### Abstract:

The Brush less Doubly-Fed Machine (BDFM) has the potential to be a more cost
effective replacement for conventional induction or synchronous machine drives. The
BDFM has two stator windings: a power winding and a control winding. An electronic
power converter of variable voltage and frequency is connected to the control winding and
allows the speed of the machine to be adjusted synchronously. The power winding, by
design, carries the majority of the current needed for operation, the control winding only a
fraction of the current, thus enabling the converter rating to be as low as 25% of the rating
of the machine depending on the speed range of operation.
To date, only one specific stator pole-pair combination has been investigated,
namely the 3/1 combination, where 3 and 1 refer to the power winding pole-pairs and the
control winding pole-pair, respectively. Since the speed of the machine is dependent on
the sum of the pole-pairs of the stator windings, a general pole numbered model is needed
to evaluate the performance of such general machines with other pole-pair number
machines. The BDFM describing system equations are transformed to the two axis (dq)
rotor reference frame using a power invariant transformation. The analysis shows an
additional term involving the common bar impedance which was not present in earlier
analyses.
The dynamic model is simplified to yield a steady state synchronous model. The synchronous frequency of analysis is investigated which results in two equivalent steady state models. The models developed can easily handle excitation of any frequency or sequence on the control winding without the use of an auxiliary model as used in previous analyses. The voltage forced model predictions match data taken for a 5 hp BDFM laboratory prototype, establishing the validity of the analysis. The model is used in illustrating the torque producing capabilities and unity power factor operation of the machine under a variety of inputs. Using the model, predictions are made on a different pole-pair combination machine (4/2 BDFM) for use as a 60 hp pump drive as an alternative to a 3/1 BDFM for the same application.