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Numerical Analysis

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Spotlight on Modern Transformer Design

Part of the book series: Power Systems ((POWSYS))

Abstract

Transformers involve magnetostatic problems. These problems can be solved by analytical and numerical techniques. The limitations of analytical techniques as well as the progress of computers facilitated the development of numerical techniques. Among the numerical techniques, the most popular method in the solution of magnetostatic problems is the finite element method. A very real advantage of the finite element method is its ability to deal with complex geometries. Another advantage is that it yields stable and accurate solutions. This chapter presents the finite element method for the solution of linear and nonlinear magnetostatic problems, the latter being very common in transformer design. Carefully selected arithmetic examples make clear the application of the finite element method to the solution of linear and nonlinear magnetostatic problems.

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References

  • Abed NY and Mohammed OA (2007) Modeling and characterization of transformers internal faults using finite element and discrete wavelet transforms. IEEE Transactions on Magnetics 43(4):1425–1428

    Article  Google Scholar 

  • Alhamadi MA and Demerdash NA (1994) Three dimensional magnetic field computation by a coupled vector-scalar potential method in brushless DC motors with skewed permanent magnet mounts – The formulation and FE grids. IEEE Transactions on Energy Conversion 9(1):1–10

    Article  Google Scholar 

  • Andersen OW (1973) Transformer leakage flux program based on the finite element method. IEEE Transactions on Power Apparatus and Systems 92(2):682–689

    Article  Google Scholar 

  • Arjona LMA and McDonald DC (1999) A new lumped steady-state synchronous machine model derived from finite element analysis. IEEE Transactions on Energy Conversion 14(1):1–7

    Article  Google Scholar 

  • Ashtiani CN (1988) Performance analysis of wound field synchronous alternators under load using finite elements. IEEE Transactions on Energy Conversion 3(2):330–334

    Article  Google Scholar 

  • Bastos JPA and Sadowski N (2003) Electromagnetic modeling by finite element methods. Marcel Dekker, New York

    Google Scholar 

  • Bergeron DA and Trahar RE Jr (1999) A static finite element analysis of substation busbar structures. IEEE Transactions on Power Delivery 14(3):890–896

    Article  Google Scholar 

  • Bergeron DA, Trahar RE Jr, Dubinich MD, Opsetmoen A (1999) Verification of a dynamic finite element analysis of substation busbar structures. IEEE Transactions on Power Delivery 14(3):884–889

    Article  Google Scholar 

  • Binns KJ, Lawrenson PJ, Trowbridge CW (1992) The analytical and numerical solution of electric and magnetic fields. Wiley, New York

    Google Scholar 

  • Bíró O, Auberhofer S, Burchgraber G, Preis K, Seitlinger W (2007) Prediction of magnetising current waveform in a single-phase power transformer under DC bias. IET Science, Measurement & Technology 1(1):2–5

    Google Scholar 

  • Brebbia CA (1984) Boundary element techniques: theory and applications in engineering. Springer-Verlag, Berlin

    MATH  Google Scholar 

  • Brebbia CA and Dominguez J (1992) Boundary elements: an introductory course. Computational Mechanics Publications, Southampton

    MATH  Google Scholar 

  • Chari MVK and Salon SJ (2000) Numerical methods in electromagnetism. Academic Press, San Diego

    Google Scholar 

  • Clough RW (1960) The finite element method in plane stress analysis. Proc American Society of Civil Engineers Conference on Electronic Computation

    Google Scholar 

  • Coulson MA (1981) Magnetic non-linearity. PhD Thesis, University of Strathclyde, UK

    Google Scholar 

  • Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of the American Mathematical Society 49

    Google Scholar 

  • de Leon F and Anders GJ (2008) Effects of backfilling on cable ampacity analyzed with the finite element method. IEEE Transactions on Power Delivery 23(2):537–543

    Article  Google Scholar 

  • Demerdash NA and Nehl TW (1979) Use of numerical analysis of nonlinear eddy current problems by finite element in the determination of parameters of electrical machines with solid iron cores. IEEE Transactions on Magnetics 15(6):1482–1484

    Article  Google Scholar 

  • Enokizono M and Soda N (1997) Finite element analysis of transformer model core with measured reluctivity tensor. IEEE Transactions on Magnetics 33(5):4110–4112

    Article  Google Scholar 

  • Erdelyi EA and Ahmed SV (1965) Flux distribution in saturated dc machines. IEEE Transactions on Power Apparatus and Systems 84(5):375–381

    Article  Google Scholar 

  • Galerkin BG (1915) Series solution of some problems of elastic equilibrium of rods and plates [In Russian]. Vestn. Inzh. Tekh. 19

    Google Scholar 

  • Gauss CF (1823) Brief an gerling. Werke 9:278–281

    Google Scholar 

  • Hameyer K and Belmans R (1999) Numerical modeling and design of electrical machines and devices. WIT Press, Southampton

    Google Scholar 

  • Hildebrand FB (1962) Advanced calculus for applications. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Ho SL, Li Y, Wong HC, Wang SH, Tang RY (2004) Numerical simulation of transient force and eddy current loss in a 720-MVA power transformer. IEEE Transactions on Magnetics 40(2):687–690

    Article  Google Scholar 

  • Holland SA, O’Connell GP, Haydock L (1992) Calculating stray losses in power transformers using surface impedance with finite elements. IEEE Transactions on Magnetics 28(2):1355– 1358

    Article  Google Scholar 

  • Hwang CC, Tang PH, Jiang YH (2005) Thermal analysis of high-frequency transformers using finite elements coupled with temperature rise method. IEE Proc Electric Power Applications 152(4):832–836

    Article  Google Scholar 

  • Kaehler C and Henneberger G (2004) Transient 3-D FEM computation of eddy-current losses in the rotor of a claw-pole alternator. IEEE Transactions on Magnetics 40(2):1362–1365

    Article  Google Scholar 

  • Kefalas TD, Georgilakis PS, Kladas AG, Souflaris AT, Paparigas DG (2008) Multiple grade lamination wound core: a novel technique for transformer iron loss minimization using simulated annealing with restarts and an anisotropy model. IEEE Transactions on Magnetics 44(6):1082–1085

    Article  Google Scholar 

  • Kladas AG, Papadopoulos MP, Tegopoulos JA (1994) Leakage flux and force calculation on power transformer windings under short-circuit: 2D and 3D models based on the theory of images and the finite element method compared to measurements. IEEE Transactions on Magnetics 30(5):3487–3490

    Article  Google Scholar 

  • Kumbhar GB and Kulkarni SV (2007) Analysis of short-circuit performance of split-winding transformer using coupled field-circuit approach. IEEE Transactions on Power Delivery 22(2):936–943

    Article  Google Scholar 

  • Kwon YW and Bang H (1997) The finite element method using MATLAB. CRC Press, Boca Raton

    Google Scholar 

  • Labridis D and Dokopoulos P (1988) Finite element computation of field, losses and forces in a three-phase gas cable with nonsymmetrical conductor arrangement. IEEE Transactions on Power Delivery 3(4):1326–1333

    Article  Google Scholar 

  • Lesniewska E (2002) The use of 3-D electric field analysis and the analytical approach for improvement of a combined instrument transformer insulation system. IEEE Transactions on Magnetics 38(2):1233–1236

    Article  Google Scholar 

  • Lin C, Xiang C, Yanlu Z, Zhingwang C, Guoqiang Z, Yinhan Z (1998) Losses calculation in transformer tie plate using the finite element method. IEEE Transactions on Magnetics 34(5):3644–3647

    Article  Google Scholar 

  • Lu S and Liu Y (1993) FEM analysis of DC saturation to assess transformer susceptibility to geomagnetically induced currents. IEEE Transactions on Power Delivery 8(3):1367–1376

    Article  Google Scholar 

  • Martic HC and Carey G (1973) Introduction to finite element analysis – Theory and applications. McGraw Hill, New York

    Google Scholar 

  • Minambres JF, Barandiaran JJ, Alvarez-Isasi R, Zorrozua MA, Zamora I, Mazon AJ (1999) Radial temperature distribution in ACSR conductors applying finite elements. IEEE Transactions on Power Delivery 14(2):472–480

    Article  Google Scholar 

  • Moallem M and Ong CM (1990) Predicting the torque of a switched reluctance machine from its finite element field solution. IEEE Transactions on Energy Conversion 5(4):733–739

    Article  Google Scholar 

  • Papagiannis GK, Triantafyllidis DG, Labridis DP (2000) A one-step finite element formulation for the modeling of single and double-circuit transmission lines. IEEE Transactions on Power Systems 15(1):33–38

    Article  Google Scholar 

  • Papazacharopoulos ZK, Tatis KV, Kladas AG, Manias SN (2004) Dynamic model for harmonic induction motor analysis determined by finite elements. IEEE Transactions on Energy Conversion 19(1):102–108

    Article  Google Scholar 

  • Pavlik D, Garg VK, Repp JR, Weiss J (1988) A finite element technique for calculating the magnet sizes and inductances of permanent magnet machines. IEEE Transactions on Energy Conversion 3(1):116–122

    Article  Google Scholar 

  • Pavlik D, Johnson DC, Girgis RS (1993) Calculation and reduction of stray and eddy losses in core-form transformers using a highly accurate finite element modelling technique. IEEE Transactions on Power Delivery 8(1):239–244

    Article  Google Scholar 

  • Peng JP and Salon S (1982) A hybrid finite element boundary element formulation of Poisson’s equation for axisymmetric vector potential problems. Journal of Applied Physics 53(11):8420–8422

    Article  Google Scholar 

  • Pern JF and Yeh SN (1995) Calculating the current distribution in power transformer windings using finite element analysis with circuit constraints. IEE Proc Science, Measurement and Technology 142(3):231–236

    Google Scholar 

  • Preis K, Bíró O, Buchgraber G, Ticar I (2006) Thermal-electromagnetic coupling in the finiteelement simulation of power transformers. IEEE Transactions on Magnetics 42(4):999–1002

    Article  Google Scholar 

  • Rausch M, Kaltenbacher M, Landes H, Lerch R, Anger J, Gerth J, Boss P (2002) Combination of finite and boundary element methods in investigation and prediction of load-controlled noise of power transformers. Journal of Sound and Vibration 250(2):323–338

    Article  Google Scholar 

  • Rayleigh L (1870) On the theory of resonance. Transactions of the Royal Society A161

    Google Scholar 

  • Reece ABJ and Preston TW (2000) Finite element methods in electrical power engineering. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Renyuan T, Yan L, Dake L, Lijian T (1992) Numerical calculation of 3-D transient eddy current field and short circuit electromagnetic force in large transformers. IEEE Transactions on Magnetics 28(2):1418–1421

    Article  Google Scholar 

  • Ritz W (1909) Uber eine neue methode zur losung gewissen variations-probleme der mathematischen physik. J. Reine Angew. Math. 135

    Google Scholar 

  • Salon S, Peaiyoung S, Mayergoyz I (1989) Some technical aspects of implementing boundary element equations. IEEE Transactions on Magnetics 25(4):2998–3000

    Article  Google Scholar 

  • Schlensok CS and Henneberger G (2004) Calculation of force excitations in induction machines with centric and excentric positioned rotor using 2-D transient FEM. IEEE Transactions on Magnetics 40(2):782–785

    Article  Google Scholar 

  • Silvester PP and Ferrari RL (1996) Finite elements for electrical engineers, 3rd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Steurer M and Fröhlich K (2002) The impact of inrush currents on the mechanical stress of high voltage power transformer coils. IEEE Transactions on Power Delivery 17(1):155–160

    Article  Google Scholar 

  • teNyenhuis EG, Girgis RS, Mechler GF, Zhou G (2002) Calculation of core hot-spot temperature in power and distribution transformers. IEEE Transactions on Power Delivery 17(4):991–995

    Article  Google Scholar 

  • Tsili MA, Kladas AG, Georgilakis PS, Souflaris AT, Paparigas DG (2006) Advanced design methodology for single and dual voltage wound core power transformers based on a particular finite element model. Electric Power Systems Research 76:729–741

    Article  Google Scholar 

  • Viana WC, Micaleff RJ, Young S, Dawson FP (1999) Transformer design considerations for mitigating geomagnetic induced saturation. IEEE Transactions on Magnetics 35(5):3532– 3534

    Article  Google Scholar 

  • Wang R and Demerdash NA (1991) A combined vector potential-scalar potential method for FE computation of 3D magnetic fields in electrical devices with iron cores. IEEE Transactions on Magnetics 27(5):3971–3977

    Article  Google Scholar 

  • Watson JF and Dorrell DG (1999) The use of finite element methods to improve techniques for the early detection of faults in 3-phase induction motors. IEEE Transactions on Energy Conversion 14(3):655–660

    Article  Google Scholar 

  • Yamazaki K (1999) Induction motor analysis considering both harmonics and end effects using combination of 2D and 3D finite element method. IEEE Transactions on Energy Conversion 14(3):698–703

    Article  Google Scholar 

  • Zachmanoglou EC and Thoe DW (1976) Introduction to partial differential equations with applications. The Williams and Wilkins Company, Baltimore

    MATH  Google Scholar 

Download references

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© 2009 Springer-Verlag London Limited

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(2009). Numerical Analysis. In: Spotlight on Modern Transformer Design. Power Systems. Springer, London. https://doi.org/10.1007/978-1-84882-667-0_3

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  • DOI: https://doi.org/10.1007/978-1-84882-667-0_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84882-666-3

  • Online ISBN: 978-1-84882-667-0

  • eBook Packages: EngineeringEngineering (R0)

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