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Permanent-magnet a.c. generatorsK.J. Binns B.Sc , A.F . I .M .A. , C. Eng. , M. I .E .E. and A. Kurdal i , B.Sc , (Eng.) .

Indexing terms: A. C. generators, Perm anen t magnetsAbstractThe development of permanent-magnet generators is reviewed and a novel multistacked form described. Thismachine is ideally suited to the production of a high airgap field from ceramic magnets, but polymer-bonded rare-earth magnets may also be used to advantage. A damping device can be incorporated to minimise load-angleoscillation. The use of capacitance to improve regulation and increase output is discussed. It is shown that theperformance of the generator can be predicted with reasonably good accuracy by a simple computer program.

List of symbols= integral of Hd l in qth. branch in magnet region

2(JHdlYq = integral of Hdl in 47th branch in iron regions 1,2 and 3= integral of Hd l in

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Early designers employed integrally cast magnets for smallmachines, which usually made use of Alnico materials magnetisedwith poles of alternate polarities, see Fig. 1. Sometimes, separateAlnico magnets were bolted to a central core by nonmagnetic bolts,see Fig. 2. Anothe r design3 had laminated pole shoes and innermetallic magnets located on a central steel hub , see Fig. 3.Some of these assemblies have been surrounded by die cast alu-minium to give rigidity.Another type of rotor, sometimes called a Lundell claw type, orimbricated construction, makes use of a cylindrical magnet which isaxially magnetised, see Fig. 4. Plates at the ends of the m agnet havefinger pieces attached, and these are interlaced radially rou nd the sidesof the magnet to form alternate N and S poles.

1Such machines havebeen made with solid magnets and two stub shafts, with the wholerotor sometimes die cast in aluminium. If there is a single shaft itmust be nonmagnetic. Traditionally, use has been made of Alnico typemagnets for such designs.1'4 Other variations on the same principlehave been developed for specialised use.A fairly recent development5 involves the incorporation of ferritemagnets tangentially magnetised into radial slots to provide alternatepolarities on rotor poles lying between adjacent slots. This form ofconstruction is also used as an inverter-fed synchronous motor underthe name 'Siemotron'. A 12-pole version is shown in Fig. 5, and it willbe seen that if the slots are sufficiently deep , the airgap density can beconsiderably higher than that in the magnet itself.

Fig. 4Lundell rotor

Fig. 5Rotor using tangentially magnetised ferrite magnetsPROC. IEE, Vol. 126, No . 7, JULY 1979

This paper describes an alternative form of construction ideallysuited to the use of ferrite or polymer-bonded rare-earth magnets. Itderives from the Lundell construction, but makes use of an assemblyof disc magnets with steel flux guides interleaved and providing aheteropolar field at the rotor surface. It is so designed that the airgapfield is maximised and the magnets suffer no irreversible loss of polaris-ation on short circuit. The machine rotor is designed for a high electro-magnetic performance by ensuring that the overall geometry is suchthat the flux is maximised from a given rotor volum e, at the same timeensuring that demagnetisation is virtually impossible. A conventionalstator is used which can conveniently be chosen from a range of induc-tion machines stators.

Fig. 6Basic construction of the multistacked rotor

T

Fig. 7Cross-section an d assembly of new rotor8 permanent-magnet materialSstee l

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2 Geometry and construction of new machineThe configuration of the newdesign6 is particularly suited tothe use of barium/strontium ferrite magnets or polymer-bonded rare-earth magnets. The high coercive force can be utilised to preventdemagnetisation on removal of the rotor, or even under the applicationof a short circuit. It also becomes possible to make use of the majormagnetisation characteristic for all operating conditions. However,magnetisation subsequent to assembly is not ruled out if a suitablymatched high-energy pulse source is available.The machine can use a conventional stator with a distributedwinding. A number of axially magnetised disc magnets are arrangedalong the rotor axis with like poles facing one another and separated

by steel discs which lead the flux to pole shoes which are connectedto the discs in such a way as to provide a field which has alternatenorth and south poles around the periphery. The basic construction ofthe rotor is shown in Fig. 6, and a possible section of the steel pole anddisc assembly is shown in Fig. 7. The design of the steel structureguiding the flux to the airgap surface provides a demanding problemin 3-dimensional nonlinear analysis. The leakage flu x has to be mini-mised for good output but is still sufficiently significant to make theprediction of the working point of the magnet require a virtuallycomplete field solution for the whole machine. Parts of the steel fluxguides work in the nonlinear region depending on the load. Becauseof the nonlinearities, an iterative numerical method is required. Twoapproaches have been undertaken, the first involving a discretisationof the magnetic circuit, and obtaining a balance between the drivingH field of the magnet less the armature reaction of the stator with thereluctance of discretised flux paths. An alternative approach involvesan integral method of field solution employing Green's functions. Anadditional feature of the new design is the incorporation of a stabilis-ing device, which essentially incorporates a section of solid pole salientsection at either or both ends of the rotor. This reduces any tendencyto hunt about a synchronous speed, and if the machine is used as aninverter-fed synchronous motor it is very beneficial. It is even possible,though not necessarily desirable, to self start as a motor on a constantfrequency supply, using the eddy currents in the stabilising section.Various sizes of machine have been constructed and tested asgenerators, and the results compared with analytical predictions. Theuse of permanent capacitance across the terminals has also beenexplored both from the aspect of increased output and also for theimprovement of regulation.The steel pole pieces can be made integral with the steel flux guidesor bolted or welded for commercial construction. The whole steelmember shown in Fig. 6b can be cast or forged but for purposes ofperformance predictions the magnetisation characteristics of the steelmembers needs to be known accurately.Another feature of the new multistacked rotor is the possibilityof incorporating a damping device serving as an endring but contain-ing salient projections for each pole. If it is clamped to a basic steelsegment carrying say, poles of N polarity. The S pole projectionsoverlapping the magnet must have sufficient clearance from the end-ring poles to prevent undue leakage. The damping plate on whichpolarities are included has induced eddy currents throughout its body,and therefore tends to damp out load-angle oscillations. It even assistsgeneration by inductor alternator action. It has been shown that astrong eddy-current action as in a solid salient pole machine can bereadily achieved.The main dimensions of a typical damping device to be added atthe end of the rotor stack are presented in Appendix 8.2 togetherwith a comparison of two designs of rotor.Though the advantages of polymer-bonded rare-earth magnets areapparent, both from the aspect of increased BH product and ease ofmachining, the ultimate choice of magnet depends on cost. Sinceceramic ferrite magnets are relatively cheap, and the proportion of thewhole volume occupied by the magnets is quite significant, the rare-earth materials result in a relatively expensive mach ine.3 Performance analysis

It is clearly important to be able to . predict performance atany power factor from the design dimensions. This makes possiblean optimium choice of construction, bearing in mind the requirementto obtain sufficient output from a given frame, a prediction of voltageregulation and assessment of the advantages of using parallel capaci-tance for output improvement.Certain assumptions are needed:(a) The demagnetisation curve must be a stabilised one with a singlevalued relationship. This, of course, is dependent on the correctoperation of the magnet, so that demagnetisation within the rangeof operation is reversible.

(b ) Eddy-current losses in the pole shoes are ignored as regards theireffect on the excitation and load characteristics.Paths of integration are chosen both for the main flux and for leakagefluxes, and for each path a balance is achieved betw een the reluctancedrop (JHdl) and the resultant m.m.f. A vector of fluxes is established,and also the magnetisation characteristics for the rotor iron andmagnet are assumed. The reluctance of the stator core is ignored, sincethe object is to design the rotor, but it could be incorporated if it wasbelieved that a precise match of stator iron cross-section with rotorgeometry was required.The number of magnets in the rotor is critical, since for a givenstator length of core, excess magnet width is a source of extra costand wasted space, and an inadequate section of rotor steel could bedisastrous. Hence, a delicate balance between steel and magnet thick-ness must be achieved.The method of analysis involves finding the reluctance of therotor flux paths for a given flux-density distribution in the airgap.The leakage flux resulting from the polarisation of the magnets affectsthe density in critical parts of the magnetic circuit and hence the use-ful flux itself. If a magnetic circuit is taken to consist of a discretenumber of branches, a set of simultaneous equations relates the mag-netic potential differences throughout the parts of each branch. Ifthe reluctance of the stator core is not included the set of equationsbecomes

- / , = o ( i )for branch q.Each magnet is surrounded by its flux carrying steel configuration,the magnetic circuit of which is shown in Fig. 6b. In this magneticcircuit, each branch carries flux, and the typical elements associatedwith the various branches are now described.3.1 Magnet representation

The density in the magnet is assumed constant but at aninitially unknown value. The assumption is reasonable if the steel fluxguides are at all adequate for directing the flux. The value Hm is foundby direct reference to the B/H curve. This assumption is reasonable,since a magnet of such properties, dimensions and initial polarisationis chosen so that it operates on its major B/H loop. This is checked byexperiment, and tests down to short circuit are made.To simplify convergence, a method described in an earlier paper7 isadopted. The B/H relation normally expressed as B = n0 H + M isinstead put in the form

B = (2)in which Br is the remanence, and n', referred to as the apparentpermeability, includes the effect of the dependence of the polarisationon the //-field.3.2 Flux paths in rotor steel

The rotor has a nonmagnetic shaft, and a typical flux paththrough the rotor steel is considered in three parts having reluctancesR[, R\ and R\. The boundaries between these regions lie on circularcylinder interfaces which are each assumed equipotential. The regionswill be referred to as 'iron paths' 1, 2 and 3, which are shown in Fig. 8.Iron path 1This disc-shaped element lies in the region between the magnets. Theflux path is considered to have a reluctance in the radial direction, thereluctance in the axial direction being negligible; this path is shown inFig. 8.Iron path 2This part of the flux path is bounded by cylindrical surfaces, one beingthe surface of flux entry to the pole. This path has a relatively sh ortlength, and the flux density in it is considered to be uniform; this pathis shown in Fig. 8.Iron path 3This iron path lies in the rotor pole. The region has to be divided intoa number of sections, and each one has a different cross-sectiondependent on the machine geometry, see Fig. 9. Flux passes throughthe pole along elemental paths. It is apparent that the cross-section ofeach path depends on the distance along the path and the overallgeometry. It was found sufficiently accurate to take 15 sections eachhaving an effective length and cross-section. It is assumed that thenormal flux density entering the pole surface does not vary axially, but

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there is of course an accumulation of flux giving rise to an axiallyvarying density in the iron pole itself. The peripheral variation in fluxdensity at the pole surface is caused by armature reaction, and theshape of the pole is very important and is discussed in the nextSection.The leakage flux paths inside the rotor include the interpolar leak-age and also the leakage between the underneath of the poles and thesteel discs; their significance is v^ry appreciable.

Fig. 8Cross-section of the steel flux guides showing the three iron pathsSiiron ftath 3& iron path 2HI iron path 1

1 2 3 j n

Fig. 9Section taken for the rotor polesPROC. IEE, Vol. 126, No. 7, JULY 1979

3.3 Armature reaction and representation of stator currentThe airgap flux wave is significantly affected by load. Toaccount for this, the surface of the pole is divided into many sections,as shown in Fig. 10. Fig. 10 also shows a typical armature m.m.f. dis-tribution and the effect of pole face configuration on the fluxdistribution into the pole face.

Fig. 10Surface pole sectiona and m.m.f. distributiona Typical armature m.m.f. patternb Effect of pole shaping on airgap permeancec Airgap region devided to n flux paths

3.4 Method of solutionBecause of the nonlinearities, an interative method of solu-tion is needed, and a digital computer is conveniently employed. Therelative position in space between the armature m.m.f. and the rotoris specified by an angle i//.Th6 problem reduces to solving a set of nonlinear equations havingi// as an independent variable. The terminal voltage is computedtogether with the load power factor related to the load current andangle \}j.The procedure for computation can be summarised as follows:

(a) The constant parameters of the flux paths are calculated from thegeometry and the winding configuration.(b) Values of the stator m.m.f. distribution over the poles are found.(c) The total magnetic flux is computed through iteration by seekingthe magnet working point at each stage of the computation usingreluctivities app ropriate to the latest flux values.(d) An underrelaxation factor is required when modifying reluctivities.(e) The rotor fluxes, the flux density waveform, the terminal voltage,the load power factor, and the fundamental of the airgap fluxdensity distribution are found.if) The angle \p is changed and steps (b) to (e) repeated until therequired value of load power factor is realised.(g) The stator current is then increased and steps (b)-(f) repeateduntil the current reaches a maximum value chosen.(/) The procedure outlined above occurs automatically and the loadcharacteristic is thus generated for a constant power factor.The program flow chart is outlined in Appendix 8.1

69 3

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Table 1MACHINES OF NOVEL TYPE

Machine A Machine BRotor diameterRotor lengthAirgap w idthMagnet materialNumber of magnets

139 mm1200-25barium-ferrite4

151 mm1400-64barium-ferrite5

4 Com parison betw een measured and predicted resultsThe aim of the computer program is to predict the character-istics of the machine, and to obtain an optimal design within con-straints such as standard magnet sizes. It is, of course, vital to comparethe results of the predictions with actual machines and this has beendone for two machines referred to as machine A and machine B.The dimensions of the machines of the novel type are given inTable 1. Fig. 11 shows the r.m.s. phase voltage and the o utpu t ofmachine A plotted against current at unity power factor. I t is seenthat a satisfactory agreement between measured and computed resultsis achieved.

Only the fundamental voltage and current are used in the computa-tion and the contribution from the harmonics is ignored. Theexperimental results give the r.m.s. values and the computationalresults are expressed in r.m.s. form. In the comparison of results, theneglect of the harmonic content of the output has little, significance indesign optimisation, and the harmonics are very load dependent. Fig.12 shows the same quantities for machine B; in both Figures, the fullline represents the calculated results and the marked points the experi-

mental results. In Fig. 12, the machine efficiency (represented by thebroken line) can be seen to be flat over a wide range of current. Thisis a desirable feature for many applications.Some of the differences between the tw o designs affect the accuracyof prediction. One significant difference is the radial airgap width; inA it is 0-25 mm, whereas in B it is 0-635 mm. This results in th e reluc-tance of the iron being a less significant par t of th e wh ole, and it is, ofcourse, the less reliable part to predict, if only because of variationsand uncertainty in the iron magnetisation characteristics. In Appendix8.2, an additional possible design is compared with design A as regardsthe achievable output.The machine characteristics are clearly affected by th e changes inthe load power factor, since the armature reaction field changes itsposition in space relative to the rotor, depending on the load powerfactor. The effect of the power factor requires consideration inpermanent-magnet machines, since the rotor field is uncontrollableexcept by complicated means. Fig. 13 shows the terminal character-istics for m achine B at different load pow er factors. The graphs showthat the maximum output could be increased significantly by changingthe load power factor from lagging to leading. The output at 0-8leading current is about seven times that at 0-8 lagging. Anotherimportan t effect is the change in regulation. The voltage drop o n loadvaries from a relatively small value for unity power factor loads topoor regulation for highly lagging pow er factor loads. A slightly leadingpower factor gives negligible voltage change over a significant range.An improvement in the machine characteristics can be obtained byadding capacitors and they could be connected in series with the loador in parallel. Series compensation improves the load power factor,

and this increases the ultimate output. However, a large capacitor isneeded (say 150/xF/phase for the rated voltage of machines A and B).

3 A 5 6phase current,A0 0

Fig. 11Terminal characteristics of machine A at unity power factorpredicted resultsa Voltageb Outputo measured voltagex measured output

1 2 3 A 5 6 7phase current.AFig. 12Terminal characteristics of machine B at unity power factor

predicted resultsa Voltageb Outputo measured voltagecalculated efficiency measured output

300

3 A 5 6stator current.A

7 -

I5oc AuoE 3

21

3 * 5 6stator current,A

Fig. 13Effect of load power factora Voltage characteristics for varying load powerb Output curves for varying load power factor(i) Curve for 0-8 lagging power factor(ii) Curve for 0-9 lagging power factor. (iii) Curve for unity lagging power factor(iv) Curve for 0-9 leading power factor(v) Curve for unity leading power factor

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Parallel capacitors improve the output by supplying capacitive currentwhich assists the rotor field. Fig. 14 shows the effect of adding abalanced 3-phase capacitor of 10/iF/phase to machine B. The increasein output is very significant; again in this Figure a comparison betweencalculated and measured results is made. The effect of parallel capaci-tance is similar in effect to an increase in the load power factor asregards output. The capacitor supplies a current which is proportionalto the terminal voltage. This shift in the armature m.m.f. relative to therotor gives an increase in the no load voltage and a better regulationup to the maximum output condition.The machine outpu t could be improved by using permanent-magnetmaterials with higher maximum if//product; one possibility is the useof rare-earth magnets. Fig. 15 shows a comparison between the com-puted output of machine B using an anisotropic ferrite magnet and apolymer-binded rare-earth magnet. Curves (i) are for terminal voltageand output power for a barium-ferrite rotor, curves (ii) represent the

Fig. 14Effect of adding parallel capacitance to machine (10 nF'/phase)output (kW) against stator currentphase voltage against stator currentphase voltage against load currentx phase voltag e against stator currento phase voltage against load current

1 2 3 A 5 6o phase current,A5 r

0 1 2 3 4 5 6 7 8 9b phase current, AFig. 15Effect of changing magnet material on machine outputa Phase voltage against phase currentb Phase outout against phase current(i) Barium-ferrite rotor(ii) The same as (i) with polymer-b onded rare-earth magnets(iii) Redesigned rotor with polymer-bonded rare-earth magnets

same with the barium-ferrite magnets replaced by polymer-bondedrare-earth magnets, whereas curves (iii) are for the same rotor size withits inside dimensions redesigned having the optimum size of rare-earthmagnets. Curve (ii) shows an improvement in maximum power ofabout 35% over (i) and the regulation is improved. As a result of theimproved regulation, the outpu t at 15% regulation is increased by 42% ;in curve (iii) the m achine is redesigned, mainly by reducing the magnetsthickness. This improved the maximum outp ut by 65% over (i) andthe reduction in the magnet volume is important because of the use ofexpensive rare-earth m agnets. Its use commercially depends on relativecost, and the ferrite magnets are much cheaper. However, other factorssuch as ease of assembly are not unimportant.The two prototype machines were investigated .experimentally andtheoretically mainly using high-coercivity barium ferrite. Bothmethods proved that, with the type of magnets used, it is safe to workunder any load conditions and no process of stabilisation is needed.The magnets could be magnetised before rotor assembly without therisk of demagnetisation in air provided the correct grade of ceramicmagnets is used (high coercivity).

5 ConclusionsThe development of permanent-magnet a.c. generators hasbeen discussed. It has been shown that a particular form of permanent-magnet generator has been developed which shows promise of signifi-cant application in the future. It can make use of relatively cheapferrite magnets, or, for higher outputs in the same frame, polymer-bonded magnets may be used. The general form of the configuration

is indicated and a method of analysis discussed.A design program has been developed and tested and the effect ofcapacitance in improving output and regulation explored.

f start J

setin it ia lvalues

callFX CALCULATE

1=1 increment

increment

Fig. 16Program flow chartPROC. IEE, Vol. 126, No. 7, JULY 1979 695

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6 AcknowledgmentsThe authors wish to acknowledge the support of NRDC andSRC in this project. They are also indebted to manufacturing firmswho have liased closely in aspects of the development. The firm ofLaurence Scott and Electromotors was the first to engage in closeco-operation, and their collaboration has been much appreciated.

7 References1 MOLE, C.J.: 'Permanent magnet generators', Electr. Times, 1956, pp. 3933982 KUMAZAWA, Y.: 'Improvements in or relating to permanent magnet rotorsfor alternating-current generators', UK Patent 12048 44,197 03 BRAINARD, M.W.: 'Synchronous machines with rotating permanent-magnetfields', Part 1\ Trans. Am er. Ints. Electr. Engrs., 1952, 71 , pp. 670-6764 WHARTON, E.: 'Unusual machine configurations' in 'Small electricalmachines'. IEE Conf. Publ. 136,1976, pp. 51 -545 SIEMENS,: Siemens Rev. 1976,66 BINNS, K.J.: 'High output stabilised permanent-magnet m achine', Britishpatent 1437348, Nov. 19767 BINNS, K.J., and JABBAR, M.A.: 'Computation of the magnetic field ofpermanent magnets in iron cores',Proc. IEE, 1975,122,(12), pp. 1377-13818 Appendix8.1 Program flow chart

The procedure for computing load characteristics is shown asa flow chart in Fig. 16. The steps in the calculation are as follows:Step 1: read machine parametersStep 2: set initial values such as the value of the flux 0 crossing themagnet surface.Step 3: call subroutine FXCALC as explained below

ye s310

give estimated value 32

M = 0

3-4 3 3

This subroutine contains the instructions to calculate interactivelythe flux 0. It is calculated 16 times as a function of geometry, thereluctivities of the iron elements and the stator discrete currents.Fig. 17 shows the flow chart which describes it. It contains thefollowing instructions:Step 3.1: compare parameter L to zeroStep 3.2: set parameter M to zeroStep 3.3: calculate the magnet flux density Bm and evaluate themagnet apparent permiability n'; set parameter N and / tozero and add one to MStep 3.4: add one to /; calculate H\ j and evaluate v 3/Step 3.5: compare / to 15Step 3.6: calculate B[, and B\ , evaluate v[ and v{Step 3.7: calculate 0; add on e to NStep 3.8: compare N to 4Step 3.9: compare M to 4Step 3.10: give initial values to the reluctivities for all materialsStep 4: check convergenceStep 5: calculate the flux density waveform in the airgap; findphase voltage and power factorStep 6: compare the calculated power factor cos 8 to the desiredpower factor cos 8dStep 7: calculate Vo and i//0 which are the voltage and \jj related tothe desired power factorStep 8: print Vo and the current /Step 9: check for stopping executionStep 10: increase the angle i//Step 11: give initial value to \j/Step 12: increase current.8.2 Comparison of rotor dimensions

A comparison was made between the main dimensions of tworotors, one being design A and the other being a rotor with a differentnumber of magnets but fitting the same stator frame. The comparisonillustrates the use of the program for comparing projected designs.Machine A1 was made prior to the development of the program.The dimensions of the two machines are given in Table 2. Themaximum output of machine A is l-7kW at 1500r/min speed andunity power factor, whereas the maximum output of machine A 1under the same conditions is 1 -1 kW. The dimensions of the stabilisingdevice used in both machines are shown in Fig. 18.Table 2DIMENSIONS OF MACHINES

Machine A Machine A 1Rotor diameterRotor lengthAirgap radial lengthMagnets axial lengthSteel guide thickness (axial)Number of magnetsNumber of poles

139 mm120 mm0-25 mm15 mm7-5 mm48

139 mm120 mm0-25 mm15 mm4-5 mm58

-0-1

A B

Fig. 17Flow chart for subroutine FXCALC

Fig. 18Stabilising device used in machine A.A = 139mmB = 125 mmC = 7 mmD = 13mmT = full pole pitchx = 0-75

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