Analytical methods of solving discrete nonlinear problems in electrical engineering

Abstract

More often than not, the non-linear problems of electrical engineering arise from discrete physical systems and are usually reducible mathematically to the solution of systems of non-linear total differential equations or to systems of non-linear integral equations. Six independent methods of solving discrete non-linear problems are given in this paper. Each method is illustrated by means of an electrical engineering problem. The illustrative examples employed pertain to a-c and d-c non-linear circuits, reluctance-induction motors, hunting of and dynamic braking of synchronous machines. References to additional methods are given in the bibliography. The 88 given references listed represent approximately ten per cent of the field, but many of the entries contain a bibliography on their respective fields. The accelerated growth of research in the field of non-linearity is due to different causes. The general advancement of science requires increasingly more precise expressions for the laws of science. Accurate non-linear equations frequently depart from the linearized or postulated linear equations which have been previously used for approximate results. The quest for perfection and generalization and the love of difficult investigations by professional mathematicians play a large part in this growth. A recent incentive is the increasingly exacting requirements of modern manufacturing. These requirements are born of the competitive necessity of producing ever improved machines and equipment in the most economical manner.