Induction motor with pole-changing windingfor variable supply frequency

Michael van der Giet and Kay HameyerInstitute of Electrical Machines, RWTH Aachen University

Schinkelstr. 4, D-52056 Aachen, Germany

Stephan RisseAirbus Deutschland GmbH

Kreetslag 10, D-21129 Hamburg, Germany

AbstractFor induction drives that are operated at two speedsthe approved Dahlander technology with pole changeable coils inthe stator of the motor can be applied. Being operated at constantsupply frequency the motor with Dahlander coils can be drivenat a speed ratio of 2:1 without using a frequency converter. Theadvantages are the simplicity and the robustness of the machineas well as the saving of weight and installation space due tothe omitted power electronic circuits, although the motor andits pole changeable coils have to be designed with particularcare. While the Dahlander winding for single frequency operationhas often been made subject of discussion, this paper presentsthe approach of an induction machine with pole-changing coilsoperating on mains supply with variable frequency for aircraftapplication. Measurements on a prototype of the machine showthat the required performance for the use as a pump drive isachieved properly.

I. INTRODUCTION

Even if the operation of a motor drive on mains withconstant frequency depicts the majority of industrial usage,drives at variable supply frequency also have a dedicated areaof application. For reliability reasons on the generating sidethe distribution of electrical energy on board of an aircraft isoften realized by a network operating in the solitary operationat inherently variable frequency. Thus, an electrical deviceconnected to this network is supplied by a frequency thatcorresponds to the current speed of the generators turbine. Thespeed of the turbine is directly dependent on the aircrafts flightphase. Idling turbines would mean 360Hz network frequencyat the minimum and the maximum value of the frequencyis reached with 800Hz at aircrafts take-off. Applying theDahlander winding [1] in this case would result in two speedranges for electrical drives instead of two fixed speeds atconstant supply frequency. For electrical drives with sophis-ticated speed control, power electronics is of course requiredto ensure the desired operating point at any rotational speedof the aircrafts main engines. If it succeeds to achieve theperformance of a drive at two speed ranges, one may savethe power electronic converter on the load side. This meansto take advantage of the benefits mentioned above which areof high interest in aircraft applications in particular.In the present case the electrical network of the new Airbus

A380 is subjected. Although the feeding pumps for coolingliquids do not have ambitious requirements with respect tospeed control they are designed as converter-fed inductionmachines. Therefore, the performance of the machines design

360 533 800Frequency (Hz)

8000

12000

16000

Spee

d(rp

m)

p=2p=4Speed too high for motor operation

Speed too low for pump performance

Fig. 1. Speed Characteristics.

with Dahlander winding is assessed by the example of a pumpdrive. The considered pump device consists of two separateinduction machines, each equipped with a pump fan wheeland working in parallel on a common liquid cooling circuit.As this exercise involves a prototype solution for an alreadyexisting system with installation constraints, stator diameterand rotor length are limited for the new motor design. Themechanical output power of the motors are P = 2 kW each,the frequency range is f = 360 800Hz and the range of themachines speed is n = 800016000 rpm. Those requirementsresult in a stator design with pole pairs p = 2 and p = 4 of theDahlander winding. The speed vs. frequency characteristics isshown in Fig. 1.The principle of pole changing windings, and the special

case of the Dahlander winding were developed at the end ofthe 19th century. A comprehensive overview of pole-changingwindings is given in [1] and [2]. In the 1950s and 60s, theprinciples were generalizes and the techniques were improved.The pole-amplitude modulation (PAM) and the pole-phasemodulation (PPM) were developed as such generalized pole-changing techniques [3], [4]. In their theory, the PPM isconsidered the most general winding design approach, ofwhich the PAM is a specialization, and again, of which theDahlander winding is a specialization. Each specializationlimits the choice of the pole ratio p1/p2. For example, theDahlander winding is only capable of generating fields of

pole ratio 2:1, a PAM winding however can generate poleratios of n : (n 1) with n as an integer. In addition tothe improvements, which were achieved in the developmentof the winding, the pole-changing winding gained new fieldsof application with upcoming power electronic devices. In the1990s pole-changing techniques were used together with aninverter supplied induction motor to extend the speed rangefor traction applications [5], [6]. These approaches representvariable-frequency pole-changing techniques, however, theycannot be compared to the approach of this paper, since thetechnical problems differ, and the inverter is the component,which is eliminated using the approach proposed here.In this paper the development of the induction machine is

depicted comprehensively, starting with the layout of the sta-tors cross-sectional geometry and the stator coils in particular.FEM analysis and simulation means have been used. Finally,the performance of the prototype is assessed on an aircraft-system integration-bench and measurements are presented.Steady state measurements show that for the depicted pumpdrive, induction machines with Dahlander winding basicallyreach similar performance than the speed-controlled motors.Slight deviations are due to the imposed design constraints.Transient measurements show that the occurring current peaksdo not exceed the values of the regular startup currents.

II. WINDING DESIGN ASPECTSA. Analytical1) General Design Procedure: The electromagnetic design

procedure of an induction machine can be divided into thefollowing steps [7]:1) Determination of the main dimensions2) Design of the stator winding3) Design of the rotor winding4) Design of the magnetic circuit5) Verification of the design by means of field calculationBased on the required characteristics rated power Pr, no-

load speed n0, rated frequency fr, rated voltage Vr andnumber of phases m, the main dimensions, such as insidediameter of stator D as well as the length of the sheet stack lare determined.The design of the stator winding is based on an assumed

value for the mean airgap flux density Bm. The airgap flux isdetermined by,

= Bm p l , (1)where p = piD2p is the pole-pitch. For the design process, theairgap flux and main machine flux m are assumed to be equaland the number of winding turns is determined as follows:

ws =2 Vh

2pifr m , (2)where f is the supply frequency and Vh is the voltage inducedby the main flux. This number of winding turns has to berealized by a parallel armature conductors, in Ns stator slots,and yields a total of

zs =2 a m ws

Ns, (3)

conductors per stator slot. The number of slots per pole andphase q is used to calculate the winding factor . Assumingthe value of the rated power factor cosr, and consideringthe maximal admissible current density in the stator windingJs, the value of the rated stator current Is,r as well as thecopper cross-section per conductor As,cu is determined. Froma given copper space factor kcu the stator-slot cross-section iscalculated:

As,slot =zs As,cu

kcu. (4)

The maximum airgap flux density is assumed to be p times itsmean value. Therefore, the minimum tooth width is calculated:

bt,min =p BmBs,t

s,slot , (5)

for saturation to be limited and the maximum flux density inthe stator tooth not to exceed Bs,t, where s,slot = piDNs is thestator-slot pitch.The design of the squirrel-cage rotor comprehends the

choice of rotor-bar material, number of rotor slots and thedetermination of slot geometry. The number of rotor slotsshould be selected carefully to reduce time and space har-monics in the total airgap field, leading to low torque rippleand vibrational force excitation. The cross-section of the rotorbars is determined by

Ar,slot = zsAs,cu cosr JsJr

, (6)

where Jr is the current density in the rotor bar and cosr is therated power factor. The minimum tooth width is determinedanalog to (5).For induction machines, the design of the magnetic circuit

corresponds to the determination of the airgap width and thethickness of stator and rotor yoke. The airgap width dependson the bearings and is calculated by:

= 0.25 mm 4Pmech/ kW , (7)

where Pmech is the mechanical power of the motor. Theminimum thickness of stator yoke is determined by

hy,min =Bm p2 Bs,y , (8)

with Bs,y being the maximum flux density in the stator yoke.The thickness of the rotor yoke is determined, analogously. Ithas to be verified that the tooth widths and the thicknesses ofthe yokes meet the requirements of the copper cross-sectionalarea.The final step in the design process is the verification of the

design by means of field computation. This can either be doneusing analytical or numerical methods. If the field computationdoes not confirm the initial design, the procedure describedabove has to be repeated.The design procedure described so far has to be altered for

the design of induction machines with pole-changing winding.For these machines, two different number of pole-pairs p resultfrom either two different no-load speeds or from two differentrated frequencies, where the latter is to be discussed in this

TABLE ICONNECTION TYPE AND RATIO OF AIRGAP FLUX DENSITIES.

Bp2/Bp1 p2 is Y p2 is YY p2 is p2 is p1 is Y 0.80 1.60 1.39 2.77p1 is YY 0.40 0.80 0.69 1.39p1 is 0.46 0.92 0.80 1.6p1 is 0.23 0.46 0.40 0.80

paper. In this case, the procedure above has to be performedtwice, once for each number of pole-pairs. Starting with (1),it can be seen that the flux for the lower number of pole-pairs is twice the flux for the higher number of pole-pairs.To determine the number of winding turns, it is necessary toknow how the induced voltage Vh depends on p. This relationhowever depends on the type of connection of the winding.The Dahlander winding is constructed by separating the

winding into two or more coils, which are reconnected.This reconnection can be in series, or in parallel. The typeof connection being used can be a Y-connection, or a -connection. For each combination, the ratio of airgap fluxdensity can be computed as follows:

Bp2Bp1

=p1 wp1 Vh,p2 p2 fp1p2 wp2 Vh,p1 p1 fp2

, (9)

where the voltage ratio results from Y- or -connection andthe turn ratio from the series or parallel connection. Note,that (9) includes the ratio of the supply frequencies. For thecommonly used case of constant frequency, this term cancelsout. In the case of constant speed, variable frequency, thefrequency is inversely proportional to p, thus (9) simplifiesto

Bp2Bp1

=p1 wp1 Vh,p2p2 wp2 Vh,p1

. (10)

Table I shows the ratios of the airgap flux density for varioustypes of connection.In [1], it is shown that the ratio of the winding factors p1p2 is

equal to 0.789 for qp1 = 2 and approaches 0.816 for qp1 .Table I is exemplarily based on p1p2 = 0.8. The choice of theratio Bp2/Bp1 depends on the application. Choosing this ratioclose to unity, for example, leads to constant torque at twodifferent numbers of pole-pairs.If the type of connection has been chosen, the design

process follows the steps 1) to 4) of the standard inductionmachine, however, the design is done for each number ofpole-pairs individually. From (2) two different zs are obtained,though one value for zs has to be chosen to be implemented inthe designed machine. The minimum value of the yoke heighthy,min from (8) is typically larger for the lower number ofpole-pairs. The cross-section of the rotor bars is determinedaccording to (6) after the stator winding has been designed.Equations (5) and (8) have to be regarded, respectively.2) Example: Now, the design process is applied to a

cooling-pump induction motor under additional design con-strains. The first requirement is not to exceed a certain outer

TABLE IIRATED PARAMETERS.

2p1 = 4 2p2 = 8

Rated power Pr 2 kW 2 kWsynchronous speed n0 12000 rpm 12000 rpmRated voltage Vr 115 V 115 VRated frequency fr 400 Hz 800 HzNumber of phases m 3 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

X2 X3 X4 X5 X6 Y8 Y9 Y10 Y11Y12 X1 Y7

7 10 111 2 3 4 5 6 8 912coil no.

Fig. 2. Winding diagram.

stator diameter, and the second is to reuse an existing rotordesign.The rated parameters of the machine are given in Table II.

Since rated power and synchronous speed of both p are equal,torque of both p has to be equal, as well. Therefore, the ratioof the airgap flux densities for both cases is to be chosen closeto unity. According to Table I, a -connection is chosen for2p1 = 4 and for 2p2 = 8 a YY-connection is chosen. Due tothe small size of the machine, the least possible number ofslots is selected:

N1 = m 2p = 3 8 = 24 . (11)This yields qp1 = 2 and qp2 = 1. The winding diagram is

shown in Fig. 2 and the circuit diagram can be seen in Fig. 3.Switching from one p to another is done by connecting all linesof the -connection to the star point of the YY-connection. Inthis way, coils 1,7 and 4,10 are brought together in the upperbranch of the YY-connection.According to (10), the ratio of airgap flux densities is

calculated for the selected type of connection:

Bp2Bp1

=0.6830.866

21 115V/

3

115V= 0.9107 . (12)

From (1) to (3), the airgap flux , the number of windingturns ws and the number of conductors per slot zs is calcu-lated. Taken the /YY-connection into account,

zs,p1 = 38 and zs,p2 = 35 (13)

are obtained. To be sure to choose the main inductance ofthe machine sufficiently large for both p, zs = 38 is selected.

2p=4 2p=8

1,7

2,8 3,9

4,10

5,11 6,12

1,7

2,8

3,9 4,10

6,12

5,11

Fig. 3. Circuit diagram.

From assumed values for the rated power efficiency r = 70%and the rated power factor cosr = 0.7, rated stator currentis computed. Using (4) the stator-slot cross-sectional requiredarea is calculated

As,slot = 112.4 mm2 . (14)

Following the design procedure, the minimum width of thestator tooth and the minimum height of the stator yoke arecomputed according to (5) and (8), respectively:

bt,min = 1.81 mm , (15)

hy,min,p1 = 3.63 mm and hy,min,p2 = 1.82 mm . (16)

The provided slot cross-section area calculated from the fixedouter stator diameter D = 80mm and hy,min = hy,min,1yields:

As,slot = 88.73 mm2 . (17)

The comparison of (14) and (17) shows that the requirementfor the slot cross-section area cannot be fulfilled under thediameter design constraint. Increasing the dimensions bt andhy increases the overall magnetic reluctivity, however, the slotcross-section, and therefore the area, which can be used forthe winding is reduced. This tradeoff becomes an additionalaspect, which will be discussed in more detail in the nextsection.

B. Optimization by means of FEA

The two different number of pole-pairs generate conflictingdemands on the usage of the available stator area. Where forthe smaller number of pole-pairs an increase of the yoke heightis most effective to increase the mean airgap flux density,for the higher number of pole-pairs the available area can beused more effectively as copper cross-section area. Anotherparameter, which may be varied, is the tooth width.To find the optimal solution for this problem the Finite

Element Analysis (FEA) is applied. The rotor is modeled asa solid cylinder and for each value combination of hy andbt, two static 2D FEA, one for each number of pole-pairs areperformed. The airgap width is increased by the Carter factorof the rotor slots. The maximum admissible current density inthe stator winding is used as excitation to the field problem.

0.0014 0.0016 0.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034Stator tooth width (mm)

0.25

0.3

0.35

0.4

0.45

0.5

Mean

airg

ap

flux

den

sity

(T)

p=2p=4

hy=3.0 mmhy=3.2 mmhy=3.5 mmhy=3.7 mmhy=4.0 mm

Fig. 4. Mean airgap flux densities (for p = 4: calculated using (12)).

Fig. 5. Flux density for p = 2.

Comparing the mean airgap flux density, the expected ratioBp2Bp1

has to be taken into account.For the induction motor presented in this paper, the mean

airgap flux density as a function of tooth width and yoke heightare shown in Fig. 4 for J = 6A/mm2. It can be seen that for

bt = 2.5 mm and hy = 3 mm (18)

the mean airgap flux densities for both p are approximatelyequal to 0.4 T. Therefore, this combination is chosen forthe presented machine. The comparatively low value of themean airgap flux density is due to the the limiting designconstraints. The optimization method could be refined by usinga combination of one static current-density excited FEA forone number of pole-pairs and one transient voltage excitedFEA using the flux determined from the first FEA.The flux density distribution for p = 2 and p = 4 excitation

are shown in Fig. 5 and 6, respectively. The plots show that inthe p = 4 case the maximum flux density is occurring in thestator teeth, where in the p = 2 case the yoke is saturating.

Fig. 6. Flux density for p = 4.

III. EXPERIMENTAL RESULTS

A. Steady State

For performance verification the pump assembly driven bytwo machines prototypes is installed on the integration rigof the cooling system. This test bench depicts the full-sizerepresentation of the cooling system as it is installed on theaircraft, allowing overall system verification as an integralpart of the design process. The pump assembly is workingon the cooling circuit where it replaces the converter suppliedone that is installed in standard configuration. The machinesare connected to an appropriate contactor circuit that servesfor switching the number of pole-pairs during operation. Thisdevice is connected to a power supply unit that allows freedemand of input voltage and frequency. In the given layouttwo motors are installed on one pump assembly. Both motorsdrive a pump wheel each and are working in parallel on onecooling circuit. This is done for reasons of redundancy andnot for increasing the flow rate. Therefore considering singlepump operation is sufficient for the measurements.The presented results are obtained at stator voltage V =

115V and startup with p = 2 for stator frequencies in therange of f = 360500Hz. Each operating point characterizedby the supply frequency is adjusted by the power supply unitssettings. When the speed of the machine reaches its limit atn = 16000 rpm the number of pole-pairs is switched to p = 4and the frequency range f = 450 800Hz is considered. Asmall overlapping range is taken into account for determiningthe most appropriate frequency for switching the number ofpole-pairs.Fig. 7 shows the measured flow rate of the cooling liquid

in dependency on the supply frequency. For V = 115V theflow characteristic is increasing continuously for both numbersof pole-pairs, p = 2 and p = 4 but is finally sloping downstarting at a frequency of f = 400Hz for p = 2 and 650Hzfor p = 4. As this behavior indicates a low voltage reservefurther tests are performed at an increased supply voltage ofV = 200V. For stator frequencies belonging to the increasing

350 400 450 500 550 600 650 700 750 800Frequency (Hz)

20

40

60

80

100

120

140

Flow

(kg/m

in)

p=2,115Vp=4,115Vp=2,200Vp=4,200V

Fig. 7. Measured pump performance.

branch of the flow characteristic, a higher supply voltage isnot leading to an increased flow-rate as it is depicted in Fig.7. In case that the flow characteristic is sloping for V = 115Van increased supply voltage induces a significant increase inthe flow-rate.Before interpreting this behavior the typical torque-speed

characteristic of an induction machine operated on terminalswith constant voltage and constant frequency has to be consid-ered. For the performed measurements it has to be emphasizedthat the pump drive is operated on separate characteristics, onefor each frequency. Following the pullout torque is decreasingat increasing supply frequencies.On the rising branch of the flow characteristic each operat-

ing point of the induction machine is determined according tothe load torque that is given by the mechanical resistance of theliquid in the ducts of the cooling circuit. For those situationsthe pullout torque is higher than the load torque. Increasing thesupply frequency at unchanged input voltage implies operatingthe induction machine on a different characteristic with alower pullout torque. At a certain frequency pullout torque asthe maximum torque is lower than the required load torque,therefore the flow is decreasing. Applying a higher statorvoltage in this situation results in an immediate increase of thepullout torque and a stable operating point is set according tothe load torque.Looking at the presented test results the following facts are

revealed:1) The maximum flow rate obtained with the Dahlander-

wound machine prototype could be determined by ex-periment. This is according to the requirements of thecooling system and is shown as dashed line in Fig. 7.

2) The layout voltage of V = 115V is obviously toolow for covering the complete frequency range with asufficient performance.

The deficiencies of the prototype design are related tothe constraints of retaining an existing rotor and of limitingthe stator diameter. With a fixed active length the machinestorque is restricted and a limited stator diameter results in iron

10.1 10.15 10.2 10.25 10.3Time (s)

-20

-15

-10

-5

0

5

10

15

20Cu

rrent(A

)

Fig. 8. Measured current waveform, transition form p=2 to p=4.

400 420 440 460 480 500 520 540 560Frequency (Hz)

-0.05

0.0

0.05

0.1

0.15

0.2

0.25

0.3

Settl

ing

time

(s)

p=4 to p=2p=2 to p=4

Fig. 9. Measured settling time.

saturation at low flux density and therefore in a low inductanceof the machine.Hence, the general applicability proof of the Dahlander-

wound induction machine is successfully verified for thepresent application although a further optimization cycle hasto be done.

B. Transient

In addition to steady state measurements (Fig. 7), the currentwaveforms during the switching process for both transitions,from the lower to the higher number of pole-pairs and vice-versa, were measured. The measured current waveform for thetransition from p = 2 to p = 4 at 115V and 550Hz is shownin Fig. 8.The exact current waveform depends on the following pa-

rameters: frequency, stator voltage, and phase angle at switch-ing time. Frequency and voltage indicate an operational point,of which the characteristics are: saturation/main inductanceand slip/load. The phase angle at switching instant influencesthe magnitude of the current peak after switch-on. The settlingtime and the largest occurring magnitude of the current peakare shown in Fig. 9 and 10, respectively.It can be seen, that in the interval, in which the switching

is supposed to be performed, the current peaks and the steady

400 420 440 460 480 500 520 540 560Frequency (Hz)

5

10

15

20

25

30

35

40

45

Curr

enta

mpl

itude

(A)

Steady State,p=2Steady State,p=4Peak,p=4 to p=2Peak,p=2 to p=4

Fig. 10. Measured current amplitude.

state currents do not differ by much. Though a more detailedtransient analysis, including the measurement of the stator-voltage in magnitude and phase, would reveal more insightinto the switching process itself. It can be concluded, that theoccurring transient current do not exceed the regular level ofstartup currents of the induction motors.

IV. SUMMARY AND CONCLUSIONSIn this paper, the design of a Dahlander-wound induction

machine for operation on mains with variable frequency waspresented. Steady state measurements show that the generalperformance of this approach meets the requirements that aregiven by a pump drive for an aircraft application. Replacing themotor that is usually operated on a power electronic converter,the presented layout offers an attractive solution for overallweight and cost saving and for increasing the reliability ofthe system. Measurements for transient operation show thatcurrent peaks after switching the pole-pairs are in an accept-able range. As the present design was limited by installationconstraints, the performance has some short comings when thepump is operated at rated voltage. Therefore, further work hasto be spent on the enhancement of the motor design.

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[3] , Neuartige polumschaltbare Dreiphasenwicklung mit sechs An-schlussenden fur elektrische Maschinen, Siemens Forschungs- und En-twicklungsberichte, vol. 7, no. 1, pp. 110, 1978.

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