Load Controlled Noise of Power Transformers: 3D Modelling of Interior and Exterior Sound Pressure Field M U S T A F A K A V A S O G L U Master of Science Thesis Stockholm, Sweden 2010 Load Controlled Noise of Power Transformers: 3D Modelling of Interior and Exterior Sound Pressure Field M U S T A F A K A V A S O G L U Masters Thesis in Numerical Analysis (30 ECTS credits) at the Scientific Computing International Master Program Royal Institute of Technology year 2010 Supervisor at CSC was Jesper Oppelstrup Examiner was Michael Hanke TRITA-CSC-E 2010:095 ISRN-KTH/CSC/E-10/095-SE ISSN-1653-5715 Royal Institute of Technology School of Computer Science and Communication KTH CSC SE-100 44 Stockholm, Sweden URL: www.csc.kth.se Abstract Noise emissions are of ever greater concern to trans- former manufacturers.Understanding the sources of the noise and prediction as well as reduction of sound emis- sion is of increasing interest. In this paper we study load- controlled noise. Empirical formulas based on the trans- former s rated power of transformers are used to predict load-controlled noise, but they are of little use for new de- signs for which measurements are not available. Accurate numerical simulations are needed for prediction.In this work an effi cient new 2D-3D computational model of the load-controlled acoustic noise of oil insulated power trans- formers is presented. Generation and propagation of trans- former noise is a complex interaction of the electromagnetic fi eld, the mechanical displacement fi eld, and the acoustic pressure fi eld. This simulation is based on a COMSOL Mul- tiphysics Finite Element Model and allows accurate fully coupled calculations of the fi elds A 2D axisymmetric mag- netic simulation for the windings on one transformer core leg is done to model the stray fi elds and Lorenz forces; these excite an axisymmetric, detailed mechanical winding model to produce the displacement fi eld. The axisymmetric dis- placement is mapped onto the transformer core, tank and exterior geometry with 120 degree phase shift between the three windings to simulate a three phase power transformer. The model is applied to an existing transformer model for which ABB has supplied data and results of earlier com- puter models, and the sensitivity to numerous parameters is assessed. It is found that accurate mechanical modeling of the clamping of the windings to the core is a pressing need to improve simulation accuracy. Referat Last-inducerat buller hos trefas-transformatorer: 3D-modellering av inre och yttre ljudtryck. Buller blir alltmer viktigt fr transformatortillverkare nr kunderna stller strngare miljcertifi eringskrav. Frst- else fr bullerkllorna och prediktion liksom reduktion av utstrlad ljudeff ekt r drfr intressant. Hr studerar vi lastinducerat buller. Prediktion av last-inducerat buller grs idag med empiriska formler baserade p transformatorns mrkeff ekt, men de r till fga hjlp vid ny-konstruktioner. Noggranna numeriska simuleringar behvs. I detta arbete presenteras en eff ektiv 2D/3D matematisk modell av lastin- ducerat buller i en oljeisolerad tre-fas krafttransformator. Alstring och spridning av transformatorbuller r en kom- plex samverkan mellan elektromagnetiska flt, mekaniska frskjutningar, och det akustiska tryck-fltet. Simulerin- gen baseras p en COMSOL Multiphysics fi nita-element- modell och ger noggranna berkningar av fullt kopplade ingende processerna. En axi-symmetrisk magnetisk mod- ell av lindningarna p ett transformatorben ger strflt och inducerade krafter; dessa exciterar en axisymmetrisk detaljerad mekanisk modell och ger frskjutningarna. Axi- symmetriska frskjutningar avbildas p 3D-modellen av kr- na, tank, olja och yttre, med 120 graders fasfrskjutning mellan de tre lindningarna fr att simulera en tre-fastrans- formator. Modellen appliceras p en befi ntlig transforma- tortyp fr vilken ABB har resultat av mtningar och tidi- gare datormodeller, och knsligheten fr de mnga parame- trarna berknas. Man fi nner att noggrannare mekanisk mod- ellering av lindningarnas fstning mot krnan r av vikt fr att frbttra simuleringsnogrannheten. Contents 1Introduction1 1.1Information about the Transformer . . . . . . . . . . . . . . . . . . .2 2Electromagnetic Model5 2.1Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2.2Short Review of Electromagnetic Fundamentals . . . . . . . . . . . .6 2.3Time Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . .7 2.3.1 Verifi cation of the computer model . . . . . . . . . . . . . . .8 2.3.2Magnetic Stray Field . . . . . . . . . . . . . . . . . . . . . . .10 2.3.3Computed Magnetic Volume Forces. . . . . . . . . . . . . .11 2.4Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 3Mechanical Modeling13 3.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 3.2Theory Background. . . . . . . . . . . . . . . . . .