Content uploaded by Ehsan Abdi
Author content
All content in this area was uploaded by Ehsan Abdi on Mar 24, 2021
Content may be subject to copyright.
Characterising Rotors for Brushless Doubly-Fed
Machines (BDFM)
Richard McMahon†*, Peter Tavner‡*, Ehsan Abdi†*, Paul Malliband†* and Darren Barker‡
† Electrical Engineering Division, Cambridge University, Cambridge, UK
‡ School of Engineering and Computing Sciences, Durham University, Durham, UK
* Wind Technologies Limited, St Johns Innovation Park, Cambridge, UK
Abstract— The brushless doubly fed machine (BDFM) is a
robust alternative to the doubly fed induction generator
(DFIG) which is widely used in wind turbines but suffers from
failures associated with its brushes and sliprings. The rotor
plays an important part in a BDFM, coupling the two stator
fields. To date, the nested loop has been almost exclusively
used in modern BDFMs, but this approach is not ideally suited
to large machines in which a form wound rotor is likely to be
preferable from a manufacturing point of view. This paper
gives a comparative study of two rotor windings. The
performance of the rotors has been predicted from theory for a
frame size 160 BDFM. Actual rotors have been built, using
identical rotor laminations, and tested, giving results which
accord well with predictions. The results give insight into the
design issues of rotors both from electrical and manufacturing
viewpoints.
I. INTRODUCTION
The brushless doubly fed machine (BDFM) is attractive
as a variable speed drive or generator because only a
fraction of the power needs to pass through the converter.
The absence of brushes and slip rings also makes the
machine attractive as a wind turbine generator as brush and
slip ring problems in the widely used doubly fed induction
generator (DFIG) have been identified as the principal
failure mode of these generators in wind turbines [1]. An
experimental scale BDFM has recently been demonstrated
in a 20 kW wind turbine [2] and the use of the BDFM as a
variable speed drive is also the subject of a recent paper [3].
The BDFM has its origins in the single-frame self-
cascaded induction machine, in which two fundamental air-
gap fields of different pole numbers share the same iron
circuit [4]. Developed by Hunt [5], the machine gained a
reputation for robustness and reliability [6]. The
contemporary BDFM, following the work of Rochelle et al.
[7], has two separate stator windings chosen with pole
numbers selected so that there is no direct coupling directly
between them, that is coupling is via the rotor only. Separate
stator windings facilitate double feeding, that is the
connection of one winding directly to the mains and the
other to the mains via an electronic converter, without any
penalty in winding utilization.
The rotor of a BDFM is a critical component. A good
rotor will couple the two fields of interest and have low
resistance and inductance. As shown in [8], there is a rotor
turns ratio which maximizes the machine output. In
addition, the rotor should be straightforward to manufacture.
Lydall [4] used two normal windings on the rotor but Hunt
[5] showed that this was wasteful of copper and described a
more complex winding with lower resistance. Broadway and
Burbidge [6] reported the nested loop type of rotor which
has been used in most subsequent BDFMs.
This type of rotor was proposed on the basis of its
similarity to the cage type rotor found in induction motors
and it was expected to share the characteristic of easy
manufacture. However, as noted by Williamson et al. [9],
the bars of a BDFM rotor must be insulated, making casting
impossible. However, the squirrel cages of large induction
motors would normally be manufactured from copper alloy
conductor and brazed but to do that for a nested loop
winding has been found to be a costly and time-consuming
process. The nested loop rotor also suffers from an unequal
distribution of currents between the nested loops and
consequential circulating currents. Roberts et al. [10]
investigated various BDFM rotor forms and showed that
another form of rotor involving series loops, was capable of
cross-coupling but the implementation described was not
optimized.
The present paper describes recent work on optimising
the design of a wound rotor for the BDFM based upon [10],
which is straightforward to manufacture and applicable to a
wide range of machine sizes. The theory underlying the
rotor design is outlined and results from experimental tests
presented to confirm the rotor's performance. In addition, its
performance is compared to that of a nested loop type of
rotor using identical rotor laminations.
II. BDFM BASICS AND CONFIGURATION
The BDFM is normally operated as a variable speed
machine in the synchronous mode with double feed, as
shown in Fig 1. The shaft speed in the synchronous mode is
given by
21
21
60 pp
ff
N+
+
= (1)
Fig 1. Block diagram showing BDFM, power winding on line and control
fed through converter (On wrong page)
XIX International Conference on Electrical Machines - ICEM 2010, Rome
978-1-4244-4175-4/10/$25.00 ©2010 IEEE
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on March 24,2021 at 14:13:34 UTC from IEEE Xplore. Restrictions apply.
Fig. 2. Simplified per-phase equivalent circuit for the BDFM from [11]
A further relationship for the so-called natural speed, that
is the synchronous speed when the control winding is fed
with DC, is given by
21
1
60 pp
f
Nn+
= (2)
The BDFM can also be operated in the cascade mode in
which one stator winding is shorted and in the simple
induction mode with one stator winding open circuit. These
two modes are useful to determine the machine parameters.
The operation of the BDFM can be described by a per-
phase equivalent circuit of the form shown in Fig. 2 [11].
Values are shown referred to the power winding and iron
losses are neglected. R1 and R2 are the resistances of the
stator windings and Rr is the rotor resistance. Lm1 and Lm2
are the stator magnetising inductances and Lr is the rotor
inductance. The use of the modifier ‘ ′ ’ denotes that the
quantity is referred. The slips s1 and s2 are defined in
section V.
An idealized form of the equivalent circuit, shown in Fig.
3, was proposed in [8] which retained only the rotor
reactance on the grounds that it was the dominant series
component in most practicable BDFMs; this approach also
allows a number of useful relationships to be derived which
can assist in BDFM design.
From the core model, an optimum value of the rotor turns
ratio nr for maximum rating can be deduced [8] given by
3
2
2
1
cos
)cos( ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛+
=
φ
δφ
p
p
nr (3)
The optimum value of nr depends on operating conditions
but a reference value can be obtained by taking the
(cos(
φ + δ
)/cos
φ
) to be unity, implying that the machine is
operated with a small load angle δ and at a power winding
power factor near unity. Another viewpoint is that in this
case the voltage drop across Lr' is small and can be
neglected.
III. BDFM ROTOR DESIGN
A. General Arrangement
The rotor has been designed for use in a 4 pole/8 pole
BDFM manufactured using the stator stack and frame from
a size 160 induction motor. The air gap diameter is 0.155 m
and the stack length 0.19 m. The stator design has been
optimized by the procedure described by Wang et al. [12];
details of the windings are given in Table I.
A p1/p2 pole-pair BDFM will have p1 + p2 sets of rotor
circuits, in this case six, each set being distributed over 60o.
The wound rotor has three concentric coils in series in each
set and the nested loop rotor has three concentric loops with
Fig. 3. The BDFM core model
a common shorting end ring. For ease of manufacture of the
wound rotor, a single layer winding with 37 strands of round
wire conductors in parallel was used. In the case of the
nested loop rotor, shaped copper bars were used with brazed
end connections. The number of rotor slots must be an even
multiple of six. A lamination with thirty six slots has been
chosen as this gives a reasonable slot pitch with the air-gap
diameter of 155 mm for the D160 machine. The measured
airgaps for the nested loop and wound rotors were is
0.33 mm and 0.34 mm respectively and a Carter factor of
1.21 was used for both the stator and rotor. The lamination
design is magnetically matched to that of the stator, which
also has 36 slots, in that the cross-sectional area of the rotor
teeth is the same as that of the stator teeth. The winding
arrangements are shown in Fig 4 and the prototype wound
and nested-loop rotors are shown in Fig. 5.
B. Turns Ratio
Using the simplified form of equation (3) in the previous
section the optimum turns ratio for a 2/4-pole-pair BDFM is
0.52/3 or 0.63. To find the actual turns ratio requires
calculation of the effective turns for the coupling to the 4
and 8-pole fields. These are shown in Table II, noting that as
the three series connected coils in each set are concentric so
the winding factors can be summed for the wound rotor. The
winding factors for each coil for the two couplings are:
⎟
⎠
⎞
⎜
⎝
⎛
=2
sin 1
1
p
kp
γ
(4)
⎟
⎠
⎞
⎜
⎝
⎛
=2
sin 2
2
p
kp
γ
(5)
The spans of the three coils or loops are 10ᴼ, 30ᴼ and 50ᴼ.
The sums of the winding factors are kwr1 = 1.44 and kwr2 =
2.19, which gives a turns ratio of 0.66, close to the optimum
value of 0.63.
TABLE I
BDFM WINDING DETAILS
Stator 1 Stator 2
Pole number 4 8
Effective turns/phase 250 272
TABLE II
WINDING FACTORS FOR ROTOR LOOPS
Coil/loop Span γ kw1 4-pole kw2 8-pole
A Inner 10 ᴼ 0.17 0.34
B Middle 30 ᴼ 0.5 0.87
C Outer 50 ᴼ 0.77 0.98
Neff 1.44 2.19
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on March 24,2021 at 14:13:34 UTC from IEEE Xplore. Restrictions apply.
(a) Wound rotor
(b) Nested-loop rotor
Fig. 4. Rotor winding diagrams
Fig. 5. Prototype wound and nested-loop rotors
The loops in the nested loop rotor have mutual couplings
which means that the calculation of the turns ratio is not
straightforward. An approximation to the turns ratio for the
nested-loop rotor can be found from considering an MMF
balance with one stator open circuit as:
C
C
B
B
A
A
C
CC
B
BB
A
AA
r
Z
kw
Z
kw
Z
kw
Z
kwkw
Z
kwkw
Z
kwkw
n2
2
2
2
2
2
21
2121
++
++
= (6)
where ZA, ZB and ZC are the impedances of the rotor loops at
a particular operating speed and the winding factors are as in
Table II. Providing that, as is usually the case, nr does not
vary significantly with speed, nr can be conveniently
evaluated at the natural speed. The data for evaluating the
bar impedances are given in sub-section D and lead to a
value for nr of 0.69, again close to the optimum.
C. Rotor Current Density
At full load, the currents in the stator and rotor windings
should reach their limiting values together. An MMF
balance can be used to find the rotor current from one of the
stator currents. It is convenient to use the 4-pole winding
which has a rated current of 5.98 A line, which, as the
machine is delta connected, translates to a phase current of
3.45 A. The MMF of a q-phase winding carrying current I
is:
p
N
I
q
MMF eff
2
4
π
= (7)
The stator is three phase but the rotor is six-phase. Hence:
rs effreffs NINI2
6
2
3
1
1= (8)
Putting in numbers for the wound rotor, noting that from
the previous section 1r
eff
N is 1.44 and from Table I 1s
eff
N is
250, gives a rotor current of 299 A. The rotor wire has a
diameter of 1.25 mm so this corresponds to a current density
of 6.6 A/mm2, slightly higher than the stator design current
density of 6 A/mm2 but acceptable as rotor cooling is
generally better.
The current densities in the nested loop rotor will be
different in each loop and will vary with operating point. At
rated output, calculation of loop currents from the rotor
impedances and winding factors shows that the currents in
loop B, the middle loop, and the inner loop A are about 2/3
and 1/4 respectively of the current in loop C, the outer loop.
Applying an MMF balance gives a maximum current of
approximately 400 A in loop C, corresponding to 5 A/mm2
for a bar section of 81.3 mm2.
D. Parameter Calculation
Parameters for the rotor are needed to enable the
performance of the overall machine to be predicted using the
equivalent circuit. The rotor turns ratio has already been
established but the turns ratios to the stator windings needs
to be calculated too. The effective turns for stators 1 and 2
are given in Table I. The two stator to rotor turns ratios, n1
and n2, are then:
3.173
1
1==
r
s
eff
eff
N
N
n (9)
2.124
2
2==
r
s
eff
eff
N
N
n (10)
This gives n1/n2 = 1.40.
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on March 24,2021 at 14:13:34 UTC from IEEE Xplore. Restrictions apply.
An estimate of the rotor resistance in the case of the
wound rotor can be found using the following relationship
for each coil and adding the values. Particular account
should be taken of the fact that the end-winding spans vary
but the total arc length in the present winding is essentially
the same as if the winding were concentric.
⎟
⎠
⎞
⎜
⎝
⎛+= w
d
A
kN
Rcoil 360
2
γπρ
(11)
where N is the number of turns, ρ the resistivity of copper
(1.72 × 10-8 Ωm), A is the cross-sectional area of the
conductor, d is the mean diameter of the rotor slots, w is the
stack length and k is a constant, taken to be 1.1. This gives a
rotor resistance per pole of 0.56 mΩ. Referral to stator 1
needs to take account of the need for a six to three-phase
transformation (division of the referred value by a factor of
two) as well as the turns ratio. The referred resistance is
8.21 Ω which equates to 2.80 Ω in a star equivalent circuit.
It now remains to find the rotor inductance. This is made
up of conventional leakage elements and harmonic
inductance terms from the space harmonics created by the
rotor. Some of the space harmonics will couple to the stator
windings so the impedance presented to the rotor will not
just be the magnetizing reactance for that space harmonic.
However, an estimate of rotor inductance can be obtained by
neglecting this effect.
The harmonic inductances can be found from:
2
0⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=p
N
ldq
g
Leff
h
π
μ
(12)
evaluated for the the harmonic pole pair numbers. The
effective turns are found for the pole number in question, g
is the air-gap and the other symbols have the same meaning
as in previous sections. The harmonic fields that can exist
(harmonic order n) are given by
{}{}{}
)()( 212211 ppmpppmpn ++++∈ U (13)
where m is an integer. In reality high pole number fields can
only exist for point conductors so in evaluating the effective
turns for a particular space harmonic, it is appropriate to
assume that the conductor current density is uniformly
distributed over a slot mouth giving a distribution factor ks
2
2
sin
p
w
p
w
k
s
s
s
⎟
⎠
⎞
⎜
⎝
⎛
= (14)
where ws is the angular width of the rotor slot mouth in
radians A summation up to 200 pole field (pole pitch 1.8ᴼ,
mouth slot pitch angle 8.16ᴼ) gives Lr(h) = 6.20 μH.
The conventional leakage inductance components,
overhang, slot and zig-zag, found using the methods
described by [13] give an additional 5.07 μH. The total
leakage reactance referred to stator 1 is then 56.4 mH (star
form).
TABLE III
INDIVIDUAL LOOP PARAMETERS FOR THE NESTED LOOP ROTOR
Loop A B C
Rr (
μΩ
) 101 112 133
Lr (
μ
H) 5.38 5.03 4.18
Xr (
μΩ
) 1127 1053 875
The resistances of the individual loops in the nested loop
rotor can be calculated using equation (11), ignoring the
effects of the common end ring, and the harmonic
inductance can be found using equation (12). The loops will
have different winding factors for harmonic fields so there
will be cross-coupling, but for simplicity this will not be
taken into account. Values of resistance, inductance and
impedance evaluated at the natural speed (a frequency of
100/3 Hz) are shown in Table III and can be used to obtain
values for ZA, ZB and ZC.
Parameters for an equivalent single loop with a winding
factor of unity can be determined by considering a short
circuit on stator 2. The effective impedance of this loop Zeq
is
1
2
1
2
1
2
1
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛++=
C
C
B
B
A
A
eq Z
kw
Z
kw
Z
kw
Z (15)
IV. EXPERIMENTAL EXTRACTION OF ROTOR PARAMETERS
The procedure for extracting the BDFM parameters in Fig
2 has been established by Roberts et al. [11]. The machine
was run in the cascade mode with the 4-pole winding
connected to the mains via a Variac and the 8-pole winding
shorted and then vice versa. Torque-speed curves were
obtained over a speed range of 200 to 1500 rpm and 200 to
750 rpm with the 4 and 8-pole windings excited
respectively. Tests were carried out at 200 V, slightly below
the rated voltage to limit saturation effects. The parameter
extraction procedure involves repeatedly recalculating
parameters for the equivalent circuit until a best fit is
obtained between the predicted and measured torque-speed
characteristics. As the stator winding resistances can be
accurately measured, they were taken as fixed and include
an allowance for temperature rise. The measured and fitted
cascade characteristics are presented in Fig 6.
A comparison between extracted, calculated and, where
available measured, parameters, including stator values, is
given in Tables V and VI. When allowance is made for
winding temperature rise during the test, the resistance
values are in good agreement. The theoretical value of the
turns ratio is a good match for the measured value.
The stator magnetizing inductances do not agree so well
but they are dependent on the air-gap measurement and the
accuracy of approximations in the Carter factors and
saturation onset in stator and rotor teeth. In addition, the fit
to the measured data in the extraction process is insensitive
to the magnetizing inductances so extracted values can vary
considerably. However, scaling the effective air-gap brings
the measured and predicted values into alignment. The rotor
reactances are reasonably close; scaling for the air-gap
makes the values closer but difficulties remain in calculating
the various leakage inductance components sufficiently
precisely. The overestimate of the inductance of the nested
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on March 24,2021 at 14:13:34 UTC from IEEE Xplore. Restrictions apply.
200 400 600 800 1000 1200 1400 1600
-20
-15
-10
-5
0
5
10
15 Wound Rotor
Speed (rpm)
Cascade Torque (Nm) - 8pole shorted
Experimental data
Fitted curve
100 200 300 400 500 600 700 800
-40
-30
-20
-10
0
10
20
30 Wo und Rotor
Speed (rpm)
Cascade Torque (Nm) - 4pole shorted
Experimental data
Fitted curve
0500 1000 1500
-40
-30
-20
-10
0
10
20
Nested-Loop Rotor
Speed
(
rpm
)
Cascade Torque (Nm) - 8pole Shorted
Experimental data
Fitted curve
670 680 690 700 710 720 730 740 750
10
12
14
16
18
20
22
24 Nested-Loop Rotor
S
p
eed
(
r
p
m
)
Cascade Torque (Nm) - 4pole Shorted
Experimental data
Fitted curve
Fig. 6. Experimental cascade torque-speed characteristics overlaid with
fitted curves
loop rotor is almost certainly a consequence of neglecting
the damping effects on certain space harmonics.
Overall, parameters can be calculated with sufficient
accuracy for initial machine design purposes.
V. TORQUE PRODUCTION
When operating the BDFM in the synchronous mode, the
aim is to utilize the synchronous torque which, referring to
the core model of Fig. 3, is given by
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛+=
1
2
11 1
cos
3f
f
IVT
r
ω
φ
(16)
This can also be expressed in the form
21
1
'
1
21
sin
3
pp
L
VVT
s
rs +
=
ω
ω
δ
(17)
which shows that the torque is dependent on a a load angle
as in a conventional synchronous machine. However, there
are also induction torques. One component, attempting to
accelerate the rotor towards the synchronous field of the
power winding is given by
11
'
2
1
1
3
s
r
im s
R
IT
ω
= (18)
TABLE V
CALCULATED AND MEASURED PARAMETERS FOR WOUND ROTOR
Parameter
Calculated
20oC
(100 K rise)
Direct
measurement
Measurement
by extraction
R1 (
Ω)
1.77 (2.46) 2.04 2.04
R2 (
Ω)
1.13 (1.57) 1.29 1.29
Lm1 (mH) 416 317 270
Lm2 (mH) 124 104 92
Rr' (
Ω)
2.80 (3.89) 3.11 3.80
Lr' (mH) 56.4 ---- 61.0
n 1.40 ---- 1.43
TABLE VI
CALCULATED AND MEASURED PARAMETERS FOR NESTED LOOP ROTOR
Parameter
Calculated
20oC
(100 K rise)
Direct
measurement
Measurement
by extraction
R1 (
Ω)
1.77 (2.46) 2.04 2.04
R2 (
Ω)
1.13 (1.57) 1.29 1.29
Lm1 (mH) 367 317 155
Lm2 (mH) 109 104 242
Rr' (
Ω)
1.54 --- 1.70
Lr' (mH) 56.4 --- 42.0
n 1.33 ---- 1.37
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on March 24,2021 at 14:13:34 UTC from IEEE Xplore. Restrictions apply.
The second component is trying to accelerate the rotor to the
cascade synchronous speed that is the natural speed. This
component is given by
n
in s
s
RIT
ω
1
3
1
2
''
2
2
1
= (19)
where ωn is 2πNn/60. The slips s1 and s2 are given by
()
21
1
1221
1pp
f
pfpf
s+
−
= (20)
()
21
2
2112
2pp
f
pfpf
s+
−
= (21)
The calculated pull-out torques for the nested loop and
wound rotors are respectively 250 and 172 Nm at natural
speed for a 240 V supply. Again based on an ideal model,
the synchronous torque at rated current (6 A) is predicted to
be 82 Nm. At natural speed and rated current the induction
torque is 11.7 Nm motoring and there is no contribution
from R2′′, which would be accelerating the rotor below
natural speed and braking it above.
The measured torques at rated currents were around
60 Nm which is in reasonable agreement given that the
calculated values are for an ideal machine. The induction
torques are not negligible and can only be reduced by
decreasing Rr′ and R2′′.
VI. DISCUSSION AND CONCLUSION
The use of a wound rotor with nested loops in series has
been shown to be a practical approach, offering
straightforward manufacture. However, Rr′ is approximately
twice that of the counterpart nested loop rotor. It is tempting
to ascribe this simply to the conductor cross-sections which
differ by a factor of 1.8. However, the inner loop of the
nested loop rotor carries only 25% of the current of the outer
loop, as confirmed experimentally for another BDFM [14].
Removing the inner loop of the wound rotor would reduce
Rr by 30% but Rr′ by only 10%.
One advantage of the nested loop winding arises from
having loops in parallel rather than series, so that current is
not forced to flow through loops which have relatively poor
couplings. The lower Lr’ of the nested loop rotor can be
attributed to the damping of harmonic fields by loop cross-
coupling, although this comes at the price of circulating
currents. The lower Lr’ & Rr′ translate into a 50% greater
pull-out torque for the nested loop over the wound loop
rotor. Both rotors have turns ratios, n, that are close to the
optimum.
An alternative design of wound rotor described in [10]
included a version with three series loops in each nest, each
loop spanning 30o displaced by 10o, which can be shown to
have a lower Rr′ but n is further from the optimum.
The investigations in this paper give insights into rotor
design for a BDFM. However, work remains to be done to
devise rotor windings which combine ease of manufacture
and good electrical parameters.
REFERENCES
[1] H. Arabian-Hoseynabadi, H. Oraee, P.J. Tavner, “Wind turbine
productivity considering electrical subassembly reliability,” in
Renewable Energy, vol. 35, no. 1, pp. 190-197, January 2010.
[2] T. Logan, J. Warrington, S. Shao and R.A. McMahon, “Practical
Deployment of the Brushless Doubly-Fed Machine in a Medium
Scale Wind Turbine,” in Proc. IEEE International Conference on
Power Electronics and Drive Systems, Taiwan, 2009, pp. 470-475.
[3] S. Shiyi, E. Abdi, R. A. McMahon, “Operation of Brushless Doubly-
Fed Machine for Drive Applications,” in Proc. 4th IET Conference on
Power Electronics Machines and Drives (PEMD), April 2008, pp.
340 – 344.
[4] Siemens Brothers and Co. Ltd. and F. Lydall, “Improvements to
polyphase induction motors,” British Patent 16839, July 1902.
[5] L. J. Hunt, “A new type of induction motor,” in Institution of
Electrical Engineers Proceedings, pp. 648-677, 1907.
[6] A. R. W. Broadway and L. Burbridge, “Self-cascaded machine: a low
speed motor or high frequency brushless alternator,” in Institution of
Electrical Engineers Proceedings, pp. 1277-1290, 1970.
[7] P. Rochelle, R. Spee and A. K. Wallace, “The effect of stator winding
configuration on the performance of brushless doubly fed machines in
adjustable speed Drives,” in Proc. IEEE Industry Application Society
Annual Meeting, Seattle, 1990, pp. 331-337.
[8] R. A. McMahon, P. C. Roberts, X. Wang, P. J. Tavner, “Performance
of BDFM as generator and motor,” in IET Proceedings, Electric
Power Applications, vol. 153, no. 2, pp. 289-299, 2006.
[9] S. Williamson and M. Boger, “Impact of inter-bar current on the
performance of the brushless doubly fed motor,” in IEEE Trans.
Industry Applications, vol. 35, no. 2, pp. 453-460, 1999.
[10] P. C. Roberts, R. A. McMahon, P. J. Tavner, J. Maciejowski, T. J.
Flack, and X. Wang, “Performance of Rotors in a Brushless Doubly-
Fed Induction Machine (BDFM),” in Proc. 16th International
Conference on Electrical Machines (ICEM 2004), Cracow, Poland,
2004, pp. 450-455.
[11] P. C. Roberts, R. A. McMahon, P. J. Tavner, J. M. Maciejowski, T. J.
Flack, and X. Wang, “An Equivalent Circuit for the Brushless Doubly
Fed Machine (BDFM) Including Parameter Estimation and
Experimental Verification,” in IET Proceedings on Electrical Power
Applications, vol. 152, pp. 933-942, 2005.
[12] X. Wang, P. C. Roberts, and R. A. McMahon, “Optimization of
BDFM Stator Design Using an Equivalent Circuit Model and a
Search Method,” in Proc. 3rd IET International Power Electronics,
Machines and Drives Conference (PEMD), March 2006, pp. 606-610.
[13] A Draper, Electrical Machines, Longmans. 2nd Edition, Longmans,
1967.
[14] E. Abdi Jalebi and R. A. McMahon, “Application of Real-Time Rotor
Current Measurements Using Bluetooth Wireless Technology in
Study of the Brushless Doubly-Fed (Induction) Machine (BDFM),” in
Proc. IEEE Industry Applications Society Annual Meeting (IAS2006),
vol. 3, pp. 1557-1561, October 2006.
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on March 24,2021 at 14:13:34 UTC from IEEE Xplore. Restrictions apply.
