Environmental Engineering Reference
In-Depth Information
conventional windings having both sides of coils in airgap slots, as well as in tor-
oidally wound machines, with only one coil side in airgap slots. The implementation
consists of selecting the number of pole pairs by controlling the phase shift between
currents in the elementary phases, where each elementary phase consists of a coil, or
a group of coils connected in series.
As opposed to Dahlander's connection, which allows only one, 2:1, ratio
between the number of pole pairs created by a single winding, the number of pole
pairs in PPM is arbitrary. The Dahlander winding is usually built with full pitch at
lower speeds of rotation, and, therefore, with half the pole pitch, that is
y
¼ t
p
/2 at
higher speeds of rotation (
y
denotes here the winding pitch and
t
p
the pole pitch,
both expressed in the number of slots). The PPM winding with conventional coils,
on the other hand, is always built to have full pitch at higher speeds, when the
number of pole pairs at lower speeds is odd, and a shortened pitch at higher speeds
of rotation, when the number of pole pairs at lower speeds is even.
The number of pole pairs PP is a function of the total number of stator slots
N
,
the phase belt
q
and the number of phases
m
according to (5.27):
N
2
qm
PP
¼
ð
5
:
27
Þ
where PP and
m
must be integers, and
q
is usually an integer. This means that an
m
-phase machine with
N
slots can be built having several pole pairs, the numbers of
which depend on the value of
q
.
In this example, a 72-slot toroidal stator is assumed, and a 12-pole/4-pole
toroidal winding is used, because a toroidal winding allows much more freedom
in PPM design than a conventional one. In this example, the IM is connected to a
9-leg, 18-switch inverter.
The toroidal machine phase belts for 12-pole and 4-pole configurations are
defined as
72
12
m
12
¼
6
m
12
,
72
4
m
4
¼
18
m
4
q
12
¼
q
4
¼
ð
5
:
28
Þ
where
m
is the number of phases, 72 is the number of stator slots and
q
is the
corresponding phase belt, expressed in a number of slots. An additional constraint
is that
q
12
¼
nq
4
ð
5
:
29
Þ
where
n
is an integer. Finally, the last condition is that the sum of all line currents is
zero.
Equation (5.28) shows that with the 72-slot machine, the maximum number of
phases (neglecting all other considerations) can be 6 for a 12-pole connection and
18 for a 4-pole connection. Having different number of phases for these two con-
figurations would lead to an inefficient use of current sensors. In order to minimize
