Fall 2002 Solutions Final Exam

Fall 2002 Solutions Final Exam - MCGILL UNIVERSITY FACULTY...

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MCGILL UNIVERSITY FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING FINAL EXAM POWER ENGINEERING, ECSE-361A DECEMBER 6, 2002: TIME 9:00 ANSWER ALL SIX QUESTIONS OPEN BOOK AND NOTES EXAM MAXIMUM POINTS = 75 Examiner: Prof. F.D. Galiana Associate Examiner: Prof. B.T. Ooi Problem 1 (10) Show how a salient pole synchronous motor can produce non-zero average torque even if the rotor current is zero. Use a simple machine model to demonstrate this. Sol: A simple machine model of a salient pole motor has an inductance matrix of the form, cos2 cos () cos ss sr sr rr LL L θθ θ  =   The torque with zero rotor current and non-zero stator current is then given by, 22 1 (,) ( c o s2) s i n2 2 ss s s s s s d Ti Li d == Thus if the stator current is a sinusoid of the form, 2 s in s it I t ω = then letting 0 m tt θω =+ , the torque becomes, 2 0 2 0 2 0 2 00 s in2 2s i n ( ) s i n ( 2 ) (1 cos(2 2 ))sin(2 ) (sin(2 ) sin(2 )cos(2 2 )) 11 (sin(2 ) sin(2 2 2 ) sin(2 2 2 )) ss s ss s s m ss s s m ss s m m s ss s m m s m s Tt LI t t t t t t t t t t t t ωθ ωω =− + + + + + + Non-zero time-average torque occurs therefore if ms .
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Problem 2 (15) A three-phase, 1kV, 20 kVA, wound rotor, induction motor operates at a no-load speed of 1490 rpm. The device operates at nominal voltage and consumes 0.9 pu real power at a lagging power factor of 0.8. The frequency of the rotor currents is 3 Hz. (a) Estimate the frequency of the stator currents and the number of poles. (b) Find the speed of rotation in rpm. (c) Find the torque in Nm produced by the motor. Sol: Part (a): At no-load the motor has no mechanical load other than that of the friction of the rotating shaft. We know that at or slightly above zero torque the motor should operate
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Fall 2002 Solutions Final Exam - MCGILL UNIVERSITY FACULTY...

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