Estimation of coefficients of multivariable power series approximating magnetic nonlinearity of AC machines

• Autorzy: Sobczyk T. J. , Warzecha A.

Identyfikatory

DOI

10.2478/aee-2015-0030

• Języki publikacji: EN

Abstrakty

EN

Energy based approach was used in the study to formulate a set of functions approximating the magnetic flux linkages versus independent currents. The simplest power series that approximates field co-energy and linked fluxes for a two winding core of an induction machine are described by a set of common unknown coefficients. The authors tested three algorithms for the coefficient estimation using Weighted Least-Squared Method for two different positions of the coils. The comparison of the approximation accuracy was accomplished in the specified area of the currents. All proposed algorithms of the coefficient estimation have been found to be effective. The algorithm based solely on the magnetic field co-energy values is significantly simpler than the method based on the magnetic flux linkages estimation concept. The algorithm based on the field co-energy and linked fluxes seems to be the most suitable for determining simultaneously the coefficients of power series approximating linked fluxes and field co-energy.

Słowa kluczowe

EN

magnetism; magnetic field co-energy; mathematical modelling; parameters estimation

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2015
• Tom: Vol. 64, nr 3
• Strony: 379--389
• Opis fizyczny: Bibliogr. 16 poz., tab., wz.

Twórcy

autor

Sobczyk T. J.

• Cracow University of Technology Institute of Electromechanical Energy Conversion ul. Warszawska 24, 31-155 Kraków, Poland

autor

Warzecha A.

• Cracow University of Technology Institute of Electromechanical Energy Conversion ul. Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• [1] Demerdash N.A., Nehl T.W., Electric Machinery Parameters and Torques by Current and Energy Perturbations from Field Computations – Part I: Theory and Formulation. IEEE Transactions on Energy Conversion 14(4): 1507-1513 (1999).
• [2] Demerdash N.A., Nehl T.W., Electric Machinery Parameters and Torques by Current and Energy Perturbations from Field Computations – Part II: Applications and Results. IEEE Transactions on Energy Conversion 14(4): 1514-1522 (1999).
• [3] Brandt S., Data Analysis: Statistical and Computational Methods for Scientists and Engineers. Springer (1999).
• [4] Sobczyk T.J., An energy-based approach to modelling the magnetic non-linearity in AC machines, part I – General formulas for the co-energy, linked fluxes and inductances. Archives of Electrical Engineering 48(1-2): 219-229 (1999).
• [5] Demenko A., Nowak L., Pietrowski W., Calculation of magnetization characteristics of a squirrel cage machine using edge element method. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 23(4): 1110-1118 (2004).
• [6] Sobczyk T.J., Methodological Aspects of Mathematical Modelling of Induction Machines. WNT, Warszawa (2004) (in Polish).
• [7] Bianchi N., Electrical machine analysis using finite elements. CRC, Taylor and Francis Group, London (2005).
• [8] Bishop Ch.M., Pattern Recognition and Machine Learning, Series: Information Science and Statistics. Springer + Business Media (2006).
• [9] Warzecha A., Multidimensional Magnetizing Characteristics in Circuital Models of Electrical Machines. Publisher Cracow University of Technology, Monograph (381), Series of Electrical & Computer Engineering (2010) (in Polish).
• [10] Węgiel T., Weinreb K., Sułowicz M., Main inductances of induction motor for diagnostically specialized mathematical models. Archives of Electrical Engineering 59 (1-2): 51-66 (2010).
• [11] Sobczyk T.J., Application of higher order forms for the description of electromechanical energy converters. Archives of Electrical Engineering 60(1): 67-75 (2011).
• [12] Burlikowski W., Hamiltonian model of electromechanical actuator in natural reference frame, Part I: Topology-based approximation algorithm. Archives of Electrical Engineering 60(3) 317-330 (2011).
• [13] Lu K., Rasmussen P.O., Ritchie E., A New Energy-Based Method for 3-D Finite-Element Nonlinear Flux Linkage Computation of Electrical Machines. IEEE Transactions on Magnetics 47(10): 3276-3279 (2011).
• [14] Mazgaj W., Warzecha A., Influence of electrical steel sheet textures on their magnetization curves. Archives of Electrical Engineering, 62(3): 425-437 (2013).
• [15] MagNet v.7.4.1, Documentation Center, http://www.infolytica.com.
• [16] Matlab R2011b, User Manual, The MathWorks, http://www.mathworks.com