clarke and park transformations through vector representation in three-phase systems|This paper presents a comprehensive pedagogical treatment of Clarke and Park transformations through systematic vector representation, designed specifically for educational purposes in power electronics and motor control courses. While these fundamental transformations are ubiquitous in modern applications–from field-oriented control of AC machines to grid-connected converter control–educational materials often present them either as matrix operations without geometric foundation, or embedded within machine-specific derivations that obscure the general mathematical structure. We address this pedagogical need by progressing systematically from three-phase voltage equations in the time domain to a spatial vector representation in three-dimensional space, deriving the Clarke transformation through explicit geometric projection onto the plane where balanced quantities reside, and, subsequently, deriving the Park transformation as a time-varying rotation of the Clarke frame. The work establishes an amplitude-invariant formulation, provides an explicit geometric interpretation of the 35.26° angle between coordinate systems, and includes workednumerical examples demonstrating complete transformations. This unified pedagogical treatment bridges the gap between practical application and mathematical foundations, providing educators with a complete geometrically intuitive framework suitable for graduate-level instruction and professional developmentČlanek predstavlja celovito obravnavo Clarkove in Parkove transformacije skozi sistematično vektorsko predstavitev, zasnovano posebej za izobraževalne namene na področju močnostne elektronike in vodenja električnih strojev. Čeprav sta ti temeljni transformaciji vseprisotni v sodobnih aplikacijah – od poljsko usmerjenega vodenja AC strojev do vodenja omrežno priključenih pretvornikov – učni materiali pogosto predstavljajo transformacije bodisi kot matrične operacije brez geometrijske osnove, bodisi v okviruizpeljav, vezanih na določene tipe strojev, kar zamegli splošno matematično strukturo. V tem delu se posvetimo tej pedagoški vrzeli z doslednim prehodom od trifaznih napetostnih enačb v časovni domeni do prostorske vektorske predstavitve v tridimenzionalnem prostoru. Clarkovo transformacijo izpeljemo kot eksplicitno geometrijsko projekcijo na ravnino, v kateri ležijo uravnotežene veličine, nato pa Parkovo transformacijo kot časovno spremenljivo rotacijo Clarkovega koordinatnega sistema. Delo vzpostavi amplitudno-invariantno formulacijo, poda jasno geometrijsko razlago 35,26° kota med koordinatnimi sistemi ter vključuje numerične primere z vsemi koraki transformacij. Ta enotna pedagoška obravnava zapolnjuje vrzel med praktično uporabo in matematičnimi temelji ter ponuja pedagoškemu kadru popolnoma geometrijsko intuitiven okvir, primeren za podiplomsko poučevanje in strokovno usposabljanjeTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Mariboru, Fakulteta za energetiko