Environmental Engineering Reference
In-Depth Information
However, as with all such brushed machines the brushes and commutator were
prone to wear out and fail, not to mention generate arcs and EMI. The induction
machine, on the other hand, has no sliding contacts and is the most rugged electric
machine available for traction applications [3].
The procedure followed above applies equally to synchronous machines and
the results have the same validity. Torque of the synchronous machine will be a
function of field flux that is either due to permanent magnet excitation, field
windings or field excitation applied via the stator windings, or a combination of
both as in the IPM machine.
7.2 Dynamics of field oriented control
To more fully appreciate FOC and understand the mechanics of its implementation,
this section will focus on the dynamic behaviour of any type of electric machine
that is given various speed and torque commands. The behaviour of the machine
under FOC is observed from the standpoint of how the machine stator currents
respond to such load changes and speed commands.
First some vector transformations are necessary to move freely between sta-
tionary and synchronous reference frames. Machine currents and voltages are
sensed as ac quantities; hence, these are stationary frame variables. Controller
commands are executed in a reference frame that rotates synchronously with the
machine rotor; hence, these are synchronous frame variables (dc in the controller).
In order to transform between a 3-phase set of variables to the controller
d-q
variables, it is necessary to define a 3- to 2-phase transformation and its inverse.
Then a vector rotator is defined to make the transition from the stationary reference
frame to the synchronous frame and back. The necessary transformations are [
T
] for
the phase conversions and [
R
] for the rotator. In matrix form these transformations
are given by (7.8) and (7.9), respectively:
2
3
1
2
1
2
r
2
3
1
4
5
p
2
p
3
½
T
¼
0
2
ð
7
:
8
Þ
2
3
1
0
p
2
r
2
3
4
5
1
2
½
T
1
¼
p
3
1
2
2
The vector operation [
T
][
T
]
1
=
I
,a2
2 identity matrix. The vector rotator
matrix is defined in terms of a rotor position variable, q, shown in Figure 7.2. The
transformation from stationary reference frame (i.e. the frame of reference for
