Rotor Design & Performance for a BDFM

Abstract

Analysis of the behaviour of the Brushless Doubly Fed Machine (BDFM) has received considerable attention in the literature. The BDFM is typified by its complex airgap flux distribution. This paper will build upon performance-prediction work, concentrating on the design and electromagnetic behaviour of the BDFM rotor, considering 2 different sizes of 4/8-pole stator machines and comparing test results from 2 different 6-pole rotor windings fitted to each of these machines, with predictions from their equivalent circuits and from FEA. The authors will use these results to conclude the important features of the rotor core and winding design for effective BDFM performance.

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Rotor Design & Performance for a BDFM
P J Tavner +, R A McMahon *, P Roberts *, E Abdi-Jalebi *, X Wang *, M Jagieła #, T Chick*
Abstract— Analysis of the behaviour of the Brushless
Doubly Fed Machine (BDFM) has received
considerable attention in the literature. The BDFM is
typified by its complex airgap flux distribution. This
paper will build upon performance-prediction work,
concentrating on the design and electromagnetic
behaviour of the BDFM rotor, considering 2 different
sizes of 4/8-pole stator machines and comparing test
results from 2 different 6-pole rotor windings fitted
to each of these machines, with predictions from their
equivalent circuits and from FEA. The authors will
use these results to conclude the important features
of the rotor core and winding design for effective
BDFM performance.
Index Terms—BDFM, Equivalent Circuit, Time-
stepping Finite Element Analysis.
I. INTRODUCTION
Analysis of the behaviour of the Brushless Doubly Fed
Machine (BDFM) has received considerable attention in
the literature, exemplified by Broadway et al [1] and
Williamson et al [2]. The BDFM is typified by its
complex airgap flux distribution. The authors have
added to this literature with recent work [3-10] which:
• Developed an equivalent circuit model for the
BDFM.
• Developed a method for extracting the parameters,
• Tested different machines, measuring both stator &
rotor quantities,
• Predicted the electric and magnetic loading and
potential ultimate rating of the BDFM.
• Compared test results, including rotor current
measurement, with performance predicted by both
the equivalent circuit and the time-stepping finite
element analysis (FEA).
Another strand of that work, included in [6], has been
the control of the BDFM, but that is not the subject of
this paper.
Peter Tavner & Tom Chick are with the New & Renewable Energy
Group, Durham University, School of Engineering, Durham, DH1
3LE, UK, peter.tavner@durham.ac.uk
Richard McMahon, Xiaoyan Wang and Ehsan Abdi Jalebi are with
Cambridge University Engineering Department, Cambridge, CB2 1PZ,
UK
Marisz Jagieła is with the Technical University, ul. Luboszycka, 45-
036, Opole, Poland
II. PRACTICAL MACHINES & ROTORS
Figure 1a, D180
frameBDFM at
Cambridge
Figure 1b, D160
frame BDFM at
Durham
Two 4/8-pole BDFM machines, with D180 and D160
frames, as shown in Figure 1, were tested at the authors’
two universities. These machines were both based upon
4-pole squirrel cage induction motor designs from the
same factory, as can be seen from the photographs, using
similar materials and manufacturing techniques. A
variety of 6-pole rotor designs were tested in these
machines as described in detail in the references [3-10].
One rotor was based on a design recommended by
earlier authors but 3 rotors incorporate new, two-layer
designs. Figure 2 shows the rotor designs adopted for
testing within the machines shown in Figure 1 and they
are described as follows:
• Rotor 1, applied to the D180 machine. Figure 2a
shows a 3 loop, nested, bar-conductor winding,
proposed by Broadway & Burbridge [1]. This had
been advocated for manufacturing reasons, because
of the simple bar and end-ring construction at one
end of the winding. However, the segmented,
brazed, end-ring construction at the other end of the
winding, visible in Figure 2a, is complex and
difficult to manufacture.
• Rotor 3, applied to the D180 machine. Figure 2b
shows a 4 turn, two-layer, bar-conductor winding,
suggested by a manufacturing arrangement used by
one of the associated companies [11]. This
arrangement allows a greater flexibility of winding
distribution and connection than is possible with the
nested-loop.
• Rotor 5, applied to the D160 machine, is a 4 turn,
two-layer, round-wire winding, which allowed
rewinding, to investigate the effect of varying
distribution factors and connections. A photograph
of Rotor 5 is shown in [10].
• Rotor 6, applied to the D160 machine, Figure 2c
shows a similar 5 turn, two-layer, round-wire
winding giving an improved MMF distribution
across the pole face.
To be presented at ICEM,
Chania, Crete, Greece,
Sept 2006

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Figure 2a, A BDFM rotor with a 6-pole, 3 loop, nested
winding. This is Rotor 1 in the D180 machine.
Figure 2b, Two D180 BDFM rotors with 6-pole, 4 turn,
two-layer windings. The right hand example is Rotor 3
in the D180 machine.
Figure 2c, A BDFM rotor with a 6-pole, 5 turn, two-
layer winding.This is Rotor 6 in the D160 machine.
III. ANALYTICAL METHODS
Roberts [5] developed a method for modelling the
machine using an equivalent circuit, as shown in Figure
3, and described a method for extracting the parameters
from the torque-speed curve measured during a cascade
test. He also proposed a method for considering
different winding designs and presented an analysis for
an optimised rotor winding design.
Figure 3, Equivalent circuit used to represent the
performance of the BDFM.
This equivalent circuit has a reduced number of
elements, as the full circuit cannot be deduced from
terminal measurements of the Torque-speed curve.
However, the forms of equivalent circuit considered in
[5, 6] are electrically equivalent but, for example,
magnetising inductances are increased , because stator
leakage reactances are absorbed into them. The
equivalent circuit allows the prediction of terminal
quantities from the machine at different applied
voltages, frequencies and rotor speeds.
Jagieła [8] proposed a method for analysing the
performance of the machine using a time-stepping FEA.
The FEA permits visualisation of the detailed magnetic
flux-plot in the rotor for different windings at different
applied voltages, frequencies and rotor speeds, allowing
the optimisation of rotor slot and yoke design.
These methods have been used to predict the behaviour
of the rotors described.
IV. EXPERIMENTAL WORK
Strong BDFM operation requires good coupling between
each stator winding and the rotor winding, associated
with no direct coupling between the stator windings. In
order to test this coupling, and demonstrate the benefits
of the different rotor and stator combinations, cascade
operation of each motor was tested. That is each
machine was supplied on one stator winding from the
mains while the other stator winding was short circuited.
The rotor torque was then measured at a variety of
speeds throughout the speed range. This test was
performed on the 4-pole winding and repeated on the 8-
pole winding. The equivalent circuit in Figure3 was
extracted from these torque-speed curves.
Figure 4 shows a comparison between the cascade
torque-speed curves of the 4 rotors studied.
The parameters of the equivalent circuit for each rotor
were extracted from the cascade torque-speed curves and
are summarised in Table 1 below.
The curves also compare the experimental performance
with that predicted using the extracted equivalent circuit.
The flux-plots for the cascade performance were
predicted using the FEA time-stepping method. The
flux-plots shown in Figure 5 were each taken at the same
point in time as the motor was running in 4-pole cascade
at the Natural Speed, 500 rev/min. Therefore in each
case the motor was running at zero torque on no-load.
The Torque-speed curves were also predicted from the
FEA and these are plotted alongside the experimental
curves in Figure 4 and there is close agreement,
confirming the validity of the FEA results.
These tests yield, for a range of rotor designs, the
potential for a detailed comparison between:
• experimental performance,
• predictions using the equivalent circuit,
• predictions using time-stepping flux-plots.
V. DISCUSSION
The novelty of this work was the range of BDFM rotors
investigated and the comparison between theory and
experiment on these rotors.
The torque-speed curves in Figure 4 and the parameters
in Table 1 demonstrate that the equivalent circuit
parameters can be extracted conveniently from the
cascade test results and that the resultant circuits
accurately represent the measured performance.
Study of the Torque-speed curves, particularly for Rotor
1 in the D180 and Rotor 6 in the D160 is instructive,
because these rotors subsequently exhibited strong
BDFM operation. Those curves both exhibit a steep
torque transition through the natural speed of 500
rev/min and the synchronous speeds of 750 rev/min (8-
pole) and 1500 rev/min (4-pole). In an induction motor
that steep transition is achieved by a high Lr’/Rr’ ratio.

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Study of Table 1 for the D180 machine shows that Rotor
1, with 3 nested-loops, had a low referred rotor
resistance, Rr’, of 1.26 Ω, and a high Lr’/Rr’ratio, 27.9.
This was higher than that for Rotor 3, with a 4 turn, two-
layer winding.
Similarly Rotor 6, with 5 turn, two-layer winding, had a
low referred rotor resistance, Rr’, of 1.47 Ω, and a high
Lr’/Rr’ratio, 19.0. This was higher than that for Rotor 5,
with 4 turn, two-layer winding.
In fact the two-layer winding in Rotor 6 of the D160
machine achieved almost as strong BDFM performance
as the nested-loop winding in Rotor 1 of the D180
machine, which had a much larger volume of copper in
its rotor circuit, compare the photographs in Figures 2a
and 2c,.
Therefore good coupling from both stator windings to
the rotor and strong BDFM performance seems to be
consistent with a steep torque transition through the
natural and synchronous speeds in the cascade test and a
high Lr’/Rr’ratio in the rotor.
Another important issue in the rotor magnetic design is
the behaviour of the rotor magnetic flux under the
complex BDFM excitation. A number of authors have
noted the importance of the rated flux in the machine
and this was considered in some detail in [7]. As in any
electrical machine, saturation in the rotor teeth and yoke
should be controlled but because of the superposition of
fields in a BDFM, due to different pole numbers, this is
complex to predict. This issue is central to consideration
of the best design for a BDFM rotor and could be
resolved by a study of the FEA flux-plots.
The no-load 4-pole, cascade, flux-plots for each motor,
in Figure 5, show a developed 6-pole field in the rotors.
For the D180 machine the flux is well-developed in the
Rotor 1. However, the width of the rotor tooth is too
narrow but in Rotor 3 the rotor yoke is very restricted
because of the extended depth of the rotor slots to
accommodate the two layers.
The no-load flux-plots for the D160 machine show that
it is hard to distinguish between Rotor 5 and Rotor 6,
despite the substantial difference in the parameters and
the marked differences in the toque-speed curves.
The theoretical and experimental data collated from the
variety of arrangements tested allows the reader to draw
conclusions about the ideal arrangement of the rotor
winding and the dimensions of the rotor slots in a
BDFM.
VI. CONCLUSIONS
Analytical and experimental work has shown the
following for the BDFM machine:
• Experimental results showed that rotors with strong
BDFM performance had a high ratio of referred
rotor winding inductance to resistance, Lr’/Rr’.
• The rotor air gap should be optimised to be as small
practicable to achieve strong BDFM operation.
• The design of the BDFM should aim to reduce the
referred rotor winding resistance, Rr’.
• Rotor slot cross-section needs to be large enough to
achieve the low referred rotor winding resistance,
Rr’.
• Rotor design needs to ensure that the rotor tooth
width at the bottom of the slot is adequate to carry
the rated flux of the machine.
• However in achieving an adequate rotor tooth width
and rotor slot cross-section the slot depth must not
restrict the depth of rotor yoke needed to carry the
main flux.
• To date the best BDFM performance from machines
at Cambridge and Durham has been achieved by
Rotor 1 in the D180 machine, with a 3 loop nested
rotor winding design, as proposed in [1].
• Two-layer rotor winding designs, as proposed in
[11], allow more freedom to adjust winding
connection and distribution, which could improve
the rotor MMF, the air-gap flux form and therefore
the output torque.
• In the D180 machine a low resistance 4 turn, two-
layer rotor winding was achieved but at the expense
of a deeper slot, reducing the rotor yoke below that
acceptable for the rated flux. The BDFM
performance of this rotor was not as good as that of
Rotor 3 with the nested-loop rotor winding.
• In the D160 machine a 4 turn, two-layer rotor
winding achieved a better balance between rotor
slot width, slot cross-section and rotor yoke depth.
A 5 turn , two-layer rotor winding achieved even
better performance, however, the full benefits in
BDFM operation were still not reached because of a
low slot fill, due to the rewindable winding,
resulting in a high rotor winding resistance.
• The tests suggest that a two-layer rotor winding can
achieve BDFM performance at least as good, if not
better than, a nested-loop if the above points are
taken into consideration in the design.
VII. ACKNOWLEDGEMENTS
The authors acknowledge the assistance of Marelli
Motori SpA & Laurence, Scott & Electromotors Ltd in
providing machines and manufacturing rotors
respectively.
VIII. REFERENCES
1. Broadway, A.R.W., and Burbridge, L.: Self-cascaded
machine: a lowspeed motor or high frequency brushless
alternator, IEE Proc, Vol 117, pp 1277–1290, 1970.
2. S Williamson, A C Ferreira, A K Wallace, Generalised
theory of the brushless doubly-fed machine. Part 1: Analysis,
IEE Proc - Electric Power Applications, Vol 144, no 2, pp
111–122, 1997.
3. P C Roberts, R A McMahon, P J Tavner, J M Maciejowski,
T J Flack, X Wang, Performance of rotors for the brushless
doubly-fed (induction) machine (BDFM), in Proc 16th Int
Conf Electrical Machines (ICEM), Cracow, Poland, pp 450–
455, September 2004.
4. P C Roberts, E Abdi-Jalebi, R A McMahon, T J Flack, Real-
time rotor bar current measurements using bluetooth
technology for a brushless doubly-fed machine (BDFM).
Proc 2nd IEE Int Conf PEMD, Edinburgh, Vol. 1, pp 120–
125, April 2004.
5. P. C. Roberts, A study of brushless doubly-fed (induction)
machines: Contributions in machine analysis, design and
control, Ph.D. dissertation, University of Cambridge, 2004,
available from http://www-control.eng.cam.ac.uk/»pcr20.
6. P C Roberts, R A McMahon, P J Tavner, J M Maciejowski,
T J Flack, Equivalent circuit for the brushless doubly-fed
machine (BDFM) including parameter estimation, IEE Proc

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- Electric Power Applications, Vol 152, no 4, pp 933–942,
July 2005.
7. R A McMahon, P C Roberts, X Wang, P J Tavner,
Performance of the BDFM as a generator & motor, IEE Proc
- Electric Power Applications, Vol 153, pp 289-299, March
2006.
8. M Jagieła, M Łukaniszyn, P J Tavner, J R Bumby,
Formation of circuit equations for inclusion in 2-d time-
stepping finite element analysis of rotating machines, Int
Conf on Fundamentals of Electrotechnics & Circuit
Theory, Poland, May 2005.
9. P J Tavner, M Jagieła, C Ingleton, A larger
motor/converter combination for higher efficiency
drives, in Proc 4th Int Conf Energy Efficiency in Motor
Driven Systems (EEMODS), Heidelberg, Germany,
September 2005.
10. P J Tavner, M Jagieła, T Chick, E Abdi-Jalebi, A Brushless
Doubly Fed Machine for use in an Integrated
Motor/Converter, Considering the Rotor Flux, Proc 3rd IEE
Int Conf PEMD, Dublin, April 2006.
11. Schwarz K K, The design of reliable squirrel cage rotors,
Publn 189, Laurence, Scott & Electromotors Ltd.
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Rotor Speed (Rev/Min)
Torque(Nm)
4-Pole Measured
4-Pole Equivalent
Circuit Predicted
4-Pole FEA Predicted
8-Pole Measured
8-Pole Equivalent
Circuit Predicted
8-Pole FEA Predicted
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Rotor Speed (Rev/Min)
Torque(Nm)
4-Pole Measured
4-Pole Equivalent
Circuit Predicted
4-Pole FEA Predicted
8-Pole Measured
8-Pole Equivalent
Circuit Predicted
8-Pole FEA Predicted
Figure 4a, Cascade performance of nested-loop Rotor 1 in
the D180 machine, taken from [6]. The air-gap flux density
in this condition was nominally 0.125 T rms.
Figure 4b, Cascade performance of two-layer winding Rotor
3 in the D180 machine, taken from [6]. The air-gap flux
density in this condition was nominally 0.125 T rms.
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0
10
20
30
0 250 500 750 1000 1250 1500
Rotor Speed (Rev/Min)
Torque (Nm)
4 Pole Measured
4 Pole Equivalent
Circuit Predicted
4 Pole Cascade FEA
Predicted
8 Pole Measured
8 Pole Equivalent
Circuit Predicted
8 Pole FEA Predicted
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20
30
0 250 500 750 1000 1250 1500
Rotor Speed (Rev/Min)
Torque (Nm)
4 pole Measured
4 Pole Equivalent
Circuit Predicted
4 Pole FEA Predicted
8 Pole Measured
8 Pole Equivalent
Circuit Predicted
8 Pole FEA Predicted
Figure 4c, Cascade performance of two-layer winding
Rotor 5 in the D160 machine. The air-gap flux density in
this condition was 0.35-0.4 T rms.
Figure 4d, Cascade performance of two-layer winding Rotor
6 in the D160 machine. The air-gap flux density in this
condition was 0.35-0.4 T rms.

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Table 1, Parameters, showing the differences in values for for all 4 different rotor designs tested.
Figure5a, No-load flux-plot from Rotor 1 in D180 machine Figure5b, No-load flux-plot from Rotor 3 in D180 machine
Figure5c, No-load flux-plot from Rotor 5 in D160 machine Figure5d, No-load flux-plot from Rotor 6 in D160 machine