The WRIG Phase Coordinate Model

The WRIG is furnished with laminated stator & rotor cores with uniform slots in which 3-phase windings are placed (Fig 2.1 below). Usually, the rotor winding is connected to copper slip-rings.

Brushes on the stator gather (or transmit) the rotor currents from (to) the rotor-side static power converter. For the time being,  the slip-ring–brush system resistances are lumped into rotor phase resistances,

& the converter is replaced by an ideal voltage source.

As a result, the main flux self-inductances of various stator &, respectively, rotor phases are not dependent on rotor position.

The stator–rotor phase main flux mutual inductances, on the other hand, vary sinusoidally with rotor position ө_er. The mutual inductances between stator phases are also independent of rotor position, as the air gap is principally uniform. The same idea is applicable for mutual inductances between rotor phases. When mentioning stator & rotor phase & leakage inductances, all phase circuit parameters are included, with the exception of parameters to account for core losses (fundamental & stray-load core losses). Winding stray-load losses are mainly caused by frequency effects in the windings & may be recorded for in the phase resistance formula. Thus the phase coordinate model of WRIG is clear-cut:

Eq (2.1)

 

The stator equations are written in stator coordinates, & the rotor equations are written in rotor coordinates, which clarify the absence of motion-induced voltages. Generator mode association of voltage signs for both stator & rotor is evident. So, delivered electric powers are of +ve value. We can easily translate Equation 2.1 into matrix form as below: