SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Fundamental Relationships
Figure C.1 shows the basic relationships in a motor. They hold for the machine as a whole but
this section concerns only a per-phase analysis.
Figure C.1 – Fundamental relationships in a motor.
For a fixed current, the space distribution of MMF f ( ) produced by the stator winding is
obviously a function of how that winding is wound on the stator; this is described by the winding
function n(θ) (also known as a winding density- or distribution- function). The rotor flux R( r)
interacts with the stator MMF to produce torque that is a function of rotor position. The rotor flux
also interacts with the winding distribution to produce the rotor-stator flux linkage R( r)
which
is a function of rotor position. Since the winding function affects both torque production and
bEMF generation, it will be studied first. Then the MMF and rotor-stator flux linkage will be
discussed in the order indicated in the figure.
Only the rotor-stator flux linkage has been mentioned as being affected by the winding function
but the stator self flux linkage is also affected. However, the result is that distributing the winding
simply reduces the self flux linkage (by a factor up to ½) [69, p.6.6]. This does not affect torque
or bEMF so it is not discussed here.
Windings
A winding may be either concentrated or distributed. In a concentrated winding all N turns are
placed into two stator slots (per pole per phase), thus each slot then has N conductors. In a
distributed winding the N turns of are distributed into different slots around the stator.
Concentrated windings are simpler and will be discussed first.
281