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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 35, NO. 3, SEPTEMBER 2020 1151

Inﬂuence of Pole-Pair Combinations on the

Characteristics of the Brushless Doubly Fed

Induction Generator

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

Salman Abdi, Member, IEEE,andSulAdemi , Member, IEEE

Abstract—The brushless doubly fed induction generator (BD-

FIG) is an alternative to the doubly fed induction generator (DFIG),

widely used in wind turbines which avoids the need for brush

gear and slip rings. The choice of pole numbers for the two stator

windings present in the BDFIG sets the operating speed, typically

in the medium speed range to eliminate a gearbox stage. This paper

focuses on how both the total number of poles and the assignment of

poles between the windings affect machine performance. Analytical

expressions have been developed for parameters including pull-out

torque, magnetizing current and back-iron depth. The results show

that the pole count can be increased without unduly compromising

pull-out torque and that in cases where more than one combination

of pole number is acceptable only the back iron depth is signiﬁcantly

affected. In addition an output factor has been introduced to enable

a direct comparison to be made with conventional DFIGs. The

torque density of a brushless DFIG is compromised to a degree

relative to a comparable DFIG as a consequence of the presence of

two magnetic ﬁelds and ﬁnite element analysis is needed to achieve

an optimized design. Finally, predictions of the performance of

multi-MW machines are made based on data from an existing

250 kW machine which show that suitable efﬁciencies can be

obtained and excessive control winding excitation can be avoided.

Index Terms—Brushless doubly-fed generator (BDFG),

electrical machine design, induction generator, power factor,

pole-pair.

NOMENCLATURE

p1,p

2Stator winding pole-pairs (principal ﬁelds).

gAir gap length.

nr,n

ropt Rotor turns ratio, general and optimal.

f,f1,f

2Frequency stator windings 1, 2.

l, d Stack length, air gap diameter.

Manuscript received February 26, 2019; revised September 18, 2019 and

January 25, 2020; accepted February 12, 2020. Date of publication March 23,

2020; date of current version August 20, 2020. This work was supported by the

European Union’s Seventh Framework Program managed by Research Execu-

tive Agency (FP7/2007-2013) under Grant 315485. Paper no. TEC-00211-2019.

(Corresponding author: Sul Ademi.)

Ashknaz Oraee is with the Department of Engineering, University of Cam-

bridge, Cambridge CB2 1PZ, U.K. (e-mail: ashknaz.oraee@gmail.com).

Richard McMahon and Sul Ademi are with the Warwick Manufacturing

Group (WMG), The University of Warwick, Coventry CV4 7AL, U.K. (e-mail:

r.mcmahon.1@warwick.ac.uk; s.ademi@warwick.ac.uk).

Ehsan Abdi is with the Wind Technologies Limited, St. John’s InnovationCen-

tre, Cambridge CB4 0WS, U.K. (e-mail: ehsan.abdi@windtechnologies.com).

Salman Abdi is with the School of Engineering, University of East Anglia,

Norwich NR4 7TJ, U.K. (e-mail: s.abdi-jalebi@uea.co.uk).

Color versions of one or more of the ﬁgures in this article are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TEC.2020.2982515

ωrRotor angular velocity.

B1,B

2RMS value of ﬂux density stator windings 1, 2.

N1,N

2Number of turns stator windings 1, 2.

BcPeak ﬂux density in core.

ycBack iron depth.

ωrRotor angular velocity.

¯

BMagnetic loading.

¯

JElectric loading.

I. INTRODUCTION

THE brushless DFIG is an alternative to the well-established

doubly fed induction generator (DFIG) for use in wind

turbines, since it offers improved reliability and reduced capital

and maintenance costs [1]. It retains the low-cost advantage of

the DFIG system as it only requires a fractionally rated converter

and does not use permanent magnet materials. The machine has

no brushed contact to the rotor, eliminating a common source of

failures, making it a particularly attractive machine for offshore

wind turbines. Moreover, the brushless DFIG is intrinsically a

medium-speed machine, enabling the use of a simpliﬁed one or

two-stage gearbox as shown in Fig. 1.

The brushless DFIG has its origins in the self-cascaded ma-

chine and has two non-coupling stator windings, referred to as

the power winding (PW) and the control winding (CW) with

different pole numbers, p1and p2creating two stator ﬁelds in

the machines magnetic circuit with different frequencies and

pole numbers [2]. A specially designed rotor couples to both

stator windings. Applications other than wind power have been

considered for this machine, for instance as a stand-alone gener-

ator for off-grid applications [3], a drive in pump applications [4]

and in shaft generator systems for ships [5].

An alternative approach is the brushless doubly-fed reluctance

generator (BDFRG) in which the short-circuited coils in the

rotor of the brushless DFIG are replaced by high-reluctance

ﬂux barriers [6]. It has been shown that any rotor type used

for synchronous reluctance machines (SynRMs) is essentially

applicable in the BDFRG, i.e., the simple salient-pole rotor [7],

axially-laminated anisotropic rotor [8] and multi-layer ﬂux-

barrier rotor [9]. The BDFRG alternative has been widely taken

into consideration [10] and several design modiﬁcations [11]

and control optimizations have been proposed [12], [13]. This

paper will, however, limit its scope to the brushless DFIG.

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1152 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 35, NO. 3, SEPTEMBER 2020

Fig. 1. Brushless DFIG drivetrain set-up for wind power applications.

The design of the brushless DFIG is not straightforward

since there are more variables to consider than in conventional

induction machine designs [14]. Attention has been given to

some aspects of design for wind power applications as reported

in [15]–[18] and several large machines have been reported.

These include a 75 kW machine [17], a 200 kW machine [19]

and the 250 kW machine built and tested by the authors of [20].

This latter, believed to be the largest to date, was conceived as a

stepping-stone towards commercial MW scale brushless DFIGs.

In a wind turbine application, the machine will be matched to

the rest of the drivetrain so the natural speed, dependent on the

sum of the pole-pairs, and the speed range around natural speed,

typically ±30%, are of interest.

This paper examines how the characteristics and performance

of the machine are affected by the choice of pole-pairs, and the

allocation of these to the two windings. Although some design

relationships were developed in [21], important characteristics

such as pull-out torque, back-iron depth and magnetizing current

were not considered. In particular, this paper considers the trends

in these parameters as a function of natural speed, as set the pole

numbers.

It was shown in [22] that to achieve the required performance

for wind turbine service, namely a power factor in the range of

0.95 lag to 0.95 lead, the CW of the 250 kW machine considered

needed to be signiﬁcantly over-excited, compromising machine

output. The rotor leakage inductance is particularly signiﬁcant in

setting the required degree of over-excitation. The ﬁnal section

of this paper looks at the performance trends of future medium-

speed MW scale brushless DFIGs. The presence of two stator

windings means that there are more variables to consider than

in a single winding machine especially when it comes to control

and stability. The dynamics, control and stability of the machine

have been reported in [20] and low voltage ride through (LVRT)

performance was considered in [23].

This paper is organized as follows. Section II describes the

brushless DFIG operation and the per-phase equivalent circuit.

The pole-number choice and effect on machine rating are pre-

sented in Section III. The effect of pole-pair split on machine

ﬁelds and back-iron considerations are reported in Section IV.

Section V details the amp-turns ratios for common (p1/p2)

pole-pair. Performance analysis of the 4/8 frame size of the D400

prototype, the pull-out torque, power factor and efﬁciency are

detailed in Section VI. Optimization design for the megawatt

(MW) BDFIGs are explored and brought into focus in Sec-

tion VII. Finally, Section VIII draws conclusions.

Fig. 2. Referred per-phase equivalent circuit of the brushless DFIG.

II. BRUSHLESS DFIG OPERATION

The brushless DFIG normally operates in the synchronous

mode in which the shaft speed is independent of the torque

exerted on the machine, as long as it is smaller than the pull-out

torque. The speed is determined by the frequency and pole-pair

numbers of the stator windings and is given by:

Nr=60(f1+f2)

p1±p2

(1)

where f1and f2are the frequencies of the supplies to the stator

windings, p1and p2are the pole-pair numbers of the windings.

A. Brushless DFIG Equivalent Circuit

The operation of the BDFG can be described by a per-phase

equivalent circuit [22] similar to the equivalent circuits of two

induction machines with interconnected rotors, as shown in

Fig. 2. In the ﬁgure R1and R2are the stator resistances, Lm1

and Lm2are the stator magnetizing inductances and L1and

L2are the stator leakage inductances. Parameters are referred

to the PW using the modiﬁer ‘’. Furthermore, the rotor can

be characterized by the rotor turns ratio nr, resistance Rrand

leakage inductance Lr, the two latter parameters are also shown

in the referred per-phase equivalent circuit of Fig. 2.

The rotor leakage inductance includes conventional leakage

elements but the space harmonics associated with common

designs of brushless DFIG rotors lead to a higher differential

leakage component compared to conventional induction ma-

chine rotors. The slips s1and s2are deﬁned as in [1].

III. POLE-NUMBER CHOICE

A. Choice of Pole Numbers

For (p1+p2) type brushless DFIGs, the choice of stator

winding pole-pair numbers to give a desired natural speed, hence

operating speed range, is the ﬁrst step in the design process. The

sum of the pole-pair combination, rounded to the nearest integer,

is given by:

p1+p2=60f1

Nr

(2)

Both the total pole-pair count and the split between the wind-

ings affect machine performance. Direct coupling between the

two stator windings must be avoided and this can be achieved

by applying the rules given in [21]. This paper considered a

range of design considerations, including the choice of pole-pair

numbers, and provided experimental validation from a D180

machine. Moreover, [21] identiﬁed a number of factors to be

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ORAEE et al.: INFLUENCE OF POLE-PAIR COMBINATIONS ON THE CHARACTERISTICS OF THE BDFIG 1153

taken into account in the design of a BDFG and these were

validated by experimental data for the D180 brushless DFIG. In

some cases, several pole number combinations are possible and

there is the choice of giving the higher or lower pole number

to the PW. The torque capability of a brushless DFIG collapses

as the speed of the machine approaches the synchronous speed

of the PW. Thus, for the widest speed range, the lower pole

number should be assigned to the PW and the frequency of

the rotor currents is reduced in this connection. However, if the

operating speed range is limited to ±30% around natural speed,

as in wind power applications, this constraint does not apply.

Furthermore, some pole-pair combinations lead to unwanted

unbalanced magnet pull and vibration effects. When there is

more than one permissible combination of pole-pair numbers,

the machine design can be modiﬁed to give a trade-off between

output torque, speed, and magnetization considerations as eval-

uated in the following sections.

B. Effect on Machine Rating

An expression for the power rating of the BDFG, calculated

from the equivalent circuit model, was derived in [1]. This

expression was based on the quadrature sum (Bquad)ofthe

two ﬁelds in the machine but an alternative approach taking

a more conservative view of the maximum allowable ﬁelds was

developed in [21] based on the simple sum of the ﬁelds. Both

relationships are given in the Appendix. Unfortunately, there is

at present no easy way of determining the maximum tolerable

ﬁelds in the machine, but experience suggests that Bsum is too

conservative [24]. The two assumptions do, however, appear in

practice to bracket the range of allowable ﬂux densities, hence

both are considered. Certain other assumptions are used in the

expressions for power rating, the most relevant here is that only

synchronous torques are produced and that the voltage drop

across the rotor is not signiﬁcant.

As the output power is proportional to the speed, it is instruc-

tive to normalize the output of the brushless DFIG to that of

a DFIG with a synchronous speed equal to the natural speed

of the brushless DFIG, both machines having the same rotor

dimensions. The induction machine therefore has (p1+p2)

poles [25]. This leads to expressions for an output factor, in effect

the ratio of available torque to that of the equivalent DFIG, again

as derived in the Appendix. The output factor is a measure of

performance that can be used to compare different machine de-

signs. The expression depends on the rotor turns ratio nrbut can

be evaluated using a value equal to the optimum value as given in

the Appendix. In the case of the simple sum basis it reduces to:

Output f actor =TBDFG

TIM

=1+p2

p1

1+p2

p11

22(3)

The corresponding expression based on the quadrature sum

method is:

Output f actor =TBDFG

TIM

=1+p2

p1

1+p2

p12

3

3

2

(4)

TAB L E I

OUTPUT FACTOR FOR VARIOUS POLE NUMBER OF BRUSHLESS DFIG

The output factors for common (p1/p2) brushless DFIGs

are given in Table I, showing that the higher the ratio of pole

numbers, the greater the output factors can be obtained. This

implies that the relative output is at minimum when p1=p2,

recognizing that such a machine is impractical, as noted in [26].

Using the sum of ﬁelds assumption, the minimum output torque

is 50% of that of a (p1+p2) induction machine but this rises to

nearly 54% for the 2/6 pole conﬁguration. For comparison, the

quadrature sum method gives substantially higher output factors,

as shown in Table I.

IV. MAGNETIC CIRCUIT CONSIDERATIONS

A. Effect of Pole-Pair Split on Machine Fields

It was shown in [1] that the two ﬁelds in a brushless DFIG

mode are related by the rotor turns ratio, pole numbers and

voltage drop across the rotor leakage inductance. If it is assumed

that this drop is small, then the ratio of the two ﬁelds is given

by:

B2

B1

=nr

p2

p1

(5)

where B1and B2are the RMS values of the fundamental p1and

p2pole-pair air gap ﬂux densities. However, in reality there can

be a signiﬁcant voltage across the rotor impedance, especially

when the machine is over-excited, hence (5) is no longer valid.

Over-excitation is particularly likely in smaller machines to

achieve an acceptable grid-side power factor [22]. In this study,

the CW voltage is limited to avoid undue over-excitation.

B. Back-Iron Considerations

The back-iron ﬂux in conventional induction machines is

deﬁned as half of the total ﬂux over one pole pitch. The peak

ﬂux density in stator or rotor core is then related to the magnetic

loading by conservation of ﬂux and for brushless DFIG it can

be calculated from:

ˆ

Bc=√2

2

d

pyc

Bsum (6)

where ycis the back-iron depth. The back-iron ﬂux density in

the brushless DFIG varies with time and position but a value for

the peak can be found using Bsum, which is divided into B1and

B2for p1and p2ﬁelds, respectively, using (5). The back-iron

depth for the brushless DFIG is then given by [15]:

yc=√2

2

d

ˆ

BcB1

p1

+B2

p2(7)

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1154 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 35, NO. 3, SEPTEMBER 2020

TAB L E II

BACK-IRON RATIO FOR VARIOUS POLE NUMBERS OF BRUSHLESS DFIG

For the brushless DFIG the back-iron depth in terms of the

total air gap ﬂux density, Bsum, can be found by re-arranging

and substituting equations (5) and (6) in (7):

yc=√2

2dBsum

ˆ

Bc⎡

⎣

p11+ 1

nr+p2(1 + nr)

2p1p2+p2

2nr+p2

1

1

nr⎤

⎦(8)

Substituting nropt from equation (23) then gives:

yc=√2

2dBsum

ˆ

Bc

⎡

⎢

⎢

⎣1+p2

p11+2p2

p11

2+p2

p1

2p2

p1+p2

p11

2+p2

p13

2

⎤

⎥

⎥

⎦

(9)

The back-iron depth ratio of the (p1/p2) brushless DFIG to a

conventional IM of (p1+p2) poles is given by:

ycBDFG

ycIM

=p1+(p2)⎡

⎣

p11+ 1

nr+p2(1 + nr)

2p1p2+p2

2nr+p2

11

nr⎤

⎦(10)

A similar approach gives the ratio of back-iron depths on the

basis of the quadrature sum method, given by:

ycBDFG

ycIM

=(p1+p2)⎡

⎣

p11+ 1

nr+p2(1 + nr)

2p1p2+p2

2nr+p2

11

nr⎤

⎦(11)

The back-iron depth ratios for common (p1/p2) pole-pair

brushless DFIGs have been calculated and are given in Table II

for both the simple and quadrature sum methods. The peak ﬂux

density in the back-iron is limited to 1.8 T.

The back-iron ratio is a minimum at p1=p2, which is not

feasible, as noted earlier. The minimum depth is twice of that of

a(p1+p2) induction machine on the simple sum basis, and 2√2

times on the quadrature sum basis which, however, gives a higher

machine output. As the ratio of pole-pair numbers increases,

there is a slight rise in the depth of back-iron required.

The results for a wide range of pole number combinations

on the basis of optimum turns ratio calculation for the sum

and quadrature sum method are shown in Fig. 3. The BDFG

needs more back iron than a corresponding DFIG as the two

machine ﬁelds have lower pole numbers. However, in any case a

certain minimum back iron depth may be mandated by structural

considerations. To determine an accurate depth requires ﬁnite

element analysis to take saturation into account [24].

Fig. 3. Back-iron ratio variation with optimum turns ratio.

V. M AGNETIZATION

A. Magnetizing Amp-Turns

For the brushless DFIG the total magnetizing amp-turns

(ATtot)forthep1and p2pole-pair ﬁelds, assuming that they

are in ratio given by equation (5), are given by:

ATtot =2g

μo

π

6p1⎡

⎢

⎣

1+p2

p12

nr

1+p2

p1nr⎤

⎥

⎦(12)

where ATtot is the product of ImagNeff ,g is the air gap length

and μois the permeability of air. The amp-turns ratio of the

(p1/p2) brushless DFIG to a conventional induction machine of

p1+p2pole-pairs is then:

ATBDFI G

ATDF IG

=p1

p1+p2⎡

⎢

⎣

1+p2

p12

nr

1+p2

p1nr⎤

⎥

⎦(13)

Substituting nropt from equation (23) for the Bsum formula-

tion gives:

ATBDFI G

ATDF IG

=p1

p1+p2⎡

⎢

⎣

1+p2

p13

2

1+p2

p11

2⎤

⎥

⎦(14)

The corresponding expression for the quadrature sum ap-

proach and substituting nropt from equation (24) is given by:

ATBDFI G

ATDF IG

=p1

p1+p2⎡

⎢

⎣

1+p2

p14

3

1+p2

p12

3⎤

⎥

⎦(15)

The amp-turns ratios for common (p1/p2) pole-pair brushless

DFIGs are calculated and given in Table III. From a magnetizing

current point of view, this ratio is a minimum at p1=p2,

however but this is impractical. On the simple sum basis the

magnetizing amp-turns are 50% of that of a (p1+p2) induction

machine, but the brushless DFIGs torque, according to (18) is

ORAEE et al.: INFLUENCE OF POLE-PAIR COMBINATIONS ON THE CHARACTERISTICS OF THE BDFIG 1155

TABLE III

AMP-TURNS RATIO FOR VARIOUS POLE-PAIR BRUSHLESS DFIG

Fig. 4. Amp-turns ratio variation with optimum turns ratio (simple sum).

only half that of the induction machine, showing that the BDFG

requires the same magnetizing AT per unit torque. Similarly, on

a quadrature sum basis, the magnetizing AT are 70.7% of those

of a DFIG, but again the output torque is only 70.7%. Whilst

there is an increase in the magnetizing AT with a greater ratio

of pole numbers, there is a corresponding rise in output factor

so a (p1/p2) BDFG requires essentially the same magnetizing

AT as a (p1+p2)DFIG.

The amp-turns ratio of the brushless DFIG to the conventional

induction machine for various pole-pair ratios using the simple

sum method is presented in Fig. 4.

VI. PERFORMANCE ANALYSIS AND RESULTS

The foregoing points are examined in the context of an

existing frame size D400, 250 kW brushless DFIG [20] by

considering designs for different speed options, i.e., pole number

combinations. The equivalent circuit model is used to represent

the steady-state performance of the machine, offering a straight-

forward method of calculating the efﬁciency and power factor to

a practical accuracy. The physical dimensions and speciﬁcations

of the D400 machine together with stator and rotor winding

details are given in Table IV.

The nested-loop rotor of this machine comprises (p1+p2)/2

sets of nests, each with ﬁve loops and the conductors being solid

bars with one common end ring. The number of rotor slots, and

hence the number of loops, will therefore depend on the pole

number count and so the machine will not necessarily be suited

for actual production and/or manufacturing.

TAB L E IV

SPECIFICATIONS OF THE 4/8 FRAME SIZE D400 BRUSHLESS DFIG

TAB L E V

DESIGN OF VARIOUS POLE NUMBER BRUSHLESS DFIGSFORFIXED PW

POWER FACTOR O F 0.95 LAGGING

A. D400 Machines

Designs for common brushless DFIG pole-pair combinations

using the same dimensions of the existing D400 prototype

machine have been investigated. Table V, provides details of the

designs with constant rated torque but different speeds and hence

powers. The PW power factor is set to 0.95 lagging, determining

the CW voltage and the balance between B1and B2is changed

by varying number of turns. The total ﬂux density, Bsum ,is

0.7 T and peak ﬂux densities in the rotor tooth and back-iron

is limited to 1.5 T. All equivalent circuit parameters, including

leakage inductances, are recalculated for each new design using

the software described in [21].

The total stator electric loading is kept at 5.7 kA/m. Fur-

thermore, the number and diameter of the stator conductors

and cross-section of the rotor bars are modiﬁed such that the

total conductor cross-sectional areas are identical to those of

the D400 machine. The stator current density is 3.5 A/mm2and

the rotor current density is 5 A/mm2. The air gap diameter and

stack length has been kept constant for all pole number designs.

It can be seen that the 2/6 pole brushless DFIG has both the

highest natural speed, power and efﬁciency, whilst producing

the same torque as the original 4/8 machine. Moreover, this

pole-pair conﬁguration requires the lowest total amp-turns for

magnetization, but needs the highest back iron depth as shown

in Table VI.

To reduce the depth of back iron, the Bsum limit can be

increased from 0.7 T to 0.8 T, without undue increase in magne-

tizing current, as seen in Table VII, which shows designs of the

1156 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 35, NO. 3, SEPTEMBER 2020

TAB L E VI

BACK IRON DESIGN OF VARIOUS POLE NUMBER BRUSHLESS DFIGS

TAB L E VI I

DESIGN OPTIMIZATION OF THE 4/8 D400 BDFIG FOR INCREASED Bsum

D400 brushless DFIG for higher Bsum for a constant torque of

3670 Nm. As stated in (5), the distribution of B1and B2ﬁelds

are dependent on the rotor turns ratio and the stator windings

number of pole-pairs. Due to the change in the number of PW and

CW turns, the total amp-turns is also changed. In the redesigns,

conductor current densities, slot dimensions and slot ﬁll are kept

constant. The peak ﬂux densities in the rotor tooth and back-iron

are limited to 1.6 T and 1.7 T, respectively.

As evident from Table VII, unity PW power factor can be

achieved at rated design CW voltage of 620 V for the 250 kW

brushless DFIG by increasing the total ﬂux density in the air

gap. To obtain unity PW power factor for a Bsum of 0.75 T and

0.8 T, B1is increased by 20% and 14%, respectively.

B. Pull-Out Torque of D400 Machines

From the previous section, the theoretically available maxi-

mum running torque depends to a degree on total pole count, as

well as the split of pole numbers. However, a further considera-

tion is the load angle at which the machine operates, related in

turn to the pull-out torque. For well-known reasons, operation

away from pull-out is desirable. In the BDFG, the pull-out torque

is primarily determined by the rotor inductance and this was

believed to increase with pole count [15].

To investigate the effect, brushless DFIGs were designed

with the same overall rotor dimensions, starting from the well-

characterized 250 kW D400 frame size machine [20], for dif-

ferent pole numbers using the design methodology reported

in [21]. The stator windings were conﬁgured to use the same

number of stator slots and the rotor slots are chosen to give

enough conductor area for the stator electrical loading to be

balanced, with the same current density in the rotor conductors

as the previous section. The design program calculates machine

parameters, notably the rotor leakage inductance, taking into

account space harmonic effects and the couplings between the

rotor loops using simple sum analysis method.

Fig. 5. Pull-out torque variation with natural speed and normal running torque

of 3.7 kNm.

Figure 5, shows the variation of pull-out torque for BDFGs

with different natural speeds and in ascending order correspond-

ing to 8/12, 4/12, 4/8 and 2/6 pole machines. As shown the 4/8

and 2/6 pole machines with natural speeds of 500 and 750 rpm,

respectively, offer somewhat higher pull-out torques allowing

easier control and improved stability due to lower rotor leakage

inductance, Lr. When designing high pole count machines, there

is a need to pay careful attention to keeping the rotor inductance

down to an acceptable level to retain a suitable margin of pull-out

torque relative to the normal running torque but this is seen to

be achievable at least to a total pole count of twenty. The normal

running full load torque for designs with natural speeds of 300,

375, 500 and 750 rpm is 3.7 kNm.

C. Power Factor

Achieving a good power factor is important and increas-

ingly wind turbines are expected to contribute to the VArs.

The selection of machine speed, and hence pole-pair count has

a signiﬁcant effect on machine operating conditions. Fig. 6,

shows the variation of the PW power factor for sums of p1and

p2pole-pairs at balanced excitation (minimum rotor currents),

preferred for low losses. It has been found that brushless DFIGs

with a lower sum pole-pairs and higher PW power factors can

be achieved. The designs used in Fig. 6 are those in Table V,

which were designed to be capable of operating at a ﬁxed power

factor of 0.95 lagging; parameters are given in the Appendix.

D. Efﬁciency

Figure 7, shows the variation of efﬁciency as the PW power

factor is improved for the existing 250 kW BDFG prototype.

Achieving a higher PW power factor comes at a price of reduced

efﬁciency, illustrating the trade-off between satisfying power

factor requirements and other performance measures.

VII. MEGAWATT MACHINES

The intention is, of course, to deploy the brushless DFIG

in large wind turbines, so it is important to know how such a

ORAEE et al.: INFLUENCE OF POLE-PAIR COMBINATIONS ON THE CHARACTERISTICS OF THE BDFIG 1157

Fig. 6. PW power factor variation with sum of pole-pairs at rated torque and

speed.

Fig. 7. Efﬁciency variation with PW power factor for 250 kW BDFIG.

machine would operate. According to recent grid codes, wind

farms have to supply reactive as well as real power to the grid.

For a brushless DFIG the power factor can be controlled by the

converter feeding the control winding, but as noted in [22] there

are some practical limits. To explore the expected performance

of large machines, designs have been developed for 2.5 MW

and 5 MW medium speed machines as tabulated in Table VIII.

The proportionately lower rotor leakage reactance allows unity

PW power factor to be achieved in both machines at rated CW

design voltages without increasing Bsum, therefore has been

kept at 0.7 T.

Figure 8, illustrates the PW power factor variation with re-

spect to the rated output power as machine size increases. The

machines are taken from Table V and Table VIII, noting that they

have different pole numbers. Each data point was recorded for

a balanced excitation condition, with each winding providing

its own magnetizing current. This condition was achieved by

adjusting the CW voltage to minimize the rotor currents, for a

given PW voltage, at full load operating conditions.

TABLE VIII

OPTIMIZED DESIGNS FOR MW BRUSHLESS DFIGS

Fig. 8. PW power factor variation with respect to the rated output power.

It is evident that smaller machines suffer from lower power

factors without an excessively high CW voltage. A line side

converter with a higher rating or capacitor banks at grid terminals

can be used to contribute to the generation of reactive power.

However, the problem becomes less critical for larger machines,

since the per unit value of the rotor reactance drops with size [27].

For the designs considered, a worst case PW power factor of 0.95

lagging is achieved at balanced excitation and a modest degree

of over-excitation of the CW will enable the export of VArs to

the grid.

VIII. CONCLUSION

This paper has examined the effect of the number of poles

and pole-pair combinations on the performance of the brushless

DFIG, especially in the context of future MW scale machines.

1158 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 35, NO. 3, SEPTEMBER 2020

The analysis presented in the paper shows that acceptable pull-

out torques can be maintained for machines with natural speeds

in the range examined, namely 300 to 750 rpm, i.e., with pole

counts from 8 to 20. The split of pole numbers between the

two windings in cases where more than one combination is

acceptable does not signiﬁcantly affect the pull-out torque. For

the same output power and speed, the brushless DFIGs require

essentially the same magnetizing ampere-turns as conventional

DFIGs and the magnetizing current does not change signiﬁcantly

with the split of pole numbers. As with conventional machines,

the back-iron depth reﬂects the choice of pole numbers, and if a

2-pole winding is present a signiﬁcantly higher back iron depth

is needed.

This paper has used both simple and quadrature sum ap-

proaches for the two ﬁelds, but the trends noted above are not

dependent on the approach adopted. However, the machine’s

output does reﬂect the maximum allowable ﬂux density and

ﬁnite element analysis is need to achieve an optimized design.

Encouragingly, designs for brushless DFIGs up to 5 MW, based

on the performance of the existing 250 kW machine show that a

good power factor can be achieved without excessive excitation

of the control winding or compromising efﬁciency.

APPENDIX

The power rating of the brushless DFIG, calculated from

the equivalent circuit model, was derived in [1] based on the

quadrature sum of ﬁelds and is given by:

Pquad =π2

√2d

22

lωrBJ ⎡

⎢

⎣

p1+p2

p11+ 1

nr1+nrp2

p121

2⎤

⎥

⎦

(16)

The power rating of a conventional induction machine with

(p1+p2) pole-pairs is found from:

PIM =π2

√2d

22

lBJ ωs

p1+p2(17)

The output power is then calculated as:

Pquad

PIM

=⎡

⎢

⎣

p1+p2

p11+ 1

nr1+nrp2

p121

2⎤

⎥

⎦(18)

Using the alternative Bsum approach, for the brushless DFIG,

maximum output power can be calculated as:

PBsum =π2

√2d

22

lωrBJ ⎡

⎣

1

p11+ 1

nr+1+nrp2

p1⎤

⎦

(19)

Hence, output power ratio is then calculated as:

PBsum

PIM

=⎡

⎣

p1+p2

p11+ 1

nr+1+nrp2

p1⎤

⎦(20)

These powers can be normalised to the output of a p1+p2

DFIG leading to output factor of:

Output f actor =TBDFI G

TIM ⎡

⎢

⎣

1+p2

p1

1+ 1

nr1+nrp2

p121

2⎤

⎥

⎦

(21)

For the quadrature sum method and:

Output factor =TBDF G

TIM 1+p2

p1

1+ 1

nr+p2

p1(1 + nr)(22)

for the sum method. The nropt is deﬁned using the method

given in [1], with the assumption of unity power factor and small

load angle operation. The turns ratio for maximum output power

is given by:

nropt =p1

p21

2

(23)

However, this is constant to the results obtained in [1]:

nropt =p1

p22

3

(24)

The actual value of nropt are 0.71 and 0.63 for the 4/8

brushless DFIG from equation (23) and (24).

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Ashknaz Oraee (Member, IEEE) receivedthe B.Eng.

degree in electrical engineering from Kings College

London, London, U.K., in 2011, and the Ph.D. degree

in electrical engineering from Cambridge University,

Cambridge, U.K., in 2015, focusing on electrical

machine design and optimization.

Her current research interests include electrical

machines and drives for renewable power generation.

Richard McMahon received the B.A. degree in elec-

trical sciences and the Ph.D. degree from the Uni-

versity of Cambridge, Cambridge, U.K., in 1976 and

1980, respectively.

Following Postdoctoral workon semiconductor de-

vice processing, he became a University Lecturer in

electrical engineering in 1989 with the Department of

Engineering, University of Cambridge, where he was

a Senior Lecturer in 2000. In 2016, he joined the War-

wick Manufacturing Group, University of Warwick,

Coventry, U.K., as a Professor of power electronics.

His current research interests include electrical drives, power electronics, and

semiconductor materials.

Ehsan Abdi (Senior Member, IEEE) received the

B.Sc. degree from the Sharif University of Tech-

nology, Tehran, Iran, in 2002, and the M.Phil. and

Ph.D. degrees, from Cambridge University, Cam-

bridge, U.K., in 2003 and 2006, respectively, all in

electrical engineering.

He is currently the Managing Director of Wind

Technologies Ltd., Cambridge, where he has been in-

volved with commercial exploitation of the brushless

doubly fed induction generator technology for wind

power applications. His main research interests in-

clude electrical machines and drives, renewable power generation, and electrical

measurements and instrumentation

Salman Abdi (Member, IEEE) received the B.Sc.

degree in electrical engineering from Ferdowsi Uni-

versity, Mashhad, Iran, in 2009, the M.Sc. degree

in electrical engineering from the Sharif University

of Technology, Tehran, Iran, in 2011, and the Ph.D.

degree in electrical machines design and modelling

from Cambridge University, Cambridge, U.K., in

2015.

He is currently a Lecturer in electrical engineering

with the University of East Anglia, Norwich, U.K. His

main research interests include electrical machines

and drives for renewable power generation and automotive applications.

Sul Ademi (Member, IEEE) received the B.Eng. and

Ph.D. degrees in electrical and electronics engineer-

ing from Northumbria University, Newcastle upon

Tyne, U.K., in 2011 and 2014, respectively.

From 2015 to 2017, he was a Lead Researcher,

engaged in knowledge exchange and transfer part-

nership activities between University of Strathclyde,

Glasgow,U.K. and GE Grid Solutions, Stafford, U.K.

He is currently a Research Scientist with the War-

wick Manufacturing Group, University of Warwick,

Coventry, U.K. His research interests include electric

motor drives, control of doubly-fed machines, and design and analysis of novel

permanent-magnet machines.