A new optimized rotor design for brushless doubly fed machines

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Abstract-- The brushless doubly fed machine (BDFM) is
an alternative to the doubly fed induction generator, widely
used in wind turbines, without use of brush gears and slip
rings. Rotor design is important for designing an optimal
multi-MW BDFM. To date, nested-loop rotors have been
extensively used in various BDFMs but they may not be
suitable for larger machines. In this paper, different
methods of BDFM rotor equivalent circuit parameters
determination are presented and validated by experimental
tests. Then, a design optimization of BDFM rotors is
proposed based on equivalent circuit analysis with the aim
of minimizing the rotor parameters. Two optimized rotors,
one bar cage rotor and one nested-loop rotor were designed
and built from the outcomes of the optimization method for
a BDFM with frame size D180. The characteristics of the
conventional and optimized rotors in terms of the rotor
equivalent circuit parameters and iron saturation at rated
operating conditions are compared using analytical and
Finite Element Analysis (FEA) methods.
Index Terms—Brushless Doubly Fed Machine (BDFM),
Finite Element Analysis (FEA), Nested loop rotor,
Equivalent circuit analysis.
I. INTRODUCTION
The BDFM shows commercial promise as both a
variable speed drive and generator. As a generator, it is
particularly attractive for wind power generation as a
replacement for doubly-fed slip-ring generators, since it
offers a key advantage of variable speed operation with
greater reliability while requiring only a fractionally rated
converter [1]. To date, there have been several attempts to
manufacture large BDFMs, for example in Brazil with a
75 kW machine [2], China with a 200 kW machine [3],
and the 250 kW BDFM reported by the authors in [4], as
stepping-stones towards a megawatt scale BDFM wind
turbine. To achieve successful large MW-scale BDFMs
with desirable performance, it is essential to optimize the
BDFM design, including its rotor characteristics.
The BDFM has two windings on a common stator
core, one connected directly to the grid, called the power
winding (PW), and the other supplied from a variable
voltage and frequency converter, called the control
winding (CW). The stator windings are configured for
different, non-coupling pole numbers (p1 and p2
associated with stator PW and stator CW, respectively). A
schematic of the BDFM grid connections is shown in Fig.
1. A special rotor is required to couple with the two stator
windings. The machine is normally run in a synchronous
mode, with an appropriate controller, in which the rotor
speed is determined by the stator supplied frequencies. In
this mode, the BDFM operates in a similar way to the
doubly fed induction generator with torque that can be
varied by adjusting the control winding voltage.
Bidirectional
Converter
1
Power Winding
(p pole pairs)
2
Control Winding
(p pole pairs)
Supply Voltage
2
ControlWinding Frequency(f )
1
Power Winding
Frequency(f )
Rotor structure,
wound
or reluctance
q=(p
1
+p
2
)/2
Fig. 1. Schematic of BDFM grid connection.
Broadway et al. proposed a number of BDFM rotor
designs in [5], among them a p1+p2 bar cage rotor was
proposed as a simple way of producing principal fields.
The nested-loop rotor was reported in [6] as a
development of the p1+p2 bar cage rotor design
comprising p1+p2 nests each with multiple concentric
loops. Nested-loop type rotors have been widely used in
recent BDFMs due to their higher torque production and
relatively simple structure [4]. In [7] where a comparison
between cage and nested-loop rotors was carried out and
various prototype rotors assessed experimentally. A rotor
design was proposed in [8] with equal current in all loops
of a nest resulting in a reduced rotor leakage inductance
but increased rotor resistance. McMahon et al. [9]
characterized BDFM rotors using an analytical parameter
calculation method using winding factors, where the
magnetizing inductances associated with harmonic fields
were neglected. Rotor parameters were compared for both
nested-loop and series wound rotors.
In this paper, various analytical and numerical
methods for rotor equivalent circuit parameters
calculation are assessed and their practicalities are
verified by performing experimental tests on three
prototype BDFMs. Then, a design optimization method is
proposed based on equivalent circuit analysis with an aim
of minimizing the rotor equivalent circuit parameters. The
optimization method is then used to design and build a
nested-loop rotor and a bar-cage rotor for a D180 frame
BDFM. The characteristics of the optimized rotors in
A New Optimized Rotor Design for Brushless
Doubly Fed Machines
Salman Abdi1, Ashknaz Oraee2, Ehsan Abdi2, and Richard McMahon1
1 Warwick Manufacturing Group (WMG), University of Warwick, Coventry, UK
2 Wind Technologies Limited, St John’s Innovation Centre, Cambridge, UK
Email: s.abdi.jalebi@gmail.com
978-1-5386-3246-8/17/$31.00 © 2017 IEEE
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terms of the rotor equivalent circuit parameters and iron
saturation at rated operating conditions are assessed and
compared with existing rotors using analytical and Finite
Element Analysis (FEA).
TABLE I
PROTOTYPE BDFMS SPECIFICATIONS
Frame size
D160
D180
D400
PW pole Number
4
4
4
CW pole Number
8
8
8
Speed range
700 rpm ± 32%
750 rpm ± 33%
500 rpm ± 36%
Rated torque
70 Nm
100 Nm
3670 Nm
Rated power
5 kW at 700
rpm
7.8 kW at 750
rpm
250 kW at 680
rpm
Efficiency
> 91 %
> 93%
> 95%
Stack length
0.19 m
0.19 m
0.82 m
Stator slots
36
48
72
Rotor slots
(nested loop)
24
36
60
Rotor slots
(bar cage)
24
30
–
II. EXPERIMENTAL BDFMS
The specifications of the prototype BDFMs used in
this study are shown in Table I. These BDFMs have four-
and eight-pole stator windings and were constructed in
frame sizes of 400, 180 and 160 with the stack lengths of
820, 190 and 190 mm, respectively. The stator windings
in all machines were connected in delta. The rotor
configurations include the nested loop rotor comprising
p1+p2 sets of nests each having concentric loops, see Fig.
2, and the cage rotor with p1+p2 bars and an enclosing
cage bars, see Fig. 3.
Nest
21
2
pp +
π
Middle loop Inner loop
Outer loopRotor coreEnd ring
(a) Schematic of the nested-loop rotor
(b) Prototype nested-loop rotor
Fig.2: D180 BDFM nested-loop rotor configuration
Nest
Rotor core
End Ring
End Ring
(a) Schematic of the bar cage rotor
(b) Prototype bar cage rotor
Fig. 3: D180 BDFM bar cage rotor configuration
III. BDFM EQUIVALENT CIRCUIT ANALYSIS
The equivalent circuit is a simple method of
representing the steady-state performance of the BDFM,
allowing rapid calculation of its operating conditions. A
simplified equivalent circuit for the BDFM is shown in
Fig. 4, where all parameters are referred to the PW side
and iron losses are neglected [10]. R1 and R2 are the stator
resistances, Lm1 and Lm2 are the stator magnetizing
inductances and L1 and L2 are the stator leakage
inductances. The circuit is valid for all the modes of
operation, including the induction, cascade, and
synchronous modes and can be utilized for the analysis of
steady-state performance of the BDFM [10]. s1 and s2 are
the power and control winding slips and are defined as
s1=
ω
1−p1
ω
r
ω
1
(1)
s
2
=
ω
2
−p
2
ω
r
ω
2
(2)
where ω1 and ω2 are the angular frequencies of the PW
and CW, and ωr is the shaft angular speed.
Rotor parameters are important in determining the
machine performance including pull out torque and low-
voltage ride through requirements in wind turbine
applications [11]. The rotor can be characterized by the
rotor turns ratio nr, resistance Rr and leakage inductance
Lr, the two latter parameters are also shown in the referred
per-phase equivalent circuit of Fig. 4. The rotor leakage
inductance is formed from conventional leakage elements
and harmonic inductance terms from the space harmonics
generated by the rotor. The harmonic nature of the BDFM
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I
1
R
1
j
ω
1
L
r
R
r
/
s1
I
r
R
2
s2
s1
I
2
s2
s12
Vj
ω
1
L
m
2
j
ω
1
L
m
1
V
1
,
ω
1
Fig. 4: Referred per phase equivalent circuit of the BDFM
rotor results in a higher differential leakage component
compared to other machines.
The rotor turns ratio is a measure of the relative
magnitudes of the magnetic field components the rotor
couples. It is shown in [12] that for given values of
machine stack length, air gap diameter, and electric and
magnetic loadings, the maximum output power can be
obtained for an optimum rotor turns ratio of:
n
r
opt
=p
1
p
2
( )
1/2
(3)
The BDFM rotor design objective is therefore to make
a rotor with turns ratio close to its optimum value. It is
also shown in [12] that the maximum machine rating is
not sensitive to the rotor turns ratio. Hence, the value of
turns ratio being close to its optimal value can be traded
off against gaining other performance measures such as
efficiency and low voltage ride-through (LVRT).
Moreover, to obtain better machine performance such as
higher efficiency and controllability, the rotor leakage
inductance and resistance must be at a minimum.
Below, different methods of obtaining the BDFM
equivalent circuit parameters including the rotor
parameters are briefly discussed. The rotor parameters are
then calculated for three experimental BDFMs, a frame
size D160 machine [12], a frame size D180 machine [13],
and a D400 250 kW machine [14]. The results are
compared with the rotor parameters obtained from
experimental tests.
A. Coupled Circuit Method (CCM)
The equivalent circuit parameters can be calculated
from the machine geometry, during the design stage,
using the method described in [10]. The procedure
involves deriving the machine’s coupled-circuit model,
followed by performing a series of transformations to
obtain the dq sequence components and equivalent circuit
parameters, respectively.
B. Winding Factor Method (WFM)
The winding factor method and its experimental
verification are described in [13]. This method of
parameter determination centres on the loops of the
nested loop or bar cage rotor, which are effectively in
parallel and have mutual couplings via the principal fields
and their space harmonics. Each loop has winding factors
for the principal fields, magnetizing inductances for each
space harmonic, emfs produced by mutual inductances for
the various space harmonics in response to the flow of
currents in other rotor loops and via coupling to the stator.
In addition, each loop has a leakage reactance, which can
be estimated by conventional means and a resistance,
which can be calculated or measured. It should be noted
that rotor parameters obtained from the winding factor
method are speed dependent. However, it is shown in [13]
that this dependency over the operating speed range is
negligible.
C. FEA/Experimental Method
The equivalent circuit parameters can also be
extracted from steady-state measures, such as torque,
speed, voltages, and currents, obtained from BDFM’s
operation in the induction and cascade modes [14], as
shown in the block diagram of Fig. 5. The steady-state
data can be obtained from numerical models e.g. Finite
Element Analysis (FEA) or experimental tests. The stator
winding resistances, R1 and R2, are either calculated from
the machine geometry at a certain operating temperature
or obtained from DC measurements. The magnetizing
inductances, Lm1 and Lm2, are obtained from the
magnetizing tests where a single stator winding is
supplied in turn while the other winding is left open and
the rotor is driven at the synchronous speed to eliminate
rotor currents. Finally, the rotor parameters L’r and R’r
are obtained from applying a curve fitting method to the
data from cascade tests, assuming the stator resistance and
magnetizing parameters are fixed [14].
DC Measurements or
Winding Details Magnetizing Tests Cascade Tests &
Curve Fitting Precess
R
1
& R
2
L
m1
& L
m2
L
'
r
& R
'
r
&Turns Ratio
Fig. 5: Extraction of equivalent circuit parameters from numerical
modeling or experimental measurements
D. Rotor Parameters for Prototype BDFMs
The rotor equivalent circuit parameters for the three
BDFMs are determined using the methods described
above, see Table II. Note that the close agreement
between the parameters calculated from analytical/FEA
methods and the parameters obtained from experimental
tests for all prototype BDFMs shows the validity of
proposed methods.
IV. BDFM ROTOR DESIGN OPTIMIZATION
A. Rotor Loop Span and Number of Loops
The aim of rotor optimization is to achieve a rotor
with near to optimum turns ratio while keeping Lr and Rr
within the desired range for maximum efficiency. The
optimization process is also restricted by the machine
design specifications such as requirements on pull-out
torque, reactive power management and low voltage ride-
through capability. In the optimization problem, turns
ratio and skin effect were taken as design constraints. In
this paper, the influence of loop span and the number of
loops on the rotor parameters for the nested-loop and the
p1+p2 bar cage rotors is studied.
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TABLE II
COMPARISON OF ROTOR PARAMETERS OBTAINED FROM DIFFERENT
EQUIVALENT CIRCUIT PARAMETERS DETERMINATION METHODS
BDFM
Parameter
CCM
WFM
FEA
Experiment
D160
R’r (Ω)
3.51
3.31
3.42
3.54
L’r (mH)
43.5
45.7
41.7
39.3
nr
0.753
0.792
0.790
0.783
D180
R’r (Ω)
1.68
1.72
1.53
1.6
L’r (mH)
56.5
56.7
56
54
nr
0.703
0.716
0.678
0.720
D400
R’r (Ω)
0.115
0.115
0.12
0.114
L’r (mH)
16
16.5
15.2
12.5
nr
0.359
0.366
0.355
0.380
The referred rotor inductance L’r in the simplified
circuit shown in Fig. 4 represents the series inductances in
the full equivalent circuit [10], including the stator PW
and CW leakage inductances and conventional rotor
leakage inductances.
The rotor resistance and conventional leakage
components of the rotor inductance do not vary
significantly with changes in the loop span. Nevertheless,
magnetizing inductance is considerably influenced by the
variation of loop spans as well as the ratio of PW and CW
pole pairs, as can be seen from (4),
L
m
=
µ
0
g
ldq
π
N
eff
p
⎛
⎝
⎜⎞
⎠
⎟
2
(4)
obtained for p pole-pair space harmonics. Neff is the
effective turns corresponds to each pole and g is the air
gap length. According to (4), the magnetizing inductance
in a machine with uniform air gap is inversely
proportional to the square of the harmonic pole pairs of
the magnetized field. The MMF, magnetizing each field is
determined by the harmonic winding factor of the
winding. The winding factor, kw, for a single rotor loop is
given by:
kw=sin(
β
p
2)sin(wsr p2)
wsr p2
(5)
where β is the coil span of the loop, p is the harmonic
pole pair and wsr is the slot mouth in radians. It should be
noted that to achieve a nested-loop rotor with six nests
and a maximum of three loops per nest, and a bar cage
rotor design with six bars and a maximum of three
internal loops, the minimum number of rotor slots must
be 36 and 42 respectively. These numbers of rotor slots
are hence considered in the following analysis.
To achieve minimum rotor L’r and R’r in a nested-loop
design, loops are added progressively to the nests and
loop spans are adjusted for equal slot spacing. The
optimization procedure is then similarly performed on the
p1+p2 bar cage rotor with arbitrary pitch and placement.
This can be achieved by adding concentric loops
progressively adjusting all the loop spans by increments
of one degree. The R’r and L’r obtained for the 36-slot
nested-loop rotor of D180 BDFM with different number
of loops are shown in Table III using coupled circuit and
winding factor methods.
It can be seen from Table III that adding loops to the
rotor nests corresponds to a lower harmonic leakage
inductance due to the addition of steps in the mmf pattern.
Furthermore, loops with larger spans have a much lower
referred rotor leakage inductance and resistance, hence
give better results on the chosen measure of the machine
performance.
A similar procedure was applied to a 42-slot bar cage
rotor of the D180 BDFM with p1+p2 bars in order to
further optimize rotor parameters. The number of slots is
chosen in a way that a maximum of three internal loops
between the two bars of the bar cage structure is
achievable and therefore a comparison of rotor parameters
obtained from these two rotor designs with the same
number of loops can be performed. Table IV shows the
effect of adding loops to the p1+p2 bar cage resulting in a
reduced referred rotor leakage inductance and resistance.
The L’r and R’r obtained for the two rotors for the
three-loop case are shown in the last columns of Table III
and IV. It is evident that both L’r and R’r are significantly
lower in a bar cage rotor than a nested-loop rotor for a
given BDFM.
TABLE III
PARAMETER CALCULATION OF 36-SLOT NESTED-LOOP ROTOR WITH
DIFFERENT NUMBER OF LOOPS FOR D180 BDFM
One loop
Two loops
Three loops
CCM
R’r (Ω)
3.47
1.87
1.54
L’r (mH)
117.7
64.1
52.4
WFM
R’r (Ω)
3.59
1.94
1.60
L’r (mH)
121.8
67.6
54.1
TABLE IV
PARAMETER CALCULATION OF 42-SLOT BAR CAGE ROTOR WITH
DIFFERENT NUMBER OF LOOPS FOR D180 BDFM
One loop
Two loops
Three loops
CCM
R’r (Ω)
3.19
1.52
1.23
L’r (mH)
108.4
55.3
43.3
WFM
R’r (Ω)
3.12
1.60
1.27
L’r (mH)
110.7
58
45.1
The optimised loops spans for the three-loop designs
are given in Table V.
TABLE V
OPTIMIZED LOOP SPANS FOR MINIMUM ROTOR PARAMETERS
Rotor type
Loop span (degree)
Inner loop
Middle loop
Outer loop
Nested-loop
27 o
42 o
54 o
Bar cage
24 o
38 o
50o
B. Saturation Effects
The optimized loop spans obtained for minimum
BDFM rotor parameters generally result in unequal rotor
teeth widths as shown in Fig. 6. This may cause iron
saturation and hence excessive rotor core losses in the
narrower rotor teeth. Therefore, special care must be
taken in determining optimized loop spans and width of
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rotor teeth in order to avoid saturation.
An approximation for the magnetic loading of the
BDFM was given in [15] as:
B=2 2
π
B
1
2+B2
2
(6)
The maximum flux densities in the teeth,
ˆ
Bt
, must be
chosen according to some criterion e.g. to avoid
saturation in the iron or to minimize core losses. It was
shown in [16] that the minimum teeth width, wt for both
the rotor and stator laminations to avoid saturation at
rated operating conditions of the machine can be
calculated using the following equation:
w
t
=2
π
d
n
s
ˆ
B
t
(B
1
+B
2
)
(7)
where d is the air gap diameter, ns is the number of rotor
or stator teeth and B1 and B2 are rms values of air gap
magnetic field density generated by PW and CW. From
(7), the minimum required rotor tooth width, wt
req, for 36-
slot and 42-slot rotors with the air gap diameter of 165
mm and magnetic loading of 0.52 T can be determined as
8.8 mm and 7.5 mm, respectively.
Fig. 6: Uneven distributions of rotor slots as a result of loop span
optimization.
Table VI shows the widths of the teeth as labelled wt1,
wt2, and wt3 in Fig. 6. As can be seen from Table VI, the
widths of teeth t2 and t3 are considerably lower than the
minimum required width to avoid saturation. In addition,
the negative value for wt3 in the case of bar cage rotor
implies that the design of a bar cage rotor with three
internal loops and optimized loop spans is not physically
practical and therefore a design with fewer number of
loops should be considered.
TABLE VI
ROTOR TEETH WIDTHS FOR THE OPTIMISED ROTOR DESIGNS
Rotor type
Tooth width (mm)
Wt
req
Wt1
Wt2
Wt3
Nested-loop
8.8 mm
25 mm
4.3 mm
0.5 mm
Bar cage
7.5 mm
21.8 mm
7.1 mm
-1.1 mm
C. Optimized Prototype Rotors
Two prototype rotors, a nested-loop and a bar cage
structure are designed for optimizing the rotor equivalent
circuit parameters while keeping the iron saturation at its
acceptable limit. The design details are shown in Table
VII. The nested-loop rotor has 36 slots and three loops per
nest. The rotor teeth have equal widths close to the
required value of Wt
req , obtained from (6). The bar cage
rotor has 30 slots and two internal loops. The teeth are
designed to have equal widths to meet saturation
requirements.
TABLE VII
SPECIFICATIONS OF THE NEW DESIGN ROTORS FOR D180 BDFM
Rotor type
Nested loop
Bar cage
No of slots
36
30
Span
Loop 1
10o
12 o
Loop 2
30 o
36 o
Loop 3
50 o
–
Tooth width
8.6 mm
10.6 mm
Wt
req from (6)
8.8 mm
10.5 mm
The BDFMs with new rotor designs are modelled
using Finite Element Analysis (FEA). Fig. 7 shows the
meshes developed for the two rotors. Non-linear models
were used to assess the magnetic circuits and saturations
levels of the machine at synchronous mode and rated
conditions. It was observed that the flux densities in
different locations of the rotor teeth and rotor back iron
regions are close to the target values set out at the design
stage. However, for the nested-loop rotor, where the rotor
teeth widths are thinner than the minimum required value,
a degree of saturation was observed specially in the roots
of the teeth at rated PW and CW voltages.
The linear FEA model is used to derive the rotors
equivalent circuit parameters. The parameters have also
been obtained using analytical CCM and WFM. The
parameters are shown in Table VIII.
V. DISCUSSION AND CONCLUSIONS
From Table VIII, it is evident that the parameters
values obtained for the optimized rotors are significantly
lower than those of previous rotors for D180 BDFM
shown in Table II. The values of nr for both optimized
rotors are close to the optimum value of 0.707.
TABLE VIII
ROTOR EQUIVALENT CIRCUIT PARAMETERS FOR D180 BDFM NEWLY
DESIGNED ROTORS
R’r (Ω)
L’r (mH)
nr
Nested Loop
Rotor
CCM
1.45
47.5
0.735
WFM
1.49
50.7
0.733
FEA
1.51
52.1
0.730
Bar Cage
Rotor
CCM
1.37
48.6
0.716
WFM
1.39
53.5
0.713
FEA
1.43
51.3
0.717
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There are four major sources of leakage permeance
considered in the analysis: slot, tooth-top, overhang and
zigzag permeances. Among the leakage terms, the slot
leakage in most cases has the largest contribution in the
winding leakage [16]. The slot leakage permeance is
inversely proportional with the slot pitch and the slot
width. Therefore, for the 30-slot bar cage rotor with larger
slot pitch and slot width than a 36-slot nested-loop rotor,
lower L’r is expected. Nevertheless, it should be noted that
higher number of loops in the nested-loop rotor has a
positive effect on L’r reduction by creating smoother
EMF. The L’r values, estimated from different methods
and shown in Table VIII, show that the difference
between the two rotor designs is not significant.
However, there is, in average, a 6.5% reduction in the
referred rotor resistance of the bar cage rotor as compared
to that of the nested-loop rotor. This is mainly due to the
increase in the rotor bars cross section as a result of lower
number of required slots. The advantage of lower rotor
resistance as well as better rotor performance in terms of
iron saturation makes the bar cage design a better rotor
choice for large-scale BDFMs.
(a) 36-slot nested-loop rotor
(b) 30-slot bar cage rotor
Fig. 7: FE modeling of D180 BDFM with new optimized rotors
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