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Krzysztof Makowski

Circuit-field formulation of single-phase shaded pole induction motors

Scientific Papers IMNiPE PWr - no. 51, Monographs - no. 14, Wrocław 2000


A circuit-field combined formulation applied to the single-phase shaded pole induction motors and its capability for analysis, design and simulation of the motors have been presented. Unlike in others circuit-fields models it is not necessary to calculate self and mutual inductance of the windings since the electromotive forces induced by the resultant magnetic flux linked with the considered winding are directly inserted into the circuit equations as variables.

Representation of the rotor bars current by the harmonic distribution of the current over periphery of the rotor enables taking into account deep bar effect and its influence on impedance of the rotor bars. It is also possible to apply skew factors, when the induced emfs are evaluated to consider the skew of the rotor bars. The magnetic vector potential has been employed to describe the distribution of magnetic field in cross-section of the motor. The results of magnetic field calculation have been used to determine the resultant emfs induced in the windings. A set of the circuit-field equations of the motor is solved for each value of slip in double iteration process. The non-linear complex potential equations and the linear complex circuit equations are solved in the internal loop and in the external loop, respectively. Except the Newton-Raphson method employed for the solution of non-linear potential equations, the approximate linearization has been developed as a first step of magnetic field evaluation. The approach may be sufficient for the preliminary design and assessment of the performance characteristics of the motor. The algorithms and block diagrams of numerical solutions of the circuit-field equations have been included. The calculated electromechanical characteristics with taking into account non-linearity of magnetic core and variations of others parameters of the motor proved the capability of the described circuit-field formulation.

The testified features of the circuit-field formulation shown its capability to deal with variety of material-structure designs of the single-phase shaded pole induction motors and proved that the method is particularly suited to a design of single-phase induction motors containing many spatial harmonics of the magnetomotive force.

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