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Published in IET Electric Power Applications

Received on 13th August 2012

Revised on 15th November 2012

Accepted on 10th December 2012

doi: 10.1049/iet-epa.2012.0238

ISSN 1751-8660

Characterising brushless doubly fed machine rotors

Richard McMahon1, Peter Tavner2, Ehsan Abdi3, Paul Malliband3, Darren Barker2

1

Department of Engineering, Cambridge University, Trumpington Street, Cambridge, CB21PZ, UK

2

School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH13LE, UK

3

Wind Technologies Ltd., St. Johns Innovation Centre, Cowley Road, Cambridge, CB40WS, UK

E-mail: peter.tavner@durham.ac.uk

Abstract: The brushless doubly fed machine (BDFM) is a robust alternative to the doubly fed induction generator, currently

widely used in wind turbines but prone to brush-gear and slip-ring failure. The rotor winding plays an important part in a

BDFM, coupling the two stator windings. To date, nested-loop (NL) rotor windings have been exclusively used in practical

BDFM. This approach may not be ideal for larger machines, in which form-wound series-loop rotor winding may be

preferable to large section bars and end-rings. This study gives a comparative analytical and experimental study of two

different brushless doubly fed 160 frame-size rotors, with NL or series-wound windings, mounted in identical rotor core

laminations operating in the same stator tested at a limited voltage (200 V line). The rotors gave a performance which accords

with theoretical predictions from two independent methods, giving insight into the design issues of the different rotor

windings from both an electrical and manufacturing viewpoint.

Nomenclature

List of symbols

X

1

,X

2

,X

r

indicating, respectively, stator1, stator 2 and

rotor winding quantities

p

1

,p

2

stator winding pole-pair numbers

qphase number

f

1

,f

2

supply frequencies

s

1

,s

2

slips of different winding systems

Nshaft speed

N

eff1,2&r

effective number of turns for the stator,

1&2

,

and rotor,

r

, windings

n

1,2&r

turns ratios of stator,

1&2

, and rotor,

r

,

windings

k

w

winding factor

k

p

pitch factor

γwinding pitch angle

R,Lwinding resistance and inductance

Zimpedance of a rotor loop

1 Introduction

The brushless doubly fed machine (BDFM) is of interest as a

variable speed generator or drive because only a fraction of

the output power needs to pass through the power

converter. The absence of brush-gear and slip-rings makes

the machine particularly attractive as a wind turbine

generator because brush-gear and slip-ring problems in the

widely used doubly fed induction generator (DFIG) have

been identiﬁed as a principal failure mode [1]. Studies

indicate that the combination of a BDFM and a two-stage

gearbox in a wind turbine would have excellent reliability

and retain low cost [2]. The authors have successfully

demonstrated a small-scale BDFM in a working 20 kW

wind turbine [3] and have built a 250 kW prototype that

has undergone witnessed tests over its full load and speed

range.

The BDFM has its origins in the single-frame

self-cascaded induction machine, in which two stator

windings of different pole numbers share the same iron

circuit with a rotor winding of related pole number [4].

Developed by Hunt [5], the machine gained a reputation

for robustness and reliability [6]. Following the work of

Rochelle et al. [7], the contemporary BDFM has two

stator windings connected to different frequency supplies,

producing different pole number magneto-motive forces

(MMF) with no direct coupling between them, coupling

being through the rotor only. The separate stator windings

facilitate double-feeding, with one winding connected to

the grid and the other via a partially rated power

electronic converter, as shown in Fig. 1, without any

winding utilisation penalty.

The BDFM rotor is a critical component. The rotor

winding carries an MMF induced by the stator windings

and the rotor and stator windings are coupled by the ﬂux

rotating in the common iron circuit. A good rotor will

couple both stator windings but have low resistance and

inductance. As shown in [8], there is a rotor turns ratio, n

r

,

which maximises the machine output, where n

r

will be

deﬁned later.

In addition, the rotor should be straightforward to

manufacture. Lydall [4] used two rotor windings, one

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IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543 535

doi: 10.1049/iet-epa.2012.0238 &The Institution of Engineering and Technology 2013

pitched for p

1

pole-pairs and the other for p

2

pole-pairs,

directly connected to each other. Hunt [5] showed this was

wasteful of copper and devised a more complex winding

with lower resistance but unfortunately also difﬁcult to make.

Broadway and Burbidge reconsidered the rotor design in

[6] and a p

1

+p

2

bar cage was identiﬁed as the simplest

concept resulting in principal ﬁelds with space harmonics,

although a rotor of this type was recently successfully used

in an experimental BDFM [9]. The nested-loop (NL) type

of rotor was proposed as a development of the p

1

+p

2

fabricated bar cage comprising multiple loops in p

1

+p

2

nests, an example being shown in Fig. 4b. This approach

reduces space harmonic generation, has been used in most

subsequently published BDFMs, was promoted because of

its similarity to the induction motor squirrel cage rotor and

was expected to share its ease of manufacture. However, as

noted by Williamson and Boger [10], the bars of the NL

rotor must be insulated, making casting difﬁcult . The cages

of large induction motors would normally be fabricated

from copper alloy conductors and brazed, but to do this for

a NL winding is time-consuming and costly. The NL rotor

also suffers from unequal current distribution between loops

[11].

Other forms of rotor winding were investigated analytically

by Roberts et al. [12] reporting the theoretical performance of

a series-loop rotor winding, following a suggestion in [6], but

implementation was not optimised. In general, rotors will

have p

1

+p

2

sets of rotor circuits and each set may be a

single winding, in which case analysis is straightforward, or

have two or more independent circuits, as in the NL,

making analysis more complex.

Large bar rotor winding designs, like a squirrel cage, make

good use of the slot area, but tend to generate higher levels of

space harmonics than conventional series-wound (SW) rotor

windings, as found in a DFIG. This will be reﬂected in an

increased rotor leakage inductance for the fabricated NL

design. However, mutual couplings can reduce the

amplitude of space harmonics, as occurs, for example in

NL rotors [11], which also lead to torque ripple and

acoustic noise.

Others have looked theoretically at conventional rotor

winding design, including Guangzhong et al. [13]who

proposed a method for considering the air-gap MMF of

cage or wound BDFM rotors, Liu et al. [14] proposing

particular connections for the rotor winding, Blazquez et al.

[15] characterised the rotor magnetic ﬁeld.

As BDFM ratings increase, the NL rotor bar cross-sections

will also increase, notwithstanding the greater number of rotor

slots. A concern then arises about bar skin effect raising rotor

resistance, especially as the rotor current frequency will be a

substantial fraction of the grid frequency. Under these

conditions multiple conductors in each slot will become

necessary and multilayer windings would be attractive.

Indeed a 75 kW prototype BDFM for a wind turbine [16]

used a stranded NL design, although the authors did not

report on the behaviour of this winding in operation.

This paper describes work to optimise the design of a

conventional BDFM with a stranded SW rotor, being more

straightforward to manufacture and applicable to larger

machine sizes, aimed at wind turbine generators >2 MW.

The experimental machine was constructed from a

MarelliMotori D160 frame induction motor described in

[17]. The rotor design theory was developed with a view to

obtaining equivalent circuit parameters analytically. Results

from experimental tests are presented to conﬁrm the

manufactured rotors’performance against analytical

parameter predictions, parameters have also been extracted

from these tests for comparison. In addition, its

performance was compared to that of a NL rotor winding

using identical rotor laminations.

2 BDFM basics and configuration

Although the BDFM rotor operates by induction, the machine

is normally operated as a variable speed machine in the

synchronous mode with double-feed, as shown in Fig. 1.In

this respect, operation is the same as the widely used DFIG

wind turbine generator. The shaft speed in the synchronous

mode is given by

N=60 f1+f2

p1+p2

(1)

In typical operation as a wind turbine generator, the rotor

speed range may be the BDFM natural speed + / −30%;

although a smaller range may be adequate for pumping

applications. A further relationship for the so-called natural

speed, that is the synchronous speed when the control

winding is fed with DC, is given by

Nn=60 f1

p1+p2

(2)

The BDFM can also be operated in the self-cascaded mode

in which one stator winding is shorted or in the simple

induction mode with one stator winding open circuit. These

two modes can be used for determining machine parameters.

The operation of the BDFM can be described by a

per-phase equivalent circuit of the form shown in Fig. 2a

[13]. Values are shown referred to the power winding and

iron losses are neglected. R

1

and R

2

are the resistances of

the stator windings and R

r

is the rotor resistance. L

m1

and

L

m2

are the stator magnetising inductances, L

1

and L

2

are

the stator leakage inductances and L

r

is the rotor inductance

(Fig. 2). The use of the modiﬁer ‘′’ denotes that the

Fig. 1 Block diagram showing BDFM, grid-connected power

winding and the control winding fed through a converter

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536 IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543

&The Institution of Engineering and Technology 2013 doi: 10.1049/iet-epa.2012.0238

quantity is referred. The slips s

1

and s

2

are deﬁned in

Section 5.

The slips s

1

and s

2

are deﬁned as follows

s1=f1p2−f2p1

f1p1+p2

(3)

s2=f2p1−f1p2

f2p1+p2

(4)

Whilst values for all these quantities can be calculated, the

leakage inductances cannot be determined unambiguously

from terminal measurements so the simpliﬁed equivalent

circuit shown in Fig. 2bwas proposed in [18]. As noted

there, L

1

and L

2

have been absorbed in L

m1&2

and

consequently the values of magnetising and rotor leakage

inductances will change, though the adjustments to the

former are small. There will also be a modiﬁcation to the

turns ratio, n

r

, and hence all referred parameters.

In most practical BDFMs the rotor leakage inductance is

the largest series impedance term in the simpliﬁed

equivalent circuit, and a core model retaining only this term

was proposed in [8]; this approach allows a number of

useful relationships to be derived which assist in BDFM

design. For normal operating conditions an optimum value

of the rotor turns ratio n

r

for maximum rating can be

deduced from [8] given by

nr=p1

p2

(2/3)

(5)

3 BDFM rotor design

3.1 General arrangement

Rotors have been designed for use in a 4/8 pole BDFM

manufactured using the stator stack and frame from a size

160 induction motor. The stator design has been optimised

and winding details are given in Table 1together with the

leading physical dimensions.

Fig. 2 Per-phase BDFM equivalent circuits

aPer-phase equivalent circuit for the BDFM from [13]

bSimpliﬁed per-phase equivalent circuit from [12]

Fig. 3 Rotor winding diagrams

aSW rotor

bNL rotor

Fig. 4 Prototype SW and NL rotors

aSW rotor

bNL rotor

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IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543 537

doi: 10.1049/iet-epa.2012.0238 &The Institution of Engineering and Technology 2013

Ap

1

/p

2

pole-pair BDFM has p

1

+p

2

sets of rotor circuits,

in this case 6. The SW rotor has three concentric coils in

series in each set whereas the NL rotor has three concentric

loops with a common shorting end ring, the loops being

effectively in parallel and rotor slot numbers an even

multiple of six. A lamination with 36 slots was chosen as

this gives a reasonable slot pitch with the D160 machine

air-gap diameter. The lamination design is magnetically

matched to that of the stator with 36 slots, in that the

cross-sectional areas of the rotor teeth are equal to that of

the stator teeth and the rotor core back depth is equal to that

of the stator. The winding arrangements are shown in Fig. 4

and the prototype wound and NL rotors are shown in Fig. 5.

For ease of manufacture of the SW rotor, a single-layer

winding with 37 strands of enameled, round wire

conductors in parallel was used to maximise the slot ﬁll and

achieve a value as close to the NL winding as possible. A

pre-assembled bundle of conductors was pressed into the

rotor slots pre-lined with Nomex and the free ends were

crimped together after removal of the enamel insulation.

For the NL rotor, shaped copper bars were fed into Nomex

slots and the end rings were brazed on.

3.2 Turns ratio

Using (5) from Section 2 the optimum turns ratio, n

r

, for a

2/4-pole-pair BDFM is 0.5

2/3

or 0.63, that rotor turns ratio

being from deﬁned [8]as

nr=N1rkw1r

N2rkw2r

(6)

where the subscripts refer to the p

1

and p

2

principal ﬁelds and

Nand k

w

are the respective turns and winding factors (WF)

<k

W

and K

w

changed to k

w

. The rotor winding has MMFs

induced in response to each stator winding MMF, the

number of turns are the same, that is N

1r

=N

2r

.Toﬁnd the

actual turn ratio requires the calculation of the effective

turns for couplings to the 4- and 8-pole ﬁelds. These are

shown in Table 2, noting that as the three SW one turn

coils in each set are concentric the WF can be summed for

the SW rotor. The two coupling WF for each coil reduce to

the pitching factor, for pitch angle γ

kp1=sin

g

p1

2

(7)

kp2=sin

g

p2

2

(8)

The turn ratio is given by

nr=k1A+k1B+k1C

k2A+k2B+k2C

(9)

The spans of the three coils are 10°, 30° and 50°. The sums

of the WF are k

wr1

= 1.44 and k

wr2

= 2.19, giving a turns

ratio for the SW rotor winding of 0.66, close to the

optimum value of 0.63.

The loops of the NL rotor winding are effectively in

parallel, as depicted in Fig. 5band have mutual couplings,

so the calculation of n

r

is not straightforward. A turn ratio

approximation for the NL rotor can be found from Fig. 5

circuit by considering an MMF balance with one stator

open circuit as

nr=kw1Akw2A/ZA

+kw1Bkw2B/ZB

+kw1Ckw2C/ZC

k2

w2A/ZA

+k2

w2B/ZB

+k2

w2C/ZC

(10)

where Z

A

,Z

B

and Z

C

are the impedances of the rotor loops at a

particular operating speed and the WF are as in Table 2,n

r

does not vary signiﬁcantly with speed so can be evaluated

at natural speed. The data for evaluating the bar impedances

are given in Section 3.5 and lead to a value for n

r

for the

NL rotor winding of 0.69, again close to the optimum.

Table 1 BDFM physical details

stator 1 pole number 4 air-gap diameter mm 155

stator 2 pole number 8 air-gap, mm 0.34/0.35

stator 1 N

eff

/phase 250 stator slots (open) 36

stator 2 N

eff

/phase 272 rotor slots (open) 36

stack length, mm 190

Fig. 5 Rotor winding schematics

aSW rotor

bNL rotor

Table 2 WF for rotor loops

Coil/loop Span γk

w1

4-pole k

w2

8-pole

AInner 10° 0.17 0.34

BMiddle 30° 0.5 0.87

COuter 50° 0.77 0.98

N

eff

1.44 2.19

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538 IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543

&The Institution of Engineering and Technology 2013 doi: 10.1049/iet-epa.2012.0238

3.3 Single equivalent loop representation

For the various rotors, it is convenient to develop a single

equivalent loop representation which directly relates to

equivalent circuit parameters. The equivalent loop will have

WF to give the desired turns ratio, resistance and

inductance electrically equivalent to the actual rotor. For

rotors with SW loops this is straightforward in that the loop

span can be chosen to give the effective turn ratio (6).

However, for rotors with loops in parallel, like the NL

rotor, parameters are rotor-speed dependent but can be

taken to be constant.

3.4 Rotor current density

At full load, the stator and rotor winding currents should reach

their limiting values together. An MMF balance can be used

to ﬁnd the rotor current from one of the stator currents. It is

convenient to use the 4-pole stator winding which has a

rated current of 5.98 A line, which as the machine is delta

connected, translates to a phase current of 3.45 A. The

MMF of a q-phase winding carrying current Iis

MMF =4

p

q

2INeff

p(11)

The stator is three phase but the rotor is six-phase, strictly

bi-three-phase, hence

3

2Is1Neffs1

=6

2IrNeffr(12)

For the SW rotor the rotor current is 299 A giving a current

density of 6.6 A/mm

2

, higher than the stator winding design

current density of 6 A/mm

2

but acceptable.

For the NL rotor currents will differ from loop-to-loop and

vary with operating point. At rated output, calculations of

loop currents from the rotor impedances and WF shows that

loop Bcurrent, the middle loop, and the inner loop A

current will be about 2/3 and 1/4, respectively, of the loop

Ccurrent, the outer loop. Applying an MMF balance gives

a maximum current of approximately 400 A in loop C

giving an acceptable current density of 5 A/mm

2

.

3.5 Parameter calculation by WF analysis

Parameters for the rotor are needed to enable the performance

of the overall machine to be predicted using the equivalent

circuit and this will be done by WF analysis. The rotor

turns ratio has already been established but the turns ratios

to the stator windings needs to be calculated too. The

effective turns for stators 1 and 2 are given in Table 1. The

two stator to rotor turns ratios, n

1

and n

2

, for the SW rotor

are then

n1=

Neffs1

Neffr

=173.3 (13)

n2=

Neffs2

Neffr

=124.2 (14)

This gives n

1

/n

2

= 1.40.

An estimate of the rotor resistance in the case of the SW

rotor can be found using the following relationship for each

coil and adding the values. Particular account should be

taken of the fact that the end-winding spans vary but the

total arc length in the present winding is essentially the

same as if the winding were concentric

Rcoil =2kN

r

A

p

d

g

360 +w

(15)

where Nis the number of turns, ρis the resistivity of copper

(1.72 × 10

−8

Ωm), Ais the cross-sectional area of the

conductor, dis the mean diameter of the rotor slots, wis

the stack length and kis a constant, taken to be 1.1. This

gives a rotor resistance per pole of 0.56 mΩ. Referral to

stator 1 needs to take account of the need for a six to

three-phase transformation, division of the referred value by

a factor of two as well as the turn ratio. The referred

resistance is 8.21 Ω, which equates to 2.80 Ωin a star

(wye) equivalent circuit.

It now remains to ﬁnd the rotor inductance. This is made up

of conventional leakage elements and harmonic inductance

terms from the space harmonics created by the rotor. Some

of the space harmonics will couple to the stator windings so

the impedance presented to the rotor will not just be the

magnetising reactance for that space harmonic. However, an

estimate of rotor inductance can be obtained by neglecting

this effect.

The harmonic inductances can be found from

Lh=

m

0

g

ldq

p

Neff

p

2

(16)

evaluated for the harmonic pole-pair numbers. The effective

turns are found for the pole number in question, gis the

air-gap length and the other symbols have the same

meaning as in previous sections. The harmonic ﬁelds that

can exist (harmonic order n) are given by

n[p1+mp

1+p2

<p2+mp

1+p2

(17)

where mis an integer. In reality, high pole number ﬁelds can

only exist for point conductors so in evaluating the effective

turns for a particular space harmonic, it is appropriate to

assume that the conductor current density is uniformly

distributed over a slot mouth giving a distribution factor k

s

ks=sin ws(p/2)

ws(p/2) (18)

where w

s

is the angular width of the rotor slot mouth in

radians. A summation up to a 200 pole ﬁeld, for a pole

pitch of 1.8° and a slot mouth pitch angle of 8.16°, gives

L

r

(h) = 5.1 μH.

The conventional leakage inductance components,

overhang, slot and zigzag, found using the methods

described by [18] give an additional 4.9 μH. The total

leakage reactance referred to stator 1 is then 50.2 mH, in

star (wye) form.

Inductance values in brackets are neglecting space

harmonics. Impedances evaluated at the natural speed

frequency of 100/3 Hz

The analysis of the NL rotor is complicated by the fact that

there are three independent loops in each nest. The resistances

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IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543 539

doi: 10.1049/iet-epa.2012.0238 &The Institution of Engineering and Technology 2013

of the individual loops in the NL rotor can be calculated using

(15), ignoring the effects of the common end ring, and

harmonic inductances can be found using (16). The loops

will have different WF for harmonic ﬁelds so there will be

cross-coupling. To establish the range of possible rotor

parameters, the evaluation has been carried out including

and excluding harmonic inductances. Values of resistance,

inductance and impedance evaluated at the natural speed are

shown in Table 3and can be used to obtain values for Z

A

,

Z

B

and Z

C

.

Parameters for an equivalent single loop with a WF of unity

can be determined by applying a short circuit in Fig. 5bto

stator 2. The effective impedance of this loop Z

eq

is

Zeq =k2

w1A

ZA

+k2

w1B

ZB

+k2

w1C

ZC

−1

(19)

For the stator, the conventional leakage inductance

components, namely the overhang, slot and zigzag

contributions, were found using the methods described by

[18]. The magnetising inductances were calculated using

(16) and winding resistances using (15).

3.6 Parameter calculation by coupled circuit (CC)

analysis

Parameters have also been obtained from the CC analysis

described in [19]. From the distribution of conductors, the

method gives position-dependent mutual inductances, which

include space harmonic effects. The model assumes that

there is a linear change of conductor density across slot

mouths. Leakage inductance components, excluding

harmonic contributions, and winding resistances are

calculated as in the previous section.

Following conversion to dq-axis form, there is a

transformation to a synchronous frame. There is then a

further conversion to extract sequence components, the

forward sequence components being the usual per-phase

equivalent circuit parameters. This is straightforward in the

case of the SW rotor but for the NL rotor a model reduction

procedure is applied to reduce the multiple dq-sets of the

rotor to a single dq-pair [11]. This reduction procedure is

based on ranking the eigenvalues of the rotor mutual

coupling matrix and retaining only the largest eigenvalues,

that is those representing the strongest couplings. Once a

single dq model has been obtained, conversion to sequence

components takes place.

3.7 Comparison of calculated and measured

parameters

WF analysis has the great advantage of being simple to

understand and implement. The predictions of parameters

for the complete equivalent circuit are compared with the

more accurate but complex CC analysis in Table 4for both

rotors, based upon equivalent circuit Fig. 2a. These were all

per-phase quantities based on a star (wye) connection.

There are small differences between the calculated values

for stator winding resistances, arising from the precise

treatment of the end windings; the measured values are a

little higher suggesting that there is more end winding

overhang than is assumed in the calculations. The same

effect is seen with the rotor resistance. All resistances were

calculated for 20°C and measurements were taken on the

machine at ambient temperature. As mentioned earlier, the

formulation for the Carter factors was chosen, with the SW

rotor, to align the predicted and measured values of

magnetising inductance. Differences in the values for stator

leakage inductances calculated by different analyses are

attributable to the precise representation of the slot shape

and placement of windings within slots.

For the SW rotor calculated rotor parameters, turns ratio,

rotor resistance and leakage inductance, are close to

measured with the exception of the leakage inductance.

For the NL rotor in the WF analysis, neglect of the mutual

harmonic coupling between loops by the two stator windings

lead to rotor parameter differences, particularly in the leakage

inductance. Coupling between loops reduces the harmonic

leakage contribution substantially and modiﬁes the effective

resistance and turns ratio. Neglect of the harmonic leakage

inductance in the WF analysis gives a closer rotor leakage

inductance value, but lower than that from CC analysis.

Therefore Table 4results show that WF analysis is

satisfactory except possibly for the prediction of the rotor

leakage inductance.

The check parameters for single equivalent loops, derived

from CC analysis are shown in Table 5. The equivalent

spans are really equal, reﬂecting the similarity in turns

ratios. The NL rotor has signiﬁcantly lower resistance and

Table 3 Individual loop parameters for the NL rotor

Loop ABC

R

r

,μΩ 105 118 132

L

r

,μH 5.02 (1.58) 4.71 (1.64) 3.94 (1.72)

X

r

,μΩ 1052 986 827

Table 4 Complete parameter set, Fig. 2a

Parameter For SW rotor For NL rotor

WF analysis Direct measurement CC analysis WF analysis Direct measurement CC analysis

R

1

,Ω1.77 2.04 1.74 1.77 2.04 1.74

L

1

, mH 5.92 —5.78 1.13 1.29 1.02

L

m1

, mH 342 317 342 333 317 372

R′

r

,Ω2.80 3.11 2.76 99 104 111

L′

r

, mH 50.2 —37.5 1.54 (1.51) —1.31

L

m2

, mH 102 104 102 49.9 (20.2) —27.9

L

2

, mH 3.92 —5.42 1.33 (1.36) —1.35

R

2

,Ω1.13 1.29 1.02 5.88 —5.97

N1.40 —1.41 3.87 —5.63

Values in brackets neglect space harmonics

www.ietdl.org

540 IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543

&The Institution of Engineering and Technology 2013 doi: 10.1049/iet-epa.2012.0238

leakage inductance. However, the structure of the NL rotor

dampens unwanted harmonics explaining the lower overall

rotor inductance.

A set of winding parameters was also devised based upon

the simpliﬁed equivalent circuit of Fig. 2b, shown in Table 6,

these considerably simplify the design of the machine. Again

the agreement between prediction and calculation is good,

with the possible exception of the rotor leakage reactance,

where the CC analysis gives better results.

4 Experimental arrangement and extraction

of rotor parameters

The experimental arrangement used for testing the

performance of rotors and for the extraction of parameters

has been described in [17]. The BDFM was connected to a

dynamometer operating in constant speed or torque mode,

giving readings of speed and torque. The p

1

winding was

connected directly to mains and the p

2

winding was fed

through a frequency converter under manual control.

A procedure for extracting Fig. 2parameters was

established by Roberts et al. [12] and in [18]. The machine

was run in the cascade mode with the 4-pole winding

connected to the mains through a variable transformer and

the 8-pole winding shorted and then vice versa. Torque–

speed curves were obtained over a speed range of 200–

1500 and 200–750 rev/min with the 4- and 8-pole

windings excited, respectively, at 200 V, slightly below the

rated voltage to limit saturation. This was done to

investigate winding parameters of the machine under linear

conditions, with the intention of resolving saturation issues

later. As the stator winding resistances can be accurately

measured, they were taken as ﬁxed, including an allowance

for temperature rise. The measured and ﬁtted cascade

characteristics are presented in Fig. 6for both rotors.

Comparisons between extracted and calculated parameters,

following conversion to values for the simpliﬁed equivalent

circuit shown in Fig. 2b, are given in Table 6and

calculated and extracted parameters are close. Parameters

modiﬁed by the conversion procedure [20] are denoted ‘*’.

Rotor resistance temperature rise must be an allowed for.

The algorithm used in Table 6treats the following as free

parameters, rotor turns ratio, the two magnetising

reactances, rotor resistance and inductance, adjusting them

to give the best ﬁt to the measured torque–speed

characteristic. Predicted stator magnetising inductances do

not agree so well with measurement in Table 6but the ﬁtto

measured torque–speed data is relatively insensitive to this

parameter, essentially because the magnetising reactances

are in shunt. So extracted magnetising reactance values can

vary considerably without affecting the torque–speed result.

The reactances were also measured independently, by

synchronous tests, and the values used as ﬁxed parameters

in the ﬁtting exercise, but again this did not radically alter

the torque–speed results.

The predicted parameters for both types of winding were

then used to calculate the torque–speed curves of the

machine operating with both rotors. Measured and

calculated torque-speed results are compared in Fig 6. The

crosses show the experimentally measured torque–speed

points and the curves have been ﬁtted to torque–speed

curves predicted from parameters, calculated as described

above and shown in Table 6.

Fig. 6demonstrates that parameters can be calculated with

sufﬁcient accuracy for machine design purposes but a more

sophisticated approach may be required for the rotor

leakage inductance and the CC analysis achieves this.

However, the WF analysis could be extended in the future

to include coupling through space harmonics.

5 Torque production

When operating the BDFM in the synchronous mode, the aim

is to utilise the synchronous torque which, from the core

model described in Section 3.1 and noting that cosφis the

power factor, is given by

T=3V1I1

cos

w

v

r

1+f2

f1

(20)

This can also be expressed in the form

T=3V1V2

sin

d

v

s1L′

r

v

s1/(p1+p2)

(21)

which shows that the torque is dependent on a load angle δas

in a conventional synchronous machine; however, induction

torques are also present. One component, attempting to

accelerate the rotor towards the synchronous ﬁeld of the

Table 5 Parameters for single equivalent loops

Rotor SW NL NL reduced fill

R

r

,μΩ 121.4 70.2 125.5 (estimated)

L

r

,μH 10.2 2.3 2.27

γ,° 40.4 43.4

n

r

0.657 0.688

Table 6 Simplified parameter sets, Fig 2b

Parameter FOR SW rotor FOR NL rotor

WF analysis CC analysis Measurement by extraction WF analysis CC analysis Measurement by extraction

R

1

,Ω1.77 1.74 2.40 1.77 1.74 2.40

L∗′

r,mH 348 348 220 339 378 180

R∗′

r,V2.90 2.86 3.80 1.60 (1.57) 1.36 1.70

L∗′

r,mH 65.6 55.2 61.0 64.3 (32.3) 44.9 42.0

L∗

m2,mH 106 107 92 103 116 195

R

2

,Ω1.13 1.02 1.50 1.13 1.02 1.50

n∗

r1.37 1.36 1.43 1.30 (1.33) 1.31 1.37

Values in brackets ignore space harmonics

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IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543 541

doi: 10.1049/iet-epa.2012.0238 &The Institution of Engineering and Technology 2013

power winding is given by

Tim =3I2

1

R′

r

s1

1

v

s1

(22)

The second component is trying to accelerate the rotor to the

natural speed. This component is given by

Tin =3I2

1R′′

2

s2

s1

1

v

n

(23)

where ω

n

is 2πN

n

/60.

The calculated pull-out torques for the NL and SW rotors

were, respectively, 250 and 172 Nm at natural speed for a

240 V supply. Again based on an ideal model, the

synchronous torque at rated current, 6 A, was predicted to

be 82 Nm. At natural speed and rated current the induction

torque was 11.7 Nm motoring and there is no contribution

from R″

2

, which would be accelerating the rotor below

natural speed and braking it above.

The measured torque at rated current but reduced line

voltage at the natural speed, N

n

, 600 rev/min summed to 60

Nm (3.8 kW), in reasonable agreement with the calculated

values for an ideal machine with these voltages and

currents. The induction torques were not negligible and can

only be reduced by decreasing R′

r

and R″

2

. The torque

available from a BDFM of given size was shown in [8]to

be 70–80% of that of a conventional induction machine,

depending on the choice of pole-pairs and assuming a

similar magnetic loading, still the subject of BDFM

research. The original MarelliMotori induction motor, from

which this BDFM was constructed, had a rated torque at

400 V line voltage and 1470 rev/min of 70 Nm (10.8 kW)

on its 4-pole winding.

6 Discussion

The use of a SW rotor has been shown as a practicable

proposition, offering straightforward manufacture compared

to the NL rotor. However, the R′

r

of the SW rotor in this

case was approximately twice that for the NL resulting in a

Fig. 6 Experimental cascade torque–speed characteristics overlaid with curves ﬁtted to points derived from calculated parameters

aSW rotor

bNL rotor

Fig. 7 Comparison between predicted L

r

′and R

r

′for rotor

windings with equal ﬁll factors, using the CC or WF analyses

aReferred rotor resistance, R′

r

,Ω

bReferred rotor inductance, L′

r

,mH

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542 IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543

&The Institution of Engineering and Technology 2013 doi: 10.1049/iet-epa.2012.0238

lower torque performance. The lower L′

r

&R′

r

translate into a

50% greater pull-out torque for the NL over the SW rotor,

both rotors having turns ratios, n

r

, that are close to the

optimum.

It is tempting to ascribe the higher resistance simply to the

greater conductor cross-section of the NL, which was 1.8

times that of the SW rotor.

However, the authors have investigated two SW and NL

rotors with identical slot ﬁll factors. Their L′

r

and R′

r

have

been calculated by the CC and WF analyses, the latter

ignoring harmonic inductances in the case of the NL rotor,

and are compared in Fig. 7. The referred rotor resistances

for the SW and NL rotors are nearly identical.

The NL inner loop carries only 25% of the outer loop

current, conﬁrmed experimentally [21]. Similarly, the inner

loop in the SW rotor adds considerable resistance but is not

well-coupled. Calculations show that a rotor with only the

two outer loops in series would reduce R

r

by 30% and R′

r

by just 10%, with a somewhat larger leakage inductance

reduction. In larger BDFMs, rotor bar size will be limited

by skin effect considerations and the simple NL design

cannot be used. Other possible designs, including the SW

rotor with three series loops, each loop spanning 30°

displaced by 10° [16], can be shown to have a lower R′

r

but

n

r

is further from the optimum.

7 Conclusions

†A stranded SW BDFM rotor winding has been compared,

experimentally and analytically, at a line voltage of 200 V,

with an identical rotor with a solid bar NL winding,

mounted in the same stator.

†Manufacture of this new stranded SW BDFM rotor

winding was straightforward.

†Stranded SW rotor winding may be of practical interest in

larger BDFM rotors requiring multiple conductors to avoid

skin effects and to facilitate manufacture.

†Experimentally measured parameters of both the SW and

NL rotor resistances and inductances were in close

agreement with analytical predictions, using either WF or

CC analyses, although the latter gives better predictions for

the rotor leakage reactance.

†Parameters extracted from the cascade tests on the BDFM

for the two designs conﬁrmed that both rotor winding

arrangements can be accurately designed.

†Experimental and analytical results from the SW rotor

winding were acceptable but the torque developed was not

as great as the equivalent NL rotor winding.

†Current and torque in this new BDFM rotor winding

design were limited by the copper cross-section achieved in

the winding.

†Prediction methods showed that if the SW rotor had an

identical rotor slot ﬁll factor to the NL rotor, the resultant

R

r

′would be similar but L

r

’somewhat higher than for the

equivalent NL rotor, so similar torque performance could

be expected.

†Further work is required to investigate the predictability of

these rotor parameters under higher saturation conditions and

taking further account of space harmonics, particularly for the

SW rotor and the WF analysis could be extended to include

coupling via space harmonics.

8 References

1 Arabian-Hoseynabadi, H., Oraee, H., Tavner, P.J.: ‘Wind turbine

productivity considering electrical subassembly reliability’,Renew.

Energy, 2010, 35, (1), pp. 190–197

2 Tavner, P.J., Higgins, A., Arabian, H., Long, H., Feng, Y.: ‘Using an

FMEA method to compare prospective wind turbine design

reliabilities’. Proc. European Wind Energy Conf. (EWEC 2010),

Poland, 2010, pp. 1–10

3 Logan, T., Warrington, J., Shao, S., McMahon, R.A.: ‘Practical

deployment of the brushless doubly-fed machine in a medium scale

wind turbine’. Proc. IEEE Int. Conf. on Power Electronics and Drive

Systems, Taiwan, 2009, pp. 470–475

4 Siemens Brothers and Co. Ltd., Lydall, F.: ‘Improvements to polyphase

induction motors’. British Patent 16839, July 1902

5 Hunt, L.J.: ‘A new type of induction motor’,Inst. Electr. Eng. Proc.,

1907, pp. 648–677

6 Broadway, A.R.W., Burbridge, L.: ‘Self-cascaded machine: a low speed

motor or high frequency brushless alternator’,Inst. Electr. Eng. Proc.,

1970, pp. 1277–1290

7 Rochelle, P., Spee, R., Wallace, A.K.: ‘The effect of stator winding

conﬁguration on the performance of brushless doubly fed machines in

adjustable speed drives’. Proc. IEEE Industry Application Society

Annual Meeting, Seattle, 1990, pp. 331–337

8 McMahon, R.A., Roberts, P.C., Wang, X., Tavner, P.J.: ‘Performance of

BDFM as generator and motor’,IET Proc., Electr. Power Appl., 2006,

153, (2), pp. 289–299

9 Poza, J., Oyarbide, E., Roye, D., Rodriguez, M.: ‘Uniﬁed reference

frame dq model of the brushless doubly fed machine’,IEE Proc.

Electr. Power Appl., 2006, 143, (5), pp. 725–734

10 Williamson, S., Boger, M.: ‘Impact of inter-bar current on the

performance of the brushless doubly fed motor’,IEEE Trans. Ind.

Appl., 1999, 35, (2), pp. 453–460

11 Wang, X., Roberts, P.C., McMahon, R.A.: ‘Optimization of BDFM

stator design using an equivalent circuit model and a search method’.

Proc. Third IET Int. Power Electronics, Machines and Drives Conf.

(PEMD), March 2006, pp. 606–610

12 Roberts, P.C., McMahon, R.A., Tavner, P.J., Maciejowski, J., Flack, T.

J., Wang, X.: ‘Performance of rotors in a brushless doubly-fed induction

machine (BDFM)’. Proc. 16th Int. Conf. on Electrical Machines (ICEM

2004), Cracow, Poland, 2004, pp. 450–455

13 Guangzhong, L., Xiaoping, D., Qianghui, X., Feng, Z.: ‘Study on rotor

magnetomotive force comparison of doubly-fed brushless machine with

cage rotor or wound rotor’. Proc Int. Conf. on Electrical Machines and

Systems, Beijing, 2005, pp. 2059–2064

14 Liu, X., Zhang, W., Jiang, F.: ‘A new rotor type of cascaded brushless

doubly-fed machine’. Proc. Int. Conf. on Electrical Machines and

Systems, Beijing, 2005, pp. 734–737

15 Blazquez, F., Veganzones, C., Ramırez, D., Platero, C.:

‘Characterization of the rotor magnetic ﬁeld in a brushless doubly-fed

induction machine’,IEEE Trans. Energy Convers., 2009, 24, (3),

pp. 599–607

16 Rüncos, F., Carlson, R., Sadowski, N., Kuo-Peng, P., Voltolini, H.:

‘Performance and vibration analysis of a 75 kW brushless double-fed

induction generator prototype’. Proc. IEEE 41st Industry Applications

Society Annual Meeting (IAS2006), October 2006, pp. 2395–2402

17 McMahon, R., Tavner, P.J., Abdi, E., Malliband, P., Barker, D.:

‘Characterising rotors for brushless doubly-fed machines (BDFM)’.

Proc. 19th Int. Conf. on Electrical Machines, Rome, 2010, pp. 1–6

18 Roberts, P.C.: ‘A study of brushless doubly-fed (induction) machines:

Contributions in machine analysis, design and control’. PhD

dissertation, University of Cambridge, 2004

19 Roberts, P.C., McMahon, R.A., Tavner, P.J., Maciejowski, J.M., Flack,

T.J., Wang, X.: ‘An equivalent circuit for the brushless doubly fed

machine (BDFM) including parameter estimation and experimental

veriﬁcation’. IET Proc. Electrical Power Applications, 2005, vol. 152,

pp. 933–942

20 White, D., Woodson, H.: ‘Electromechanical energy conversion’

(Wiley, 1959)

21 Abdi Jalebi, E., McMahon, R.A.: ‘Application of real-time rotor current

measurements using Bluetooth wireless technology in study of the

brushless doubly-fed (induction) machine (BDFM)’. Proc. IEEE

Industry Applications Society Annual Meeting (IAS2006), October

2006, vol. 3, pp. 1557–1561

www.ietdl.org

IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 535–543 543

doi: 10.1049/iet-epa.2012.0238 &The Institution of Engineering and Technology 2013