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The brushless doubly fed induction generator (BDFIG) is an alternative to the doubly fed induction generator (DFIG), widely used in wind turbines which avoids the need for brush gear and slip rings. The choice of pole numbers for the two stator windings present in the BDFIG sets the operating speed range but also affects the torque capability, magnetizing currents and back iron depth. Analytical expressions are developed for these effects and a comparison is made between the BDFIG and the conventional DFIG. The torque capabilities and magnetizing currents are not strongly dependent on the choice of pole numbers but the back iron depth is significantly affected. The torque density of the BDFIG is somewhat reduced compared to a similarly sized DFIG but magnetizing currents per unit torque are the same. However, the required back iron depths are greater. The work also shows that multi-megawatt machines are expected to work within the desired range of power factors at acceptable efficiencies.
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Influence of Pole-Pair Combinations on the
Characteristics of the Brushless Doubly Fed
Induction Generator
Ashknaz Oraee, Member, IEEE, Richard McMahon, Ehsan Abdi, Senior Member, IEEE,
Salman Abdi, Member, IEEE,andSulAdemi , Member, IEEE
Abstract—The brushless doubly fed induction generator (BD-
FIG) is an alternative to the doubly fed induction generator (DFIG),
widely used in wind turbines which avoids the need for brush
gear and slip rings. The choice of pole numbers for the two stator
windings present in the BDFIG sets the operating speed, typically
in the medium speed range to eliminate a gearbox stage. This paper
focuses on how both the total number of poles and the assignment of
poles between the windings affect machine performance. Analytical
expressions have been developed for parameters including pull-out
torque, magnetizing current and back-iron depth. The results show
that the pole count can be increased without unduly compromising
pull-out torque and that in cases where more than one combination
of pole number is acceptable only the back iron depth is significantly
affected. In addition an output factor has been introduced to enable
a direct comparison to be made with conventional DFIGs. The
torque density of a brushless DFIG is compromised to a degree
relative to a comparable DFIG as a consequence of the presence of
two magnetic fields and finite element analysis is needed to achieve
an optimized design. Finally, predictions of the performance of
multi-MW machines are made based on data from an existing
250 kW machine which show that suitable efficiencies can be
obtained and excessive control winding excitation can be avoided.
Index Terms—Brushless doubly-fed generator (BDFG),
electrical machine design, induction generator, power factor,
2Stator winding pole-pairs (principal fields).
gAir gap length.
ropt Rotor turns ratio, general and optimal.
2Frequency stator windings 1, 2.
l, d Stack length, air gap diameter.
Manuscript received February 26, 2019; revised September 18, 2019 and
January 25, 2020; accepted February 12, 2020. Date of publication March 23,
2020; date of current version August 20, 2020. This work was supported by the
European Union’s Seventh Framework Program managed by Research Execu-
tive Agency (FP7/2007-2013) under Grant 315485. Paper no. TEC-00211-2019.
(Corresponding author: Sul Ademi.)
Ashknaz Oraee is with the Department of Engineering, University of Cam-
bridge, Cambridge CB2 1PZ, U.K. (e-mail:
Richard McMahon and Sul Ademi are with the Warwick Manufacturing
Group (WMG), The University of Warwick, Coventry CV4 7AL, U.K. (e-mail:;
Ehsan Abdi is with the Wind Technologies Limited, St. John’s InnovationCen-
tre, Cambridge CB4 0WS, U.K. (e-mail:
Salman Abdi is with the School of Engineering, University of East Anglia,
Norwich NR4 7TJ, U.K. (e-mail:
Color versions of one or more of the figures in this article are available online
Digital Object Identifier 10.1109/TEC.2020.2982515
ωrRotor angular velocity.
2RMS value of flux density stator windings 1, 2.
2Number of turns stator windings 1, 2.
BcPeak flux density in core.
ycBack iron depth.
ωrRotor angular velocity.
BMagnetic loading.
JElectric loading.
THE brushless DFIG is an alternative to the well-established
doubly fed induction generator (DFIG) for use in wind
turbines, since it offers improved reliability and reduced capital
and maintenance costs [1]. It retains the low-cost advantage of
the DFIG system as it only requires a fractionally rated converter
and does not use permanent magnet materials. The machine has
no brushed contact to the rotor, eliminating a common source of
failures, making it a particularly attractive machine for offshore
wind turbines. Moreover, the brushless DFIG is intrinsically a
medium-speed machine, enabling the use of a simplified one or
two-stage gearbox as shown in Fig. 1.
The brushless DFIG has its origins in the self-cascaded ma-
chine and has two non-coupling stator windings, referred to as
the power winding (PW) and the control winding (CW) with
different pole numbers, p1and p2creating two stator fields in
the machines magnetic circuit with different frequencies and
pole numbers [2]. A specially designed rotor couples to both
stator windings. Applications other than wind power have been
considered for this machine, for instance as a stand-alone gener-
ator for off-grid applications [3], a drive in pump applications [4]
and in shaft generator systems for ships [5].
An alternative approach is the brushless doubly-fed reluctance
generator (BDFRG) in which the short-circuited coils in the
rotor of the brushless DFIG are replaced by high-reluctance
flux barriers [6]. It has been shown that any rotor type used
for synchronous reluctance machines (SynRMs) is essentially
applicable in the BDFRG, i.e., the simple salient-pole rotor [7],
axially-laminated anisotropic rotor [8] and multi-layer flux-
barrier rotor [9]. The BDFRG alternative has been widely taken
into consideration [10] and several design modifications [11]
and control optimizations have been proposed [12], [13]. This
paper will, however, limit its scope to the brushless DFIG.
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Fig. 1. Brushless DFIG drivetrain set-up for wind power applications.
The design of the brushless DFIG is not straightforward
since there are more variables to consider than in conventional
induction machine designs [14]. Attention has been given to
some aspects of design for wind power applications as reported
in [15]–[18] and several large machines have been reported.
These include a 75 kW machine [17], a 200 kW machine [19]
and the 250 kW machine built and tested by the authors of [20].
This latter, believed to be the largest to date, was conceived as a
stepping-stone towards commercial MW scale brushless DFIGs.
In a wind turbine application, the machine will be matched to
the rest of the drivetrain so the natural speed, dependent on the
sum of the pole-pairs, and the speed range around natural speed,
typically ±30%, are of interest.
This paper examines how the characteristics and performance
of the machine are affected by the choice of pole-pairs, and the
allocation of these to the two windings. Although some design
relationships were developed in [21], important characteristics
such as pull-out torque, back-iron depth and magnetizing current
were not considered. In particular, this paper considers the trends
in these parameters as a function of natural speed, as set the pole
It was shown in [22] that to achieve the required performance
for wind turbine service, namely a power factor in the range of
0.95 lag to 0.95 lead, the CW of the 250 kW machine considered
needed to be significantly over-excited, compromising machine
output. The rotor leakage inductance is particularly significant in
setting the required degree of over-excitation. The final section
of this paper looks at the performance trends of future medium-
speed MW scale brushless DFIGs. The presence of two stator
windings means that there are more variables to consider than
in a single winding machine especially when it comes to control
and stability. The dynamics, control and stability of the machine
have been reported in [20] and low voltage ride through (LVRT)
performance was considered in [23].
This paper is organized as follows. Section II describes the
brushless DFIG operation and the per-phase equivalent circuit.
The pole-number choice and effect on machine rating are pre-
sented in Section III. The effect of pole-pair split on machine
fields and back-iron considerations are reported in Section IV.
Section V details the amp-turns ratios for common (p1/p2)
pole-pair. Performance analysis of the 4/8 frame size of the D400
prototype, the pull-out torque, power factor and efficiency are
detailed in Section VI. Optimization design for the megawatt
(MW) BDFIGs are explored and brought into focus in Sec-
tion VII. Finally, Section VIII draws conclusions.
Fig. 2. Referred per-phase equivalent circuit of the brushless DFIG.
The brushless DFIG normally operates in the synchronous
mode in which the shaft speed is independent of the torque
exerted on the machine, as long as it is smaller than the pull-out
torque. The speed is determined by the frequency and pole-pair
numbers of the stator windings and is given by:
where f1and f2are the frequencies of the supplies to the stator
windings, p1and p2are the pole-pair numbers of the windings.
A. Brushless DFIG Equivalent Circuit
The operation of the BDFG can be described by a per-phase
equivalent circuit [22] similar to the equivalent circuits of two
induction machines with interconnected rotors, as shown in
Fig. 2. In the figure R1and R2are the stator resistances, Lm1
and Lm2are the stator magnetizing inductances and L1and
L2are the stator leakage inductances. Parameters are referred
to the PW using the modifier ‘’. Furthermore, the rotor can
be characterized by the rotor turns ratio nr, resistance Rrand
leakage inductance Lr, the two latter parameters are also shown
in the referred per-phase equivalent circuit of Fig. 2.
The rotor leakage inductance includes conventional leakage
elements but the space harmonics associated with common
designs of brushless DFIG rotors lead to a higher differential
leakage component compared to conventional induction ma-
chine rotors. The slips s1and s2are defined as in [1].
A. Choice of Pole Numbers
For (p1+p2) type brushless DFIGs, the choice of stator
winding pole-pair numbers to give a desired natural speed, hence
operating speed range, is the first step in the design process. The
sum of the pole-pair combination, rounded to the nearest integer,
is given by:
Both the total pole-pair count and the split between the wind-
ings affect machine performance. Direct coupling between the
two stator windings must be avoided and this can be achieved
by applying the rules given in [21]. This paper considered a
range of design considerations, including the choice of pole-pair
numbers, and provided experimental validation from a D180
machine. Moreover, [21] identified a number of factors to be
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taken into account in the design of a BDFG and these were
validated by experimental data for the D180 brushless DFIG. In
some cases, several pole number combinations are possible and
there is the choice of giving the higher or lower pole number
to the PW. The torque capability of a brushless DFIG collapses
as the speed of the machine approaches the synchronous speed
of the PW. Thus, for the widest speed range, the lower pole
number should be assigned to the PW and the frequency of
the rotor currents is reduced in this connection. However, if the
operating speed range is limited to ±30% around natural speed,
as in wind power applications, this constraint does not apply.
Furthermore, some pole-pair combinations lead to unwanted
unbalanced magnet pull and vibration effects. When there is
more than one permissible combination of pole-pair numbers,
the machine design can be modified to give a trade-off between
output torque, speed, and magnetization considerations as eval-
uated in the following sections.
B. Effect on Machine Rating
An expression for the power rating of the BDFG, calculated
from the equivalent circuit model, was derived in [1]. This
expression was based on the quadrature sum (Bquad)ofthe
two fields in the machine but an alternative approach taking
a more conservative view of the maximum allowable fields was
developed in [21] based on the simple sum of the fields. Both
relationships are given in the Appendix. Unfortunately, there is
at present no easy way of determining the maximum tolerable
fields in the machine, but experience suggests that Bsum is too
conservative [24]. The two assumptions do, however, appear in
practice to bracket the range of allowable flux densities, hence
both are considered. Certain other assumptions are used in the
expressions for power rating, the most relevant here is that only
synchronous torques are produced and that the voltage drop
across the rotor is not significant.
As the output power is proportional to the speed, it is instruc-
tive to normalize the output of the brushless DFIG to that of
a DFIG with a synchronous speed equal to the natural speed
of the brushless DFIG, both machines having the same rotor
dimensions. The induction machine therefore has (p1+p2)
poles [25]. This leads to expressions for an output factor, in effect
the ratio of available torque to that of the equivalent DFIG, again
as derived in the Appendix. The output factor is a measure of
performance that can be used to compare different machine de-
signs. The expression depends on the rotor turns ratio nrbut can
be evaluated using a value equal to the optimum value as given in
the Appendix. In the case of the simple sum basis it reduces to:
Output f actor =TBDFG
The corresponding expression based on the quadrature sum
method is:
Output f actor =TBDFG
The output factors for common (p1/p2) brushless DFIGs
are given in Table I, showing that the higher the ratio of pole
numbers, the greater the output factors can be obtained. This
implies that the relative output is at minimum when p1=p2,
recognizing that such a machine is impractical, as noted in [26].
Using the sum of fields assumption, the minimum output torque
is 50% of that of a (p1+p2) induction machine but this rises to
nearly 54% for the 2/6 pole configuration. For comparison, the
quadrature sum method gives substantially higher output factors,
as shown in Table I.
A. Effect of Pole-Pair Split on Machine Fields
It was shown in [1] that the two fields in a brushless DFIG
mode are related by the rotor turns ratio, pole numbers and
voltage drop across the rotor leakage inductance. If it is assumed
that this drop is small, then the ratio of the two fields is given
where B1and B2are the RMS values of the fundamental p1and
p2pole-pair air gap flux densities. However, in reality there can
be a significant voltage across the rotor impedance, especially
when the machine is over-excited, hence (5) is no longer valid.
Over-excitation is particularly likely in smaller machines to
achieve an acceptable grid-side power factor [22]. In this study,
the CW voltage is limited to avoid undue over-excitation.
B. Back-Iron Considerations
The back-iron flux in conventional induction machines is
defined as half of the total flux over one pole pitch. The peak
flux density in stator or rotor core is then related to the magnetic
loading by conservation of flux and for brushless DFIG it can
be calculated from:
Bsum (6)
where ycis the back-iron depth. The back-iron flux density in
the brushless DFIG varies with time and position but a value for
the peak can be found using Bsum, which is divided into B1and
B2for p1and p2fields, respectively, using (5). The back-iron
depth for the brushless DFIG is then given by [15]:
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For the brushless DFIG the back-iron depth in terms of the
total air gap flux density, Bsum, can be found by re-arranging
and substituting equations (5) and (6) in (7):
p11+ 1
nr+p2(1 + nr)
Substituting nropt from equation (23) then gives:
The back-iron depth ratio of the (p1/p2) brushless DFIG to a
conventional IM of (p1+p2) poles is given by:
p11+ 1
nr+p2(1 + nr)
A similar approach gives the ratio of back-iron depths on the
basis of the quadrature sum method, given by:
p11+ 1
nr+p2(1 + nr)
The back-iron depth ratios for common (p1/p2) pole-pair
brushless DFIGs have been calculated and are given in Table II
for both the simple and quadrature sum methods. The peak flux
density in the back-iron is limited to 1.8 T.
The back-iron ratio is a minimum at p1=p2, which is not
feasible, as noted earlier. The minimum depth is twice of that of
a(p1+p2) induction machine on the simple sum basis, and 22
times on the quadrature sum basis which, however, gives a higher
machine output. As the ratio of pole-pair numbers increases,
there is a slight rise in the depth of back-iron required.
The results for a wide range of pole number combinations
on the basis of optimum turns ratio calculation for the sum
and quadrature sum method are shown in Fig. 3. The BDFG
needs more back iron than a corresponding DFIG as the two
machine fields have lower pole numbers. However, in any case a
certain minimum back iron depth may be mandated by structural
considerations. To determine an accurate depth requires finite
element analysis to take saturation into account [24].
Fig. 3. Back-iron ratio variation with optimum turns ratio.
A. Magnetizing Amp-Turns
For the brushless DFIG the total magnetizing amp-turns
(ATtot)forthep1and p2pole-pair fields, assuming that they
are in ratio given by equation (5), are given by:
ATtot =2g
where ATtot is the product of ImagNeff ,g is the air gap length
and μois the permeability of air. The amp-turns ratio of the
(p1/p2) brushless DFIG to a conventional induction machine of
p1+p2pole-pairs is then:
Substituting nropt from equation (23) for the Bsum formula-
tion gives:
The corresponding expression for the quadrature sum ap-
proach and substituting nropt from equation (24) is given by:
The amp-turns ratios for common (p1/p2) pole-pair brushless
DFIGs are calculated and given in Table III. From a magnetizing
current point of view, this ratio is a minimum at p1=p2,
however but this is impractical. On the simple sum basis the
magnetizing amp-turns are 50% of that of a (p1+p2) induction
machine, but the brushless DFIGs torque, according to (18) is
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Fig. 4. Amp-turns ratio variation with optimum turns ratio (simple sum).
only half that of the induction machine, showing that the BDFG
requires the same magnetizing AT per unit torque. Similarly, on
a quadrature sum basis, the magnetizing AT are 70.7% of those
of a DFIG, but again the output torque is only 70.7%. Whilst
there is an increase in the magnetizing AT with a greater ratio
of pole numbers, there is a corresponding rise in output factor
so a (p1/p2) BDFG requires essentially the same magnetizing
AT as a (p1+p2)DFIG.
The amp-turns ratio of the brushless DFIG to the conventional
induction machine for various pole-pair ratios using the simple
sum method is presented in Fig. 4.
The foregoing points are examined in the context of an
existing frame size D400, 250 kW brushless DFIG [20] by
considering designs for different speed options, i.e., pole number
combinations. The equivalent circuit model is used to represent
the steady-state performance of the machine, offering a straight-
forward method of calculating the efficiency and power factor to
a practical accuracy. The physical dimensions and specifications
of the D400 machine together with stator and rotor winding
details are given in Table IV.
The nested-loop rotor of this machine comprises (p1+p2)/2
sets of nests, each with five loops and the conductors being solid
bars with one common end ring. The number of rotor slots, and
hence the number of loops, will therefore depend on the pole
number count and so the machine will not necessarily be suited
for actual production and/or manufacturing.
A. D400 Machines
Designs for common brushless DFIG pole-pair combinations
using the same dimensions of the existing D400 prototype
machine have been investigated. Table V, provides details of the
designs with constant rated torque but different speeds and hence
powers. The PW power factor is set to 0.95 lagging, determining
the CW voltage and the balance between B1and B2is changed
by varying number of turns. The total flux density, Bsum ,is
0.7 T and peak flux densities in the rotor tooth and back-iron
is limited to 1.5 T. All equivalent circuit parameters, including
leakage inductances, are recalculated for each new design using
the software described in [21].
The total stator electric loading is kept at 5.7 kA/m. Fur-
thermore, the number and diameter of the stator conductors
and cross-section of the rotor bars are modified such that the
total conductor cross-sectional areas are identical to those of
the D400 machine. The stator current density is 3.5 A/mm2and
the rotor current density is 5 A/mm2. The air gap diameter and
stack length has been kept constant for all pole number designs.
It can be seen that the 2/6 pole brushless DFIG has both the
highest natural speed, power and efficiency, whilst producing
the same torque as the original 4/8 machine. Moreover, this
pole-pair configuration requires the lowest total amp-turns for
magnetization, but needs the highest back iron depth as shown
in Table VI.
To reduce the depth of back iron, the Bsum limit can be
increased from 0.7 T to 0.8 T, without undue increase in magne-
tizing current, as seen in Table VII, which shows designs of the
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D400 brushless DFIG for higher Bsum for a constant torque of
3670 Nm. As stated in (5), the distribution of B1and B2fields
are dependent on the rotor turns ratio and the stator windings
number of pole-pairs. Due to the change in the number of PW and
CW turns, the total amp-turns is also changed. In the redesigns,
conductor current densities, slot dimensions and slot fill are kept
constant. The peak flux densities in the rotor tooth and back-iron
are limited to 1.6 T and 1.7 T, respectively.
As evident from Table VII, unity PW power factor can be
achieved at rated design CW voltage of 620 V for the 250 kW
brushless DFIG by increasing the total flux density in the air
gap. To obtain unity PW power factor for a Bsum of 0.75 T and
0.8 T, B1is increased by 20% and 14%, respectively.
B. Pull-Out Torque of D400 Machines
From the previous section, the theoretically available maxi-
mum running torque depends to a degree on total pole count, as
well as the split of pole numbers. However, a further considera-
tion is the load angle at which the machine operates, related in
turn to the pull-out torque. For well-known reasons, operation
away from pull-out is desirable. In the BDFG, the pull-out torque
is primarily determined by the rotor inductance and this was
believed to increase with pole count [15].
To investigate the effect, brushless DFIGs were designed
with the same overall rotor dimensions, starting from the well-
characterized 250 kW D400 frame size machine [20], for dif-
ferent pole numbers using the design methodology reported
in [21]. The stator windings were configured to use the same
number of stator slots and the rotor slots are chosen to give
enough conductor area for the stator electrical loading to be
balanced, with the same current density in the rotor conductors
as the previous section. The design program calculates machine
parameters, notably the rotor leakage inductance, taking into
account space harmonic effects and the couplings between the
rotor loops using simple sum analysis method.
Fig. 5. Pull-out torque variation with natural speed and normal running torque
of 3.7 kNm.
Figure 5, shows the variation of pull-out torque for BDFGs
with different natural speeds and in ascending order correspond-
ing to 8/12, 4/12, 4/8 and 2/6 pole machines. As shown the 4/8
and 2/6 pole machines with natural speeds of 500 and 750 rpm,
respectively, offer somewhat higher pull-out torques allowing
easier control and improved stability due to lower rotor leakage
inductance, Lr. When designing high pole count machines, there
is a need to pay careful attention to keeping the rotor inductance
down to an acceptable level to retain a suitable margin of pull-out
torque relative to the normal running torque but this is seen to
be achievable at least to a total pole count of twenty. The normal
running full load torque for designs with natural speeds of 300,
375, 500 and 750 rpm is 3.7 kNm.
C. Power Factor
Achieving a good power factor is important and increas-
ingly wind turbines are expected to contribute to the VArs.
The selection of machine speed, and hence pole-pair count has
a significant effect on machine operating conditions. Fig. 6,
shows the variation of the PW power factor for sums of p1and
p2pole-pairs at balanced excitation (minimum rotor currents),
preferred for low losses. It has been found that brushless DFIGs
with a lower sum pole-pairs and higher PW power factors can
be achieved. The designs used in Fig. 6 are those in Table V,
which were designed to be capable of operating at a fixed power
factor of 0.95 lagging; parameters are given in the Appendix.
D. Efficiency
Figure 7, shows the variation of efficiency as the PW power
factor is improved for the existing 250 kW BDFG prototype.
Achieving a higher PW power factor comes at a price of reduced
efficiency, illustrating the trade-off between satisfying power
factor requirements and other performance measures.
The intention is, of course, to deploy the brushless DFIG
in large wind turbines, so it is important to know how such a
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Fig. 6. PW power factor variation with sum of pole-pairs at rated torque and
Fig. 7. Efficiency variation with PW power factor for 250 kW BDFIG.
machine would operate. According to recent grid codes, wind
farms have to supply reactive as well as real power to the grid.
For a brushless DFIG the power factor can be controlled by the
converter feeding the control winding, but as noted in [22] there
are some practical limits. To explore the expected performance
of large machines, designs have been developed for 2.5 MW
and 5 MW medium speed machines as tabulated in Table VIII.
The proportionately lower rotor leakage reactance allows unity
PW power factor to be achieved in both machines at rated CW
design voltages without increasing Bsum, therefore has been
kept at 0.7 T.
Figure 8, illustrates the PW power factor variation with re-
spect to the rated output power as machine size increases. The
machines are taken from Table V and Table VIII, noting that they
have different pole numbers. Each data point was recorded for
a balanced excitation condition, with each winding providing
its own magnetizing current. This condition was achieved by
adjusting the CW voltage to minimize the rotor currents, for a
given PW voltage, at full load operating conditions.
Fig. 8. PW power factor variation with respect to the rated output power.
It is evident that smaller machines suffer from lower power
factors without an excessively high CW voltage. A line side
converter with a higher rating or capacitor banks at grid terminals
can be used to contribute to the generation of reactive power.
However, the problem becomes less critical for larger machines,
since the per unit value of the rotor reactance drops with size [27].
For the designs considered, a worst case PW power factor of 0.95
lagging is achieved at balanced excitation and a modest degree
of over-excitation of the CW will enable the export of VArs to
the grid.
This paper has examined the effect of the number of poles
and pole-pair combinations on the performance of the brushless
DFIG, especially in the context of future MW scale machines.
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The analysis presented in the paper shows that acceptable pull-
out torques can be maintained for machines with natural speeds
in the range examined, namely 300 to 750 rpm, i.e., with pole
counts from 8 to 20. The split of pole numbers between the
two windings in cases where more than one combination is
acceptable does not significantly affect the pull-out torque. For
the same output power and speed, the brushless DFIGs require
essentially the same magnetizing ampere-turns as conventional
DFIGs and the magnetizing current does not change significantly
with the split of pole numbers. As with conventional machines,
the back-iron depth reflects the choice of pole numbers, and if a
2-pole winding is present a significantly higher back iron depth
is needed.
This paper has used both simple and quadrature sum ap-
proaches for the two fields, but the trends noted above are not
dependent on the approach adopted. However, the machine’s
output does reflect the maximum allowable flux density and
finite element analysis is need to achieve an optimized design.
Encouragingly, designs for brushless DFIGs up to 5 MW, based
on the performance of the existing 250 kW machine show that a
good power factor can be achieved without excessive excitation
of the control winding or compromising efficiency.
The power rating of the brushless DFIG, calculated from
the equivalent circuit model, was derived in [1] based on the
quadrature sum of fields and is given by:
Pquad =π2
p11+ 1
The power rating of a conventional induction machine with
(p1+p2) pole-pairs is found from:
PIM =π2
lBJ ωs
The output power is then calculated as:
p11+ 1
Using the alternative Bsum approach, for the brushless DFIG,
maximum output power can be calculated as:
PBsum =π2
p11+ 1
Hence, output power ratio is then calculated as:
p11+ 1
These powers can be normalised to the output of a p1+p2
DFIG leading to output factor of:
Output f actor =TBDFI G
1+ 1
For the quadrature sum method and:
Output factor =TBDF G
TIM 1+p2
1+ 1
p1(1 + nr)(22)
for the sum method. The nropt is defined using the method
given in [1], with the assumption of unity power factor and small
load angle operation. The turns ratio for maximum output power
is given by:
nropt =p1
However, this is constant to the results obtained in [1]:
nropt =p1
The actual value of nropt are 0.71 and 0.63 for the 4/8
brushless DFIG from equation (23) and (24).
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Ashknaz Oraee (Member, IEEE) receivedthe B.Eng.
degree in electrical engineering from Kings College
London, London, U.K., in 2011, and the Ph.D. degree
in electrical engineering from Cambridge University,
Cambridge, U.K., in 2015, focusing on electrical
machine design and optimization.
Her current research interests include electrical
machines and drives for renewable power generation.
Richard McMahon received the B.A. degree in elec-
trical sciences and the Ph.D. degree from the Uni-
versity of Cambridge, Cambridge, U.K., in 1976 and
1980, respectively.
Following Postdoctoral workon semiconductor de-
vice processing, he became a University Lecturer in
electrical engineering in 1989 with the Department of
Engineering, University of Cambridge, where he was
a Senior Lecturer in 2000. In 2016, he joined the War-
wick Manufacturing Group, University of Warwick,
Coventry, U.K., as a Professor of power electronics.
His current research interests include electrical drives, power electronics, and
semiconductor materials.
Ehsan Abdi (Senior Member, IEEE) received the
B.Sc. degree from the Sharif University of Tech-
nology, Tehran, Iran, in 2002, and the M.Phil. and
Ph.D. degrees, from Cambridge University, Cam-
bridge, U.K., in 2003 and 2006, respectively, all in
electrical engineering.
He is currently the Managing Director of Wind
Technologies Ltd., Cambridge, where he has been in-
volved with commercial exploitation of the brushless
doubly fed induction generator technology for wind
power applications. His main research interests in-
clude electrical machines and drives, renewable power generation, and electrical
measurements and instrumentation
Salman Abdi (Member, IEEE) received the B.Sc.
degree in electrical engineering from Ferdowsi Uni-
versity, Mashhad, Iran, in 2009, the M.Sc. degree
in electrical engineering from the Sharif University
of Technology, Tehran, Iran, in 2011, and the Ph.D.
degree in electrical machines design and modelling
from Cambridge University, Cambridge, U.K., in
He is currently a Lecturer in electrical engineering
with the University of East Anglia, Norwich, U.K. His
main research interests include electrical machines
and drives for renewable power generation and automotive applications.
Sul Ademi (Member, IEEE) received the B.Eng. and
Ph.D. degrees in electrical and electronics engineer-
ing from Northumbria University, Newcastle upon
Tyne, U.K., in 2011 and 2014, respectively.
From 2015 to 2017, he was a Lead Researcher,
engaged in knowledge exchange and transfer part-
nership activities between University of Strathclyde,
Glasgow,U.K. and GE Grid Solutions, Stafford, U.K.
He is currently a Research Scientist with the War-
wick Manufacturing Group, University of Warwick,
Coventry, U.K. His research interests include electric
motor drives, control of doubly-fed machines, and design and analysis of novel
permanent-magnet machines.
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on March 24,2021 at 11:31:54 UTC from IEEE Xplore. Restrictions apply.
... However, this hardly applies to BDFMs with regards to being alternatives to DFIGs in wind turbines. To use fractionally rated converters, the BDFM maximum speed will typically be lower than the synchronous speed of the higher pole [29]. ...
... However, optimization results in [38] indicate that the p 1 /p 2 = 2/4 combination performs better than the p 1 /p 2 = 4/6 combination for a BDFM in a D180 frame size. Analytical estimations in [29] also point to better performance from the p 1 /p 2 = 2/4 combination, compared to the p 1 /p 2 = 4/6 in terms of power and efficiency. ...
... The BDFM power ratings expression in [5] is used to predict about a quarter reduction of the power rating in BDFMs, compared to conventional DFIGs of the same size. The influence of pole pair combinations on this disparity in power between BDFMs and DFIGs is investigated in [29]. It is suggested that combinations with lower (p 1 /p 2 ) pole ratios have slight reduction in this disparity. ...
Full-text available
Research interest on brushless doubly fed induction machines (BDFMs) is increasing, as they offer higher reliability compared to doubly fed induction generators (DFIGs) in wind turbines. At the moment, BDFMs do not have a definitive structure nor design process, as literature is rife with different approaches to designing BDFMs. In this paper, a comprehensive review of the design of BDFMs from available literature is conducted. The evolution of cascade induction machine systems to contemporary BDFMs is first illustrated. Pioneering research work in the evolution which have influences on modern BDFM designs are highlighted. Relevant research on different aspects of present day BDFM design are then discussed. BDFM design and optimization methodologies applied in available literature are also explored.
... They serve as the foundation of industrial production and play a crucial role in countries' economic wellbeing. Moreover, induction generators are increasingly employed in environmentally friendly applications like the harnessing of wind [2], hydro [3], and tidal energy [4]. Despite their reputation for affordability, reliability, and sturdiness, induction motors often operate under adverse conditions, including high ambient temperatures, elevated humidity levels, and overloads. ...
... The machine model is developed in the natural a-b-c coordinates, using its electrical parameters, including resistances, leakage, self, and mutual inductances of the rotor and stator. The state-space machine model is given in Equations (1) and (2), which originate from Kirchhoff's voltage law [35]. An illustrative diagram of the DFIG model, created using MATLAB/Simulink, is presented in Figure 1. ...
Full-text available
This paper introduces a novel approach for detecting inter-turn short-circuit faults in rotor windings using wavelet transformation and empirical mode decomposition. A MATLAB/Simulink model is developed based on electrical parameters to simulate the inter-turn short circuit by adding a resistor parallel to phase “a” of the rotor. The resulting high current in the new phase indicates the presence of the short circuit. By measuring the rotor and stator three-phase currents, the fault can be detected as the currents exhibit asymmetric behavior. Fluctuations in the electromagnetic torque also occur during the fault. The wavelet transform is applied to the rotor current, revealing an effective analysis of sideband frequency components. Specifically, changes in amplitude and frequency, particularly in d7 and a7, indicate the presence of harmonics generated by the inter-turn short circuit. The simulation results demonstrate the effectiveness of wavelet transformation in analyzing these frequency components. Additionally, this study explores the use of empirical mode decomposition to detect faults in their early stages, observing substantial changes in the instantaneous amplitudes of the first three intrinsic mode functions during fault onset. The proposed technique is straightforward and reliable, making it suitable for application in wind turbines with simple electrical inputs.
... The airgap flux density and electric loading combination for the 75 KW BDFM is relatively high, potentially leading to saturation from an undersized machine. Pole pair combinations also play a big role in BDFM torque production [35], [37]. ...
... Such designs would require additional/over-excitation to achieve unity power factor at desired power ratings. In [37], it is noted that the 250 kW BDFM tested in [42] required significant over-excitation to operate within grid code requirements. The rotor leakage is identified as a significant factor contributing to the need for over-excitation. ...
In this paper, it is proposed that design evaluations of brushless doubly fed machines (BDFMs) be conducted at unity power factor in the synchronous generating mode, for wind turbine applications. In the build up to this idea, differences in power output at asynchronous, synchronous motoring, and synchronous generating modes are highlighted and discussed. The changes in generated power at varying grid side power factor of BDFMs are also demonstrated. Different designs of doubly fed induction generators (DFIGs) and BDFMs are simulated to highlight these variations. Potential issues that can arise from insufficient design evaluations are discussed. Experimental measurements from a 160L frame 2/3 BDFM are also used for validation.
... As a new type of motor, BDFM [1][2][3][4][5][6][7] can realize multiple operation modes such as asynchronous, synchronous, and double-fed. It can be used as a motor in alternating current (AC) speed-regulating transmission systems, and can also be used in power generation systems. ...
Full-text available
The paper presents the state-space (SS) model of the brushless double-fed machine (BDFM) by taking the negative conjugate (NC) transformation of the power machine’s correlation variable when the current source of the control machine is supplied in the m-t reference frame. Based on this, the testing method of machine parameters is given, and the SS model described by five parameters is obtained. The derivation process and realization method of the slip-frequency vector feedback linearization control (SFV-FLC) strategy are given. Then, researching the SS equation in the m-t reference frame by the control machine rotor field-oriented, the relationship between the maximum and minimum output torque and the control machine rotor flux amplitude and slip velocity, the machine parameters are given considering power supply constraints. Finally, the validity of the theoretical analysis is verified by simulation and experiment, and the feasibility of the decoupling control method are also demonstrated.
The brushless doubly-fed machine (BDFM) can be used in the variable speed constant frequency field. For BDFM, the choice of the pole-pair combination and the design of the rotor are significant. The output factor of the BDFM with 1/5 pole-pair combination is higher than that of the 2/4 pole-pair counterpart. However, the rotor of the BDFM with 1/5 pole-pair combination is hard to design for its wide pole-pair ratio. This paper presents a 1/5 pole-pair combination BDFM used in hydro power with a three-phase symmetrical wound rotor to solve the design challenge. First, the magnetic field modulation theory of the BDFM and the optimal output power in terms of different pole-pair combinations are introduced. Then, the slot-number phase diagram and the ampere-conductor wave method are applied to design windings of a BDFM with 1/5 pole-pair combination. Finally, the finite element (FE) models of the 1/5 and the 2/4 pole-pair combination BDFMs are established for comparison. A prototype of the 1/5 pole-pair combination is manufactured based on the proposed design scheme. Simulated and experimental results verified the feasibility of the design scheme.
The brushless doubly fed generator (BDFG) shows great potential for the variable speed constant frequency ship shaft power generation applications due to its high reliability and low system costs. The rotor topology, which directly couples two stator magnetomotive forces (MMFs) with different pole pairs, is essential for the BDFG. However, existing rotor topologies cannot have both strong magnetic field coupling ability and simple structure. To address this problem, this paper proposes a simplified three-phase wound rotor that can produce two MMFs with different pole pairs simultaneously. Useless harmonics are also eliminated to achieve strong magnetic field coupling ability. The complete design method of a novel integral-slot single-layer winding acting as a basic unit of the compound wound rotor is presented. Two sets of basic winding units are merged into one according to the principle of Ampere-conductor wave, whose approaches are also thoroughly developed with the design example. The maximum number of winding layers and the coil types are reduced to simplify the winding layout. Steady-state performances of a prototype generator are analyzed by both finite element simulations and experimental tests, which verify proposed design methods and schemes.
In this paper, a new dual-stator brushless doubly-fed induction machine with a staggered dual cage rotor is proposed, with emphasis on the general interconnection rule of the conductor bars for the staggered dual cage rotor. Since the squirrel cage rotor offers the merits of robustness, reliable structure, high slot filling factor, and low rotor resistance comparing to the wound rotor, it is introduced to the dual-stator brushless doubly-fed induction machine to solve the problems of high copper loss and unreliable rotor structure for the dual-stator brushless doubly-fed induction machine with a wound rotor. The originality of this article is to investigate the interconnection rule of conductor bars between the inner and outer cages. The constraint condition that is supposed to be satisfied is deduced by using the rotating magneto-motive force theory, based on which diverse slot/pole combinations are investigated. The performance comparison between the existing and proposed machines is conducted. Finally, a prototype is designed and fabricated. The experimental results verify the effectiveness of the proposed topology.
Brushless doubly-fed generator (BDFG) shows great potential in the field of wind power due to its high reliability and cost advantages. The rotor is the basis of BDFG electromechanical energy conversion, and plays the role of “pole-number converter”. In order to improve the magnetic field modulation ability of the BDFG rotor, combining the advantages of different types of rotor structures of BDFG, this paper proposes a series cage bar assisted magnetic barrier rotor structure, the series cage bar and the radial magnetic barrier have an effect on the air gap magnetic field, which enhances the magnetic field modulation ability commonly. The structural characteristics of this kind of generator are introduced in detail, and the mapping law between the rotor structural parameters and the magnetic field modulation ability of the BDFG is studied. Finally, simulation research has verified the superiority of the above-mentioned generator structure and is suitable for application in the field of wind power generation.KeywordsBrushless doubly-fed generators (BDFG)New hybrid rotorStructural parametersMagnetic field modulation ability
Full-text available
The brushless doubly-fed machine(BDFM) is a family of multiport electric machines with two ac electrical ports and a common mechanical port. Different from the conventional singly-fed machines whose synchronous speed is solely determined by a single supply frequency and the actual pole pair number, the BDFM has two supply frequencies and two different pole pair numbers to control the rotor speed. By the two accessible electrical ports, all BDFMs are endowed with more degrees of freedom for speed and power control, inherent fault-tolerant capability and high reliability. The BDFM in its broad sense has been extensively investigated as a promising alternative to the conventional slip-ring doubly-fed induction machine(DFIM) during the past decades, for both limited and wide speed range applications. This paper presents a new theoretical framework of the BDFM within which all topological variants can be closely linked by the similarities in working principle. The individualities of each machine topology are presented first, followed by the commonalities such as the modeling techniques, modes of operation, design considerations and control strategies. The challenges are identified and highlighted based on recent developments and possible opportunities are predicted considering the unique nature of this special AC machine type.
Full-text available
This paper presents an optimized design method for the magnetic circuit of brushless doubly fed machines (BDFMs). The BDFM is an attractive electrical machine, particularly for wind power applications, as a replacement for doubly fed slip-ring generators. This study shows that the conventional design methods for the BDFM stator and rotor back iron can be modified, leading to a lighter and smaller machine. The proposed design concepts are supported by analytical methods, and their practicality is verified using two-dimensional finite-element modeling and analysis. Two BDFMs with frame sizes D180 and D400 are considered in this study.
Full-text available
A procedure has been established for obtaining equivalent circuit parameters for the brushless doubly fed machine, also known as the brushless doubly fed induction machine, by transforming a reduced coupled-circuit model into a sequence component form. This approach takes advantage of the model reduction procedure's ability to reduce a complex rotor structure to a single equivalent loop without significant loss of accuracy. An alternative method based on winding factors has also been developed and includes coupling via harmonic fields. Parameters determined in both ways are in close agreement with those determined from finite element analysis and experimentally. The advantages of each method are discussed in the conclusion section.
Full-text available
This article studies the converter rating requirement of a Brushless doubly-fed induction generator (DFIG) for wind turbine applications. Practical constraints such as the generator torque-speed requirement, reactive power management and grid low-voltage ride-through (LVRT) are considered. Experimental data have been used to obtain a realistic system model of a Brushless DFIG in a wind turbine. The study shows that there is a minimum converter rating, dependant on operating point, but this may not be achievable without machine derating. The use of a capacitor bank enables the converter ratings to be reduced without compromising the machine's performance. The effect of the machine's leakage inductance on the interplay of LVRT, achievable system power factor, converter rating and losses is investigated.
This paper contributes to the characterisation of the brushless doubly fed induction generator (BDFIG), which is attractive as a variable speed generator in applications (offshore wind turbine) with minimum maintenance requirements. The BDFIG has two three-phase stator windings of different pole numbers housed within the same stator slots and a shortcircuited rotor winding capable of coupling fields of different pole numbers. The stator windings and rotor winding create a magnetic field distribution with a range of characteristics different to those of conventional induction generators. This paper presents an analysis to identify the field characteristics and discusses their impact on the analysis and design of the BDFIG. The characteristics are determined from an analysis of the sum of two rotating sinusoidal field waveforms and confirmed by comparison with time-stepping finite element results and measured magnetic flux density data.
The brushless Doubly-Fed Induction Machine (DFIM) provides an interesting alternative to the commonly applied conventional DFIM in modern multi-MW wind turbines. This paper presents a literature survey on the brushless DFIM. The evolution of the cascaded induction machine into the modern brushless DFIM is discussed, as well as several theories explaining this machines complex operating principles. Nowadays, brushless DFIM research is mainly focussed on the development of a commercially competitive brushless DFIM based drive for multi-MW wind turbine applications. An overview of the latest developments in the fields of brushless DFIM modeling, design, and control is provided. Based on this, a qualitative comparison is presented of the brushless DFIM and other well-established generator systems for wind turbines and the challenges for future research are explored.
The brushless Doubly-Fed Induction Machine (DFIM) shows great potential as a generator in large-scale wind turbines. The motion of the magnetic field in this machine is not a simple rotation, which makes it not so straight forward to understand its operating principles. This paper develops an analytical magnetic field model for the brushless DFIM that includes the effects of rotor time-harmonics and space-harmonics due to the winding distribution and slotting. By using a case study machine, the developed analytical model is then validated by comparison to FE calculations. Additionally, a two-dimensional spectral analysis is applied to the FE derived radial air-gap magnetic field as a function of time. This analysis verifies the space-time relations of the rotating magnetic field components in the air-gap of the brushless DFIM. Lastly, the developed analytical magnetic field model is used to analyse the brushless DFIM operating principles. The interaction of the stator magnetic field with the rotor nested-loops is explained, as well as the development of electromagnetic torque.
A design procedure for the Brushless Doubly Fed machine is based on equations derived from a simplified equivalent circuit. The method allows the many variables in the design of this machine to be handled in straightforward way. Relationships are given for the division of slot area between the two stator windings and for the design of the magnetic circuit. The design method is applied to a frame size 180 machine. In particular, calculated values for flux densities in the machine have been verified by time stepping finite element analysis for actual operating conditions. The approach outlined can also be used as part of a design optimization routine.
This paper deals with the electromagnetic modeling and design aspects of brushless doubly fed reluctance machines (BDFRM). It presents the development and the experimental validation of a semi-analytical model (SAM) used for sizing new machine designs. The SAM is an optimization-oriented model implemented using analytical approaches and a deterministic optimization algorithm to find an optimal machine by solving iteratively an objective function, whereas satisfying several output constraints simultaneously. It is fast and accurate for pre-design stages, premises that are confirmed by both simulation and experimental results.