SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

do not contain a common-mode component. In the next section the ideal waveforms do not
contain a ZS component so this is no harm, and in the next chapter, the space vector model will
take care of this.
The phase-variable simulation model will be used to develop concepts and to compare torque
production in sinusoidal and trapezoidal motors. A summary of the models used in this report is
as follows.
- The single-phase equivalent (SPE) model (introduced in the next chapter) represents one
phase of the machine in operation. It is likely the most familiar model of a three-phase
machine but it is valid only for a sinusoidal motor driven by sinusoidal currents and
operating in steady-state. The SPE model cannot be used with salient machines.
- The phase-variable model described above can describe a nonsinusoidal machine in
transient conditions but it is difficult to work with and does not provide very intuitive
results unless solved on a computer. The form shown above is useful for basic torque
analysis (shown in the next section) but will be most useful for deriving the space vector
model.
- The space vector model incorporates the combined action of each phase, like the threephase
simulation model, but it is condensed into a two-phase equivalent version that is
easier to work with. It is valid for arbitrary currents, even in transient operation, but can
only describe sinusoidal motors. The space vector model is simply the complex-valued
representation of the traditional “two-axis synchronous” model; both will be examined in
the next chapter.
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