A Review of the Advancements in the Design of Brushless Doubly Fed Machines

Abstract

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.

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Citation: Olubamiwa, O.I.; Gule, N.
A Review of the Advancements
in the Design of Brushless Doubly
Fed Machines. Energies 2022,15, 725.
https://doi.org/10.3390/en15030725
Academic Editor: Marcin Kaminski
Received: 18 November 2021
Accepted: 24 December 2021
Published: 19 January 2022
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energies
Review
A Review of the Advancements in the Design of Brushless
Doubly Fed Machines
Oreoluwa I. Olubamiwa and Nkosinathi Gule *
Department of Electrical and Electronic Engineering, Stellenbosch University, Stellenbosch 7600, South Africa;
19469462@sun.ac.za
*Correspondence: nathie@sun.ac.za
Abstract:
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.
Keywords:
wind power generation; brushless doubly fed machines; pole pair combinations; nested
loop rotors
1. Introduction
Doubly fed induction generators (DFIGs) are the most widely employed generators in
medium and large wind turbines. This is due to their low cost, variable speed operations,
and the use of fractionally rated converters in their setup [1]. However, DFIG based wind
turbines have the highest operational and maintenance (O&M) costs, because of DFIG
slip ring and brush assembly failures [
2
]. This is further compounded in remote areas
like offshore wind sites, which have low accessibility. It is worth noting that offshore
wind power is getting increasing attention, and a significant expansion in offshore wind
installations is projected in the coming years [3].
Brushless doubly fed machines (BDFMs) have similar advantages with DFIGs, and the ab-
sence of slip ring and brush assemblies in their setup increases their reliability [
4
]. As a
result, the O&M costs of wind turbines using BDFMs would potentially be reduced. How-
ever, BDFMs have complex structures with lower power densities, compared to DFIGs [
5
].
There is also no consensus regarding certain critical aspects of BDFM design.
The development of BDFMs can be traced to machines preceding DFIGs, and these
machines were mostly used for motoring purposes. In this paper, the historical evolution
of BDFMs is first outlined to paint a clear picture of the development of BDFM design.
The influence of the shift from cascade motoring to doubly fed generating operations on
BDFM features is discussed. A thematic review of published literature considering the
design of contemporary BDFMs is then presented. The different BDFM components are
comprehensively examined, as well as design and optimization procedures employed in
literature. The overarching aim of this paper is to provide perspective on contemporary
BDFM structures, and a comprehensive overview of BDFM design.
It is recognized that general reviews on BDFMs are available in literature such as [
6
–
8
].
These reviews cover a broad array of subjects like brief histories, electromagnetic design,
modelling techniques, modes of operation, and control strategies. Consequently, the BDFM
design considerations in these reviews are not exhaustive. Doubly fed reluctance machines
Energies 2022,15, 725. https://doi.org/10.3390/en15030725 https://www.mdpi.com/journal/energies

Energies 2022,15, 725 2 of 19
are also discussed in these reviews. However, in this paper, there is a comprehensive
focus on the design of BDFMs, and the procedures involved. Doubly fed machines with
reluctance rotors, hybrid rotors and dual stators are not considered.
This paper is divided into two main sections:
1.
The evolution of cascaded IMs to contemporary BDFM topologies. In this section,
significant contributions to the present day BDFM topologies are highlighted, with
the underlying reasons for these design developments.
2.
Discussions on the aspects of BDFM design. A comprehensive run-down of recent
developments and approaches employed in the design of BDFMs, are presented in
this section.
2. Development of BDFMs from Cascade Induction Motors
At the turn of the 19th century, polyphase induction motors (IMs) were increasing
in industry usage, due to their simplicity and reliability [
9
]. Squirrel cage induction
motors (SCIMs) were preferred in environments like mining industries, where rough and
rigorous handling of equipment were required [
10
]. However, SCIMs were only relevant
for constant speed and moderate starting torque operations. This was before the advent
of power electronics, and variable speed motoring operations commonly employed direct
current motors [
11
,
12
]. Wound rotor (slip ring) induction motors using rheostatic control
also seem to have been used for variable speed applications at the time [
13
,
14
]. Slip ring IM
setups with rheostatic control had performances analogous to shunt motors [
12
], however
with significant losses [15].
Cascade motors were developed in the pursuit of the robustness of SCIMs, and the
variable speed functionality of slip ring IMs with rheostatic controls [
10
,
14
]. Cascade motor
origins can be traced to cascade systems, which consisted of two or more motors having a
common connecting shaft. A good example of these cascade systems is the Steinmetz cas-
cade IM system, which was patented in 1897 [
16
]. These motors were connected according
to different configurations to achieve different speed and power configurations. Examples
of these connections are illustrated in Figure 1. In Figure 1a, the stator of the secondary
motor is connected to the rotor of the primary motor. By this connection, a starting torque
almost double one of the motors is achievable without the losses common with rheostatic
controls. The connection in Figure 1b enables speed control capabilities similar to the
series-parallel control of DC motors; Figure 1c likewise, with more options [16].
12
Rheostats
Switching
cylinder
Rotor
winding
Rotor
winding
Stator
winding
Stator
winding
Supply
(a)
12
Rheostats
Rotor
windings
Stator
winding Stator
winding
Switching cylinder
Supply
(b)
Supply
12
Rheostats
Rotor
windings
Stator
winding
Stator
winding
Switching cylinder
12
Stator
winding
Stator
winding
Rotor
windings
(c)
Figure 1.
Steinmetz cascade system examples: (
a
) two motors with rotor of primary motor connected
to secondary stator, (
b
) two motors with both rotors connected to each other, and (
c
) four motors [
16
].

Energies 2022,15, 725 3 of 19
Cascade systems however had disadvantages of high cost, low efficiency, low power
factor, and poor overload capacity [
14
]. Over time, different machines were designed
with inspiration from cascade systems, from which modern day BDFMs were eventually
developed. In the following subsections, distinct pioneering machines are highlighted,
with their major contributions to the development of BDFMs underscored. A summary of
the shift from cascade operations to synchronous doubly fed operations is also given.
2.1. The Thompson Motor
A motor patented by S. Thompson in 1901, was highlighted in [
14
] as essentially being
equivalent to a two motor cascade. The stator was divided into segments occupied by the
primary and secondary windings. Alternate segments had different windings preventing
mutual induction, as illustrated in Figure 2. The primary windings were connected directly
to the main supply, while the secondary windings were connected to regulating resistances.
The rotor had a wave winding which coupled with the primary stator field and induced a
field on the secondary stator winding. Placing all the windings on one core was to reduce
the setup cost, as opposed to two separate machines connected in cascade. The Thompson
motor helped shape the shift from multiple motors in a cascade system to a single motor
with cascaded operations.
B
A
C
C
U
V
W
W
Figure 2. Thompson motor winding illustration [14].
2.2. The Lydall Motor
A patent for a polyphase motor which could be operated at three speeds without
rheostatic loss, was accepted in 1903 [
13
]. This motor was developed by the Siemens
brothers & Co. Limited and Francis Lydall, with two stator windings which had different
pole numbers preventing direct inductive coupling. The rotor also had two windings
wound in similar fashion as the stator, with connections made possible by slip rings. A
schematic illustration of the Lydall motor is given in Figure 3. In reality, the “switching
controller” in Figure 3consisted of 3 barrel switches used to achieve desired connections.
The synchronous speed of S1 was achieved by connecting the supply to S1, S2 to R1,
and R2 to the starting rheostats; the synchronous speed of S2 was achieved by swapping
these connections (S2 to the supply, S1 to R2, R1 to rheostats). A cascade speed was
achieved by connecting S1 to the supply, shorting S2 and R2, and connecting R1 to the
starting rheostats.

Energies 2022,15, 725 4 of 19
S1
Rheostats
Rotor
windings
Stator windings
Switching controller
S2
R1
R2
Supply
Figure 3. Schematic representation of the Lydall motor [13].
The difference in pole numbers made segmentation of the stator windings unnecessary,
as one could be placed on top the other. However, there was increased copper losses from
the two sets of windings (on the stator and rotor), and increased magnetic leakage due
to deeper slots, especially from the winding farthest from the air-gap [
14
]. Despite this, it
should be noted that present day BDFMs use the Lydall type of stator, with windings of
different pole numbers; one on top of the other.
2.3. The Hunt Motor
L.J. Hunt introduced a cascade motor in [
14
], with single stator and rotor windings.
This motor had regulating resistances connected to tappings on the stator winding, and did
not need slip rings. Slip rings could however be employed if more efficient speeds were
desired. The special stator winding allowed for reduction of magnetic leakage and copper
losses incurred by the two stator windings in prior cascade motors. Hunt continued to
work on the development of this motor, fine tuning the design and making it more practical.
Upon the successful construction and usage of large numbers of these machines,
another paper [
10
] was published in 1914. This paper gave more details as to the design of
the hunt motor, and also notably a brief guide into the selection of the number of poles on
the stator. In Figure 4, the coil group connections to obtain 4 poles, 8 poles, and (
4+8
) poles
configurations from a star wound single stator are illustrated. In 1921, F. Creedy published
a paper [
17
], which shed more light on the pole number selections, paving the way for new
combinations. Improved rotor and stator winding designs for this type of cascade motor
were also discussed in [
17
]. The works of L.J. Hunt and F. Creedy were foundational for
the selection of suitable pole pair combinations for BDFM stator windings.
T1T2T3
A
A
B
B
C
C
Supply
(a)
T1T2T3
A
A
B
B
C
C
Supply
(b)
T1T2
T3
B
C
Supply
B
C
A
A
(c)
Figure 4. Hunt motor stator connections: (a) 4 poles, (b) 8 poles, and (c) (4 + 8) poles [10].

Energies 2022,15, 725 5 of 19
2.4. The Broadway & Burbridge Motor
In [
18
], Broadway and Burbridge sought to design cascade motor rotors that were sim-
pler compared to the irregularly grouped double layer wound rotors in the Hunt/Creedy
motors. Two single layer winding rotors, the graded winding rotor and the multicircuit
winding rotor, were investigated. The winding arrangements of these rotors are illustrated
in Figure 5. Although, the coils of the graded winding rotor in Figure 5a are not short
circuited together, the graded winding rotor prototype in Figure 6a has a common end-ring
for all the coils. The graded winding rotor in Figure 6a is built for a (6 + 2) poles cascade
machine. A multicircuit rotor for a (18 + 12) poles machine is also built in [
18
], as shown in
Figure 6b. These rotors presented in [
18
], which are now more commonly called the nested
loops (NL) and cage+NL rotors respectively, are currently the most widely used rotors in
contemporary BDFMs.
Rotor nest
(a)
End-ring Common bar
Loops
(b)
Figure 5.
Broadway & Burbridge rotor winding arrangements: (
a
) Graded winding rotor and
(b) multicircuit winding rotor [18].
(a) (b)
Figure 6.
Broadway & Burbridge rotor prototypes: (
a
) Graded winding rotor for (6 + 2) poles machine,
and (b) multicircuit rotor for (18 + 12) poles machine [18].
2.5. Cascade Systems to Brushless Doubly Fed Operations
The cascade IM systems/cascade motors were conceived at a time before power
electronic converters. Early cascade systems/motors were developed to achieve efficient
motor operations at different (usually low) speeds. The cascade motors were also developed
with the view of obtaining robustness and reliability similar to SCIMs [14,18].
The synchronous operation of machines similar to S. Thompson’s motor, were detailed
by B.H. Smith in 1966-7 [
19
,
20
]. These motors used by B.H. Smith, were at the time called
twin stator induction machines, and the stator windings were both fed with three phase
supplies at different frequencies. This was the first of analyses of what were hitherto
cascade motors, operating similarly to doubly fed induction machines. Slip frequency
excitation from a low power frequency converter was discussed for harnessing slip power
from the machine rotors.

Energies 2022,15, 725 6 of 19
In 1970 [
18
], Broadway and Burbridge also discussed the synchronous operations of
cascade machines. However, these synchronous operations were limited to the machine
synchronous speed, such that AC was applied to one stator winding, and DC to the other.
Full load performances of the cascade machines in synchronous operations were notably
superior to asynchronous operations of equivalent multipole IMs. Also, there was an
increase in power factor compared to asynchronous operations.
The first traceable mention of the term “brushless doubly fed machine (BDFM)” is
in [
21
], a 1989 paper about a dynamic model of BDFMs. In 1994, Brune et al. tested the
possibilities of using BDFMs in a variable speed wind turbine in [
22
]. The use of a BDFM
in a wind turbine was an attempt to obtain the benefits of a DFIG in with a more robust
structure, which is still the main reason for the recent push in research about BDFMs. A
1.5 kW prototype was built to demonstrate the viability of BDFM based wind turbines. In
the following sections, the discussion is shifted to recent (mainly post 90s) developments in
the design of BDFMs. Research challenges with the design and approaches to solving these
issues are also discussed.
3. Recent BDFM Design Development
In a push towards commercial MW rated BDFMs, the authors in [
23
] presented a
250 kW
rated BDFM. This being the largest BDFM/BDFIG tested to date, showed expected
performances and stable control, and thus the viability of the technology.
Although the BDFM is not yet at a commercial scale of implementation, the prospects
of usage in wind turbines have piqued the interests of several research groups globally.
As a result, a number of notable developments in the design of BDFMs have occurred. A
large portion of these developments have had focusses on suitable pole pair combinations
and optimum rotor design. Maximizing the power density and reduction of harmonics
have also received their fair share of attention. Furthermore, different design approaches of
BDFMs have been presented, and all these aspects are discussed in the subsequent sections.
3.1. Stator Winding Development
Up until around 1989, the L.J. Hunt type of stator windings [
10
] were used for BDFMs,
in which coil groups were interconnected in a way to accommodate two AC supplies (or
pole pairs) [
21
]. However in [
24
], it was suggested that the L.J. hunt type of stator winding
was better suited for applications in which only one set of terminals were connected to a
power source at a time.
For synchronous BDFM operations, with two AC supplies connected to the terminals,
there are unbalances in the Hunt type of stator, which lead to internal circulating currents.
Therefore, reverting to isolated stator windings like in the Lydall motor was recommended
in [
24
]. This helped in avoiding the circulating currents, while affording greater simplicity
and flexibility.
Consequently, contemporary BDFM stators have two isolated windings, the power
winding (PW) and the control winding (CW). The stator windings do not couple directly,
but are cross-coupled by a special rotor (see Section 3.2). As already suggested in [
14
], the
winding which is farthest from the airgap has increased leakage. Placing the PW at the
bottom layer would have significant effects on the converter ratings, as higher leakage
would increase the difficulty in controlling the grid side power factor as noted in [
25
]. Thus,
the PW with
p1
pole pairs typically occupies the bottom layer (closest to the airgap) of the
stator slots, while the CW with
p2
pole pairs occupies the top layer. This type of stator for a
p1/p2= 2/3 BDFM, is illustrated in Figure 7.

Energies 2022,15, 725 7 of 19
Figure 7. Stator winding arrangement of a BDFM with p1/p2=2/3.
3.1.1. Relative Winding Pole Size
Typically,
p1
is lower than
p2
for a number of reasons. A significant reason for using
the lower pole as
p1
is the higher magnetizing requirements with increasing poles [
26
–
28
].
Thus higher poles for
p1
can increase the power ratings of the converters used. Furthermore,
the lower pole number for
p1
affords better winding distribution, as the PW and CW occupy
the same number of slots, and this helps reduce unwanted harmonics.
The BDFM torque breaks down at the synchronous speed of a
p1
machine, thus
favouring a lower
p1
for a wider operating speed range [
27
]. 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].
The rotor field frequency (ωrf) is calculated from the formula in [30,31],
ωrf=ω1−p1ωr=−ω2+p2ωr, (1)
where,
ω1
&
ω2
are the electrical angular speeds of the PW and CW respectively, while
ωr
is mechanical angular speed of the rotor. It can be observed that
ωrf
is higher if
p1
is lower
than
p2
. This leads to higher core losses [
32
,
33
], and rotor impedances considering that
skin effect is lower at lower frequencies. The disparity between
p1
and
p2
should not be
too high to reduce copper losses due to skin effect [32].
3.1.2. Unbalanced Magnetic Pull and Magnetic Coupling
In [
34
], it was established that when a
x
-pole pair field is combined with a (
x+y
)-pole
pair field, a force imbalance occurs when
y
= 1. This imbalance, now commonly called
an unbalanced magnetic pull (UMP), was then illustrated (Figure 8) with a 2/3 pole pair
combination. It can be observed from the force diagram in Figure 8, that a strong force
zone is directly opposite to a weak zone, giving rise to the imbalance. If
y>
1, there will be
equal ystrong and weak zones [34], and UMPs can be avoided.
The harmonics generated by the PW and CW are given respectively as
hpw =p1(2t−1),t∈N,
hcw =p2(2t−1),t∈N.(2)
If the windings have no common harmonic, they do not couple inductively. A bit
more nuance about selecting pole pair combinations towards ensuring non coupling is
provided in [
30
]. However, the rules given in [
30
] only apply when series windings are
used. The use of parallel coil group connections can enable direct coupling of the PW and
CW, which produces circulating currents. Practical connections of coil groups in parallel

Energies 2022,15, 725 8 of 19
while avoiding direct coupling are discussed in [
35
], and these parallel paths can help
mitigate UMPs.
1
2
3
4
5
Weak zones
Strong zones
BDFM
Figure 8. Force diagram for p1/p2=2/3 (adapted from [34]).
3.1.3. Commonly Used Pole Pair Combinations
Pole pair combinations which do not produce UMPs were tested using 2D FE BDFM
models in [
36
] to highlight suitable combinations. Although the
p1/p2
= 2
/
4 pole pair
combination is used for a 250 kW BDFM prototype in [
37
], the results in [
36
] suggest that the
p1/p2
= 4
/
6 combination is more suitable in terms of power, efficiency and torque ripple.
However, optimization results in [
38
] indicate that the
p1/p2
= 2
/
4 combination performs
better than the
p1/p2
= 4
/
6 combination for a BDFM in a D180 frame size. Analytical
estimations in [
29
] also point to better performance from the
p1/p2
= 2
/
4 combination,
compared to the p1/p2= 4/6 in terms of power and efficiency.
In spite of these, the
p1/p2
= 2
/
3 is the preferred combination for the D180 frame
BDFM in [
38
,
39
], as it produces the best performance in terms of efficiency and generated
torque. The
p1/p2
= 2
/
3 combination in [
38
] also has considerably lower torque ripple
and time harmonic distortions, compared to the
p1/p2
= 2
/
4 combination. Concerns of
UMP with the
p1/p2
= 2
/
3 combinations were considered minor in [
38
], due to the small
size of the machine. In [
40
], the
p1/p2
= 4
/
6 is the preferred combination for a 3.2 MW
BDFM, due to the less coupling of higher space harmonics compared to the
p1/p2
= 2
/
4
combination, and the absence of UMP, which is present in the
p1/p2
= 2
/
3 combination.
The lower harmonic content in the 4
/
6 combination relative to the 2
/
4 combination is also
alluded to in [
41
], however the PW has the higher pole number. A summary of the relative
performances of the 2/3, 2/4 and 4/6 pole pair combinations as described in literature, is
given in Table 1.
Table 1. Relative performance of popular BDFM pole pair combinations.
Parameters Pole Pair Combinations (p1/p2)
2/3 2/4 4/6
Power density [29,38,39] High Medium Low
Efficiency [29,38,39] High Medium Low
Torque ripple [38] Low High Low
Harmonic distortion [40,41] Low High Low
UMP [35,36] Present - -

Energies 2022,15, 725 9 of 19
3.2. Rotor Winding Development
The nested loop (NL) and cage+NL rotors, whose origins are traced to [
18
], are cur-
rently deemed the most suitable for BDFMs [
6
,
30
,
42
]. The NL rotor winding arrangement
and a prototype are shown in Figure 9a,b respectively. The cage+NL rotor winding ar-
rangement has already being illustrated in Figure 5b, and a prototype is shown in Figure 9c.
The winding arrangement in Figure 9a differs from that in Figure 5a by the presence of a
common end ring, with the rotor illustrated in Figure 5a now sometimes called an isolated
loop (IL) rotor [
30
]. These (NL, IL, & cage+NL) rotor types have robust builds with better
torque performance and lower losses, compared to wound rotors [6].
A rotor similar to the NL rotor, but with double layers of bars, is highlighted
in [30]
.
It is suggested that this double layer bar rotor has a larger torque envelope than the NL
rotor; also higher efficiency due to less excess harmonic reactance. However, the increased
complexity has manufacturing and control implications. The double layer bar rotor winding
arrangement is illustrated in Figure 10a, while a prototype is shown in Figure 10b.
Whilst considering the high harmonic reactance and potential considerable skin effect
in large BDFMs using NL rotors, series wound (SW) rotors are compared with NL rotors
in [
42
]. The winding arrangement of the SW rotor is illustrated in Figure 11a, with a
prototype shown in Figure 11b. Although the SW rotor has lower harmonic content and
no skin effect issues, it has higher impedance and develops lower torque. Despite this, the
performance of the SW rotor is deemed acceptable. It is also indicated that with similar slot
fill factors, the SW and NL rotors will have similar torque performance due to identical
referred rotor resistance. Also in [
43
], details of the design of a 60 kW BDFM with a special
“double-sine” rotor are given. This rotor was designed as a potential BDFM rotor with
greatly reduced harmonic content.
Although, the cage+NL rotor has similar advantages with the NL rotor, the NL config-
uration is more commonly used [
6
]. In [
44
,
45
], the NL and cage+NL rotors are compared
based on their rotor equivalent circuit parameters, and it is suggested that the cage+NL ro-
tors provide better performance due to their lower impedances. This advantage of cage+NL
rotors is shown in [
46
] to be more evident when the disparity between
p1
and
p2
is greater.
In cases where the
p1
value is close to
p2
, the NL rotor may perform better due to lower
leakage inductance.
Initial guidelines for loop design of the NL and cage+NL rotors are given in [
47
]. It is
suggested that loops with spans closer to the pitch of the higher pole number in the BDFM,
are more efficient and effective in torque production. It is also suggested in [
47
], that loops
with small spans have minor contributions to torque production, similar to suggestions
in [44,48,49].
Loops Rotor nest
(a) (b)
Cage End-ring
Cage bar Common End-ring
(c)
Figure 9.
Widely used BDFM rotors: (
a
) NL rotor winding arrangement for
p1+p2=
5, (
b
) NL rotor
prototype [42], and (c) Cage + NL rotor prototype.

Energies 2022,15, 725 10 of 19
5 6 7 8 9 10 11 12 13 14 15 16 17 18
Rotor slots
Single coil pitch
Rotor 'phase'
(a) (b)
Figure 10.
Double layer bar rotor: (
a
) Winding arrangement for
p1/p2=
2
/
4, and (
b
) prototype [
30
].
(a) (b)
Figure 11. SW rotor: (a) Winding arrangement for p1+p2=5, and (b) prototype [42].
Observations in [
44
,
47
,
48
] indicate that the rotor loops should not necessarily be evenly
spaced, and the width of the outer loops should be maximized. An increase in rotor loops
per nest helps to mitigate space harmonics in BDFMs [
27
,
48
], and helps with better current
distribution in BDFM rotors [27].
3.3. BDFM Sizing and Power Ratings
By analyzing the stator magnetic fields in BDFMs using a per phase equivalent circuit,
a composite magnetic loading based on the stator fields is derived in [
5
]. Expressions for
the BDFM power rating as a function of the pole pairs, stack length, airgap radius, electric
and magnetic loadings, are given in [
5
]. The magnetic loading derivation in [
5
] was further
modified in [
27
], as the loading derived in [
5
] was deemed too conservative, leading to
over-sizing. Other aspects of the BDFM geometric sizing such as the slot teeth width and
core height/depth are given in [27].
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 (
p1/p2
) pole ratios
have slight reduction in this disparity. These observations are somewhat echoed in [
50
],
however, the analysed MW rated BDFMs have more than a quarter increase in mass when
compared with DFIGs of similar power and operating speed. BDFMs also suffer a reduction
in efficiency compared to DFIGs, as they have more windings, and consequently higher
winding losses [6].
The impact of pole combination choices on the BDFM core depth is also characterized
in [
29
]. For the pole pair combinations investigated in [
29
], it is observed that the BDFM core

Energies 2022,15, 725 11 of 19
depths are at least two times bigger than DFIG core depths. However, it is also observed
that as
p1
gets closer to
p2
, the core depth ratio between BDFMs and DFIGs of similar
speeds gets smaller. Also, it is demonstrated in [
51
], how sections of an NL rotor core which
do not contribute to the rotor magnetic circuit can be removed for weight reduction.
The effects of rotor leakage inductances on inverter ratings are illustrated in [
25
]. An in-
crease in the rotor leakage inductance reduces the inverter ratings required for crowbar-less
low voltage ride through (LVRT) requirements, but reduces the power factor management
abilities. A trade-off between LVRT and power factor management requirements is there-
fore advocated in the choice and design of BDFM rotors. The use of magnetic wedges in
optimizing inverter ratings is also discussed in [
37
,
52
]. However, it is worth noting that
magnetic wedges are brittle and less reliable than non-magnetic wedges.
3.4. Vibrations and Harmonics Mitigation
In [
53
], it is affirmed that the combination of two magnetic fields of different poles
in BDFMs produces extra vibrations not present in single field induction machines. It is
further revealed that the bending forces on the stator back iron, which are significantly
dependent on the pole pair combinations, contribute greatly to these vibrations. Apparently,
combinations with pole numbers which are close, tend to produce higher vibrations. A
method to mitigate these vibrations is also given, such that the machines are “stiffened” by
increasing the stator core depth. This solution would have to be applied with caution, as
BDFMs already have longer core depths compared to DFIGs [29].
In [
54
], it is stated that the most significant source of torque ripple in BDFMs is the
winding distribution space harmonics; the excessive space harmonics present in the nested
loop rotor structure being a major culprit. In [
41
,
44
,
48
], it is suggested that increasing the
rotor loop spans helps in reducing harmonic content in BDFMs. Also, an increase in rotor
loops per nest helps to mitigate space harmonics in BDFMs [
27
,
48
]. Using a coupled circuit
(CC) model, the effect on torque ripple of NL and cage+NL rotor loop spans relative to the
PW and CW pole pitches, is illustrated in [
49
]. It is shown how the CC model can be used
to find suitable rotor designs for specific BDFM applications.
Slot types have effects on torque ripple [
54
]. Also, a double layer CW is expected to
reduce torque ripple according to [
55
]. It is shown analytically in [
56
], that rotor skews help
to reduce torque ripple. The effects of rotor skewing are further investigated in [
57
], and it
is determined that skewing has little effects on losses, however, there is a slight reduction
in the average torque.
As noted in Section 3.1, suitable pole pair combinations are investigated for torque
ripple and harmonic content in [
36
,
38
,
40
]. Pole pair combinations that are multiples of the
2/3 combination have low harmonic content [
6
,
36
,
38
,
40
], however, the 2/3 combination
itself suffers from UMP.
3.5. BDFM Design and Optimization Procedures
A proposed design procedure for a 6 MW BDFM is presented in [
4
], as illustrated
in Figure 12. The power rating is selected because the largest DFIG generators used in
wind turbines are rated similarly. In the design process, the BDFM equivalent circuit
in [
58
] is used to obtain an initial design from the determined machine specifications. A
coupled circuit (CC) BDFM model is then employed to evaluate the designed nested loop
rotor. Finite element analysis (FEA) of the design is conducted to investigate the peak flux
densities in the different iron parts, and obtain a close estimate of the magnetizing current.
Thermal evaluation of the BDFM design is also recommended, alongside discussions with
machine manufacturers, to aid practicality. System performances such as dynamics, control
stability and LVRT capabilities are then considered in a fine-tuning of the design. This
design procedure was reportedly employed for the 250 kW built and tested in [23].

Energies 2022,15, 725 12 of 19
Initial design
Specifications
Analytical design
software
Discussion with
machine
manufacturer
Equivalent circuit
analysis
Coupled circuit
analysis
LVRT & Grid
connection
Final design
Thermal modelling
Control
optimization
Finite element
analysis
System dynamics
Figure 12. Proposed design procedure for a 6-MW BDFM [4].
Available BDFM electric equivalent circuit (EEC) models are limited in evaluating
saturation, and FEA models are computationally costly. In light of these, a design approach
for BDFMs using an EEC alongside a magnetic equivalent circuit (MEC) model is presented
in [
59
]. The MEC developed in [
60
], is used to determine the flux distribution by the PW
and CW, while the EEC model uses the MEC results to determine the machine performance.
It was noted in [
61
], that investigations on the design of BDFMs are limited in avail-
able literature. To that effect, a comprehensive BDFM design procedure considering the
electromagnetic and thermal aspects of the BDFM, is presented in [
61
], with details of
some of the models used given in [
62
]. A flowchart of the design procedure is given in
Figure 13a
. An EEC model is used to evaluate stator and rotor currents, while a static MEC
as
presented [62]
, is used to analyze the flux density distributions and core loss caused by
these currents.
Temperature analysis is conducted in the design process in [
61
] using a lumped
parameter thermal model illustrated in Figure 13b. The machine sections are designated
as resistances, with the losses identified as heat sources. The description of the thermal
model components are given in Table 2. A simple vibration analysis is also used to estimate
vibrations in designs, and the optimization results are verified using 2-D FEA.
An optimization process using the imperialist competitive algorithm is used to max-
imize the power to weight ratio, efficiency, power factor, while minimizing the voltage
regulation and rotor differential leakage inductance in [
61
]. Feasibility of different aspects
of the BDFM design are monitored, such as the stator and rotor slots, the airgap length,
shaft diameter etc. However, it is the CW power factor that was being maximized. The CW
is also seemingly placed closest to the airgap.
An iterative (Tabu search) method is used to optimize the stator of a 180 frame size
BDFM based on its per phase equivalent circuit model in [
63
]. The optimization was used
to demonstrate how appropriate division of the stator slot area between the PW and CW,
can enable BDFM operation at the magnetic and electric loading limits. This maximizes the
power output, as was demonstrated by the 21 % increase in power from the original design.
This method of optimization is also applied to a D160 frame BDFM in [
64
], to optimize the
electric and magnetic loadings. The maximum motoring torque with a lower limit on the
PW power factor of 0.75 is used for machine evaluation in the optimization process.

Energies 2022,15, 725 13 of 19
Min.
shaft
diameter
Slot
height
Execute EEC and perform
magnetic, thermal and
vibration analysis
Generating
criteria
Magnetic
limitations
Temperature,
vibration and
CW rating
Compute OF(x)
Convergence
criteria
Stop
Set solver parameters
Start
Select PW rating, V1& F1
Set min and max
boundaries of design
variables
Solver sets the values of
design variables
Calculate other
dimensions from design
variables
Feasibility
of stator slot
Feasibility
of rotor slot
and winding
Min.
mechanical
airgap
length
X
X
OF(x)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
No No
(a)
External frame
Stator core
CW
PW
Rotor
Bar
Rotor
core
Shaft
θenv
θenv
θenv
θenv
θenv
θenv
θenv
θenv
Non Drive-End
Drive-End
Rs0
Rs1
Rs2 Rs3 Rs4
Rs6 Rs5
Rag
Rs10 Rs9 Rs7 Rs8
Rr1
Rr2
Rr7
Rr6
Rr3
Rs2
Rr5 Rr6
Pfe,s
Pfric.
Pcu,ew
pw Pcu,ew
pw
Pcu,slot
pw
Pcu,slot
cw
Pcu,ew
cw Pcu,ew
cw
Pcu,ew
r
Pcu,ew
r
Pcu,slot
r
Pfe,r
(b)
Figure 13.
Design process and thermal model in [
61
]: (
a
) Design flow chart, and (
b
) Radial equivalent
thermal network of a BDFM .
Table 2. Resistance descriptions in thermal model [61].
Component Description
Rs0 Thermal resistance between external frame and
environment with thermal resistance of external frame
Rs1 Thermal resistance of stator core
Rs2 Thermal resistance of coil insulator
Rs3/Rs5 Thermal resistance of PW & CW end-winding to
Rs7/Rs9 middle of slot at drive end/non-drive end sections
Rs4/Rs6 Thermal resistance between PW & CW end-winding and
Rs8/Rs10 environment at drive end/non-drive end sections
Rag Thermal resistance between rotor and stator
Rr1 Thermal resistance of rotor slot insulator
Rr2/Rr4 Thermal resistance of rotor end-winding to
middle of slot at drive end/non-drive end sections
Rr3/Rr5 Thermal resistance between rotor end-winding and
environment at drive end/non-drive end sections
Rr6 Thermal resistance of rotor core
Rr7 Thermal resistance between shaft and environment
Pfe,(s/r), Pfric Stator/rotor iron, frictional losses
Pcu,ew, Pcu,slot End-winding, slot copper losses

Energies 2022,15, 725 14 of 19
A magnetostatic FE BDFM model is presented in [
39
,
65
] to enable computationally
efficient and accurate optimization processes. The non-dominated sorting genetic algorithm
(NSGA-II) is used in [
39
] alongside the magnetostatic FE model to optimize the torque and
efficiency of a BDFM designed for a D180 frame size. Geometric variables such as the stator
inner radius and the ratios of slot/yoke height are used in the optimization process. The
NSGA-II is also used in an optimization process in [
40
] to optimize the material cost and
efficiency of a 3.2 MW BDFM. Similar geometric variables and magnetostatic FE models
like in [39], are used in the optimization process in [40].
Both optimization processes in [
39
,
40
] are illustrated in Figure 14; A & B representing
the optimized BDFM performances in [
39
,
40
] respectively. Different pole pair combinations
(
p1/p2
= 1/3, 2/3, 2/4 & 4/6) are tested in the optimization process in [
39
], with the 2/3
combination having the superior performance. However the 4/6 pole pair combination
is used for the 3.2 MW BDFM in [
40
], because of the effects of the presence of UMP using
the 2/3 combination. It is worth noting that the machines in [
39
,
40
] are optimized at the
maximum torque operation points.
In [
66
], the authors of this paper presented a BDFM design process. A modified
version of that process is presented here. The design process of a BDFM is represented
with two intertwined processes; the geometric and winding design process illustrated
in
Figure 15a
, and the power density optimization process illustrated in Figure 15b. The
geometric process is used for each design iteration in the optimization process. Given
the absence of specific values for the stack aspect ratio, electric and magnetic loadings in
literature, practical values are identified during an optimization process, and these values
are used in the final geometric and winding design of the BDFM.
In this design process, the CC model developed in [
49
] is used to determine the appro-
priate rotor type and structure (number of loops) for individual design applications. The
optimization process which also employs the NSGA-II is used to maximize the efficiency
and power density at power output constraints. It is demonstrated in [
67
], how the power
output of BDFMs varies with PW power factor, such that the maximum generated power
from a design may be much larger than the power generated at PW unity power factor. As
a result, power output at PW unity power factor is used in the optimization process in [
66
].
A response surface approximation (RSA) developed from 2-D transient FEA results is used
with the NSGA-II. The RSA is used to enable computational efficiency in the optimization
process. A summary of the listed design and optimization procedures is given in Table 3.
Optimization input parameters
•Construction variations
•Geometry parameters
•Material properties
Machine geometry model
Static FE BDFM model
BDFM Performance
A
•Power,
Torque
•Efficiency
Pareto optimal designs
Multi-objective optimization
•Evaluate objectives
•Generate new set of designs
B
•Efficiency
•CapEx cost
Figure 14. NSGA-II optimizations flow chart. Optimization processes in [39,40].

Energies 2022,15, 725 15 of 19
Start
Determine design specifications
Determine design input variables
(aspect ratio, electrical and magnetic
loadings, flux densities)
Calculate stator bore diameter
and stack length
Calculate PW and CW
parameters (Turns numbers and
currents)
Calculate stator & rotor slot and
core dimensions
Determine maximum number of
loops for either rotor type in
specific application
Torque and torque ripple
evaluation for all number of loops
using CC model
Rotor
topology
selected?
Stop
No
Yes
Rotor topology
selection
Select suitable rotor type and
number of loops
(a)
Start
Determine objectives and
variables
Determine variable ranges
Develop DOE for variables
Develop geometric and
winding designs from DOE
FEA evaluation of designs
Develop RSA from FEA
results
Run optimization with
RSA
Stop
No
RSA
refinement
Add refinement
points to DOE
Satisfactory
RSA
performance?
Satisfactory
performance
obtained?
Yes
Adjust DOE
and/or
Objectives
No
Yes
(b)
Figure 15.
Design process proposed by authors: (
a
) Geometric and winding design process and
(b) optimization process.
Table 3. Summary of design and optimization procedures.
Description Relevant References Models/Analytical
Methods Applications/Advantages Limitations
6 MW BDFM design [4,23,58]
Equivalent circuit
models, CC models,
FEA
Comprehensive MW
rated BDFM design
Impractical for
smaller designs
BDFM design with EEC
and MEC models [59,60] EEC and MEC models
Computationally cheap
Limited functionality
Electromagnetic and
thermal design of
BDFMs
[61,62]
EEC, MEC & thermal
models, vibration
analysis, 2D FEA,
imperialist competitive
algorithm
Robust design
procedure; broad
functionality
Complex
implementation
BDFM rotor design and
power density
optimization
[49,66,67]
CC model, Transient
FEA, NSGA-II,
Response surface
approximations
Rotor type selection;
Systematic power
output evaluation;
computationally cheap
optimization
No thermal
considerations; slightly
complex
implementation
Electric and magnetic
loading optimization [63,64]
Equivalent circuit
model, Tabu search
method
Maximizing power
output, easy
implementation
Power factor constraint
too low
Multi-objective
optimizations [39,40,65]Magnetostatic FEA,
NSGA-II
Computationally cheap
optimizations; material
cost, efficiency &
torque optimizations
No power factor
consideration

Energies 2022,15, 725 16 of 19
4. Conclusions and Future Research
This review on the design of BDFMs can be divided into two parts; the evolution of
cascade motors to BDFMs, and the recent developments in BDFM design. BDFMs have a
rich history in terms of development, which has been laid out. The evolution was detailed
in a way to provide the reader with perspective on BDFM development by highlighting
pioneering designs and prototypes. Contemporary developments in the design of BDFMs
are also described. These recent developments have revolved around the stator winding
pole pair combinations, rotor topology and performance optimizations.
Recurring themes in recent BDFM design related articles include the selection of
suitable pole pair combinations for the stator windings, vibrations & harmonic mitigation,
and optimization of machine power density & efficiency. The stator structure design seems
to be settled on the electrically isolated windings occupying different layers in the stator
slots, with the PW typically closest to the airgap, and the CW closer to the core. However,
there is no clear candidate for the pole pair combinations of these windings. Researchers
are split between the 2/4 and 4/6 combinations for different reasons which are detailed.
Thus, further insight on suitable pole pair combinations is crucial. The use of fractionally
distributed windings for harmonics mitigation also needs to be further investigated.
On the other hand, a lot of research is still being conducted on the type and structure
of BDFM rotors. Two rotor types, the NL and cage+NL rotors, are the leading choices of
rotor types. The number of loops per nest for either rotor type is not fixed, and varies
for reasons like harmonics, vibrations and torque performance. There is a possibility of
significant skin effect in large BDFMs using NL or cage+NL rotors, and this needs to be
investigated. Also, a comprehensive performance comparison between the NL, IL and
cage+NL rotors is important.
BDFM sizing is detailed in available literature. However, the equations used for
parameters like the airgap flux density or core depths are not definitive. To this effect,
investigations across different power ratings may be required to identify the saturation
tolerances of BDFMs. This will also help provide a more accurate basis for power density
comparisons between BDFMs and DFIGs.
Different models have been used for design purposes, giving researchers interested in
BDFM designs a variety of options. However, many require individual implementation, as
they are unavailable in software form for public use, or in commercial software packages.
This generally makes the design of BDFMs a longer process than conventional machines.
Different design procedures have also been presented, and these provide useful insight
into the design of BDFMs. Finally, it is reckoned that a robust design process for BDFMs
would involve both machine and converter designs.
Author Contributions:
Conceptualization, O.I.O. and N.G.; methodology, O.I.O. and N.G.; software,
O.I.O.; validation, O.I.O.; formal analysis, O.I.O.; investigation, O.I.O.; resources, N.G.; data curation,
O.I.O.; writing—original draft preparation, O.I.O.; writing—review and editing, O.I.O. and N.G.;
visualization, O.I.O.; supervision, N.G.; project administration, N.G.; funding acquisition, N.G. All
authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the Centre for Renewable and Sustainable Energy Studies
(CRSES), at Stellenbosch University, South Africa, and the Department of Science and Innovation
(DSI) in South Africa.
Conflicts of Interest: The authors declare no conflict of interest.

Energies 2022,15, 725 17 of 19
Abbreviations
The following abbreviations are used in this manuscript:
BDFM Brushless doubly fed machine
CC Coupled circuit
CW Control winding
DFIG Doubly fed induction generator
EEC Electric equivalent circuit
FEA Finite element analysis
IL Isolated loops
IM Induction machine
LVRT Low voltage ride through
MEC Magnetic equivalent circuit
NL Nested loops
NSGA-II Non dominated sorting genetic algorithm
O&M Operational and maintenance
p1PW pole pairs
p2CW pole pairs
PW Power winding
RSA Response surface approximation
SCIM Squirrel cage induction motor
SW Series wound
UMP Unbalanced magnetic pull
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