Superconducting AC generator with a magneticsteel outer rotor

J.R. Bumby, B.Sc, Ph.D, C.Eng., M.I.E.E.

Indexing terms: Generators, superconductivity,

Abstract: The specific power output per unit length of large superconducting AC generators is limited by thematerial properties, of the outer rotor. By manufacturing this component from a high strength magnetic steel,such as is used in. conventional turbogenerator rotors, the diameter of this component can be increasedproducing an increase in the specific power output. This paper demonstrates the feasibility of using amagnetic outer rotor and shows that advantages are to be gained in respect of generator systems performanceand ease of manufacture as well as improved specific power output.

List of symbols

A = electric loading, A/mAz = axial component of vector potentialBo = flux density at axial centre of air-cored super-

conducting AC generator, T. Bo = /JL0 K O / 2Br = radial component flux density, THr — radial component magnetic, field, A/mHQ = tangential component magnetic field, A/mKo = superconducting field winding linear current

density, A/mL'a = subtransient inductance, HLs = synchronous; inductance of generator with mag-

netic outer rotor, HLso

= synchronous inductance of generator with non-magnetic outer rotor, H

P = power output, WR = winding resistance, O,Tph = number of turns in series/phaseki = magnetic outer rotor factorkw = winding factorkr = radial flux density environmental screen factorke = trangential flux density environmental screen

factor/ = generator length, mn =• generator speed, rev/sr — radius of field point, mri = inner radius outer rotor, mr2 = outer radius outer rotor, mrD — mean radius outer rotor, mr0 = mean radius superconducting field winding, mrs = mean radius armature windings, mrx = inner radius environmental screen, mt = winding thickness, m6 = circumfrential position, radHi = incremental permeabilityHo = permeability of free space H/mHr = relative permeabilityp = resistivity, flmao.2 = 0.2% (300K) proof stress of inner rotor N/mm2

i// = internal power factor angle, rad

1 Introduction

Superconducting turbogenerators are currently beingdeveloped as a means of both increasing generator

Paper 1101C, first received 17th April and in revised form 5thAugust 1980The author is with the Department of Engineering Science,University of Durham, Science Laboratories, South Road, DurhamDHI 3LE, England

IEEPROC, Vol. 128, Pt. C, No. 1, JANUAR Y1981

efficiency, and offering a generator with developmentpotential well in excess of the 2000 MVA anticipated of theconventional generator with present day technology. Theelimination of the. excitation I2R loss is the main reason foran increase in generator efficiency of typically 0.6% [1]. Inorder to produce the. most effective design, machines withlarge specific outputs per unit length are sought whereas themanufacture of the different generator components inmaterials with, which significant experience has been gainedin similar applications is further advantageous.

In the superconducting generator designed by theInternational Research and Development Co. Ltd., [1,2]the superconducting rotor excitation winding is supportedin slots in an austenitic stainless steel rotor forging and isprotected from armature negative sequence and faultfluxes by an ambient-temperature outer rotor. This outerrotor also serves as a vacuum containment vessel, thevacuum being required to limit convection heat transferbetween the inner and outer rotors. Radiation heat transferis reduced by a radiation screen, at a typical temperature of70K, situated between the inner and outer rotors.Surrounding the outer rotor is the armature winding, inthis case supported in an epoxy-concrete core [1] and, toprotect the environment from stray magnetic fields, alaminated iron environmental screen is placed outside thearmature winding.

The rotor screening system, consisting of the outerrotor and the radiation screen, presents an intriguingproblem in the design of superconducting machines as itmust carry the full short-circuit force whilst maximisingnatural damping of rotor-hunting oscillations and minimisingflux-density variations at the superconductor. Such a designrequirement can be met by using a double-rotor construction[3-6] . In this the outer rotor is designed to withstand 95%of the short-circuit forces, to screen armature negative-sequence fluxes and reduce substantially the flux-densityvariations at 50 Hz seen by the radiation screen during afault. The radiation screen is then designed to reduceflux-density variations at hunting frequency, typically1.5 Hz, such that any armature-induced flux-densitychanges at the superconductor are acceptable for theparticular winding design.

One outer rotor design that meets the above requirementis a composite structure manufactured from an aus.teni.ticstainless steel cylinder, proof stress 650 N/mm2, lined byaluminium, the stainless steel providing the strength and thealuminium improving the screening function [3].

In Section 2 of the paper the limitation on poweroutput per unit length is described and shown to beprimarily due to the strength of the outer rotor stainless

0143-7046/81/01001+11 $01-50/0

Table 1: Magnetic field distributions produced by field winding

Region 1 r < r0

1 +D

cos 0

1 + sin 0

Region 2 rl > r > r0

cos 0

Region 3 r2 > r > r,

Hr — Koro COS 0

sin 0

Region 4 rx > r > r2

cos 0

Hd = sin 0

steel support cylinder. It would be beneficial if the strengthof this component could be increased. An additionaladvantage would result if the outer rotor could bemanufactured from a single material, without recourse toan aluminium liner to improve the screening function.There is therefore an incentive to investigate the feasibilityof using a high-strength ferritic steel in the outer rotorconstruction. The higher proof stress of such a steel wouldallow an increase in the rotor diameter and the higherconductivity could render the use of an aluminium linerunnecessary.

As ferritic steel is magnetic additional flux from thesuperconductor will be required to saturate the outer rotorand force flux through to the armature. In order toestablish the feasibility of such a magnetic outer rotor itis necessary not only to examine the flux-shunting aspectof the outer rotor on machine design (Sections 4 and 5) butalso to investigate generator performance following asudden short circuit (Section 6). A deterioration in thesystem performance and/or a substantial reduction in theflux Unking the armature winding could outweigh the

advantage of using such a high-strength material for theouter rotor. It is with establishing the feasibility of such amagnetic outer rotor that this paper is concerned. Two-pole designs are assumed throughout.

2 Rotor design concept

In order to achieve maximum power output per unit lengthlarge turbogenerators are designed to have the maximumdiameter consistent with practical design limitations. In thecase of the superconducting AC generator the power outputof a two-pole machine can be expressed as

P = 2\/2~TT2 kwkr(Borl) A In cos (1)

where kw is the winding factor, A the armature electricloading, / the generator active length and n the speed ofrotation in r.p.s. BQr\ refers to the product of the fluxdensity at the axial centre of an air-cored machine and thesquare of the effective winding radius of the super-conducting rotor winding, kr is a geometric factor relatingto the effect of the environmental screen on the flux

IEEPROC, Vol. 128, Pt. C, No. 1, JANUAR Y1981

density at the armature winding \j/, the internal-power-factorangle, is a function of synchronous reactance and external-power-factor angle. A two-dimensional analysis of themagnetic fields inside the generator, assuming the super-conducting field winding to be represented by an infinitelylong sinusoidal current sheet Ko Sin 6, gives the environ-mental screen factor, kr, [3, 7, 8] as

(2)kr= i + M-

In the superconducting AC generator maximum poweroutput per unit length is obtained when the productBQr% is maximised. In practice the maximum value ofBo is related to the superconductor characteristic whereasr0 is determined by stress considerations in the inner andouter rotors.

1.5

P £

1.0

0.5

0.2 0.3 0.4 0.5rotor tooth tip radius, R

0.6 0.7

Fig. 1 Influence of rotor radius on magnetic moment of innerrotor (from Reference 9).

ao2 = 400N/mm2, 300 KNb/Ti superconductor, 5 Kminimum bursting speed ratio 1.7rJR = 0.2

Earlier work [9] on a 1300 MW machine, accounting forthe superconductor characteristic and maximum allowablestress in the inner rotor, produced the variation of Borlwith tooth-tip radius as shown in Fig. 1. In obtainingFig. 1 it is assumed that the minimum bursting speed of theinner rotor is 1.7 times rated speed and the rotor bore todiameter ratio is 0.2. With these assumptions, and using a0.2% proof stress for the inner rotor material at ambienttemperature of 400N/mm2, Fig. 1 shows that an innerrotor diameter of 1.2 m is required to maximise generatoroutput.

In the design of Reference 3 the outer rotor material wasan austentic stainless steel with a proof stress of650N/mm2. When account is taken of the rotational andshort-circuit stresses in the outer rotor the allowablediameter and thickness of this component limits thediameter of the inner rotor to values well below that whichmaximises BQr\\ typical values of Bor\ being 0.6 to0.8 Tm2. If the value of Bor% could be increased by theintroduction of an outer rotor manufactured from amaterial with greater proof stress then greater rotordiameters and consequently specific power outputs couldbe obtained. One possible material is a ferritic steel, 35% Ni,Cr Mo, V, such as used in conventional turbogenerators forLP spindles and rotor forgings [1], which is capable of aproof stress of 850N/mm2. A further advantage associatedwith this material is that substantial experience has beengained from its use in similar situations so potentiallyincreasing the reliability of the generator.

3 Rotor electromagnetic model

To quantify the amount of flux required to saturate theouter rotor, and so establish the electromagnetic feasibilityof using a magnetic outer rotor material, a two-dimensionalsolution for the magnetic fields inside the generator isobtained. The problem is formulated in cylindrical polarcoordinates and an analytical solution obtained for themagnetic fields using the vector potential Az, and solvingLaplaces equation,

ori_ ax

dr= 0 (3)

with the following assumptions:(a) The field winding is represented by an infinitely-long

sinusoidal current sheet, Ko sin d, at the geometric meanwinding radius. As magnetic fields substantially removedfrom the excitation winding are of interest, neglectingwinding thickness is acceptable while harmonic fieldsreduce with the radius as (Vo/r)n+1 such that their effect onthe magnetic fields at the armature is small compared tothe fundamental.

(b) The laminated environmental screen, of inner radiusrx, is infinitely long in the axial direction and has zeroconductivity and infinite permeability.

(c) The outer rotor is uniformly saturated such that itspermeability can be considered constant. In practice,permeability of this component will vary both circum-ferentially and radially but the assumption of constantpermeability facilitates a straightforward solution. Theinner radius of this component is designated rx and theouterr2.The solution of Laplaces equation obtained by the methodof separation of variables produces the magnetic-fielddistributions in the generator as shown in Table 1. Howeverthe equations contain an unknown in /ir, the relativepearmeability of the outer rotor.

To determine the relative permeability value to usein Table 1 consider the physical process by which theouter rotor is saturated. On initial excitation flux from thefield winding enters the outer rotor radially. This flux isthen magnetically short circuited by the magnetic outerrotor, flux flowing circumferentially inside the magneticouter rotor. It is the reluctance of the outer rotor, in thecicumferential direction, that is predominant indetermining the amount of rotor flux penetrating through

IEEPROC, Vol. 128, Pt. C, No. 1, JANUARY 1981

to the armature. Consequently the relative permeabilitycalculated on the interpolar axis is used in the magnetic-field expressions in Table 1. A solution for the relativepermeability is obtained by solving for the tangentialflux density in the outer rotor iteratively with the B/Hcurve of the material, Fig. 2, at the interpolar axis until avalue for the relative permeability converges to an accuracyof 0.01.

If the relative permeability in the outer rotor is unity themagnetic field expressions in Table 1 are identical to thoseobtained for a generator with a nonmagnetic outer rotor[ 3 , 7 , 8 ] .

6 8 10 12magnetic field, A /m (x105)

Fig. 2 Magnetisation curve for outer rotor material

4 Magnetic field distributions

4.1 Comparison of analytical and numerical methods

The validity of the magnetic field expressions in Table 1 areestablished by comparison with magnetic field obtainednumerically using the magnet design computer programGFUN [10] allowing for permeability variations in theouter rotor material. The rotor model used by GFUNrepresents each quadrant of the outer rotor by 96 discreteelements each of which has a different, constant value ofrelative permeability. The outer rotor and superconductingfield winding are assumed to be infinitely long, soeliminating axial variations, but account is taken of therotor slotting geometry. For the 1300MW generatordescribed by design 1, Table 2, the radial and tangentialmagnetic field variations computed using GFUN are

5

4i—

oCD 3

o

flux

densi

t;ra

dial

0

-

, <

vVA-AA 1—

0.2 0.4 0.6 0.8radiUs.m

1.0 1.2 1.4

Fig. 3 Comparison of analytical and numerical methods at 100%excitation. No environmental screen

GFUNanalytical

compared with the value obtained from the analyticexpressions of Table 1 in Figs. 3 and 4, respectively, for100% rotor excitation. To simplify the discussion theeffects of the environmental screen is not included in thesefigures but its influence on the three-dimensional magneticfields is discussed in Section 4.3.

10

9

H- 8

x10"1Z. 6o£5<D 4

I 3a 2

02 0.4 0.6 0.8 1.0radius, m

1.2 1.4

Fig. 4 Comparison of analytical and numerical methods at 100%excitation. No environmental screen. GFUN

analytical

The magnetic field distributions of Figs. 3 and 4 indicatethat at radii remote from the rotor radius, i.e. typicalarmature winding radii, both numerical and analyticalmethods give similar results but large differences occurclose to the superconducting winding. This is due to thesuperconducting winding being represented by a sinusoidalcurrent sheet of zero radial thickness and fundamentalspace harmonic. Consequently the analytical method gives

' position of maximum field

Fig. 5 Variation of relative permeability in the magnetic outerrotor calculated by GFUN at 100% excitation (no armaturereaction

IEEPROC, Vol. 128, Pt. C, No. 1, JANUARY 1981

a constant value for the flux density in the inner rotor,falling off with increasing radius from the winding whereas,when winding thickness is taken into account, the fieldchanges in going through the winding and there is nosudden change at the winding radius. The effect of therotor slots is to produce local changes in flux density nearto, and in, the superconducting winding such that themaximum flux density is at the bottom corner of theoutermost slot as shown on Fig. 5. In this case themaximum flux density being 6.22T (1.35 x the centralflux density.)

The variation of relative permeability throughout theouter rotor is shown in Fig. 5 where pole face permeabilitiesare seen to be greater than in the interpolar axis. Fig. 6demonstrates the agreement obtained between thenumerical and analytical methods for the relativepermeability on the interpolar axis as a function ofexcitation.

Table 2: 1300 MW AC generator design parameters

Design 1 Design 2

MVA rating 1530MVA 1530MVAPower factor 0.85 lagging 0.85 laggingTerminal voltage, r.m.s./phase 16 kV 15.5kVArmature current, r.m.s./phase 16 kV 16.5 kVNumber of phases 6 6Number of conductors in

series/phase 24 24Field winding radius 0.423 m 0.446 mRadiation screen radius 0.49 m 0.515 mRadiation screen time constant 2.16s 2.16sOuter rotor:

outer radius 0.65 m 0.675minner radius 0.533 m 0.563 mresistivity 85 X 10~8ftm 27 X 10~8ftmtime constant 0.06 s 0.19s

Outer rotor liner:thickness 0.018 m —resistivity 3.0 X 10"8 fim —time constant 0.23 s —

Armature mean winding radius 1.03m 1.15 mInner radius of iron environmental

screen 1.4 m 1.52 mActive length 3.67m 3.48mInertia constant 2.3 s 2.3 s

When a magnetic outer rotor is used with Design 1 no liner isnecessary

I5oa>6 4

i.

20°/. 40°/. 60°/. 80°/. 100 °/«

°/o full load excitation

Fig. 6 Comparison of relative permeability calculated analyticaland numerically at 0 = "

relative permeability at 6 = j from GFUNanalytical

4.2 Comparison of magnetic and nonmagnetic outerrotors

The generator design is modified to that of design 2,Table 2, to take advantage of the increased strengthproperties of the magnetic outer rotor and a comparisonmade for the generator with and without a magnetic outerrotor using the analytic field expressions of Table 1.

Figs. 7 and 8 show the variation of radial and tangentialflux density, respectively, in the generator at 100%excitation again with the environmental screen absent. An

10r

~ 4

02 0.4 0.6 0.8radius.m

1.0 1.2

Fig. 7 Comparison of magnetic and nonmagnetic outer rotorsat 100% excitation. No environmental screen

nonmagentic outer rotormagnetic outer rotor

xifj1

Fig. 8 Comparison of magnetic and nonmagnetic outer rotorsat 100% excitation. No environmental screen

nonmagnetic outer rotormagnetic outer rotor

IEEPROC, Vol. 128, Pt. C, No. 1, JANUARY 1981

increase in the central flux density of 0.25 T or 6% isproduced by the magnetic outer rotor whereas magneticfields outside the outer rotor are reduced by approximately3%. To obtain the same flux density at the stator as withthe nonmagnetic outer rotor an overall increase in thecentral flux density of about 8.5% is incurred. In thetangential flux-density variations of Fig. 8 the abruptchange in the flux density of 2T corresponds to thesaturation flux density in the magnetic outer rotor.

The effect of excitation on the flux density at thearmature is shown in Fig. 9. Because of the essential air-cored nature of the machine synchronous reactances of0.5 p.u. and below are typical. This in turn requires onlysmall changes in field current to counteract armaturereaction effects, no-load field current being typically60—70% of full-load current. Over the no-load to full-loadexcitation range the rotor flux lost because of the fluxshunting effect of the magnetic outer rotor is between 3and 5%.

= 10m

1.1m

0.1 -

20 AOVo 60 V. 80*/.

Vofull load excitationlOOVo

Fig. 9 Variation of flux density from the superconductor at thestator as a function of excitation for a generator with and without amagnetic outer rotor

nonmagnetic outer rotormagnetic outer rotor

4.3 A comparison of two-dimensional and three-dimensional magnetic-field calculations

In Fig. 10 and Fig. l l a comparison is made of the radialand tangential flux densities calculated by the analyticexpressions of Table 1 and computed numerically by

GFUN for design 2, Table 2. The magentic fields arecalculated at 100% excitation, and an armature-windingradius of 1.1 m, for different combinations of outer rotormaterial and environmental screen. Account is taken offinite length effects within the generator by GFUN. Alsoshown on these diagrams is the relative position of the rotorend windings, outer rotor and iron environmental screen.The analytical and numerical methods compare well at thecentre of the generator when an iron environmental screenis present regardless of whether the outer rotor ismagnetic. This is particularly true as regards radial fluxdensity, where the difference is less than 1% while

environmental . ,screen / / / / A 1.6

1.5 2.0 2.5axial position.m

Fig. 10 Axial variation of radial component of flux densityproduced by superconducting winding at 100% excitation

Relative position of the rotor end windings and environmentalscreen shown to scaleA = analytical; nonmagnetic outer rotor, environmental screenB = analytical; magnetioiouter rotor, environmental screen.C = numerical; nonmagnetic outer rotor, environmental screenD = numerical; magnetic outer rotor, environmental screenE = numerical; magnetic outer rotor, no environmental screenF = analytical; magnetic outer rotor, no environmental screen

1.6

1.2

1.0 •

E0.8^

0.6°

0A

0.2

3.0 3.5

3??!

lux

dens

ityco

nduc

ting

13 cl

Ol

1.6

1A

1.2

10

0.8

0.6

0A

02

0

/ / environmental •/ / / screen / /

A

= B

C r\• ' ' " ^ 1 "

F

/ / X

/ / A 1

-

-/ /outer r o t o r / / ! .

^S. rotor end^v windings

0.5 1.0 1.5 2.0 2.5axial position.m

Fig. \\ Axial variation of tangential component of flux densityproduced by superconducting winding at 100% excitation

Relative position of the rotor end windings and environmentalscreen shown to scaleA = analytical; magnetic outer rotor, no environmental screenB = numerical; magnetic outer rotor, no environmental screenC = analytical; nonmagnetic outer rotor, environmental screenD = analytical; magnetic outer rotor, environmental screenE = numerical; nonmagnetic outer rotor, environmental screenF = numerical; magnetic outer rotor, environmental screen

IEEPROC, Vol. 128, Pt. C, No. 1, JANUARY 1981

tangential flux densities at the same radius differ by lessthan 4.5%. Both radial and tangential flux densities remainsensibly constant over the centre two metres of thegenerator reducing with axial position until about 1 moutside the end of the rotor excitation winding themagnetic fields are < 0.05 T. As the introduction of an ironenvironmental screen presents a circumferential flux pathof low reluctance the radial flux density in such agenerator is increased and the tangential flux densityreduced as demonstrated by curves D & E in Fig. 10 andcurves B & F in Fig. 11, the increase in radial flux densityat the machine centre being, in this case, 44% from a valueofO.765tol.1T.

For a generator with no environmental screen thecomparison between the two-dimensional analytic and thethree-dimensional numerical magnetic field computations ispoor at the machine centre, the radial flux density in thethree dimensional case being increased by about 8%. This isbecause the flux produced by the rotor end windingsincreases the resultant radial flux density at the centreof the generator in the three-dimensional calculation. Inthe two-dimensional computation these end turns areeffectively at infinity and consequently have no effect onthe magnetic fields at the centre of the machine.

The influence of the iron environmental screen and themagnetic outer rotor on the axial flux density is shown inFig. 12 at different radii. Fig. 12 shows the axial fluxdensity to be zero at the machine centre increasing to amaximum over the rotor end windings and then reducingwith axial length until at about 1 m outside the end turnsthe flux density is about 0.05 T with the peak value of fluxdensity decreasing as radius increases. Introducing the ironenvironmental screen into the design tends to reduce theaxial flux density from the rotor end turns, in this case by30% from 0.425 T to 0.39 T at a radius of 1.1 m, and preventdeep penetration of axial flux into the generator. Inconsequence the rotor end turns contribute very little tothe central flux density when the environmental screen is

i.6r -environmental/ screen

1.2

1.0P ,

>> 0.6

•o 0.A

o 0.2so

/A ni.6

\.U

1.2

1.0

0.8

0.6

0.4

0.2

1.0 2.0axial position,m

3.0

Fig. 12 Axial variation of axial component of flux densityproduced by the superconducting winding at 100% excitation

Relative position of the rotor end windings and environmentalscreen shown to scaleA = radius = 0.9 m\B = radius = 1.1 ml Numerical: magnetic outer rotor,C — radius = 1.3 mj environmental screenD = numerical; Radius = 1.1m, magnetic outer rotor, noenvironmental screenE = numerical Radius = 1.1 m, nonmagnetic outer rotor,environmental screen

IEEPROC, Vol. 128, Pt. C, No. 1, JANUARY 1981

present, so that the two-dimensional and three-dimensionalcomputations are comparable at the machines centre.

At the ends of the generator outboard of the rotor endwindings, Figs. 10, 11 and 12 indicate that the effect of theenvironmental screen is the reduce the radial, tangentialand axial fields and so help confine the flux within theenvironmental screen length. Introducing the magneticouter rotor further tends to reduce these end fieldsbecause of the flux shunting effect of the outer rotor. Sucha reduction in these end fields is beneficial as it reduces themagnitude of the rotor fields at the armature endconnection so reducing the eddy-current loss in thesemembers.

5 Modification of the output equation to account forthe magnetic outer rotor

The radial magnetic field given in Table 1 for region 4 canbe written in the form

Br = kfirBo ( — I cos 6 tesla* e

(4)

where kt is a magnetic outer rotor factor and is given by

(5)kt can now be introduced into the power ouput equation togive

P = 2\[2 n2 kwkrki (Borl) A In cos \p (6)

with kt being found iteratively by the method described inSection 3. Typical values of k{ are 0.9 to 0.99, indicatinga reduction in generator specific power output due to theflux shunting effect of the outer rotor. However, the higherproof stress available from the magnetic steel, as comparedto stainless steel, allows an increase in outer rotor diameter,and consequently inner rotor diameter, such that anincrease in specific power output is possible with anincrease of 20% having been reported [1]. Comparison ofthe two designs in Table 2 indicates a reduction in theactive length of 0.2 m with the magnetic outer rotor leadingto a 5% increase in specific power output.

6 Performance aspects of a superconducting ACgenerator with a magnetic outer rotor

6.1 Synchronous & subtransient inductance

To determine a synchronous inductance expression fromeqn. 11 the problem of assigning an appropriate outer rotorpermeability value is again encountered. In steady-stateoperation with just the field winding excited the outerrotor is very heavily saturated, Figs. 4 & 5, with a relativepermeability of two and minimum flux density in excessof 3 T. The B/H curve for the outer rotor material, Fig. 2,shows that normal operation is far beyond the knee of theB/H curve with the outer rotor incremental permeabilitybeing unity. To drive the outer rotor out of saturationsubstantial demagnetisation would be necessary.

When armature current is drawn some redistribution offlux, particularly within the pole-face region, will occur.

However because of the very high degree of saturation, andthe large short-circuit ratio, associated with these machines,typically about two, the outer rotor can be regarded ashaving an incremental permeability that is constant fromno-load to rated-load condition. It is this incrementalpermeability that is used in evaluating the synchronousinductance from the general inductance expression, eqn 11,to give

of the subtransient reactance expression is then the same asfor a generator with a nonmagnetic outer rotor, namely [11]

(9)

Ls = 3non 1 + 1 *-*•01,+ D*-r-M d - ^ - o - ^ ) h+r-L

The effect of the incremental permeability on thesynchronous inductance is shown in Fig. 13 where thevariation of synchronous inductance is expressed as a ratioof the equivalent inductance for the generator with anonmagnetic outer rotor, for design 1 of Table 2. Thelimiting value of synchronous inductance as thepermeability tends to infinity is

Ls = Ls (8)

with Lso being the synchronous inductance of theequivalent generator but with a nonmagnetic outer rotor.

During a terminal fault condition eddy-current effectsdominate magnetic effects so that flux from the armatureis deflected round the outside of the outer rotor. The form

1 8 r

1.6

s 1 A

ffi.2

CQ8

0.6

5- 0.2

100relative X

increment*!

Fig. 13 Variation of inductance ratio with pearmeability forgenerator with magnetic outer rotor

Dhenrys/metre

(7)

6.2 Damping and screening

6.2.1 Modelling technique To investigate damping of rotor-hunting oscillations and the screening of the super-conductor a digital-computer simulation of the generatorand power system is used, the generator being representedby two-axis model with the inner rotor body, radiationscreen and outer rotor being represented by up to 15 nestedcoils in each of the direct and quadrature axes, each with itsown inductance and resistance [3].

In evaluating inductance values from eqn. 11 to be usedin this part of the study it is again necessary to specify anappropriate outer rotor permeability. The problem isfurther aggravated as, during a system fault, substantialcurrents flow both in the armature and in the rotor screenscausing a continuously changing distribution of flux withinthe magnetic outer rotor. To accomodate these effects on acontinuous basis would be difficult and require extensivecomputer time.

Section 6.1 demonstrated the extremely high degree oiouter rotor saturation to be dominated by the flux fromthe superconducting winding. Because of this, and becauseof the air-cored nature of the machine limiting armaturereaction effects, outer rotor incremental permeability isagain used in calculating all winding inductance values foruse during the transient period.

In order to account for the flux shunting affect of theouter rotor on flux produced by the superconductingfield winding the initial steady state operating condition isestablished using a field/armature mutual inductance valuecalculated using outer rotor relative permeability. Thevariation of this field/armature inductance with outer rotorrelative permeability, expressed as a ratio of thecorresponding inductance of a generator with a nonmagneticouter rotor, is shown in Fig. 13 for design 1, Table 2.

Similarly the variation of magnetic field at the super-conductor produced by the individual windings iscomputed using outer rotor incremental permeability for allwindings except the superconducting field winding. For thiswinding changes in magnetic field are computed using outerrotor incremental permeability with the initial magneticfield obtained using the outer rotor relative permeabilityvalue. The total nett field at the superconductor is found atany instant by summing algebraically the magnetic fieldfrom each winding [3].

The power system model used assumes the generatorto be connected through a transformer of leakage reactance0.2 p.u. and a double circuit transmission line of reactance0.05 p.u. to an infinite busbar. A three phase to earth faultis applied on the high voltage side of the generator

IEEPROC, Vol. 128, Pt. C.No. 1, JANUARY 1981

transformer and cleared after 140 ms by switching out thefaulted line. The effect of such a fault on the generatorof design 1, Table 2, with and without a magnetic outerrotor is investigated. In the generator model the relativepermeability of the magnetic outer rotor is taken as 2 andthe incremental permeability unity. Two rotor layers areused to model the outer rotor and one layer the radiationscreen.

6.2.2 Rotor hunting oscillations In earlier work Lawrensonet al, [5] using an eigenvalue technique, and Bumby [3],using transient rotor angle results, demonstrated that anouter rotor time constant of typically 0.1 to 0.3 s wasrequired, depending on generator parameters, to achievemaximum damping of rotor hunting oscillations. Dampingof rotor hunting oscillations was also shown to increase asthe coupling between the outer rotor and radiation screendecreased.

The natural damping of rotor hunting oscillations withthe composite nonmagnetic outer rotor is shown in Fig. 14and is primarily produced by the aluminium liner of timeconstant 0.23 sees at an effective radius of 0.525 m.Replacing this composite outer rotor by one manufacturedfrom ferritic steel of resistivity 27 x 10~8 £2 removes theneed for an aluminium liner to limit short circuit forces onthe radiation screen. The outer rotor time constant is now0.19 s, approximately the same as for the nonmagneticouter rotor, but the effective radius of the outer rotor hasnow increased to 0.594 m. This leads to reduced couplingwith the radiation screen and increased coupling with thearmature winding such that the damping of rotor huntingoscillations is marginally improved, Fig. 14, with aconceptually simpler outer rotor design. The logarithmicdecrement being 0.09 with the nonmagnetic outer rotorand 0.18 with the magnetic outer rotor.

100

t 80

*5 60

' 20

0

-20

1.0 2.0time, s

3.0 4.0

Fig. 14 Rotor angle swing curves following a three-phase toearth fault on generator transformer for 140 ms

nonmagnetic outer rotormagnetic outer rotor

6.2.3 Screening of the superconductor Field-currentvariations following a three phase to earth fault are shownin Fig. 15 with an increase in field current of 1.4% beingrequired to saturate the outer rotor. Subsequent variationsthen show that the improved natural damping with themagnetic outer rotor leads to a reduction in the size of thefield-current oscillations at rotor swing frequency andhence better overall screening of the superconducting fieldwinding.

Tangential flux-density variations at the superconductor

in the direct axis are shown in Fig. 16 with the maximumflux-density variation of the first 'true' oscillation beingapproximately 0.2 T. Flux-density variations then decaymore rapidly with the magnetic outer rotor because of theimproved natural damping characteristic of this machine.The magnetic outer rotor also tends to reduce the steady-state value of the tangential flux density at the super-conductor, in this case by about 6%, such that variations ofthe direct-axis tangetial flux density, during a fault is at alower level than with the nonmagnetic outer rotor.

As the flux linkage of the superconducting field windingremains constant during the fault period the net radialflux density at the superconductor remains unaltered atits steady state value of 4.75 T. The corresponding valuewith the nonmagnetic outer rotor was 4.38T, thedifference being due to the magnetic outer rotor.

6.3 r

c 6,2

6.1

6.0

5.9

5.81.0 2.0

time, s3.0 4.0

Fig. 15 Variation of field current after a three-phase fault toearth on the generator transformer for 140 ms

nonmagnetic outer rotormagnetic outer rotor

5.0 r

4.0

Fig. 16 Time variation of peak tangential flux density in thedirect axis after a three-phase to earth fault on the generatortransformer

nonmagnetic outer rotormagnetic outer rotor

6.2.4 Comparison of designs Sections 6.2.2 and 6.2.3described the influence of the outer rotor material ondamping and screening using design 1 as the reference. Asone of the major benefits of using a ferritic material is inthe greater rotor diameter that can be employed it ishelpful to examine the effect of this geometry changeon both damping and screening. The performance of thegenerator with a magnetic outer rotor, design 2, iscompared with design 1 for a nonmagnetic outer rotor.

In arriving at the parameters in design 2 account is taken

IEEPR0C, Vol. 128, Pt. C, No. 1, JANUARY 1981

of the increased radial flux density near the field windingdue to the magnetic outer rotor. The time constant of theradiation screen, 2.16 s, is selected to give acceptablescreening of the superconductor. With this screeningsystem maximum variations in direct axis tangetial fluxdensity is about 0.2 T at rotor swing frequency and issimilar to that shown in Fig. 16 for design 1. However,the initial value of this flux density is 4.18 T compared to4.34 T in design 1 while damping of rotor oscillations isimproved. The logarithmic decrement now being 0.14.

6.3 Negative sequence loss

The variation of relative permeability around the outerrotor shown in Fig. 5 indicates that in the pole face regionpermeability values are greater than on the interpolar axis.The significance of this higher permeability in the poleface region on the distribution of negative sequence lossround the outer rotor can be appreciated by assuming theouter rotor to be inductance limited to negative sequencefluxes when, considering a semi-infinite flat plate [11], thepower loss is inversely proportional to skin depth butdirectly proportional to resistivity, i.e.

or" 2

(10)

where fit is the incremental permeability. Consequently fora generator of the same dimensions the specific power lossis reduced by about 40% in a magnetic outer rotor ofresistivity 27 x 10~8 fim, incremental permeability ofunity, compared with a stainless steel outer rotor ofresistivity 85 x 10~8 fim. However due to the increase inpermeability in the pole face the loss in this area will begreater than on the interpolar axis but with the expectedtotal negative sequence loss being less than in the generatorwith a stainless steel outer rotor.

7 Conclusion

The feasibility of a superconducting AC generator with amagnetic outer rotor has been established. The use of ahigh-strength magnetic material, such as i\% Ni, Cr, Mo, Vferritic steel, for the manufacture of the outer rotor hasbeen shown to offer advantages over a composite stainlesssteel/aluminium outer rotor in terms of overall design andperformance, improved strength, greater materialknowledge and ease of manufacture.

It has been demonstrated that the magnetic outer rotorreduces the flux density at the armature by approximately3% but that the increase in diameter more than compensatesfor this producing an increase in generator specific poweroutput; a typical increase being 340/MVA/m to410 MVA/m [ 1 ] . In addition a conceptually simplerouter rotor design than the composite design previouslyproposed [3] is possible while natural damping of rotorhunting oscillations is increased.

8 Acknowledgments

The work was carried out while the author was employedby the Electrical Engineering Department of I.R.D. It was

carried out in collaboration with CEGB. and NEI. Parsons.The author would particularly like to acknowledge theadvice given by J.S.H. Ross of IRD. and W. Trowbridgeand J. Simpkin of the Rutherford Laboratory for producingthe GFUN results.

References

1 ROSS, J.S.H.: 'The engineering design of large superconductinga.c. generators', International conference on electrical machines,Vienna, Sept., 1976

2 APPLETON, A.D., LORCH, H.O., REECE, A.B.J., SMITH, D.A.and STEEL, J.G.: 'Advanced turbine-generators. An assessment',CIGRE, International conference on large high voltage electricalsystems', 1976 Aug/Sept., Paper 11-02

3 BUMBY, J.R.,: The influence of system operating conditionson the rotor screening requirements of superconducting a.c.generators', International Conference on Electrical Machines,Vienna, Sept., 1976

4 BUMBY, J.R.,: British Patent No. 34854/76 relating to screeningin superconducting a.c. generators

5 LAWRENSON, P.J., MILLER, T.J.E., STEPHENSON, J.M.,and ULA, A.H.M.S.,: 'Damping and screening in the synchronoussuperconducting a.c. generator", Proc. IEE, 1976, 123, (8),pp. 787-794

6 KIRTLEY, J., and FURUYAMA, M.: "A design concept forlarge superconducting altermatores", IEEE. Trans., 1975,PAS-94, (4), pp. 1264-1269

7 HUGHES, A., and MILLER, T.J.E.: 'Analysis of fields andinductances in air-cored and iron-cored synchronous machines',Proc. IEE, 1977, 124, (2), pp. 121-126

8 BRATOLJIC, T., FURSICH, H., and LORENZEN, H.W.:'Transient and small perturbation behaviour of superconductingturbogenerators', IEEE. Trans., 1977, PAS-96, (4), pp.1418-1427

9 APPLETON, A.D., ANDERSON, A.F., and ROSS, J.H.S.: 'Adiscussion on large superconducting a.c. generators',International Conference Electrical Machines, LONDON, Sept.1975, paper A4

10 ARMSTRONG, A.G.A.M., COLLIE, C.J., DISERNS, N.J.,NEWMAN, M.J., SIMPKIN, J., and TROWBRIDGE, C.W.: 'Newdevelopments in the magnet design computer program GFUN',5th International Conference on magnet technology, Frascati,Rome, 1975

11 MILLER, T.J.E., and HUGHES, A.: 'Comparative design andperformance analysis of air-cored and iron-cored synchronousmachines', Proc. IEE, 1977, 124, (2), pp. 127-132

12 STOLL, R.: The analysis of eddy currents' (Clarendon Press,1974)

10 Appendix

10.1 Inductance calculations

The inductance expressions required to assess generatorterminal performance are obtained by calculating the fluxlinkage of individual windings to give the generalinductance expression

I = — henrys per metre (11)IT i

where Br is either a self radial flux density at the windingor mutual radial flux density depending whether self ormutual inductance is required. The relevant radial flux-density values are given in Table 1 for windings inside themagnetic outer rotor while for the windings outside theouter rotor, e.g. the armature winding, the magnetic fieldexpressions of Table 3 are obtained- using similarassumptions about the magnetic outer rotor, iron

10 IEE PROC, Vol. 128, PL C, No. I.JANUARY 1981

R =4irp \Tk

rt 7Tohms per metre (12)

environmental screen and excitation windings as inSection 3.

10.2 Winding resistance

The resistance per unit length of an infinitely long winding To represent a rotor screen coil the number of turnsof T turns, radius r, thickness t and winding factor kw selected is arbitrary as it is the time constant of the screenis [3] only that is important.

Table 3: Magnetic field distributions produced by armature winding

Region 1 r < r,

cos e

Region 2 r2 > r > r,

i i+rc o s e

= -K, sin 0

Region 3 rs > r > r.

Ksr = —r 2

He =

r\ \rcos 0

"-̂ - sin

Region 4 rx > r > rs

r 2

(1-M?)(r22-rf) 1 + P-

(1-M?)(r22-rf) 1 + M-

A-v/ Vy

— cos dr2

— sin 0r2

IEEPROC, Vol. 128, Pt. C, No. 1, JANUARY 1981 11