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final 2004

# final 2004 - 1 DEPARTMENT OF ELECTRICAL AND COMPUTING...

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1 DEPARTMENT OF ELECTRICAL AND COMPUTING ENGINEERING FINAL EXAMINATION ELECTROMECHANICAL ENERGY CONVERSION ECSE-462B Examiner: Professor B.T.Ooi Associate Examiner: Professor F.D.Galiana Date: December 10, 2004 Time : AM (3 hours) INSTRUCTIONS: OPEN BOOK EXAMINATION Answer all six questions. Trigonometric Identities cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-cosAsinB [ Systeme Internationale or MKS units are used. Field vectors are represented by bold letters, for example B and K . The directional vectors in cylindrical co-ordinates are: u r , u ϕ and u z . The superscript T denotes “transpose”. State vectors are also represented in bold, for example v dq , λ dq , i dq .] Questions #1 & #2 refer to an electric machine consisting of a cylindrical rotor inside an annular stator. They are separated by an airgap “g” at a mean radius “R”. The stack length is “L”. The permeability of the iron is infinite and the permeability of the airgap is μ o . Question 1 An electric machine has only one 4-pole stator winding carrying current i S α which produces a sheet current K S α = u z i S α B S sin( 2 ϕ ) where B S is the Fourier coefficient of the fundamental space harmonic and where the position ϕ =0 0 is fixed to the stator . (a) What is the magnetic field density distribution B S α around the airgap? The rotor has two 4-pole windings carrying currents i R α and i R β which produce sheet currents K R α = u z i R α B R sin(2 ϕ 1 + δ ) and K R β = u z i R β B R sin(2 ϕ 1 + δ +90 0 ), where B R is the Fourier coefficient of the fundamental space harmonic and where the position ϕ 1 =0 0 is fixed to the rotor .

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2 (b) What are the magnetic field density distributions B
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final 2004 - 1 DEPARTMENT OF ELECTRICAL AND COMPUTING...

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