Characterising brushless doubly fed machine rotors

Abstract

The brushless doubly fed machine (BDFM) is a robust alternative to the doubly fed induction generator, currently widely used in wind turbines but prone to brush-gear and slip-ring failure. The rotor winding plays an important part in a BDFM, coupling the two stator windings. To date, nested-loop (NL) rotor windings have been exclusively used in practical BDFM. This approach may not be ideal for larger machines, in which form-wound series-loop rotor winding may be preferable to large section bars and end-rings. This study gives a comparative analytical and experimental study of two different brushless doubly fed 160 frame-size rotors, with NL or series-wound windings, mounted in identical rotor core laminations operating in the same stator tested at a limited voltage (200 V line). The rotors gave a performance which accords with theoretical predictions from two independent methods, giving insight into the design issues of the different rotor windings from both an electrical and manufacturing viewpoint.

Full text

Published in IET Electric Power Applications
Received on 13th August 2012
Revised on 15th November 2012
Accepted on 10th December 2012
doi: 10.1049/iet-epa.2012.0238
ISSN 1751-8660
Characterising brushless doubly fed machine rotors
Richard McMahon1, Peter Tavner2, Ehsan Abdi3, Paul Malliband3, Darren Barker2
1
Department of Engineering, Cambridge University, Trumpington Street, Cambridge, CB21PZ, UK
2
School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH13LE, UK
3
Wind Technologies Ltd., St. Johns Innovation Centre, Cowley Road, Cambridge, CB40WS, UK
E-mail: peter.tavner@durham.ac.uk
Abstract: The brushless doubly fed machine (BDFM) is a robust alternative to the doubly fed induction generator, currently
widely used in wind turbines but prone to brush-gear and slip-ring failure. The rotor winding plays an important part in a
BDFM, coupling the two stator windings. To date, nested-loop (NL) rotor windings have been exclusively used in practical
BDFM. This approach may not be ideal for larger machines, in which form-wound series-loop rotor winding may be
preferable to large section bars and end-rings. This study gives a comparative analytical and experimental study of two
different brushless doubly fed 160 frame-size rotors, with NL or series-wound windings, mounted in identical rotor core
laminations operating in the same stator tested at a limited voltage (200 V line). The rotors gave a performance which accords
with theoretical predictions from two independent methods, giving insight into the design issues of the different rotor
windings from both an electrical and manufacturing viewpoint.
Nomenclature
List of symbols
X
1
,X
2
,X
r
indicating, respectively, stator1, stator 2 and
rotor winding quantities
p
1
,p
2
stator winding pole-pair numbers
qphase number
f
1
,f
2
supply frequencies
s
1
,s
2
slips of different winding systems
Nshaft speed
N
eff1,2&r
effective number of turns for the stator,
1&2
,
and rotor,
r
, windings
n
1,2&r
turns ratios of stator,
1&2
, and rotor,
r
,
windings
k
w
winding factor
k
p
pitch factor
γwinding pitch angle
R,Lwinding resistance and inductance
Zimpedance of a rotor loop
1 Introduction
The brushless doubly fed machine (BDFM) is of interest as a
variable speed generator or drive because only a fraction of
the output power needs to pass through the power
converter. The absence of brush-gear and slip-rings makes
the machine particularly attractive as a wind turbine
generator because brush-gear and slip-ring problems in the
widely used doubly fed induction generator (DFIG) have
been identified as a principal failure mode [1]. Studies
indicate that the combination of a BDFM and a two-stage
gearbox in a wind turbine would have excellent reliability
and retain low cost [2]. The authors have successfully
demonstrated a small-scale BDFM in a working 20 kW
wind turbine [3] and have built a 250 kW prototype that
has undergone witnessed tests over its full load and speed
range.
The BDFM has its origins in the single-frame
self-cascaded induction machine, in which two stator
windings of different pole numbers share the same iron
circuit with a rotor winding of related pole number [4].
Developed by Hunt [5], the machine gained a reputation
for robustness and reliability [6]. Following the work of
Rochelle et al. [7], the contemporary BDFM has two
stator windings connected to different frequency supplies,
producing different pole number magneto-motive forces
(MMF) with no direct coupling between them, coupling
being through the rotor only. The separate stator windings
facilitate double-feeding, with one winding connected to
the grid and the other via a partially rated power
electronic converter, as shown in Fig. 1, without any
winding utilisation penalty.
The BDFM rotor is a critical component. The rotor
winding carries an MMF induced by the stator windings
and the rotor and stator windings are coupled by the flux
rotating in the common iron circuit. A good rotor will
couple both stator windings but have low resistance and
inductance. As shown in [8], there is a rotor turns ratio, n
r
,
which maximises the machine output, where n
r
will be
defined later.
In addition, the rotor should be straightforward to
manufacture. Lydall [4] used two rotor windings, one
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pitched for p
1
pole-pairs and the other for p
2
pole-pairs,
directly connected to each other. Hunt [5] showed this was
wasteful of copper and devised a more complex winding
with lower resistance but unfortunately also difficult to make.
Broadway and Burbidge reconsidered the rotor design in
[6] and a p
1
+p
2
bar cage was identified as the simplest
concept resulting in principal fields with space harmonics,
although a rotor of this type was recently successfully used
in an experimental BDFM [9]. The nested-loop (NL) type
of rotor was proposed as a development of the p
1
+p
2
fabricated bar cage comprising multiple loops in p
1
+p
2
nests, an example being shown in Fig. 4b. This approach
reduces space harmonic generation, has been used in most
subsequently published BDFMs, was promoted because of
its similarity to the induction motor squirrel cage rotor and
was expected to share its ease of manufacture. However, as
noted by Williamson and Boger [10], the bars of the NL
rotor must be insulated, making casting difficult . The cages
of large induction motors would normally be fabricated
from copper alloy conductors and brazed, but to do this for
a NL winding is time-consuming and costly. The NL rotor
also suffers from unequal current distribution between loops
[11].
Other forms of rotor winding were investigated analytically
by Roberts et al. [12] reporting the theoretical performance of
a series-loop rotor winding, following a suggestion in [6], but
implementation was not optimised. In general, rotors will
have p
1
+p
2
sets of rotor circuits and each set may be a
single winding, in which case analysis is straightforward, or
have two or more independent circuits, as in the NL,
making analysis more complex.
Large bar rotor winding designs, like a squirrel cage, make
good use of the slot area, but tend to generate higher levels of
space harmonics than conventional series-wound (SW) rotor
windings, as found in a DFIG. This will be reflected in an
increased rotor leakage inductance for the fabricated NL
design. However, mutual couplings can reduce the
amplitude of space harmonics, as occurs, for example in
NL rotors [11], which also lead to torque ripple and
acoustic noise.
Others have looked theoretically at conventional rotor
winding design, including Guangzhong et al. [13]who
proposed a method for considering the air-gap MMF of
cage or wound BDFM rotors, Liu et al. [14] proposing
particular connections for the rotor winding, Blazquez et al.
[15] characterised the rotor magnetic field.
As BDFM ratings increase, the NL rotor bar cross-sections
will also increase, notwithstanding the greater number of rotor
slots. A concern then arises about bar skin effect raising rotor
resistance, especially as the rotor current frequency will be a
substantial fraction of the grid frequency. Under these
conditions multiple conductors in each slot will become
necessary and multilayer windings would be attractive.
Indeed a 75 kW prototype BDFM for a wind turbine [16]
used a stranded NL design, although the authors did not
report on the behaviour of this winding in operation.
This paper describes work to optimise the design of a
conventional BDFM with a stranded SW rotor, being more
straightforward to manufacture and applicable to larger
machine sizes, aimed at wind turbine generators >2 MW.
The experimental machine was constructed from a
MarelliMotori D160 frame induction motor described in
[17]. The rotor design theory was developed with a view to
obtaining equivalent circuit parameters analytically. Results
from experimental tests are presented to confirm the
manufactured rotors’performance against analytical
parameter predictions, parameters have also been extracted
from these tests for comparison. In addition, its
performance was compared to that of a NL rotor winding
using identical rotor laminations.
2 BDFM basics and configuration
Although the BDFM rotor operates by induction, the machine
is normally operated as a variable speed machine in the
synchronous mode with double-feed, as shown in Fig. 1.In
this respect, operation is the same as the widely used DFIG
wind turbine generator. The shaft speed in the synchronous
mode is given by
N=60 f1+f2
p1+p2
(1)
In typical operation as a wind turbine generator, the rotor
speed range may be the BDFM natural speed + / −30%;
although a smaller range may be adequate for pumping
applications. 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
Nn=60 f1
p1+p2
(2)
The BDFM can also be operated in the self-cascaded mode
in which one stator winding is shorted or in the simple
induction mode with one stator winding open circuit. These
two modes can be used for determining machine parameters.
The operation of the BDFM can be described by a
per-phase equivalent circuit of the form shown in Fig. 2a
[13]. Values are shown referred to the power winding and
iron losses are neglected. R
1
and R
2
are the resistances of
the stator windings and R
r
is the rotor resistance. L
m1
and
L
m2
are the stator magnetising inductances, L
1
and L
2
are
the stator leakage inductances and L
r
is the rotor inductance
(Fig. 2). The use of the modifier ‘′’ denotes that the
Fig. 1 Block diagram showing BDFM, grid-connected power
winding and the control winding fed through a converter
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536 IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543
&The Institution of Engineering and Technology 2013 doi: 10.1049/iet-epa.2012.0238

quantity is referred. The slips s
1
and s
2
are defined in
Section 5.
The slips s
1
and s
2
are defined as follows
s1=f1p2−f2p1
f1p1+p2
 (3)
s2=f2p1−f1p2
f2p1+p2
 (4)
Whilst values for all these quantities can be calculated, the
leakage inductances cannot be determined unambiguously
from terminal measurements so the simplified equivalent
circuit shown in Fig. 2bwas proposed in [18]. As noted
there, L
1
and L
2
have been absorbed in L
m1&2
and
consequently the values of magnetising and rotor leakage
inductances will change, though the adjustments to the
former are small. There will also be a modification to the
turns ratio, n
r
, and hence all referred parameters.
In most practical BDFMs the rotor leakage inductance is
the largest series impedance term in the simplified
equivalent circuit, and a core model retaining only this term
was proposed in [8]; this approach allows a number of
useful relationships to be derived which assist in BDFM
design. For normal operating conditions an optimum value
of the rotor turns ratio n
r
for maximum rating can be
deduced from [8] given by
nr=p1
p2

(2/3)
(5)
3 BDFM rotor design
3.1 General arrangement
Rotors have been designed for use in a 4/8 pole BDFM
manufactured using the stator stack and frame from a size
160 induction motor. The stator design has been optimised
and winding details are given in Table 1together with the
leading physical dimensions.
Fig. 2 Per-phase BDFM equivalent circuits
aPer-phase equivalent circuit for the BDFM from [13]
bSimplified per-phase equivalent circuit from [12]
Fig. 3 Rotor winding diagrams
aSW rotor
bNL rotor
Fig. 4 Prototype SW and NL rotors
aSW rotor
bNL rotor
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Ap
1
/p
2
pole-pair BDFM has p
1
+p
2
sets of rotor circuits,
in this case 6. The SW rotor has three concentric coils in
series in each set whereas the NL rotor has three concentric
loops with a common shorting end ring, the loops being
effectively in parallel and rotor slot numbers an even
multiple of six. A lamination with 36 slots was chosen as
this gives a reasonable slot pitch with the D160 machine
air-gap diameter. The lamination design is magnetically
matched to that of the stator with 36 slots, in that the
cross-sectional areas of the rotor teeth are equal to that of
the stator teeth and the rotor core back depth is equal to that
of the stator. The winding arrangements are shown in Fig. 4
and the prototype wound and NL rotors are shown in Fig. 5.
For ease of manufacture of the SW rotor, a single-layer
winding with 37 strands of enameled, round wire
conductors in parallel was used to maximise the slot fill and
achieve a value as close to the NL winding as possible. A
pre-assembled bundle of conductors was pressed into the
rotor slots pre-lined with Nomex and the free ends were
crimped together after removal of the enamel insulation.
For the NL rotor, shaped copper bars were fed into Nomex
slots and the end rings were brazed on.
3.2 Turns ratio
Using (5) from Section 2 the optimum turns ratio, n
r
, for a
2/4-pole-pair BDFM is 0.5
2/3
or 0.63, that rotor turns ratio
being from defined [8]as
nr=N1rkw1r
N2rkw2r
(6)
where the subscripts refer to the p
1
and p
2
principal fields and
Nand k
w
are the respective turns and winding factors (WF)
<k
W
and K
w
changed to k
w
. The rotor winding has MMFs
induced in response to each stator winding MMF, the
number of turns are the same, that is N
1r
=N
2r
.Tofind the
actual turn ratio requires the calculation of the effective
turns for couplings to the 4- and 8-pole fields. These are
shown in Table 2, noting that as the three SW one turn
coils in each set are concentric the WF can be summed for
the SW rotor. The two coupling WF for each coil reduce to
the pitching factor, for pitch angle γ
kp1=sin
g
p1
2
 (7)
kp2=sin
g
p2
2
 (8)
The turn ratio is given by
nr=k1A+k1B+k1C
k2A+k2B+k2C
(9)
The spans of the three coils are 10°, 30° and 50°. The sums
of the WF are k
wr1
= 1.44 and k
wr2
= 2.19, giving a turns
ratio for the SW rotor winding of 0.66, close to the
optimum value of 0.63.
The loops of the NL rotor winding are effectively in
parallel, as depicted in Fig. 5band have mutual couplings,
so the calculation of n
r
is not straightforward. A turn ratio
approximation for the NL rotor can be found from Fig. 5
circuit by considering an MMF balance with one stator
open circuit as
nr=kw1Akw2A/ZA

+kw1Bkw2B/ZB

+kw1Ckw2C/ZC




k2
w2A/ZA

+k2
w2B/ZB

+k2
w2C/ZC



(10)
where Z
A
,Z
B
and Z
C
are the impedances of the rotor loops at a
particular operating speed and the WF are as in Table 2,n
r
does not vary significantly with speed so can be evaluated
at natural speed. The data for evaluating the bar impedances
are given in Section 3.5 and lead to a value for n
r
for the
NL rotor winding of 0.69, again close to the optimum.
Table 1 BDFM physical details
stator 1 pole number 4 air-gap diameter mm 155
stator 2 pole number 8 air-gap, mm 0.34/0.35
stator 1 N
eff
/phase 250 stator slots (open) 36
stator 2 N
eff
/phase 272 rotor slots (open) 36
stack length, mm 190
Fig. 5 Rotor winding schematics
aSW rotor
bNL rotor
Table 2 WF for rotor loops
Coil/loop Span γk
w1
4-pole k
w2
8-pole
AInner 10° 0.17 0.34
BMiddle 30° 0.5 0.87
COuter 50° 0.77 0.98
N
eff
1.44 2.19
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3.3 Single equivalent loop representation
For the various rotors, it is convenient to develop a single
equivalent loop representation which directly relates to
equivalent circuit parameters. The equivalent loop will have
WF to give the desired turns ratio, resistance and
inductance electrically equivalent to the actual rotor. For
rotors with SW loops this is straightforward in that the loop
span can be chosen to give the effective turn ratio (6).
However, for rotors with loops in parallel, like the NL
rotor, parameters are rotor-speed dependent but can be
taken to be constant.
3.4 Rotor current density
At full load, the stator and rotor winding currents 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 stator 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 Iis
MMF =4
p
q
2INeff
p(11)
The stator is three phase but the rotor is six-phase, strictly
bi-three-phase, hence
3
2Is1Neffs1
=6
2IrNeffr(12)
For the SW rotor the rotor current is 299 A giving a current
density of 6.6 A/mm
2
, higher than the stator winding design
current density of 6 A/mm
2
but acceptable.
For the NL rotor currents will differ from loop-to-loop and
vary with operating point. At rated output, calculations of
loop currents from the rotor impedances and WF shows that
loop Bcurrent, the middle loop, and the inner loop A
current will be about 2/3 and 1/4, respectively, of the loop
Ccurrent, the outer loop. Applying an MMF balance gives
a maximum current of approximately 400 A in loop C
giving an acceptable current density of 5 A/mm
2
.
3.5 Parameter calculation by WF analysis
Parameters for the rotor are needed to enable the performance
of the overall machine to be predicted using the equivalent
circuit and this will be done by WF analysis. 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 1. The
two stator to rotor turns ratios, n
1
and n
2
, for the SW rotor
are then
n1=
Neffs1
Neffr
=173.3 (13)
n2=
Neffs2
Neffr
=124.2 (14)
This gives n
1
/n
2
= 1.40.
An estimate of the rotor resistance in the case of the SW
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
Rcoil =2kN
r
A
p
d
g
360 +w
 (15)
where Nis the number of turns, ρis the resistivity of copper
(1.72 × 10
−8
Ωm), Ais the cross-sectional area of the
conductor, dis the mean diameter of the rotor slots, wis
the stack length and kis 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 turn ratio. The referred
resistance is 8.21 Ω, which equates to 2.80 Ωin a star
(wye) 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
magnetising 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
Lh=
m
0
g
ldq
p
Neff
p

2
(16)
evaluated for the harmonic pole-pair numbers. The effective
turns are found for the pole number in question, gis the
air-gap length and the other symbols have the same
meaning as in previous sections. The harmonic fields that
can exist (harmonic order n) are given by
n[p1+mp
1+p2

<p2+mp
1+p2

(17)
where mis 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 k
s
ks=sin ws(p/2)

ws(p/2) (18)
where w
s
is the angular width of the rotor slot mouth in
radians. A summation up to a 200 pole field, for a pole
pitch of 1.8° and a slot mouth pitch angle of 8.16°, gives
L
r
(h) = 5.1 μH.
The conventional leakage inductance components,
overhang, slot and zigzag, found using the methods
described by [18] give an additional 4.9 μH. The total
leakage reactance referred to stator 1 is then 50.2 mH, in
star (wye) form.
Inductance values in brackets are neglecting space
harmonics. Impedances evaluated at the natural speed
frequency of 100/3 Hz
The analysis of the NL rotor is complicated by the fact that
there are three independent loops in each nest. The resistances
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of the individual loops in the NL rotor can be calculated using
(15), ignoring the effects of the common end ring, and
harmonic inductances can be found using (16). The loops
will have different WF for harmonic fields so there will be
cross-coupling. To establish the range of possible rotor
parameters, the evaluation has been carried out including
and excluding harmonic inductances. Values of resistance,
inductance and impedance evaluated at the natural speed are
shown in Table 3and can be used to obtain values for Z
A
,
Z
B
and Z
C
.
Parameters for an equivalent single loop with a WF of unity
can be determined by applying a short circuit in Fig. 5bto
stator 2. The effective impedance of this loop Z
eq
is
Zeq =k2
w1A
ZA
+k2
w1B
ZB
+k2
w1C
ZC

−1
(19)
For the stator, the conventional leakage inductance
components, namely the overhang, slot and zigzag
contributions, were found using the methods described by
[18]. The magnetising inductances were calculated using
(16) and winding resistances using (15).
3.6 Parameter calculation by coupled circuit (CC)
analysis
Parameters have also been obtained from the CC analysis
described in [19]. From the distribution of conductors, the
method gives position-dependent mutual inductances, which
include space harmonic effects. The model assumes that
there is a linear change of conductor density across slot
mouths. Leakage inductance components, excluding
harmonic contributions, and winding resistances are
calculated as in the previous section.
Following conversion to dq-axis form, there is a
transformation to a synchronous frame. There is then a
further conversion to extract sequence components, the
forward sequence components being the usual per-phase
equivalent circuit parameters. This is straightforward in the
case of the SW rotor but for the NL rotor a model reduction
procedure is applied to reduce the multiple dq-sets of the
rotor to a single dq-pair [11]. This reduction procedure is
based on ranking the eigenvalues of the rotor mutual
coupling matrix and retaining only the largest eigenvalues,
that is those representing the strongest couplings. Once a
single dq model has been obtained, conversion to sequence
components takes place.
3.7 Comparison of calculated and measured
parameters
WF analysis has the great advantage of being simple to
understand and implement. The predictions of parameters
for the complete equivalent circuit are compared with the
more accurate but complex CC analysis in Table 4for both
rotors, based upon equivalent circuit Fig. 2a. These were all
per-phase quantities based on a star (wye) connection.
There are small differences between the calculated values
for stator winding resistances, arising from the precise
treatment of the end windings; the measured values are a
little higher suggesting that there is more end winding
overhang than is assumed in the calculations. The same
effect is seen with the rotor resistance. All resistances were
calculated for 20°C and measurements were taken on the
machine at ambient temperature. As mentioned earlier, the
formulation for the Carter factors was chosen, with the SW
rotor, to align the predicted and measured values of
magnetising inductance. Differences in the values for stator
leakage inductances calculated by different analyses are
attributable to the precise representation of the slot shape
and placement of windings within slots.
For the SW rotor calculated rotor parameters, turns ratio,
rotor resistance and leakage inductance, are close to
measured with the exception of the leakage inductance.
For the NL rotor in the WF analysis, neglect of the mutual
harmonic coupling between loops by the two stator windings
lead to rotor parameter differences, particularly in the leakage
inductance. Coupling between loops reduces the harmonic
leakage contribution substantially and modifies the effective
resistance and turns ratio. Neglect of the harmonic leakage
inductance in the WF analysis gives a closer rotor leakage
inductance value, but lower than that from CC analysis.
Therefore Table 4results show that WF analysis is
satisfactory except possibly for the prediction of the rotor
leakage inductance.
The check parameters for single equivalent loops, derived
from CC analysis are shown in Table 5. The equivalent
spans are really equal, reflecting the similarity in turns
ratios. The NL rotor has significantly lower resistance and
Table 3 Individual loop parameters for the NL rotor
Loop ABC
R
r
,μΩ 105 118 132
L
r
,μH 5.02 (1.58) 4.71 (1.64) 3.94 (1.72)
X
r
,μΩ 1052 986 827
Table 4 Complete parameter set, Fig. 2a
Parameter For SW rotor For NL rotor
WF analysis Direct measurement CC analysis WF analysis Direct measurement CC analysis
R
1
,Ω1.77 2.04 1.74 1.77 2.04 1.74
L
1
, mH 5.92 —5.78 1.13 1.29 1.02
L
m1
, mH 342 317 342 333 317 372
R′
r
,Ω2.80 3.11 2.76 99 104 111
L′
r
, mH 50.2 —37.5 1.54 (1.51) —1.31
L
m2
, mH 102 104 102 49.9 (20.2) —27.9
L
2
, mH 3.92 —5.42 1.33 (1.36) —1.35
R
2
,Ω1.13 1.29 1.02 5.88 —5.97
N1.40 —1.41 3.87 —5.63
Values in brackets neglect space harmonics
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540 IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543
&The Institution of Engineering and Technology 2013 doi: 10.1049/iet-epa.2012.0238

leakage inductance. However, the structure of the NL rotor
dampens unwanted harmonics explaining the lower overall
rotor inductance.
A set of winding parameters was also devised based upon
the simplified equivalent circuit of Fig. 2b, shown in Table 6,
these considerably simplify the design of the machine. Again
the agreement between prediction and calculation is good,
with the possible exception of the rotor leakage reactance,
where the CC analysis gives better results.
4 Experimental arrangement and extraction
of rotor parameters
The experimental arrangement used for testing the
performance of rotors and for the extraction of parameters
has been described in [17]. The BDFM was connected to a
dynamometer operating in constant speed or torque mode,
giving readings of speed and torque. The p
1
winding was
connected directly to mains and the p
2
winding was fed
through a frequency converter under manual control.
A procedure for extracting Fig. 2parameters was
established by Roberts et al. [12] and in [18]. The machine
was run in the cascade mode with the 4-pole winding
connected to the mains through a variable transformer and
the 8-pole winding shorted and then vice versa. Torque–
speed curves were obtained over a speed range of 200–
1500 and 200–750 rev/min with the 4- and 8-pole
windings excited, respectively, at 200 V, slightly below the
rated voltage to limit saturation. This was done to
investigate winding parameters of the machine under linear
conditions, with the intention of resolving saturation issues
later. As the stator winding resistances can be accurately
measured, they were taken as fixed, including an allowance
for temperature rise. The measured and fitted cascade
characteristics are presented in Fig. 6for both rotors.
Comparisons between extracted and calculated parameters,
following conversion to values for the simplified equivalent
circuit shown in Fig. 2b, are given in Table 6and
calculated and extracted parameters are close. Parameters
modified by the conversion procedure [20] are denoted ‘*’.
Rotor resistance temperature rise must be an allowed for.
The algorithm used in Table 6treats the following as free
parameters, rotor turns ratio, the two magnetising
reactances, rotor resistance and inductance, adjusting them
to give the best fit to the measured torque–speed
characteristic. Predicted stator magnetising inductances do
not agree so well with measurement in Table 6but the fitto
measured torque–speed data is relatively insensitive to this
parameter, essentially because the magnetising reactances
are in shunt. So extracted magnetising reactance values can
vary considerably without affecting the torque–speed result.
The reactances were also measured independently, by
synchronous tests, and the values used as fixed parameters
in the fitting exercise, but again this did not radically alter
the torque–speed results.
The predicted parameters for both types of winding were
then used to calculate the torque–speed curves of the
machine operating with both rotors. Measured and
calculated torque-speed results are compared in Fig 6. The
crosses show the experimentally measured torque–speed
points and the curves have been fitted to torque–speed
curves predicted from parameters, calculated as described
above and shown in Table 6.
Fig. 6demonstrates that parameters can be calculated with
sufficient accuracy for machine design purposes but a more
sophisticated approach may be required for the rotor
leakage inductance and the CC analysis achieves this.
However, the WF analysis could be extended in the future
to include coupling through space harmonics.
5 Torque production
When operating the BDFM in the synchronous mode, the aim
is to utilise the synchronous torque which, from the core
model described in Section 3.1 and noting that cosφis the
power factor, is given by
T=3V1I1
cos
w
v
r
1+f2
f1
 (20)
This can also be expressed in the form
T=3V1V2
sin
d
v
s1L′
r
v
s1/(p1+p2)

(21)
which shows that the torque is dependent on a load angle δas
in a conventional synchronous machine; however, induction
torques are also present. One component, attempting to
accelerate the rotor towards the synchronous field of the
Table 5 Parameters for single equivalent loops
Rotor SW NL NL reduced fill
R
r
,μΩ 121.4 70.2 125.5 (estimated)
L
r
,μH 10.2 2.3 2.27
γ,° 40.4 43.4
n
r
0.657 0.688
Table 6 Simplified parameter sets, Fig 2b
Parameter FOR SW rotor FOR NL rotor
WF analysis CC analysis Measurement by extraction WF analysis CC analysis Measurement by extraction
R
1
,Ω1.77 1.74 2.40 1.77 1.74 2.40
L∗′
r,mH 348 348 220 339 378 180
R∗′
r,V2.90 2.86 3.80 1.60 (1.57) 1.36 1.70
L∗′
r,mH 65.6 55.2 61.0 64.3 (32.3) 44.9 42.0
L∗
m2,mH 106 107 92 103 116 195
R
2
,Ω1.13 1.02 1.50 1.13 1.02 1.50
n∗
r1.37 1.36 1.43 1.30 (1.33) 1.31 1.37
Values in brackets ignore space harmonics
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IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543 541
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power winding is given by
Tim =3I2
1
R′
r
s1
1
v
s1
(22)
The second component is trying to accelerate the rotor to the
natural speed. This component is given by
Tin =3I2
1R′′
2
s2
s1
1
v
n
(23)
where ω
n
is 2πN
n
/60.
The calculated pull-out torques for the NL and SW rotors
were, 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, was predicted to
be 82 Nm. At natural speed and rated current the induction
torque was 11.7 Nm motoring and there is no contribution
from R″
2
, which would be accelerating the rotor below
natural speed and braking it above.
The measured torque at rated current but reduced line
voltage at the natural speed, N
n
, 600 rev/min summed to 60
Nm (3.8 kW), in reasonable agreement with the calculated
values for an ideal machine with these voltages and
currents. The induction torques were not negligible and can
only be reduced by decreasing R′
r
and R″
2
. The torque
available from a BDFM of given size was shown in [8]to
be 70–80% of that of a conventional induction machine,
depending on the choice of pole-pairs and assuming a
similar magnetic loading, still the subject of BDFM
research. The original MarelliMotori induction motor, from
which this BDFM was constructed, had a rated torque at
400 V line voltage and 1470 rev/min of 70 Nm (10.8 kW)
on its 4-pole winding.
6 Discussion
The use of a SW rotor has been shown as a practicable
proposition, offering straightforward manufacture compared
to the NL rotor. However, the R′
r
of the SW rotor in this
case was approximately twice that for the NL resulting in a
Fig. 6 Experimental cascade torque–speed characteristics overlaid with curves fitted to points derived from calculated parameters
aSW rotor
bNL rotor
Fig. 7 Comparison between predicted L
r
′and R
r
′for rotor
windings with equal fill factors, using the CC or WF analyses
aReferred rotor resistance, R′
r
,Ω
bReferred rotor inductance, L′
r
,mH
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542 IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543
&The Institution of Engineering and Technology 2013 doi: 10.1049/iet-epa.2012.0238

lower torque performance. The lower L′
r
&R′
r
translate into a
50% greater pull-out torque for the NL over the SW rotor,
both rotors having turns ratios, n
r
, that are close to the
optimum.
It is tempting to ascribe the higher resistance simply to the
greater conductor cross-section of the NL, which was 1.8
times that of the SW rotor.
However, the authors have investigated two SW and NL
rotors with identical slot fill factors. Their L′
r
and R′
r
have
been calculated by the CC and WF analyses, the latter
ignoring harmonic inductances in the case of the NL rotor,
and are compared in Fig. 7. The referred rotor resistances
for the SW and NL rotors are nearly identical.
The NL inner loop carries only 25% of the outer loop
current, confirmed experimentally [21]. Similarly, the inner
loop in the SW rotor adds considerable resistance but is not
well-coupled. Calculations show that a rotor with only the
two outer loops in series would reduce R
r
by 30% and R′
r
by just 10%, with a somewhat larger leakage inductance
reduction. In larger BDFMs, rotor bar size will be limited
by skin effect considerations and the simple NL design
cannot be used. Other possible designs, including the SW
rotor with three series loops, each loop spanning 30°
displaced by 10° [16], can be shown to have a lower R′
r
but
n
r
is further from the optimum.
7 Conclusions
†A stranded SW BDFM rotor winding has been compared,
experimentally and analytically, at a line voltage of 200 V,
with an identical rotor with a solid bar NL winding,
mounted in the same stator.
†Manufacture of this new stranded SW BDFM rotor
winding was straightforward.
†Stranded SW rotor winding may be of practical interest in
larger BDFM rotors requiring multiple conductors to avoid
skin effects and to facilitate manufacture.
†Experimentally measured parameters of both the SW and
NL rotor resistances and inductances were in close
agreement with analytical predictions, using either WF or
CC analyses, although the latter gives better predictions for
the rotor leakage reactance.
†Parameters extracted from the cascade tests on the BDFM
for the two designs confirmed that both rotor winding
arrangements can be accurately designed.
†Experimental and analytical results from the SW rotor
winding were acceptable but the torque developed was not
as great as the equivalent NL rotor winding.
†Current and torque in this new BDFM rotor winding
design were limited by the copper cross-section achieved in
the winding.
†Prediction methods showed that if the SW rotor had an
identical rotor slot fill factor to the NL rotor, the resultant
R
r
′would be similar but L
r
’somewhat higher than for the
equivalent NL rotor, so similar torque performance could
be expected.
†Further work is required to investigate the predictability of
these rotor parameters under higher saturation conditions and
taking further account of space harmonics, particularly for the
SW rotor and the WF analysis could be extended to include
coupling via space harmonics.
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IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543 543
doi: 10.1049/iet-epa.2012.0238 &The Institution of Engineering and Technology 2013