ELECTRO-MAGNETIC FIELD ANALYSIS OF ELECTRICAL MACHINES BY FINITE ELEMENT METHOD

Abstract

A detailed study of finite element method as applied to field problems in electrical machines has been carried out. The topics covered are, (i) Development of Finite Element Method as applied to electro-magnetic field problems, (ii) Development of solution algorithms and computer programmes for linear and nonlinear steady-state and transient problems, development of the method and solution algorithms for materially nonlinear problems, (iv) Development of solution algorithms to solve the eddy-current problems, using complex magnetic vector potential approach. \ :y To satisfy various types of boundary conditions some special elements such as incremental, pocket node, interface 311(1 ijifinrte_j2lements have been developed. For the symmetric and anti-symmetric periodicity conditions suitable modifica tions in element properties are suggested. The choice between the use of different types of elements is difficult. Some times physical features dictate the use of smaller elements than those required. Mesh refinements over a region of rapidly varying field loads to bad numerical conditioning due to the use of same type of elements with higher aspect ratios and large variations in sizes. The use of different order elements and unorthodox mesh grading has been recommended. Anew but very simply approach to mesh grading and mixed graded elements has been presented. The basic element properties have been suitably modified for the constraint conditions. A Fortran programme has been developed. It is a general field analysing system, which includes all the above discussed refinements. Reluctance and conductance matrices are evaluated by using numerical integration. Twodimensional fields, axi-symmetric fields, and fields with varying thickness can ^oo analysed. The elements are isoparametric with linear, parabolic or cubic variations and can be used separately or in combination. Analysis of transient eddy currents behaviour to include the effect of impact voltage excitation directly has been carried out. A simplified approach based on field intensity is presented and the formulation is verified experimentally. It is possible to analyse the field by using either the magnetic vector potential or field intensity approach. A wide choice of algorithms based on Newton-Raphson method such as iterative method, incremental-i/teraitive method and modified Newton-Raphson method is available. A new formulation of the Newton-Raphson method, in which only incrjmgnd^aljtangential reluctance matrix is formed at every stage of iteration, is proposed. 'Alpha-constant' method has also been developed for analysing electro-magnetic fields. This method has yielded reliable and fast solutions of field problems. A new finite element approach 'Generalized Reluctivity' method has been suggested for the electro-magnetic field problems. In the method the shape functions and gradient matrix is evaluated only once at all the Gaussian points and only the generalized reluctivity and field intensity matrices are formed for different elements. The saving in time for forming the reluctance matrix once is approximately 35'/. for parabolic quadrilateral elements. The equations obtained for solving the steady state eddy current problems are of complex nature, i.e. consisting of real and imaginary parts. The solution of these equations is possible either by using complex mathematical operations or by separating the real and imaginary parts and using real operations. Efforts have been made to solve the steady state eddy current problems by using reluctance and conductance matrices.