Investigation of AC Electrical Machine Stators with Fractional Conductor Windings HENRIK GROP Licentiate Thesis Stockholm, Sweden 2010 Electrical Machines and PowerElectronics TRITA-EE 2010:013 School of Electrical Engineering, KTH ISSN 1653-5146 Teknikringen 33 SE-100 44 Stockholm ISBN 978-91-7415-602-7 SWEDEN Akademisk avhandlingsommedtillst(cid:229)nd avKungl Tekniskah(cid:246)gskolanframl(cid:228)gges tillo(cid:27)entliggranskningf(cid:246)ravl(cid:228)ggandeavteknologielicentiatexamentorsdagenden 29 April 2010 klockan 15.00 i H1, Kungl Tekniska h(cid:246)gskolan, Teknikringen 33, Stockholm. ' Henrik Grop, Mars 2010 Tryck: Universitetsservice US AB iii Abstract Industryalwayssearchestheleastexpensivesolutionforamachinedesign. Therefore,thereisaneedforintegratingdi(cid:27)erentcustomerorderedmachines within the same frame, while keeping the foundation of the mechanical de- sign constant. Since the winding design inelectrical machines is essential for the performance and relatively inexpensive to adapt, it can be used to meet di(cid:27)erentcustomer demands. This thesis investigates the foundations of a special winding named frac- tionalconductorwinding. Anexpressionforwindingfactors forcertainkinds of these windings is developed. Calculations showed thatthe selection of the winding distribution has e(cid:27)ect on the air gap space harmonics produced by the winding. In some cases, the (cid:28)fth and seventh space harmonics can be eliminated by the use of fractional conductor windings in combination with short pitching. The construction of a prototype fractional conductor wound induction motor was documented andis presented inthis thesis. The air gap (cid:29)uxdensityin a dualslotted fractional conductor woundin- ductionmotorrunningatnoloadisstudied. Analyticalmodelsarecompared to results obtained by (cid:28)nite elements and measurements. It was found that analytical results overestimated the peak of the fundamental (cid:29)ux density by 13.5%. Theoverestimationwascausedbytheironreluctanceofthemain(cid:29)ux path as well as saturation. Leakage was found to be a minor cause of this overestimation. Slot leakage and di(cid:27)erential leakage in machines having these windings are studied. The analytical models were evaluated, with mostly good agree- ments, compared to (cid:28)niteelement modeling as well as measurements. Keywords: Windings, Leakage, Large machines, Induction motor construc- tion. v Sammanfattning Industrins(cid:246)keralltiddenmestkostnadse(cid:27)ektival(cid:246)sningnenp(cid:229)enmaskins konstruktion. D(cid:228)rf(cid:246)r (cid:28)nns ett behov att bygga olika kunders maskiner, med f(cid:246)ljaktligen varierande speci(cid:28)kationer, i samma maskinstomme och d(cid:228)rmed anv(cid:228)nda en gemensam grundkonstruktion. Eftersom lindningen i en maskin (cid:228)r avg(cid:246)rande f(cid:246)r prestanda samt dess utf(cid:246)rande (cid:228)r relativt billig att g(cid:246)ra (cid:228)ndringar i, kan denanpassas till att uppfylla olika kunderskrav. Denh(cid:228)rlicentiatavhandlingenutredergrundernaf(cid:246)renspeciellsortslind- ning kallad delvarvslindning. Ett uttryckf(cid:246)r lindningsfaktorn f(cid:246)r vissa typer avdessalindningarh(cid:228)rleds.Ber(cid:228)kningarvisarattvaletavlindningsf(cid:246)rdelning p(cid:229)verkarstorlekenp(cid:229)deavlindningenproducerade(cid:246)verv(cid:229)gornailuftgapet.I vissa fallkandenfemteochdensjundeordningens(cid:246)verv(cid:229)geliminerasgenom anv(cid:228)ndandetavdelvarvslindning i kombination med h(cid:228)rvstegsf(cid:246)rkortning. Byggetavendelvarvslindadasynkronmotorprototypdokumenteradesoch beskrivs i dennalicentiatavhandling. Vidare unders(cid:246)ks (cid:29)(cid:246)dest(cid:228)theten i luftgapet med sp(cid:229)rning av stator och rotor i prototypen. En j(cid:228)mf(cid:246)relse med m(cid:228)tningar och (cid:28)nita elementmeto- denvisarattdenanalytisktber(cid:228)knade(cid:29)(cid:246)dest(cid:228)theten(cid:246)verskattasmed13.5% beroende p(cid:229) j(cid:228)rnreluktans och m(cid:228)ttning. L(cid:228)ckning visar sig endast p(cid:229)verka resultatet marginellt. Sp(cid:229)rl(cid:228)ckningochdi(cid:27)erentielll(cid:228)ckningimaskinermeddessalindningarun- ders(cid:246)ks. Analytiska modeller utv(cid:228)rderas med mestadels goda resultat genom j(cid:228)mf(cid:246)relse med (cid:28)nitaelementmetoden och m(cid:228)tningar. S(cid:246)kord: Lindningar, L(cid:228)ckning, Stora maskiner, Konstruktion av asynkro- nmotorer. Acknowledgment This project is conducted at the department of Electrical Machines and Power Electronics at the Center of Excellence in Electric Power Engineering through the High Performance Drives program. First of all, I would like to thank my supervisor Assoc. Prof. Juliette Soulard aswellasmyco-supervisorProf. ChandurSadaranganiforallhelpandinspiration during the project. Secondly, I wish to thank all important people at ABB Au- tomationProducts,DivisionMachineswhowereinvolvedintheproject. Especially Holger Perssonfor suggesting the topic and Dr Marguerite Holmberg for supervis- ing me at ABB in the beginning of the project. Further on, I am very grateful for all support I got at ABB by Djordje Savinovic, Bj(cid:246)rn Lindberg, Magnus Lundin, Dr Eva M(cid:229)rtensson, Hans ¯ke Eriksson, Bengt Eriksson and John Seppas. A spe- cialthanks to Lars (cid:214)hrnwho I commuted with during the six months in V(cid:228)ster(cid:229)s. Many thanks to all employees in the factory of ABB Machines, especially the sta(cid:27) workinginthe winding factoryandthe test roomwhereIspentmanyjoyfulhours. Thanks to all employees at the Department of Electrical Machines and Power Electronics who have been very helpful and friendly. A special thanks to my of- (cid:28)ce mate and friend Dmitry Svechkarenko, with whom I have solved the World’s problems severaltimes but never remembersthe solution. Thanks to my colleague and friend Alexander Stening for his inputs in discussions and also for his great sense of humor. I am very happy having worked together with my colleague and friend Rathna Chitroju. The department secretary Eva Pettersson has been very helpful in administrative tasks, thank you for this. A huge thanks goes to Olle Br(cid:228)nnvall for the many interesting discussions in the sauna and elsewhere, I hope your shoulder will heal soon. Iamverygratefultomymotherandfatherforalwaysbeingsupportivewhenever I need. Lastbutnotleast,IwouldliketothankKatharina,whohasbeenagreatpartner and friend during these years. vii Contents Acknowledgment vii Contents viii 1 Introduction 1 1.1 AC-armature windings . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Main contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Bene(cid:28)ts and issues associated with fractional conductor windings 9 2.1 Investigation of di(cid:27)erent phase group patterns. . . . . . . . . . . . . 11 2.2 Conclusions from the winding investigations. . . . . . . . . . . . . . 19 3 Winding factors for fractional conductor windings 21 3.1 Introduction of the coil factor . . . . . . . . . . . . . . . . . . . . . . 21 3.2 The coil factor for a simple winding . . . . . . . . . . . . . . . . . . 22 3.3 General expression of the coil factor for winding A . . . . . . . . . . 25 3.4 The coil factor for space harmonics . . . . . . . . . . . . . . . . . . . 27 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4 Modellingof air gap (cid:29)ux density at no load including stator and rotor slotting 33 4.1 Air gap (cid:29)ux density in the prototype . . . . . . . . . . . . . . . . . . 33 4.2 In(cid:29)uence of slotting . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3 Search coil measurements and comparison to analytical and FEM models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5 Stator slot and di(cid:27)erential leakage 47 5.1 The slot-model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.2 Veri(cid:28)cation of slot energy by FEM modeling. . . . . . . . . . . . . . 49 viii CONTENTS ix 5.3 Di(cid:27)erential leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.4 Measurements of slot leakage . . . . . . . . . . . . . . . . . . . . . . 62 5.5 Measurement details . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.6 Validation of FEM model . . . . . . . . . . . . . . . . . . . . . . . . 67 5.7 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.8 Measurement Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6 Construction of a full scale prototype 77 6.1 Punching of sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.2 Stacking of sheets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.3 Stator coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.4 Winding the stator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.5 Connection of the stator winding . . . . . . . . . . . . . . . . . . . . 81 6.6 Vacuum pressure impregnation (VPI) . . . . . . . . . . . . . . . . . 83 6.7 Insertion of rotor bars . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.8 Machine assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.9 Sensors and tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 7 Conclusions and Future Work 91 Appendices 92 A Derivation of the coil factor for winding A 93 Bibliography 97 List of Figures 100