The Phasor Diagram of a Superconducting Synchronous Electrical Machine

Abstract

This paper describes a universal method proposed by the author for the evaluative analytical calculation of the main parameters of synchronous electrical machines, including superconducting ones. Traditional methods for analytical calculation of parameters to build a phasor diagram of electrical machines require a calculation of all dimensions of the active zone, tooth-slot zone and frontal parts of armature windings. All sizes and local states of magnetic circuit saturation are necessary for the calculation of magnetic conductivities. Traditional analytical methods use, among other things, empirical formulas and non-physical coefficients and allow one to calculate only standard machines with classic tooth-slot zones and armature winding types. As a result of drawing a phasor diagram using traditional methods, the angle between the electromotive force and voltage is calculated, which is the machine’s internal parameter and has no major significance for users. The application of modern computer programs for simulation requires a preliminary analytical calculation in order to obtain all dimensions of the three-dimensional model. FEM simulation programs are expensive, require expensive high-performance computers and highly paid skilled personnel. Fast analytical techniques are also required to assess the correctness of the obtained automatic computer simulation results. The proposed analytical method makes it possible to quickly obtain all the main parameters of a newly designed machine (including superconducting ones and those of non-traditional design) without a detailed calculation of the dimensions of the tooth-slot zone and armature end-windings. The characteristic values of load angles are set according to the results of simple calculations, and the desired values, obtained via plotting, represent the inductive resistances of armature winding and inductive voltage drop across it. Results of practical significance, calculated from the voltage diagram, are as follows: the inductor’s magnetomotive force necessary to maintain the nominal load voltage value, regardless of the magnitude (including double overload) and type of the connected load, or the main dimensions of the active zone.

Simplified Current-Equivalent Circuit Models of Synchronous Reluctance Machines and Salient Pole Synchronous Machines Considering the Reluctance Torque

“…Salient pole machines are often modeled based on the Clarke transform and the Park transform [33][34][35][36][37][38][39][40]. The Clarke transform represents the three alternating magnetic fields as one rotating magnetic field, where the rotation is described by two sine waves representing two directional axes in the stator reference frame.…”

“…Note that this is a phasor model and not a vector model [39]. The magnetic flux linkage Ψ phasor will rotate in the same angular phase as the current phasor I.…”