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# Phase Domain Synchronous Machine | Model Overview

- The stator is composed of N parallel windings per phase, all connected to ground with a ZN impedance. The N parallel windings of one phase are spatially distributed around the stator. Their positions is used to compute the winding functions necessary for the self and mutual inductance parameters.
- The rotoric circuit is composed of the field winding and one damper winding in the direct axis while the quadrature axis contains one or two damper windings for saliant or round rotors respectively.
- All damper windings are shorted. The block diagram of the phase-domain machine is shown in Figure 5 - 5.
- The stator reactance matrix for a single winding per phase machine is given as:

where Xls is the leakage reactance, XAxx and XBxx are the constant and time-variant part of the self reactance while XAxy and XBxy are for the mutual reactances. Finally, θ is the rotor electrical angle. The XA and XB parameters are calculated from the winding functions. The mutual reactance matrix between the stator and the rotor, refered to the stator for a salient-pole machine, is:

where Xmd and Xmq are the magnetizing reactance for the direct and quadrature axis respectively. Finally, the rotor reactance matrix, referred to the stator takes the following form.

Xlkq, Xlfd and Xlkd are the leakage reactance for the q-axis damper, the field winding and the daxis damper.

Phase-Domain Syncrhonous Machine Block Diagram (Healthy Machine)

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