Design and Performance of Brushless Doubly-fed Machine Based on Wound Rotor with Star-polygon Structure

doi:10.4236/epe.2013.54B015

Paper Menu >>

Journal Menu >>

Energy and Power Engineering, 2013, 5, 78-82

doi:10.4236/epe.2013.54B015 Published Online July 2013 (http://www.scirp.org/journal/epe)

Design and Performance of Brushless Doubly-fed Machine

Based on Wound Rotor with Star-polygon Structure

Chaohao Kan

College of Electrical & Automatic Engineering, Hefei University of Technology, Hefei, China

Email: [email protected]

Received September, 2012

ABSTRACT

The star-polygon bru shless doubly-fed machine (SPBDFM) is a new type of wound-rotor machine and is attractive fo r

variable-speed constant-frequency shaft generation system. The structure of rotor for the machine may b e impro v ing the

conductor availability of th e rotor windings. The kirchhoff laws is employed to illuminate the princip le and some com-

binations of different slots and poles are presented as the examples. Harmonic analysis is also employed to analyze the

magnetic motive force (MMF) waveform of rotor winding with the structure of star- polygon. Finally, the results are

used to reveal that the SPBDFM is attractive for shaft generation system.

Keywords: Polygon; BDFM; Wound Rotor; Magnetic Motive Force

1. Introduction

The brushless doubly-fed machine (BDFM), having ad-

vanced recently, is a new type AC-excited motor, with

the characteristics of synchronous motor and induction

motor. There are two sets of symmetrical AC windings in

the stator: the control winding with 1 pole-pair is

connected via a power electronic converter and the pow-

er winding with 2 pole-pair is connected directly to

the grid, and a set of symmetrical AC windings in the

rotor. There haven’t the direct contact between the two

sets of stator wind ings on voltage or cur rent, but through

the couple of rotor magnetic field to realize modulation

of two sets of stator rotating magnetic field which have

different pole-pair, achieving the motor electrical and

mechanical energy conversion and transmission [1-4]. A s

a generator, the variable-speed constant-voltage constant-

frequency sound generation features make its in the wind

power generation, marine shaft power generation area; as

a motor when the precise timing of its features make it in

the higher speed requirements of place has a broad ap-

plicatio n p rospect s.

The structure of rotor winding is a k ey factor affecting

the performance of a BDFM, therefore rotor winding

needs to be specially desig ned to achiev e the requirement

that rotor MMF couple the MMF generated by the stator

control winding and power winding [5-8]. When a rotor

with r

bars is subjected to rotating magnetic fields of

1 pole-pair, the indu ced rotor MMF contains main slot

spatial harmonic of 1r pole-pair. When 1

ppZ0



,

the rotation direction of the harmonic field is against the

main field of pole-pair relative to the rotor. Obvi-

ously, choose 21r

pZp





precisely to meet synchro-

nous operation requirement with the BDFM, therefore,

the rotor can choose 12



slots.

While the sum of stator pole-pair numbers is small, if

the number of rotor slots is choice as 12

, the in-

duced harmonic MMFs of rotor winding is abundant, the

leakage reactance may be weaken by increasing the slot

number. When the rotor slot number increase to r

pp







pp (

a positive integer), We have, by the

principles of BDFM winding design, each

adjacent

rotor slot is a basic unit, which is a minimum slot number

group, named the smallest slot number group, also it is

known as a phase of rotor winding. Obviously, each

smallest slot number group has same winding connection

means.

Current the design, it is known as the ‘nested-loop’

design. As a example, a rotor 54 slots, 1/2 pole-pairs

‘nested-loop’ is shown as Figure 1. It has 3 nests, and

there are 6 loops in each nest.

Figure 1. bdfm with rotor 54slots 1/2- pole pair winding

with the connection of nested loop.

C. H. Kan 79

Both the nested loop structure and the reluctance

structure of BDFM are “magnetic field” type which by

adjusting the flow path to achieve the rotor to couple the

magnetic field of the two sets of stator winding. Because

of the air gap is sinusoidal alternating magnetic field,

rotor winding could not preferable realized coupling two

kinds of stator magnetic field only by change the mag-

netic flux path. the “magnetic field” type structure has

defect, such as follows: abundant harmonic MMFs; strong

sub-pressure effect; for the relatively small pole-pair

number, the winding pitch (nested loop) or the equivalent

winding pitch (reluctance) is smaller, especially in the

difference between two pole-pair is big, therefore, it is

weak that the effect of magnetic coupling for the smaller

of the pole - p a ir number.

In this paper, the rotor winding with “star-polygon”

structure of the BDFM is presented. In the novel machine,

the “star-polygon” topology is employed, by using this

method, the phase current vector of rotor winding will

shift a specified angle, and this shift will change the vec-

tor of rotor winding MMF, and improve the magnetic

field distribution.

2. Structure and Working Principle of the

Rotor

By Kirchhoff law, it’s obviously that the phase current

and the line current have a certain phase angle difference

in time domain for the connection of polygon circuit.

And motor rotor windings also have a certain phase dif-

ference in space. If using the space on the phase differ-

ence to compensate for the phase difference in time do-

main, it may be making the two parts of windings MMF

generated by superimposed in space, then the windings

are star - polygon connection can increase the number of

pole-pair corresponding phase windings of the distribu-

tion coefficient, thus to improve the utilization of con-

ductors.

To achieve the above functions, the specific winding

connection is requ ired. As mentioned above, for the con-

trol winding 1 pole-pair and the power winding

pole-pair, the rotor winding is divided into 12



phases and each phase winding is divided into two

groups. The subscripts d, s denote this two groups. The

rotor winding parameters of one phase are defined as

follows: is the coil win ding number of the polygon

part and rs is the coil winding number of the star part;

rd is each phase winding turns per coil turns of the

polygon part and rs is each phase winding turns per

coil turns of the star part. The star-polygon structure of

the rotor winding is shown in Figure 2.

As shown in Figure 2, rdi and rsi are the ith

phase rotor winding induction electromotive force of the

polygon part an d star part respectively, where i = 1,2, ...,

E E

1rs





rsm





2rs





1rd





rdm





2rd





Figure 2. Structure of wound rotor in the form of star- po-

lygon.

m. The number of rotor winding phase is 12

mp p





and 12



is supposed.

The principle of the rotor winding with the star-poly-

gon structure is illustrated as follows. When the stator

windings of 1 pole-pair are imposed with the currents,

the gap space will generate the 1 pole-pair air-gap

magnetic field [9,10]. The expression of each phase in-

duced electromotive force for the rotor windings is given

by Equation (1).



211

211 1

11 1

rd rd

rdm rd

rs rs

rsm rs

EEp

EEmp

EEp

EEpp

EEmpp

















 







 



 





(1)

where rd and rs are each phase induced electromo-

tive force amplitude of the polygon part winding and the

star part winding respectively. Since each phase rotor

winding is connected in the same manner, the amplitude

of the induction electromotive force for the star part and

polygon part are equal respectively. 1

E E



is the mechani-

cal rotor shaft angle.



is the angle between the me-

chanical axis of the star part and polygon part for one

certain phase rotor winding.

It can be seen from the symmetry of topological struc-

ture that the current of star part and polygon part are

symmetry distribution respectively. Using equal (1) the

rotor winding current may be written as

C. H. Kan



211 0

11 0

211 0

11 0

rd rd

rdm rd

rs rs

rsm rs

IIp

IImp

IIp

IImp















 



 







 



 





(2)

where rd

and rs

are the current amplitude which are

produced by the polygon part winding and the star part

winding of each phase respectively. 0



is the angle

which is between the electromotive force vector and the

current vector. By the simplification, we define00





It’s obvious that the angle 11







 (see appendix).

In order to ensure that the ampere conductors per slot are

the same value, the ratio of the current amplitude is

rd rsrsrd

IWW approximately.

The axis of polygon part for first-phase winding is

counted as the coordinate origin for the space angle. For

the vth MMF harmonic may be written as equal (3).





21 1111

111 11

111

21111 11

1111

cos cos

cos( 1)cos( 1)

cos cos

cos( 1)

rd vdvr

rdmv dvr

rs vsvr

rsmv sv

fF vpt

fF vpptp

fF vpmptmp

fF vppt

fF vppptp

fF vpmpp





 

 

 







 











cos( 1)

rtm p













 



(3)

where dv



and



are the pulsating MMFs that are

produced by the polygon part winding and the star part

winding of each phase respectively. By the ratio of the

rotor winding current amplitude rd

and rs

, it can be

seen that rdrdvrs rsv

dv sv

FNkkN





 

, where rdv

and rsv are the polygon part winding and the star part

winding of the rotor winding vth harmonic winding fac-

tor respectively. r



is the frequency of the magnetic

field in the rotor reference frame, hence the rotor fre-

quencies in the referred circuit are equal in the magnitude.

When , the combination of m phase MMFs is 1v





111

cos

Ftp

mF tp p















(4)

when 21

vpp, the pole-pair of the combination of

phase is , because the 2 pole-pair magnetic field is

inverse with the pole-pair magnetic field in the ro-

tating direction, we have



222

cos

sp r

Ftp

mF tp p















(5)

From equation (4) and (5), it is can be seen that the

angle of MMFs which are produced by star part and po-

lygon part of the same rotor phase winding are adjusted



. We have

22 0

222

ppp

mpp

















 

 









(6)

Form the equation (4), (5) and (6), it is can be seen

that the MMF angle between star part and polygon part

of each phase is increased by



for 1 pole-pair,

which is bound to reduce the composite MMFs; and the

MMF angle that between star part and polygon part of

each phase is reduced by



for 2 pole-pair, which is

bound to increase the composite MMFs. Because



, the decrease in value of 1 pole-pair MMF is

less than the increase in value of pole-pair MMF.

When the three-phase symmetrical voltage sources

impose on the 2 pole-pair stator windings, it will form

2 pole-pair MMF in the air-gap magnetic field, ac-

cording to the equation (1) ~ (6), and the similar conclu-

sion can be proved: for 1 pole-pair, the MMF angle

that between star part and polygon part of each phase is

increased by



. For 2 pole-pair, the MMF angle that

between star part and polygon part of each phase is re-

duced by



To sum up, the two kinds of air gap magnetic field

produced by the 1 and 2 pole-pair rotor winding

are rotating in the opposite direction, and the angle be-

tween the magnetic of star part winding and the magnetic

of circular part winding will increase while the rotor

winding produces the 1 pole-pair magnetic field, or

reduce while the rotor winding produces the 2 pole-

pair magnetic field. Since 1, 2 are the fix number,

the angle

p p



only has one value. If 12

, the sum of

windings distribution coefficients will increase. If 12

the sum of windings distribution coefficients of the

winding connected in the above mentioned method will

reduce. So it doesn’t fit for the rotor winding connection.

pppp

3. Prototype Test

The designed rotor winding has been wound in an

YZR225 induction machine, as shown in Figure 3(a).

The stator has 72 slots, in which two windings of 11p



and 22p



pole-pair are separately placed. The rotor

has 54 slot and its winding connection diagram is shown

in Figure 3(b), where y = 15.

C. H. Kan 81

As a comparison, the rotor winding connection dia-

gram in the general structure is shown in Figure 4.

It is listed in Table 1 that the comparison of harmonic

analysis for the resultant MMF produced by three kinds

of winding (as shown in Figure3(b), Figure 4 and Fig-

ure 1). The coil s pans are cho sen as 15 slo ts (y = 15) for

the former two.

As listed in Table 1, the rotor winding coefficient is

decreased by 0.091 as form 1 pole-pair, and the rotor

winding coefficient is increased by 0.128 as form 2 pole-

pair. Obviously, the star - polygon structure can improve

the overall utilization rate of the rotor windings effec-

tively. Comparable to nested loop winding, the winding

coefficient is decreased as form 1 pole-pair, just as form

2 pole-pair. But, the important, the star-polygon connec-

tion has significantly smaller in high harmonic MMFs.

(a) Prototype machine

39 40

3837

2019

46 47

2625

(b) Winding structure

Figure 3. Prototype machine and star-polygon structure of

the 54 slots 1/2 pole-pair prototype.

39 40

46 47

43 48

28 29262530

Figure 4. A wound-rotor 54 slots and 1/2 pole pairs winding

with a general structure.

Table 1. Comparison of the results of MMF harmonic anal-

ysis of rotor winding with a structure in the form of

star-polygon, general, and nested LooP.

star – polygon general nested loop

Pole-p

airs Winding

factor Resultant

MMF（%） Winding

factor Resultant

MMF（%）

Winding

factor Resultant

MMF（%）

1 0.615 –149.4 0.706 -202.7 0.642 –139.8

2 0.824 100 0.696 100 0.918 100

4 0.021 –1.29 0.042 -3.04 0.204 -11.1

5 0.047 2.28 0.093 5.37 0.255 11.1

7 0.043 –1.48 0.036 –1.48 0.296 –9.21

8 0.067 2.03 0.077 2.76 0.072 1.97

10 0.055 –1.33 0.063 –1.80 0.008 –0.18

11 0.028 0.62 0.024 0.62 0.124 2.45

(a) Magnetic field

00.02 0.040.06 0.080.1

-200

-150

-100

-50

100

150

200

time(sec)

voltage(V)

(b) Voltage curve

Figure 5. magnetic field and voltage curve as 2 pole-pair

output 5 kw.

800 1000 1200

line voltage of control

，

speed

，

rpm

(a) Control voltage

80090010001100 1200

current in control

，

speed, rpm

(b) Control current

Figure 6. Control voltage and control current as power

winding OUTPUT 5 KW (cosφ = 1).

In the experiment, the 2 pole-pair winding is used as

the power winding with a line voltage of 200 V rms (the

phase voltage 115.5 V rms correspond). We keep the

power winding output 5 kW (cos 1



). As the rotor

speed is 1200 rpm, the magnetic field is shown as in

Figure 5(a); the power winding voltage (named v1, v2

and v3) and contro l voltage (named v4, v5 and v6) curv e

are shown as in Figure 5(b) based on FE analysis. As the

C. H. Kan

[1] P. C. Roberts and R. A. McMahon, “Performance of

BDFM as Generator and Motor, IEE Proceedings, Elec-

tric Power Application, Vol. 153, No. 2, 2006, pp.

289–299.

rotor speed is from 800 to 1200 rpm, the control voltage

vs. speed is shown in Figure 6(a); the control current vs.

speed is shown in F igure 6( b ).

As shown in Figure 6(a), the experimental data are

consistent with the calculated results based on FE analy-

sis. Obviously, the star-polygon BDFM can realize the

function of variable-speed constant-voltage constant-

frequency generation.

[2] S. Williamson, A. C. Ferreira and A. K. Wallace, “Gener-

alized Theory of the BDFM. Part 2: Model Verification

and Performance,” IEE Proceedings- Electric Power Ap-

plication, Vol. 144, No. 2, 1997, pp. 123–129.

doi:10.1049/ip-epa:19971052

[3] A. K. Wallace, P. Rochelle and R. Spee, “Rotor Modeling

and Development for BDFMs,” Conference of Record

of the International Conference on Electrical Machines,

Cambridge, Vol. 1, 1990.

4. Conclusions

This paper has presented, for the first time, a new type

rotor winding connection, named star-polygon, for

BDFM. The BDFM with “star- polygon” structure of

rotor windings has the following five characteristics: 1, It

is increased that the rotor winding distribution coefficient

which corresponding to the stator power windings; 2, A

set of rotor slot conductors is used repeatly, improving

the actual utilization of the rotor slot conductors; 3, The

choice of winding pitch is freedom; 4, The connection of

rotor winding is flexible; 5, The content of harmonic

MMFs is low. So this new type structure of rotor wind-

ings has great development prospects.

[4] X. Wang and P. C. Roberts, “Optimization of Bdfm Sta-

tor design Using an Equivalent Circuit Model and a

Search Method,” In Proc, IEE 3th Int. Conf. Power Elec-

tronics, Machines and Drives, Dublin, Ireland, 2006, pp.

606-610.

[5] X. Wang, R. A. McMabon and P. J. Tavner, “Design of

the Brushless Doubly-fed (induction) Machine,” IEEE

Interaction Election Machines &Drives Conference,

IEMDC’07, Vol. 2, 2007, pp.1508-1513.

[6] X. F. Wang, “A New BDFM with a Wound-rotor Chang-

ing-pole Winding,” Proceedings of the CSEE, Vol. 23,

No. 6, 2003, pp. 108-111.

5. Acknowledgements [7] S. C. Yang, “Feature of Electromagnetic Design for

BDFMs,” Proceedings of the CSEE, Vol. 21, No. 7, 2001,

pp. 107-110.

This work was supported by the Surface of Natural Sci-

ence Fund Program projects of Anhui Province (NO.12

08085ME62), by the Doctoral Degree in Special Re-

search Fund Program projects of hfut (NO. 2011HGBZ-

0935).

[8] F. G. Zhang, F. X. Wang and Z. Wang, “Comparative

Experiment Study on the Performance of Doubly-fed),”

Proceedings of the CSEE, Vol. 22, No. 4, 2002, pp.

52-55.

The authors wish to thank the China Changjiang Na-

tional Shipping Group Motor Factory for the provision of

the prototype machine and fabrication of the rotor.

[9] C. H. Kan and X. F. Wang, “Harmonic Anslysis for

Wound-rotor Winding in Induction Manchine,” Large

electric manchine and hydraulic turbine., Vol. 4, 2007,

pp. 18–23.

[10] S. Z. Xu, “Windings Theory of A.C. Machines,” Publish-

ing House of Machinery Industry, 1985.

REFERENCES

Appendix phase are symmetry, the value of



is not a result of

the chosen reference point of change.

The parameters compute of



：

The current vectors, such as 1rd

, 2rd

and 1rs

, in-

tersect at the same node, by Kirchhoff current law, we

have 21rdrs rd



1rd

2rd

1rs





II, As shown in Figure 7.

Because of 1rdrd 2

I, we have11









. It is

can be seen from Figure 7 that





. So the



given as11







 . As the rotor windings of each Figure 7. The vector of current.