The Analysis of Electric Machines Electro-Mechanic Processes

Abstract

The rapid development of modeling of various electromechanic energy transformers (power transformers, electric machines) over the past years created the necessity to develop the systematic method of quality and quantity model analysis. Typical analysis of model includes the following stages: the calculation of transient processes, the calculation of established processes, the evaluation of static stability, and the parametric sensitiveness defining. Nowadays, only the analysis of transient processes is performed continuously, i.e. in the state cognate with the physical nature of a process. Other stages are studied in discrete time. The variety of mathematical apparatus used on each stage complicates the analysis and requires significant expenses. In this article, the author describes the method of solving all four tasks on the basis of a unified mathematic apparatus - general theory of differential equations based on a unified algorithm. The completion of first three stages is illustrated on example of the induction machine, the mathematical model of which is arranged to the normal Cauchy form in order to avoid inversion of coefficient matrix on each integration step. By using the affine coordinate system the physical meaning of stator variables has been preserved and the rank of model equation system has been reduced. Stationary electromechanic process is defined by solv ing the twopoint Tperiodic boundary problem leaded do wn on period to Cauchy problem with initial conditions clarification by Newton iterations. The response matrix for the initial conditions, that is the basic element of the Newton formula, is defined from the analytical solving of homogeneous system of linear variation equations. The transient electro� mechanic process will result from the integration of state equations defining on time longer than period. The static stability of the process is defined by the multipliers of response matrix to the initial conditions. The matrix should be calculated for variables values of the last step in the integration process on period. The suggested method can be freely generalized for the analysis of complicated electromechanic schemes. Keywords: energy transformer, power transformer, electric machine, model analysis, unified mathematic apparatus, induction machine, electromagnetic proc ess, Tperiodic boundary problem, Cauchy problem.