SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure C.8 – Ampèrian loop; modified from [42, p.172].
The total enclosed current can be written in terms of the winding density function and the
winding current i, as shown in Equation (C.4).
H(2 G) Ienclosed N( ) id (C.4)
The winding density function in Equation (C.4) is responsible for ensuring the correct polarity of
current in each conductor. The convention established earlier is that positive current flow in a
winding is out of the page for conductors marked with . Given that hole flow is considered
positive current, it is required that the path of integration be traversed in the counterclockwise
direction per the right-hand rule in order to yield a positive value of field strength for current out
of the page [31, p.695], [44, p.203]. The sign convention used in this report is that an airgap
magnetic quantity (B, Φ, H, F) is positive when traveling from the rotor to the stator. When used
with the current polarity convention, the right hand rule also produces a positive value of MMF
thus all of these conventions agree. Finally, the airgap MMF can be found by evaluating Equation
(C.4), where it is recognized that the definition of field strength is MMF-per-length (which is 2G
since there are two airgaps across which the MMF acts).
CFP
The MMF of the CFP winding (Figure C.5-a) can be found visually with the help of Figure C.8
and the integral is unnecessary. The total MMF (across two airgaps) is found to be equal to the
product N·i over the interval (–π/2,π/2). The MMF across each gap plotted in developed form in
Figure C.9, where the peak value is given by Equation (C.5).
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