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Permanent-magnet generators for wind turbines

J. Rizk M. H. Nagrial

School of Mechatronic, Computer and Electrical Engineering

University of Western Sydney, NepeanP.O. Box 10, Kingswood, NSW 2747

AUSTRALIAEmail: j.rizk@eng.nepean.uws.edu.au

Abstract

Wind power generates electricity from an unlimited source, the wind. This has many benefits including savingthe environment because it does not rely on fossil fuels. Also, wind turbines do not require the large areas thatconventional power stations require. As wind turbines become increasingly cost effective their use in thenational supply grid becomes greater. The finite element method is a numerical method for solvingelectromagnetic field problems, which are too complex to be solved using analytical techniques, especially thoseinvolving non-linear material characteristics. This paper deals with Finite Element analysis and the design of apermanent magnet wind generator. Finite element method is used to accurately predict the electromagneticbehaviour of the designed machine. The details of the permanent magnet generator are presented.

Key words: Finite element method, permanent magnet machines and wind generators

1 Introduction

The energy authorities in Australia have beenundertaking an active wind energy program forseveral years. The program has included windmonitoring, analysis of existing wind data,

installation and testing of small wind generators inremote homestead power systems, and installation ofup to 100 kW wind generators.

In Australia [1-3], current installed capacity is about2.7 MW. The Ten-Mile Lagoon wind farm atEsperance on Western Australia's south coast is thelargest wind farm. This wind farm has nine VestaV27 wind turbines with a total output of 2.025 MW.Total project cost, including transmission line, was$5.8 million, and electricity generation cost over thelife of the wind farm is estimated at 8 cents/kW. Thelargest individual wind generator in Australia is the

150 kW Windmaster at Malabar, Sydney, New SouthWales. A 60 kW pilot wind generator situated atBreamlea, near Geelong in Victoria, is producing95,000 kWh of electricity a year, enough to meet theneeds of 20 houses. Wind farms are vast areas ofland dotted with hundreds of wind generators, whichusually feed electricity directly into the supplynetwork. Large sections of the southern Australiancoast are ideal wind-generation sites. At Esperance inWestern Australia this country's first wind farm wasestablished in 1986. Comprising six Australian-builtWestwind turbines, the farm produces over one

million kilowatt-hours of electricity each year for thetownship of Esperance.

Wind turbines can be divided into two basic

configurations depending on the position of the rotor:horizontal axis and vertical axis (or Darieus type)wind turbines (HAWTs and VAWTs, respectively).HAWT are the most common units manufactured.Both types use aerodynamic lift to extract powerfrom the wind. They also have the same sub-systems[4-12].

Modern finite element software is extremely robustand accurate. It offers great advantage in thesimplicity of changing geometry of machinesstructure and the effects of the modifications atdifferent stages and with different parameters. In the

case of PM machines, FEM can be used to study theinfluence of design parameters such as the magnetlength, the magnet width and the magnet positionwithin the rotor core on the performance of themachine.

Due to recent development in permanent magnetmaterials, especially Nd-Fe-B, high efficiency PMgenerators can be manufactured for windapplications. The present paper is aimed to outlinethe design, analysis of such a PM generator. Thegenerator that is being used will be an 8-pole

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permanent magnet generator rated at 5 kW and usingNdFeB for the field excitation. This is beingdesigned using a new finite element packagedeveloped by MSC-Ansoft. The generator will becoupled to the blades via a 1:5.5 gearbox. This willgive a higher rotational speed to the generator toallow it to generate more electricity at lower windspeeds. Figure 1 a) presents the cross section of thedesigned permanent magnet generator.

2 Finite element method

The Finite element method is a numerical method ofsolving linear and non-linear partial differentialequations. It offers an accurate and powerful designtool, allowing material properties, nonlinearities and

structural details to be taken into account. Themethod basically involves the discretisation of themachine cross section into smaller finite elements.The spatial variation of magnetic potentialthroughout the machine is described by a non-linearpartial differential equation derived from Maxwellequation [14-19].

The finite element method (FEM) can be used tochange the structure of the machine, the materialproperties, and the excitation in the rotor and thestator of machine. The solution of a continuumproblem by the FEM process always follows anorderly step-by-step process [20-22]. The first step is

to divide the continuum or solution region intoelements. A variety of element shapes may be used,and different element shapes may be employed in thesame solution region. The finite element modelcontains information about the device to be analysedsuch as geometry (subdivided into finite elements),materials, excitations, and constraints. The materialproperties, excitations, and constraints can often beexpressed quickly and easily, but geometry is usuallydifficult to describe. The finite elements can be verysmall where small geometric details exist, such as airgaps and can be much larger elsewhere.

The corners of the finite elements are called gridpoints or nodes. These nodes are assigned to eachelement and then the interpolation function chosen torepresent the variation of the field variable over theelement. The field variable may be scalar, a vector,or a higher order tensor. Often, the polynomials areselected as interpolation functions for the fieldvariable because they are easy to integrate and

differentiate. The degree of the polynomial chosendepends on the number of nodes assigned to theelement, the nature and number of unknowns at eachnode, and certain continuity requirements imposed atthe nodes and along the element boundaries. Themagnitude of the field variables, as well as themagnitude of its derivatives, may be the unknowns atthe nodes. Once the finite element model has beenestablished (i.e. once the elements and theirinterpolation functions have been selected), thematrix equations expressing the properties of theindividual elements are determined.

To find the properties for the overall system modeledby the network of elements, the element propertiesmust be assembled. The matrix equations expressingthe behaviour of the elements are combined and formthe matrix equations expressing the behaviour of theentire system. The matrix equations for the system

have the same form as the equations for an individualelement, except that they contain many more termsbecause they include all nodes.

Before the system equations are ready for solutionthey must be modified to account for the boundaryconditions of the problem. Each degree of freedom ata grid point may be unconstrained (unknown) orconstrained. The assembly process gives a set ofsimultaneous equations that we solve to obtain theunknown nodal values of the problem. If the problemdescribes steady or equilibrium behaviour then wemust solve a set of linear or non-linear algebraic

equations. If the problem is unsteady, the nodalunknowns are a function of time, and a set of linearor non-linear ordinary differential equations must besolved.

The solution of the system equations can be used tocalculate other important parameters. For example, inelectromagnetic problems, the nodal unknowns arethe components of magnetic flux density. From thesecomponents the induction, the torque, and otherelectromagnetic parameters can be calculated [7-9].Fig. 1 shows the cross section and the fluxdistribution of the designed machine. Fig. 2 shows

the cogging torque of the machine when it is excitedonly with the permanent magnet and Fig. 3 shows themagnetic flux density around the core. In the case ofwind generator the cogging torque is a veryimportant parameter as it is the parameter that candefine the minimum strength of wind that can beenough to move the rotor of the generator.

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a) b)

Figure 1: Cross section of the wind generator a) and the flux distribution b)

Figure 2: Cogging torque in the designing wind generator

Figure 3: Magnetic flux density in the stator yoke

-2.0

-1.0

0.0

1.0

2.0

0 2 4 6 8 10 12 14 16

Theta, deg

C

og.

torque,

N.m

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3. Permanent magnet generators

Permanent magnet (PM) machines are a well-knownclass of rotating and linear electric machines used inboth the motoring and generating modes. PM

machines have been used for many years inapplications where simplicity of structure and a lowinitial cost were of primary importance. Morerecently, PM machines have been applied to moredemanding applications, primarily as the result of theavailability of low-cost power electronic controldevices and the improvement of permanent magnetcharacteristics. In general, modern PM machines arecompetitive both in performance and cost with manytypes of machines.

The term permanent magnet machine is used toinclude all electromagnetic energy conversion

devices in which the magnetic excitation is suppliedby a permanent magnet. Energy converters usingpermanent magnets come in a variety ofconfigurations and are described by such terms asmotor, generator, alternator, stepper motor, linearmotor, actuator, transducer, control motor,tachometer, brushless dc motor, and many others.Permanent magnet machines are rapidly findingnumerous applications as alternators, automotiveapplications, vehicular electric drive motors, smallappliances, and control motors, printed circuit motorsand computer and robotics applications. The stator ofthe machine is identical to the stator of a multiphaseAC machine. The new component is the rotor, which

in contrast to conventional rotors relies on permanentmagnets as the source of excitation rather than anelectric current in windings. The optimum rotorconfiguration, rotor electromagnetic and mechanicaldesign, and the stator electromagnetic design must bematched to achieve a higher efficient machine of thedesired load characteristics, high power factor, andhigh efficiency and performance.

The PM machines can be surface mounted or exteriorPM machines and interior PM machines [14, 19].Inburied or interior PM machines the machine isrobust, rugged and well-suited for flux weakeningcontrol for a wide speed-torque range, essential formany applications. The surface-mounted PMmachine has magnets at the airgap surface and isliable to damage at high speeds or even in theassembly and fabrication process. The rotor structurefor an interior PM rotor will tend to have a smoothrotor design similar to or better than inductionmachines. Thus, windage losses will be equal to orlower than those of conventional induction machines.In this paper we present the performance of designedinterior permanent magnet machine. The statoremployed is of an equivalent induction motor, ratedat the same power.

Modern wind turbines can be divided into two basicconfigurations depending on the position of the rotor:horizontal axis and vertical axis (or Darieus type)wind turbines (HAWTs and VAWTs, respectively).HAWT are the most common units manufactured.Both types use aerodynamic lift to extract powerfrom the wind. They also have the same sub-systems,illustrated in figure 4.

The wind turbine will be built with 2 blades takenfrom a Bell helicopter. The tower will be 9m hightruss construction to allow greater weight above.This wind turbine that will be built is an upwind

horizontal axis wind turbine (HAWT). This meansthat the blades will be subject to the wind before therest of the wind turbine. Figure.5 shows an upwind &downwind HAWT. [9]

4. Conclusions

A permanent magnet wind generator is analysedusing the finite element method. The simulationresults are being used in the fabrication of themachine. The fabricated machine will be tested andthe experimental results will be reported soon.

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Figure 4: Schematic overview of wind turbine components

Figure 5: Upwind HAWT and Downwind HAWT

6. References

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2. Lemon J. H. Ecologically SustainableDevelopment (ESD) working groups. Finalreport, energy production, Canberra, 16-18April, 1991

3. Kaneff S. Renewable Energy options forsustainability. PP 48-100 Canberra: Center forresources and Environmental studies AustralianNational University.

4. Wind Energy Technical Information Guide.SERI, Golden Colorado, USA, December 1989.

5. World Energy Council New Renewable EnergyResources, Kogan Page Limited, 1994.

6. Paul Gipe, Wind energy comes of age, JohnWiley & Sons, INC, 1995.

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7. Michael Peevey, address before American WindEnergy Association conference, Windpower, 91,palm Springs, CA, September, 1991

8. Grosveld, F. W., 1985 Prediction of BroadbandNoise from Horizontal Axis Wind Turbines,AIAA Journal of Propulsion and Power, Vol. 1,No 4.

9. Richardson, D. R and McNerney, G. M. WindEnergy Systems. IEEE, March, 1993

10. Eggleston, D.M and Stoddard, F.S. WindTurbine Engineering Design. Van NostrandReinhold, 1987.

11. Nacfaire, H. Grid-Connected Wind Turbines.Elsevier Applied Science Publishers LTD, 1988.

12. Jenkins, N. Engineering Wind Farms. PowerEngineering, April 1993.

13. Bureau of Meteorology: Wind Data in PenrithArea: 01/01/96 27/09/98

14. J. Rizk and M. Nagrial, Analysis and design of

permanent magnet machines using finite elementmethod, Power Systems World 97, Sep. 6-12,1997, Baltimore, pp USA, IMO3.2-1 IMO3.2-7

15. L. Chang, A. R. Easthan and G. E. Dawson(1989) "Permanent Magnet Synchronous Motor,Finite Element Torque calculation, San Diego,IEEE/IAS, October, pp. 69-73.

16. M. Marinescu and N. Marinescu (1988)"Numerical computation of torque in PMMotors", IEEE, Mag. vol. 29 No.1, pp. 463-466.

17. J. Mizia, K. Adamiak, A.R. Easthan and G.E.Dawson (1988) "Finite Element Force

calculation: comparison of methods for ElectricMachines", vol. MAG-24, No.1, pp. 447-450.

18. J. Rizk and M. H. Nagrial (1997) FiniteElement Modeling of permanent magnetmachines Third International Conference onModeling and Simulation (MS97),), Melbourne,Australia, pp. 295-299, Oct. 29-31

19. J. Rizk and M. H. Nagrial (1997) Torquecalculation in permanent magnet machines usingFinite Element Method 2nd International Powerelectronics and motion control conference,IPEEM97, Nov 3-6, 1997, Hangzhou, China

20. P.P. Silvester (1983), Finite elements forelectrical engineers, Cambridge UniversityPress.

21. T. Sebastian, G. R. Slemon and M. A. Rahman(1986) Modeling of permanent magnetsynchronous motors, IEEE, Mag. vol. 22No.5, pp. 1069-1071.

22. D. A. Lowther, and P. P. Silvester, (1986)Computer-aided Design in Magnetics,

Springer-Verlag, New York.23. L.Chang, A.R.Easthan, and G. E. Dawson

(1989) "Permanent magnet synchronous motor.Finite element torque calculation, San Diego,IEEE/IAS, October, pp. 69-73.

24. M.Marinescu and N. Marinescu (1988)"Numerical computation of torque in PMmotors", IEEE, Mag. vol. 29 No.1, pp. 463-466.

25. J.Mizia, K. Adamiak, A.R. Easthan and G.E.Dawson (1988) "Finite element forcecalculation: comparison of methods for electricmachines", vol. MAG-24, No.1, pp. 447-450.

APPENDIX A GENERATOR SPECIFICATIONS

poles number 8 poleRated power, kW 5 kWRated speed 750 RpmRated voltage, v 415 v (Delta connected), 720 v (Y connected)

Stator inner diameter, mm 165Length of stator stack, mm 100Air gap length, mm 0.6Stator slots 36No of turns/slot 96

Phase resistance, 3.7 Magnet dimensions, mm 15X30X100