A cascade equivalent A-H-circuit of a synchronous salient-pole electric machine

Abstract

Cartesian and cylindrical laminated models are well known in electromagnetic calculations of electric machines. In such models, general solutions of partial differential equations are transformed into four-terminal circuit equations, and this makes possible to synthesize cascade equivalent circuits of the electric machines. In salient-pole machines, solutions of partial differential equations are formed on the base of piecewise continuous Sturm-Liouville eigenfunctions. However, in this case, cascade equivalent circuits cannot be synthesized since it needs many piecewise continuous eigenfunctions in a zone of poles and many smooth functions in a zone of an air gap for ensuring uniqueness of a solution. Meanwhile the author of this paper had offered an approximate method on the base of a single piecewise continuous Sturm-Liouville eigenfunction in a zone of poles and many smooth functions in a zone of the air gap. This method allows transforming an analytic solution of a partial differential equation into four-terminal circuit equations and synthesizing cascade equivalent circuits of salient-pole electric machines. In this paper, a synthesis of an active cell of a cascade equivalent A-H-circuit of a synchronous salient-pole electric machine is considered. The active cell of the corresponding exciting field is synthesized by means of a solution of Poisson’s equation with a single piecewise continuous Sturm-Liouville eigenfunction.