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Performance of Rotors in a Brushless Doubly-Fed Induction
Machine (BDFM)
P.C. Roberts (pcr20@cam.ac.uk), R.A. McMahon , P.J. Tavner*, J.M. Maciejowski, T.J. Flack,
X. Wang
Cambridge University Engineering Department, Trumpington Street, Cambridge, CB2 1PZ, UK
* University of Durham, School of Engineering, South Road, Durham, DH1 3LE, UK
Abstract-The paper presents experimental results
to assess the performance of a variety of rotors
used in a Brushless Doubly Fed Machine
(BDFM). In the experiments the torque-speed
characteristics were measured on a BDFM fitted
with four rotors with five different windings. The
measurements were made of the machine excited
with just one stator supply with the second stator
supply first open circuit, and then short-
circuited. The results give valuable insight into
how different rotors, including a novel design of
BDFM rotor, will perform in a BDFM configured
as a variable speed generator. The results
highlight important differences between the
rotors related to their winding construction.
I. INTRODUCTION
The BDFM is attractive as a variable speed
generator for wind turbines. In this application, one
stator winding is connected to the grid and the other
is fed with a variable frequency supply by an
inverter. The BDFM operates in synchronous mode
with a fixed relationship between the shaft speed,
grid frequency and the output frequency of the
inverter. In common with the currently used
double-fed induction generator (DFIG), the BDFM
requires an inverter with a rating which is only a
fraction of the total electrical output. However, the
BDFM has the important advantage that there is no
brushgear. The BDFM is therefore of particular
interest for off-shore wind turbine applications
where servicing costs are high and it is desirable to
avoid brushgear maintenance.
However, to date only relatively small prototype
BDFM machines have been demonstrated, the
largest being a 160 frame size machine reported by
Williamson et al [1]. The authors have recently
increased the size of the BDFM by constructing a
180 frame machine as a step towards the
construction of a machine with a rating similar to
that of existing DFIGs, see Figure 1. The authors’
BDFM uses a commercial frame with a stator
incorporating four and eight pole windings of equal
rating, see Figure 2.
The rotor configuration and performance is the most
challenging aspect of the design of a BDFM as the
action of the rotor is crucial in determining the
overall performance of the machine. For BDFM
operation, the rotor must couple to both stator
windings and the effectiveness of this coupling
depends on rotor configuration. In this paper the
authors show how rotor performance can be
assessed from measured torque-speed
characteristics. The performance of three candidate
BDFM rotors has been studied and compared. In
addition, to act as benchmark, the performance of
the cage rotor normally fitted to that 180 frame size
machine has been determined.
The paper answers the following questions:
• What are the relative torques developed by
the different rotors and windings in a
BDFM?
• How large are these torques, compared to
those developed by a normal cage rotor in
the same machine?
Figure 1, The 180 size BDFM Machine used in these
experiments, in an early test configuration.
Figure 2, The 180 size BDFM Machine showing the two
stator windings in conventional slots.
II. PROTOTYPE BDFM MACHINE
To be presented at International Conference of
Electrical Machines, 2004, Cracow, Poland
The details of the prototype machine shown in Figs
1 to 5 are given in Table I, the detailed design of the
rotors is discussed in Section III.
Table I Prototype Details
Parameter Value
Frame size D180
Stator core
length
190mm
Stator slots 48
Stator winding 1
4 pole, 16 x 10 turn coils, series
connected
Stator winding 2
8 pole, 16 x 20 turn coils, series
connected
Rated Stator
Voltage &
Connection
230 Vrms (phase), 50 Hz, star
connected
Air gap 0.50-0.58 mm
depending on rotor
Rotor slots 36
Rotor 1 6 nested loops spanning 1/6
rotor circumference, as Wallace
[6] & Broadway [2], see Fig 3.
Rotor 2 18 independent progressive
loops each spanning 7/36 of the
rotor circumference.
Rotor 2a As Rotor 2 but with every third
loop omitted making 6 groups of
2 independent loops.
Rotor 3 Novel design consisting of 6
progressively wound groups of
coils spanning 1/6 of rotor
circumference, see Fig 4.
Rotor 4 Conventional squirrel cage rotor
with Boucherot type slots, see
Fig 5.
III. BDFM ROTOR DESIGNS
For effective BDFM action, the rotor must cross-
couple the stator fields of two different pole
numbers. This means that if, for example, the 4 pole
winding is excited, you would expect a significant
amount of 8 pole field to be produced via the rotor,
and vice-versa. Cross-coupling has two
requirements:
• That the particular rotor winding links a
stator field of one pole number.
• That the resultant current distribution in the
rotor winding is constrained in such a way
as to link the stator field of the other pole
number.
In the present work, four rotor designs were
considered. The design of rotors was discussed by
Broadway and Burbridge [2], who first proposed the
‘nested-loop’ design of rotor. In the case of 4 & 8-
pole stator windings the rotor winding has 6 such
nests. The work of [2] focussed attention on single
layer designs suitable for manufacture by casting, as
is common for the fabrication of ordinary small cage
rotors. Almost all subsequent BDFMs have used this
nested loop rotor design proposed by Broadway [2],
further investigated by Wallace at al. [3] and
Williamson et al. [1]. The authors have constructed
a rotor of this design as shown in Fig 3.
Figure 3, Rotor 1 with nested winding, like [1] & [2].
In [2] the stated aim of the rotor design was to
produce a rotor with a single layer construction to
minimise manufacturing costs. However in [2] it
was noted that a superior design might be obtained
using a double layer but the design was ruled out on
economic grounds, which are valid for smaller
machines. However, this constraint does not apply
to larger machines, so the authors have
manufactured rotors with double layer windings,
Rotors 2 & 3 are of this type.
Rotor 2, with 18 progressive loops pitched over 7
slots was constructed to demonstrate the effects of
limited cross-coupling. Loops of pitch 70
o
were
finally chosen for manufacturing reasons and link
both 4 and 8 pole fields fulfilling only one of the
two requirements for cross-coupling. The current
distribution in this winding is relatively
unconstrained, as in a squirrel cage rotor, when the
rotor is excited with a 4 pole field, so only a 4 pole
field is produced. Similarly under excitation from
the 8 pole field only an 8 pole current distribution is
produced.
rotor ’phase’
single coil pitch
rotor core
Slot no.
187 9 14 e
tc
13121110865 151617etc
Figure 4, Rotor 3, novel progressive loop design
An additional rotor, identical to Rotor 2 was also
available, Rotor 2a. Every third loop of the winding
was omitted to enforce 6-fold symmetry on the
rotor, ensuring that the right harmonic fields are
produced to cross couple between 4 and 8 pole
fields. Rotors 2 & 2a serve to illustrate the two
requirements for cross-coupling of different pole
number fields.
The authors have also designed and constructed a
novel rotor design, Rotor 3, developed from design
notes in [2]. The rotor comprises
21
ppN
+
=
‘phases’, or sets of progressive loops, rather like a
single pole of a distributed winding, with each coil
pitched across
)/(2
21
pp
+
π
radians, where
21
p&p are the pole pair numbers of the two stator
windings. The prototype machine has 8 and 4 pole
stator windings, hence N=6, so the new rotor design
comprises 6 sets of progressively wound coils
pitched at 60
o
. Simulation studies performed
suggested that better performance might be obtained
by the removal of the outer conductor from each set
of loops. Various options were simulated, from
removing no loops, to removing 3 loops. Removing
two loops from each set was chosen as it gave good
performance.
The pitch of the loops within each phase could, in
principal, be changed, however under the
assumption that the two different pole number fields
are of equal magnitude, the maximum total flux
linked, summing both pole number fields, as a
function of coil pitch, is achieved with a pitch of
)/(2
21
pp +
π
radians. Figure 4 depicts the final
design.
Figure 5, Rotor 4 with conventional cage.
IV. ROTOR PERFORMANCE
The effectiveness of cross-coupling in a rotor can be
studied by comparing the operation of the BDFM
running in two conditions:
• Simple induction mode where one stator
winding is energised while the second is
left open circuit
• Cascade induction mode where one stator
winding is energised while the second is
short-circuited.
The production of torque by cross-coupling is
revealed by the tests in the cascade mode. In
contrast, in an ideal rotor there would be no torque
produce in the simple induction mode. The ratio of
the peak cascade torque to the peak simple induction
torque is therefore an indicator of the ideality of the
rotor for use in a BDFM. The absolute magnitude
of the cascade torque is also an issue; for a BDFM
of a given frame size to have a similar rating to a
cage rotor machine, or a DFIG, then the cascade
torques must be similar to the torque obtained from
a conventional cage rotor. Following on from the
author’s work of [4] it can be shown that by
comparing the torque-speed curves of the machine
in both modes, it is possible to make these
assessments.
These tests were all carried out on the machine
shown in Fig 1 with the details shown in Table I at a
reduced supply voltage of 90 Vrms (phase), 50 Hz,
star connected. This was done to limit currents to
acceptable values throughout all the tests and ensure
that all the results were obtained at approximately
the same flux conditions. The applied voltage gave a
nominal airgap flux density throughout the tests of
about 0.125 T rms. In the simple induction tests
only one fundamental field component was present
but in the cascade mode two fundamental field
components were present but in all cases the peak
flux density was well below a level at which
saturation of the iron circuit could occur.
0 500 1000 1500
-15
-10
-5
0
5
Rotor S
p
eed
(
r
p
m
)
Torque (Nm)
Rotor 1
Rotor 2
Rotor 2a
Rotor 3
Rotor 4
Figure 6, Measured 4 Pole Simple Induction.
0 500 1000 1500
-6
-4
-2
0
2
4
Rotor S
p
eed
(
r
p
m
)
Torque (Nm)
Rotor 1
Rotor 2
Rotor 2a
Rotor 3
Rotor 4
Figure 7, Measured 8 Pole Simple Induction.
0 500 1000 1500
-20
-15
-10
-5
0
5
10
Rotor S
p
eed
(
r
p
m
)
Torque (Nm)
Rotor 1
Rotor 2
Rotor 2a
Rotor 3
Rotor 4
Figure 8, Measured 4 Pole Cascade.
0 500 1000 1500
-10
-5
0
5
Rotor S
p
eed
(
r
p
m
)
Torque (Nm)
Rotor 1
Rotor 2
Rotor 2a
Rotor 3
Rotor 4
Figure 9, Measured 8 Pole Cascade.
Figure 6 shows Rotors 1-3 running in simple
induction mode when supplied from the 4 pole
winding, compared to the standard cage, Rotor 4, at
the same supplied voltage.
Figure 7 shows Rotors 1-3 running in simple
induction mode when supplied from the 8 pole
winding, again compared to Rotor 4.
Figure 8 & 9 show the rotors running in cascade,
supplied successively from the 4 and 8 pole
windings, again compared to the standard cage
rotor.
V. DISCUSSION
The results shown in Figures 5-8 exhibit a number
of important features as follows:
• Simple induction action:
o All five rotors show some simple
induction action. Rotor 4 was the
strongest, because it was designed for
that purpose, Rotor 2 also showed
strong induction action.
o The peaks of the 4 pole and 8 pole
Torque-Speed curves of Rotor 4 differ
due to differing pole numbers and
equivalent circuit impedances.
o The peak torques of the 4 pole and 8
pole Torque-Speed curves of Rotor 2
are slightly different to those of rotor
4. The relatively lower torque of the 4
pole characteristic is due to the
increased chosen pitch of 70
o
.
• Cascade action:
o Rotors 1 & 3 exhibit strong cascade
action as predicted by Williamson [1]
& Broadway [2], again because they
were designed for that purpose.
However, they both exhibit weak
simple induction action.
o Rotor 2a exhibits weak cascade action
with the same structure as Rotors 1 &
3 but reduced amplitude, particularly
with the 8 pole stator excited. This is
due to the weak cross-coupling present
in the rotor.
o Rotors 1, 3 & 2a show the Torque-
Speed curve passing through zero at
three points:
The cascade synchronous
(natural) Speed 500 rev/min
The Synchronous Speed,
1500 rev/min when energised
on the 4 pole winding, 750
rev/min when energised on
the 8 pole winding.
An intermediate speed
between the Natural and
Synchronous Speeds.
o Rotors 2 & 4 exhibit no measurable
cascade action.
o Rotors 1 & 3 in cascade action exhibit
torques in motoring and generation
equal to or greater than developed by
the conventional squirrel cage Rotor 4.
There is no diminution in the torque
capability in the cascade mode.
VI. ROTOR PERFORMANCE
In the case of Rotor 4, the standard cage rotor, the
peak torque and the speed at which it was generated
can be estimated from calculations using equivalent
circuit parameters. As the BDFM windings are such
that a given excitation produces very nearly the
same flux as in the normal induction motor, within
1% for the 4-pole winding and 3% for the 8-pole
winding, it is reasonable to use the manufacturer’s
given parameters for rotor quantities. However, as
the cage rotor has closed Boucherot type slots, the
parameters will vary with slip. Nevertheless, an
estimate of expected torque can be obtained using
normal running parameters.
The BDFM has two stator windings and so the
resistances of the individual windings will be higher
than the resistance of the stator winding in the
induction motor. Measured values have been used
for the two windings. It is not possible to determine
the stator leakage reactance in a simple way and so
the usual approximation of making it equal to the
rotor leakage reactance has been used in the first
instance. As the air gap in the present BDFM is
slightly different to that in the standard induction
motor, a value for the magnetizing reactance was
determined from a No Load Test. The Test results
are shown below in Table 2.
Table 2 Rotor 4, Initial Parameter Values
4-pole operation
R
2
’ = 0.459 Ohm X
2
’ = 1.88 Ohm
R
1
= 3.47 Ohm X
1
= 1.88 Ohm
X
m
= 76.65 Ohm
8-pole operation
R
2
’ = 2.18 Ohm X
2
’ = 6.03 Ohm
R
1
= 5.08 Ohm X
1
= 6.03 Ohm
X
m
= 85.6 Ohm
From these values, the results in Table 3 were
obtained.
Table 3 Rotor 4, Torques Measured & Predicted Using
Initial Parameters
4-pole motoring
Theory: 8.5 Nm
@ 1365 rev/min
Measured: 6.3 Nm
@ 1400 rev/min
4-pole generating
Not calculated
8-pole motoring
Theory: 8.5 Nm
@ 625 rev/min
Measured: 3.5 Nm
@ 700 rev/min
8- pole generating
Not calculated
From the results in Table 3 it can be seen that the
predicted torques are rather greater than measured.
The predicted torques for Rotor 4 in the BDFM
frame are lower than those obtained in the normal
configuration, principally because the stator
resistance in the BDFM is higher. It is possible that
the stator leakage reactance is also greater than the
simple estimate and such an increase would also
reduce the predicted torques. The observed
magnetizing inductance, determined from open
circuit tests, is 250 mH as opposed to 150 mH
quoted by the Manufacturer, so we can argue that
we have a smaller effective air gap. We can further
argue that leakage reactances should be increased in
the same proportion. The parameters then become as
shown below.
Table 4 Rotor 4, Modified Parameter Values
4-pole operation
R
2
’ = 0.459 Ohm X
2
’ = 3.13 Ohm
R
1
= 3.47 Ohm X
1
= 3.13 Ohm
X
m
= 76.65 Ohm
8-pole operation
R
2
’ = 2.18 Ohm X
2
’ = 10.05 Ohm
R
1
= 5.08 Ohm X
1
=10.05 Ohm
X
m
= 85.6 Ohm
Using these values, the results in Table 5 were
obtained.
Table 5 Rotor 4, Torques Measured & Predicted Using
Modified Parameters
4-pole motoring
Theory: 7.3 Nm
@ 1404 rev/min
Measured: 6.3 Nm
@ 1400 rev/min
4-pole generating
Theory: 21.5 Nm
@ 1596 rev/min
Measured: 16.5 Nm
@ 1594 rev/min
8-pole motoring
Theory: 3.0 Nm
@ 671 rev/min
Measured: 3.6 Nm
@ 703 rev/min
8-pole generating
Theory: 4.9 Nm
@ 829 rev/min
Measured: 5.4 Nm
@ 826 rev/min
From the results in Table 5 it can be seen that the
predicted torques are generally close to the
measured torques. Overall, we can conclude that
Rotor 4 is delivering close to expected torques in the
BDFM frame when the airgap dimension and stator
resistances are correctly considered.
VII. CHARACTERISATION
The previous section has shown how a conventional
induction motor can be analysed and designed using
an equivalent circuit model, the parameters for
which can be elicited from classical No-Load (Open
Circuit) and Locked Rotor (Short Circuit) Tests.
The BDFM is clearly a more complex machine, as
can be seen from the Torque-Speed characteristics
presented. However the measurements have shown
that the Torque-Speed characteristics of the motor in
cascade are related to the simple induction
characteristic and should submit to an equivalent
circuit model, related to that produced for the
conventional induction machine. The parameters for
such an equivalent circuit can then be obtained from
the Torque-Speed curve measured in cascade
operation. An additional aid to the process of
parameter extraction is that the authors have
perfected the means to measure the current flowing
in the rotor winding, see [5]. It is proposed that the
next step in this work will be to find that equivalent
circuit and predict the performance from the
parameters obtained.
VIII. CONCLUSIONS
It is clear from the measured results that Rotors 1
and 3 are viable BDFM rotors, as they both exhibit
strong cross-coupling torques. The measurements
have also shown that these torques are similar to
those developed by a conventional cage, Rotor 4, at
similar levels of excitation. The measurements give
confidence that the performance of a BDFM can be
represented by an equivalent circuit model, similar
to a conventional induction motor and that the
equivalent circuit could be derived from the Torque-
Speed characteristic measured in cascade action.
ACKNOWLEDGEMENT
The authors acknowledge the assistance of FKI
Energy Technology, particularly their subsidiaries
Marelli Motori SpA and Laurence, Scott &
Electromotors Ltd for the provision of the prototype
motor and fabrication of the rotors.
REFERENCES
[1] Williamson S, Ferreira A C, Wallace A K,
Generalised theory of the brushless doubly-fed
machine. Part 2: Model verification and performance,
Proc IEE, EPA, 1997, Vol 144, No 2, pp123-129.
[2] Broadway A R W, Burbridge L, Self-cascaded
machine: a low-speed motor or high frequency
brushless alternator, Proc IEE, 1970, Vol 117,
pp1277-1290.
[3] Wallace A K, Rochelle P, Spee R, Rotor modelling
and development for brushless doubly-fed machines,
ICEM, August 1990, Cambridge, MA, USA.
[4] Roberts P C, Flack T J, Maciejowski J M, Mc Mahon
R A, Two stabilising control strategies for the
brushless doubly-fed machine (BDFM), IEE
Conference, 1
st
PEMD, 2002, Bath, Pubn 487,
pp341-346.
[5] Roberts P C, Abdi Jalebi E, Mc Mahon R A, Flack T
J, Real time rotor bar current measurements using
blue tooth technology for a BDFM. IEE Conference,
2
nd
PEMD, 2004, Edinburgh, Pubn 498, pp120-125.
[6] Wallace A, Rochelle P, Spee R, Rotor Modelling and
Development for Brushless Doubly-Fed Machines,
Proc. Int. Conf. Elec. Mach. (ICEM), 1990 August
12-15, Cambridge, MA, USA, Vol 1.
