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IEEE TRANSACTION ON ENERGY CONVERSION

1

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 gear and slip ring. Rotor

design is important for achieving an optimal multi MW BDFM.

To date, nested-loop rotors have been exclusively used in various

BDFMs, although they may not be ideal for larger machines. This

paper studies, both analytically and experimentally, different

rotors for the D160 and D400 frame size BDFMs. An

optimization on the rotor equivalent circuit parameters is carried

out and verified with different parameter extraction methods. A

comparison of the performance of the suggested rotors is also

presented.

Index Terms—Brushless doubly fed machine (BDFM),

Electrical machines, Nested-loop rotor, Optimization.

I. INTRODUCTION

he BDFM is a promising replacement for the widely used

conventional DFIG 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 BDFM requires no brushed contact to

the rotor, eliminating a common source of failures making it a

particularly attractive machine for offshore wind turbines.

The BDFM has two non-coupling stator windings with

different pole numbers, p1 and p2, (where p1 and p2 are the

power winding, PW, and control winding, CW, pole pairs

respectively) and a specially designed rotor, coupling both

stator fields. The BDFM rotor is thus an important component

of the machine as its winding carries the mmf induced by both

stator PW and CW, as shown in Figure 1. However, limited

literature is available on the rotor design of the BDFM.

Broadway and Burbidge considered rotor designs in [2] and

a p1+p2 bar cage rotor was identified as the simplest concept

resulting in principal fields with space harmonics. The nested-

Ashknaz Oraee and Richard McMahon are with Electrical Engineering

Division, Cambridge University, 9 JJ Thomson Avenue, Cambridge CB3

0FA, UK (e-mail: ao331@cam.ac.uk; ram1@cam.ac.uk).

Ehsan Abdi and Peter Tavner are with Wind Technologies Ltd, St John’s

Innovation Park, Cambridge CB4 0WS, UK (e-mail:

ehsan.abdi@windtechnologies.com; peter.tavner@durham.ac.uk).

loop rotor was proposed as a development of the p1+p2

fabricated bar cage 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 [3]. Several series-wound and

nested-loop rotors have also been studied [4]. A comparison

between cage and nested-loop rotors was carried out in [4] and

various prototype rotors assessed experimentally. The design

and behavior of various 6 pole rotor windings for two different

sizes of 4/8 pole BDFMs was analyzed in [5] with predictions

from their equivalent circuits. Gorginpour et al. [6] proposed a

new rotor configuration for the BDFM with equal current in

all loops of a nest. The loops were connected in series

resulting in a reduced rotor leakage inductance but increased

rotor resistance. McMahon et al. [7] characterized BDFM

rotors with the winding factor method, a new analytical

parameter calculation method. It was assumed that there is no

coupling via harmonic fields and the magnetizing inductances

associated with harmonic fields were neglected. Rotor

parameters were then compared for both nested-loop and

series wound rotors. It was shown that the rotor resistance of

the series wound rotor is almost twice that for the nested-loop,

both having turns ratios close to optimum, resulting in lower

torque performance.

Figure 1: Brushless doubly fed machine configuration

Various BDFMs have been reported in the literature, some

specially designed for wind power applications [8,3].

Nevertheless, attempts have been made to manufacture larger

machines, beginning in Brazil with a 75 kW machine by

Stator Power

Winding (PW)

Fractionally

rated

converter

Grid

Rotor Winding BDFM

Stator Control

Winding (CW)

Rotor Design Optimization for the BDFM

Ashknaz Oraee, Student Member, IEEE, Richard McMahon, Ehsan Abdi, Senior Member, IEEE, and

Peter Tavner, Senior Member, IEEE

T

IEEE TRANSACTION ON ENERGY CONVERSION

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Carlson et al. [9] and more recently in China with the design

of a 200 kW machine by Liu and Xu [10].

This paper analytically examines various BDFM rotors,

mainly a cage rotor with p1+p2 bars and a nested-loop rotor by

modeling analysis on the rotor structure and winding

arrangements. The equivalent circuit parameters are extracted

using the winding factor method and the coupled circuit model

and verified using experimental results for existing BDFM

prototypes.

Optimization on the rotor equivalent circuit parameters are

performed with the aim of minimizing rotor resistance and

inductance whilst keeping the turns ratio close to its optimum

value. Design objectives and constraints are investigated

further for MW wind turbines generators. Moreover, rotor

equivalent circuit parameters are extracted for the optimized

design and machine performance is analyzed in this study.

Finally, the effects of loop span and pole pair combination

for different rotor configurations are investigated and a

comparison on the rotor parameters is also presented.

II. BDFM BACKGROUND AND CONFIGURATION

A. BDFM equivalent circuit

The operation of the BDFM can be described by a per-

phase equivalent circuit similar to the equivalent circuits of

two induction machines with interconnected rotors, shown in

Figure 2 [7]. R1 and R2 are the stator resistances, Lm1 and Lm2

are the stator magnetizing inductances and L1 and L2 are the

stator leakage inductances. Parameters are referred to the PW

using the modifier ‘′’. The slips are defined as:

s1=

ω

1−p1

ω

r

ω

1

(1)

s2=

ω

2−p2

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. The leakage

inductances cannot be measured directly therefore a simplified

equivalent circuit is proposed in [11].

Furthermore, 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 Figure 2. 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 rotor results in a

higher differential leakage component compared to other

machines.

Figure 2: Referred per phase equivalent circuit of the BDFM

B. Design objectives and constraints

The design objective is to produce a rotor with turns ratio

close to its optimum value. Moreover, for better machine

performance i.e. higher efficiency and controllability, the rotor

leakage inductance and resistance must be at a minimum.

The power rating of the BDFM is given in [4]. However,

experience has shown that using a peak flux density of

2𝐵!"#, as a single field machine, gives an underestimate of

the peak flux density in the airgap which can lead to excessive

saturation in the teeth. An alternative approach is to use a limit

of 𝐵!"# defined as:

Bsum =B

1+B2

(3)

Therefore, for the BDFM, power rating can be calculated

as:

P

c=2

π

d

2

!

"

#$

%

&

2

l

ω

rBsum Jc

p1+p2

p1(1+1

nr

)(1+nr

p2

p1

)

!

"

#

#

#

#

$

%

&

&

&

&

(4)

From the above relation, machine rating is determined by

the stack length l, airgap diameter d, magnetic loading B!"#,

electric loading J, pole pairs and the rotor turns ratio.

With the assumptions of unity power factor and small load

angle operation, the value of nr giving the maximum output

power may be obtained by solving !!!

!!!

=0. The turns ratio for

maximum output power is therefore given by:

nr

opt =p1

p2

( )

1/2

(5)

This is in contrast to the result obtained in [1]. The reason

for this change is using an alternative approach of 𝐵!"# limit

instead of peak flux density of 2𝐵!"#. The actual values of

n!!"#!are 0.71 and 0.63 for the 4/8 BDFM from equation (5)

and [1], respectively. An optimum rotor for the purpose of

maximum machine rating has minimum resistance and leakage

inductance with a turns ratio close to an optimum value.

However, equation (4) does not show the sensitivity of the

maximum machine rating to the variation of rotor turns ratio.

Table I shows how the rotor turns ratio varies within a range

I1R1j1L1

j1Lm1

V1 1

j1Lrj1L2

Rr/s1IrR2

s2

s1I2

s2

s12

VV 1

rV2

rj1Lm2

IEEE TRANSACTION ON ENERGY CONVERSION

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of 2% and 5% of the maximum output power for different pole

pair machines. It is evident from Table I that the maximum

machine rating is not sensitive to the rotor turns ratio. Hence,

the value of the turns ratio being close to its optimal can be

traded off against gaining other performance measures.

Table I: Variation of rotor turns ratio for maximum power

rating

BDFM (p1/p2)

(p1/p2)1/2

2% range

5% range

1/2

0.71

0.53-0.95

0.45-1.12

1/3

0.58

0.43-0.78

0.36-0.93

1/4

0.50

0.37-0.68

0.31-0.81

III. ROTOR MODELING

A. Rotor structure and winding arrangement

Cage rotor with p1+p2 bars is identified as the simplest

concept with an enclosing cage and concentric loops

connected to the end ring from one side. Figure 3a shows

winding configuration of a p1+p2 bar cage rotor with two loops

per nest. The nested-loop rotor was proposed as a

development of the p1+p2 fabricated bar cage comprising

multiple loops in p1+p2 nests. An example of a nested-loop

rotor winding arrangement with three loops per nest is shown

in Figure 3b.

Rotors have been designed and built for the 4/8 D160 and

D400 frame size BDFMs. Specifications of the nested-loop

and p1+p2 bar cage prototype rotors for the D160 and D400

BDFMs are given in Table II and Table III. The existing

prototype rotors are shown in Figure 4.

a. p1+p2 bar cage rotor

b. Nested-loop rotor

Figure 3: BDFM rotor arrangements

Table II: D160 BDFM specifications

PW pole pair

2

Rated speed, rev/min

700

CW pole pair

4

Stator slots

36

Stack length, mm

190

Rotor slots (nested-loop)

24

Rated power, kW

1.4

Rotor slot (bar cage)

24

Rated torque, Nm

40

Table III: D400 BDFM specifications

PW pole pair

2

Rated speed, rev/min

680

CW pole pair

4

Stator slots

72

Stack length, mm

820

Rotor slots (nested-loop)

60

Rated power, kW

250

Rotor nests

6

Rated torque, Nm

3670

a. p1+p2 bar cage rotors

b. Nested-loop rotor

Figure 4: BDFM rotor prototypes

B. Winding factor method

To assess the performance of the overall machine, rotor

parameters are required and they can be extracted using the

equivalent circuit model. The winding factor method predicts

rotor parameters by calculating rotor loop impedances referred

to the stator winding when CW is short-circuited. The

impedance of individual loops, n, in the nested loop rotor

taking into account rotor and stator coupling via space

harmonics is calculated as:

Nest

Rotor coreEnd Ring

End Ring

Nest

21

2

pp +

π

Middle loop Inner loop

Outer loopRotor coreEnd ring

IEEE TRANSACTION ON ENERGY CONVERSION

4

Zeff1

Zeff2

!

Zeffn

!

"

#

#

#

#

#

$

%

&

&

&

&

&

=

kw1,1

I1

'

(

)*

+

,

kw1,2

I2

'

(

)*

+

,

!

kw1,n

In

'

(

)*

+

,

!

"

#

#

#

#

#

#

#

#

#

#

$

%

&

&

&

&

&

&

&

&

&

&

(6)

where Ix is the current flowing through each individual rotor

loop and kw is the winding factor for a single loop in a nest of

a particular loop. Furthermore, the equivalent impedance

presented by one nest for the ith harmonic pole pair is given

by:

Zeq =kw1i

2

Zeffi

i=1

n

∑

"

#

$

$

%

&

'

'

−1

(7)

A transformation from p1+p2 phase system of the nested

loop rotor to a three-phase system of the stator is then

required. Note that these parameters are at rotor frequency, i.e.

speed dependent.

The turns ratio for the nested loop rotor is calculated using

mmf balance with one stator winding open circuit, as given in

[6]:

nr=

kww1ikww2i

Zi

kww2i

2

Zi

i=1

n

∑

(8)

To extract rotor parameters for the p1+p2 bar cage rotor, the

phase relationship between coils must be investigated. The

phase change between the peak flux in the coils is:

2

π

p1+p2

2

(9)

For the 4/8 pole BDFM, the phase change between the

loops is !!

! or 120 degrees. The same phase shift will apply

between the emfs induced in the bars of the p1+p2 cage rotor.

The induced emfs in the bars by the p1 pole pair field must

have the same phase sequence as those induced by the p2 pole

pair field for a functional BDFM. Therefore, the currents

flowing in the set of loops or in the bars must have the same

phase delay. For the p1+p2 bar cage rotor, shown in Figure 4a,

to produce the same mmf pattern each slot must contain the

same amp-conductors. Since the two rotors produce identical

mmf patterns, the rotor turns ratio must also be identical.

Hence, in the winding factor method this is equivalent to

multiplying the effective impedance of the outer loop by the

scaling factor of equation (10).

scale =(cos(0) −cos( 2

π

p1+p2

2

))2+(sin(0) −sin( 2

π

p1+p2

2

))2

(10)

For example, in the 4/8 BDFM this factor evaluates to 3.

The effective loop impedance is then calculated as:

Zeffbarcage =Zeff1:n−1zeffn×scale

[ ]

(11)

Therefore, the equivalent impedance presented by one nest

for a bar cage rotor changes to:

Zeq =kw1i

2

Zeffbarcage,i

i=1

n

∑

"

#

$

$

%

&

'

'

−1

(12)

For the p1+p2 bar cage rotor, equation (8) must be modified

to:

nr=

kww1ikww2i

Zbarcage,i

kww2i

2

Zbarcage,i

i=1

n

∑

(13)

C. Coupled circuit model

An alternative method of obtaining the equivalent circuit

parameters is the coupled circuit model that relates the stator

and rotor voltages and currents by using a transformation into

complex sequence components. The coupled circuit approach

is based on the model reduction procedure starting from a

coupled circuit model which leads to a single set of dq

parameters for the rotor, independent of the operating speed.

The coupled circuit model of the BDFM for various rotors is

studied in [12].

The rotor inductance matrix, Mrr, is calculated as:

Mrr =Mrr

coupled coils +Mrr

leak

(14)

where M!!!"#$ is the conventional leakage component and

M!!!"#$%&'!!"#$% is the magnetizing and mutual inductance

IEEE TRANSACTION ON ENERGY CONVERSION

5

component. The conventional leakage component of the rotor

inductance arises from leakage effects due to magnetic flux

not linking stator and rotor conductors. The latter consists of

slot, overhang and zig-zag, for each rotor loop and can be

calculated using methods described in [13]. M!!!"#$ for each

nest of the nested loop rotor is given by:

Mrr

leak =

Lloop 0!0

0Lloop " #

# " " 0

0!0Lloop

!

"

#

#

#

#

#

$

%

&

&

&

&

&

(15)

where Lloop is the diagonal matrix of nest leakage

inductances.

The rotor resistance is found by calculating the resistance of

the bar using its cross-sectional area and length. The rotor

resistance matrix is therefore calculated by finding the

resistance of each rotor loop with zero off-diagonal terms

similar to the rotor leakage inductance matrix of equation (15).

The rotor resistance matrix for each nest of the nested loop

rotor is formed using (16):

Rr=

Rloop 0!0

0Rloop " #

# " " 0

0!0Rloop

!

"

#

#

#

#

#

$

%

&

&

&

&

&

(16)

where Rloop is the diagonal matrix of nest resistances. It is

assumed that the resistance matrix has a constant value

throughout the machine operation. For example for nested

loop rotor of the D400 BDFM with 5 rotor loops and 6 nests,

M!!!"#$ and Rr matrices have dimensions of 30×30.

In both nested loop and p1+p2 bar cage rotors the

magnetizing and mutual leakage components dominate over

conventional leakage inductance due to the higher harmonic

components of the magnetic field. Since the p1+p2 bar cage

rotor must also produce the same mmf pattern as the nested

loop rotor, the magnetizing and mutual inductance component

of the rotor leakage inductance remains the same. However,

the resistance and conventional leakage inductance matrices

will change to have the following form:

Mrr

leak =

2Lbar +2Lend −Lbar 0−Lbar

−Lbar 2Lbar +2Lend −Lbar 0

0−Lbar 2Lbar +2Lend −Lbar

−Lbar 0−Lbar 2Lbar +2Lend

"

#

$

$

$

$

$

%

&

'

'

'

'

'

(17)

Rr=

2Rbar +2Rend −Rbar 0−Rbar

−Rbar 2Rbar +2Rend −Rbar 0

0−Rbar 2Rbar +2Rend −Rbar

−Rbar 0−Rbar 2Rbar +2Rend

"

#

$

$

$

$

$

%

&

'

'

'

'

'

(18)

where Rbar and Rend are the resistances and Lbar and Lend are

the inductances due to bar and end ring respectively.

The effective turns ratio is defined as the square root of the

fundamental space harmonics leakage terms for the rotor and

the stator. Using the p1+p2 bar cage rotor instead of a nested

loop results in changes in the rotor inductance matrix Mrr,

hence, the turns ratio of a cage rotor is different to a nested

loop rotor. This difference is due to the change in the ratio of

the number of turns of the rotor to stator.

IV. PARAMETER EXTRACTION AND EXPERIMENTS

The two previously mentioned methods of obtaining rotor

parameters are applied to the nested loop rotor of the 4/8 D400

BDFM prototype and the p1+p2 bar cage rotor of the 4/8 D160

BDFM, shown in Figure 4. The D400 nested loop rotor has 5

loops per nest with spans of 54∘, 42∘, 30∘, 18∘ and 6∘. The

D160 p1+p2 bar cage rotor has a cage and a central loop with

spans of 60∘ and 30∘.

A. Comparison of parameter values

The winding factor method includes coupling via harmonic

fields. However, the rotor-stator coupling has a very small

effect on the rotor parameters and therefore it can be

neglected.

For the coupled circuit model, the stator to rotor couplings

is assumed to take place only via the principal p1+p2 fields but

couplings between rotor loops via harmonic fields are

included. The values obtained from the two models are

compared to those determined experimentally.

The equivalent circuit parameters are measured for each

rotor using the procedure proposed by [11]. The experimental

arrangement and procedure for the extraction of parameters

has been described in [7]. A comparison between coupled

circuit and winding factor method is carried out on the D400

[3] and the D160 BDFMs. The parameters are calculated from

the machine geometry and are given in Table IV.

IEEE TRANSACTION ON ENERGY CONVERSION

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Table IV: D160 and D400 experimental parameters

Parameter

D160

D400

R1 (Ω)

2.1

0.0907

R2 (Ω)

1.3

0.667

L1 (mH)

34.7

0.576

Lm1 (mH)

329

89.3

L2 (mH)

27.4

13.1

Lm2 (mH)

83

286

For the speed dependent winding factor method, the

parameters are evaluated at natural speed, defined as the

synchronous speed when the CW is fed with DC. Table V

gives rotor parameters calculated from the coupled circuit

model and the winding factor method. It can be seen that both

methods produce similar rotor equivalent circuit parameters

for the D160 and D400 prototype BDFMs.

Table V: Comparison of complete equivalent circuit rotor

parameters

Machine

Parameter

Coupled Circuit

Winding Factor

D160

R′r (Ω)

xxx

xxx

L′r (mH)

xxx

xxx

nr

xxx

xxx

D400

R′r (Ω)

0.112

0.110

L′r (mH)

5.94

5.86

nr

0.401

0.409

As mentioned previously in section III, rotor parameters

obtained from the winding factor method are speed dependent.

Table VI shows the variance in rotor parameters at different

rotational speeds. It is evident from the table that the effect on

rotor parameters is negligible.

Table VI: Comparison of rotor parameters for different

operating speeds

Speed

(rev/min)

D160

D400

L′r (mH)

R′r (Ω)

L′r (mH)

R′r (Ω)

350

xxx

xxx

0.5863

0.1097

500

xxx

xxx

0.5859

0.1103

650

xxx

xxx

0.5857

0.1109

B. Experimental parameter extraction

Machine parameters were extracted from the D160 and

D400 frame BDFMs by cascade tests using a procedure

described by Roberts et al. [11] in which parameters were

obtained from experimentally determined torque-speed

characteristics in the cascade mode.

Experimentally extracted parameters are for the reduced

form of the equivalent circuit, whereas the parameters

obtained in the previous section are for the full model.

Converting the full model to the reduced model using the

method described in [14] enables a comparison to be made

with the experimentally determined values and those using the

coupled circuit and winding factor methods. The results are

shown in Table VII. Comparison of the results from the

coupled circuit model and the winding factor method given in

Table VII shows good agreement.

Table VII: Reduced form of extracted rotor parameters

Machine

Parameter

Coupled

Circuit

Winding

Factor

Experiment

D160

R′r (Ω)

xxx

xxx

4.05

L′r (mH)

xxx

xx

127.5

nr

xxx

xxx

1.17

D400

R′r (Ω)

0.114

0.114

0.114

L′r (mH)

8.64

8.75

12.5

nr

0.386

0.393

0.380

V. ROTOR DESIGN OPTIMIZATION

A. Optimization parameters and constraints

The rotor design theory is developed with a view to

obtaining equivalent circuit parameters, enabling the

assessment of the overall machine design and performance.

The rotor optimization aims to achieve a rotor with near to

optimum turns ratio while keeping Lr and Rr within the desired

range for maximum efficiency.

As mentioned previously, the rotor leakage inductance

consists of a conventional leakage component as well as space

harmonics manifested as magnetizing and mutual inductances.

The magnetizing inductance is significantly affected by the

variation of loops span as well as the ratio of PW and CW pole

pairs, as can be seen from (19):

Lm=

µ

0

g

ldq

π

Neff

p

!

"

#$

%

&

2

(19)

evaluated for p pole-pair space harmonics. The effective

turns corresponds to each pole and g is the airgap length.

To achieve optimum rotor Lr and Rr in a design, loops are

added progressively to the nested-loop design 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 loop spans

by increments of one degree.

The rotor optimization is determined by the design

IEEE TRANSACTION ON ENERGY CONVERSION

7

specifications such as the 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.

B. Effect of loop span

The influence of loop span on the rotor parameters for the

nested loop and the p1+p2 bar cage rotors of Figure 4 is

investigated in this section.

The rotor resistance and conventional leakage component of

the rotor inductance do not vary significantly with changes in

the loop span. However, the harmonic component of the rotor

inductance changes considerably. According to equation (19),

the magnetizing inductance in a machine with uniform airgap

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, 𝑘!, for a single rotor loop in a

nest is given by:

kw=sin(

β

p

2)

sin(wsr p

2)

wsr p

2

(20)

where 𝛽 is the coil span of the loop, p is the harmonic pole

pair and w!" is the slot mouth in radians.

It can be seen from Figure 5 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. The spans have

been optimized for 5 loops to give minimum rotor parameters,

given in Table VIII. Similar procedure can be applied if a

p1+p2 bar cage rotor is employed in the D400 BDFM to further

optimize rotor parameters. Figure 6 shows the effect of adding

loops to the p1+p2 bar cage resulting in a reduced referred

rotor leakage inductance and resistance. The optimized rotor

loop spans for the p1+p2 bar cage rotor is given in Table IX.

a. Rotor leakage inductance

b. Rotor resistance

Figure 5: D400 nested loop rotor parameter variation with

number of loops

xxx

a. Rotor leakage inductance

xxx

b. Rotor resistance

Figure 6: D400 p1+p2 bar cage rotor parameter variation with

number of loops

12345

0

0.01

0.02

0.03

0.04

Number of Loops

Lrprime (H)

12345

0

0.05

0.1

0.15

0.2

0.25

Number of Loops

Rrprime (ohms)

IEEE TRANSACTION ON ENERGY CONVERSION

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Table VIII: Minimum rotor parameters for optimized spans of

nested loop rotor

Nested loop spans

59∘

53∘

46∘

39∘

28∘

𝐿!

! (mH)

4.5

𝑅!

!

(Ω)

0.05

𝑛!

xxx

Table IX: Minimum rotor parameters for optimized spans of

p1+p2 bar cage rotor

Nested loop spans

𝑥∘

𝑥∘

𝑥∘

𝑥∘

𝑥∘

𝐿!

! (mH)

xxx

𝑅!

!

(Ω)

xxx

𝑛!

xxx

C. Effect of pole pair

Important performance measures such as output torque,

speed and magnetization considerations determine the most

appropriate BDFM pole pair combination. To achieve the

most appropriate BDFM pole combination with minimum

rotor inductance and resistance a comparison is conducted.

The complete equivalent circuit rotor parameters of the nested

loop and p1+p2 bar cage rotor for common BDFM pole pair

combinations are given in Tables X and XI, respectively.

Figure 7 shows that for the same physical dimensions, the 2/6

pole machine gives lowest referred rotor inductance and

resistance for the nested loop rotor. Figure 8 shows the p1+p2

bar cage rotor arrangement giving lower rotor inductance and

resistance on machines with further away poles.

Table X: Referred rotor parameters for nested loop rotor

Machine

2/6

4/8

4/12

8/12

𝐿!

! (mH)

4.2

5.6

8.3

8.6

𝑅!

!

(Ω)

0.07

0.11

0.25

0.29

𝑛!

0.53

0.68

0.52

0.80

Table XI: Referred rotor parameters for p1+p2 bar cage rotor

Machine

2/6

4/8

4/12

8/12

𝐿!

! (mH)

xxx

xxx

xxx

xxx

𝑅!

!

(Ω)

xxx

xxx

xxx

xxx

𝑛!

xxx

xxx

xxx

xxx

a. Rotor leakage inductance

b. Rotor resistance

Figure 7: D400 BDFM nested loop rotor parameter variation

with pole number (p1/p2)

xxx

a. Rotor leakage inductance

xxx

b. Rotor resistance

Figure 8: D400 BDFM p1+p2 bar cage rotor parameter

variation with pole number (p1/p2)

BDFM pole (p1/p2)

8/12 4/12 4/8 2/6

Lrprime (mH)

0

2

4

6

8

10

BDFM pole (p1/p2)

8/12 4/12 4/8 2/6

Rrprime (ohms)

0

0.1

0.2

0.3

0.4

IEEE TRANSACTION ON ENERGY CONVERSION

9

VI. CONCLUSIONS AND DISCUSSION

Modeling analysis and experiments on rotor winding

arrangements of the D160 and D400 BDFM prototypes have

been used to verify different methods of obtaining rotor

equivalent circuit parameters in this investigation. A

comparison between rotor parameters obtained from the

coupled circuit model and the winding factor method was

conducted to prove good agreement with experimental

parameters.

Furthermore, optimization with the aim of minimizing rotor

parameters on the nested loop rotor and the p1+p2 bar cage

rotor was carried out. The effect of loop span and number of

loops was studied for different rotors and it was shown that

increasing the loop span results in lower referred inductance

and resistance. Comparing results from the nested loop and the

cage rotor shows that the cage rotor has significantly lower

referred resistance for the same filled slots. Design studies

were performed to find optimum number of loops per nest for

nested loop and bar cage rotor and parameters were extracted

and compared using different methods. It was shown that

using a cage configuration offers dramatic reduction in rotor

impedance due to highest possible loop span and phasor

addition of currents in rotor bars. Therefore, for a MW scale

BDFM this suggests rotor design of p1+p2 bar cage with loops

offering better machine performance.

In addition, the effect of pole pair combination on rotor

parameters was investigated for the nested loop and p1+p2 bar

cage rotor. It was shown that for machines with further away

pole pairs, the cage rotor offers lower inductance and

resistance, however, as the pole numbers become closer nested

loop type rotors are more favorable.

ACKNOWLEDGMENT

The research leading to these results has received funding

from the European Union's Seventh Framework Program

managed by REA – Research Executive Agency

(FP7/2007_2013) under Grant Agreement N.315485.

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