The cascade equivalent A-H-circuit of the salient-pole electric machine on the base of Laplace’s equation in dimensionless Cartesian coordinates

Abstract

For electromagnetic calculations of electric machines, the laminated models and the cascade equivalent circuits are often used. In the laminated model, each layer corresponds to the certain structural zone of the electric machine. Analyzing the solutions of the partial differential equations for each layer, we can conclude that these solutions may be reduced to the equations of the four-terminal circuit. Thereupon, the cascade equivalent circuit of the laminated model will be synthesized. In salient-pole machines, the solutions of partial differential equations are usually formed on the base of the piecewise continuous Sturm- Liouville eigenfunctions. Unfortunately, in this case, the cascade equivalent circuits cannot be synthesized since it needs many piecewise continuous functions in the zone of poles and many smooth functions in the zone of the air gap for ensuring the uniqueness of the solution. However, the author offers the 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 synthesizing the cascade equivalent circuits of the salient-pole electric machines. In this paper, the synthesis of the cascade equivalent A-H-circuit of the synchronous salient-pole electric machine on the base of the Cartesian model is considered. In this model, the exciting field is generated with current sheets that are located on the rotor yoke The active cell corresponding the exciting field is synthesized by means of Laplace’s equation with the single piecewise continuous Sturm-Liouville eigenfunction.