Exciting field and quadrature-axis armature reaction in a cascade equivalent A-H-circuit of a salient-pole generator

Abstract

Cartesian and cylindrical laminated models are well known in calculations of electric machines. In such models, general solutions of partial differential equations are transformed into four-terminal network equations, and this makes possible to synthesize cascade equivalent circuits of 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 the zone of poles and many smooth functions in the zone of the air gap for ensuring uniqueness of a solution. Meanwhile the author of this paper had offered an approximate method on the base of the single piecewise continuous Sturm-Liouville eigenfunction in the zone of poles and many smooth functions in the zone of the air gap. This method allows transforming a solution of a partial differential equation into four-terminal network equations and synthesizing cascade equivalent circuits of salient-pole machines. In this paper, electromagnetic field of a synchronous salient-pole generator is calculated with a cascade equivalent A-H-circuit. The cell that corresponds to rotor poles is synthesized on the base of a solution of Laplace's equation with the single piecewise continuous Sturm-Liouville eigenfunction.