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To design a six-phase machine, it is a common strategy to split the stator winding into two through phase belt splitting namely, abc and xyz having the angular displacement of α = 30°, to have asymmetrical winding [4, 18, 19]. Rotor of the machine remains same having the field winding fr and damper windings kd and kq along d-q axes, respectively. While going onward for the mathematical modeling, some of the important simplifying assumptions are considered [21, 22]:

 Both the three-phase stator windings (abc and xyz) are symmetrical balanced having a perfectly sinusoidal distribution in the air-gap.

 Flux and mmfs are sinusoidal with no space harmonics.

 Saturation and hysteresis effects are ignored.

 No skin effect, i.e., winding resistance, is not dependent on frequency.

Although, voltage and electromagnetic torque can be mathematically expressed in terms machine variables, which results in non-linear differential equations [22]. The non-linearity is due to the time varying inductance term. For simplicity, with constant inductance terms, concept of reference frame theory is used, and equations are preferably written in rotor reference frame using Park’s equation. Mathematically, voltages and flux linkage per second of a six-phase synchronous machine using Park’s variables are as follows [21–23]: