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assignment3 - (2 Eq(2 can be split into two as follows L...

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1 ASSIGNMENT 3 Trigonometric Identities cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-cosAsinB Question 1 The inductance of a single-phase reluctance machine is: ] 2 cos [ d B A a L L L θ + = The single-phase winding is excited by a current t I i a ω cos = Let the rotor turn at synchronous speed so that δ ω θ + = t d (i) What is the electromechanical torque e T ? (ii) What is the time invariant component ) ( δ f T ave e = ? Sketch ) ( δ f T ave e = for o 180 . . . 180 + ° δ . (iii) What are the even harmonic pulsating components of torque, even e T ? (iv) The reluctance motor has a moment of inertia J and drives a load L T . The mechanical equation of motion is: L e m T T dt d J = ω (1) Let the rotor speed be the sum of a term at synchronous speed ω and perturbation terms m ω Δ due to the even harmonic pulsating torque components. Substituting in (1) L even e ave e m T T T dt
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