SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Part I – Sinusoidal BPMS Motors with Sinusoidal Currents
Part I reviews the nonsalient sinusoidal synchronous machine operating on balanced sinusoidal
current in the steady state. It is similar to the standard treatment found in most machine texts
except that the field winding has been replaced with a permanent magnet and there are no
damper/amortisseur windings or starting cage. First the general physical structure of the PMSM is
presented including conventions for winding directionality and magnetic axes. A brief discussion
of wye and delta connections is given next. The rotating stator MMF distribution is then
developed, both graphically and mathematically; this includes a discussion of the relationship
between electrical and mechanical angular measures. A common expression for electromagnetic
torque is formulated and the phasor-based electrical model (the single-phase equivalent) is
developed.
Physical Construction and Windings
The general structure of the three-phase brushless permanent magnet synchronous machine is
exactly like that presented in the previous chapter except that there are two additional phase
windings on the stator as shown in Figure 3.1. Per the convention given in Appendix C, the
buried coilsides are used to indicate the center of the sinusoidal windings. Note that the phase
order of the axes increases in a counter-clockwise direction. This convention is not universal in
the literature but it is by far the most convenient mathematically and graphically thus is used here.
Figure 3.1 – Stator of three-phase sinusoidal synchronous machine.
Similar to any general three-phase load, the windings of a three-phase motor may be connected in
wye (Y) or delta (Δ); if connected in wye the center connecting point (the neutral) may or may
63