EJM – 159
*EJM159*
I Semester M.E. (PES) Degree Examination, March 2013 (2K8 Scheme) Power and Energy Systems PS 112 : ELECTRICAL MACHINE DYNAMICS Time : 3 Hours
Max. Marks : 100 Instruction : Answer any five full questions.
1. a) For a reluctance motor, find an expression for current i in terms of reluctance, maximum flux, angular velocity, time t and δ . Develop an expression for the average torque in terms of reluctance and maximum flux. Neglect resistance. 10 b) Two windings, one mounted on the starter and the other on the rotor have the following self and mutual inductances : Lss = 2.2 H Lrr = 1.0H Msr = 1.414 cos θ H where θ is the angle b/w the windings. The rotor is short circuited and the current in the winding is is = 14.14 sin ω t.
i) if the rotor is stationary derive the expression for the instantaneous torque on the rotor in terms of the angle θ , 10 ii) determine the average torque when θ = 45°.
2. a) Derive an expression for the average torque in a variable capacitance single phase electro static machine. 10 b) Find the electromagnetic system, shown in Fig. 2b, the air gap flux density under steady state condition is β( t ) = Bm sin ω t find i) coil voltage ii) the force of field origin as a function of time. 10
Fig. 2b
P.T.O.
*EJM159*
EJM – 159
3. a) Show that poly phase rotating axis can be transformed to stationary two axes by using parks transformation.
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b) A 230 V dc series motor running at 150 radians/sec takes 30A from supply. The combined resistance of armature and field winding is one ohm. Moment of inertia = 5 kg – m2 D = 0.02 Nm- sec/rad. i) Calculate rotational mutual inductance M and load torque. ii) If the supply voltage is suddenly reduced to 200V, the load torque remaining constant. Find the speed as a function of time. 10 4. a) Using generalised machine theory, obtain the impedance matrix of a DC shunt motor for steady state operation. Obtain also the characteristics of i) speed Vs torque and ii) torque Vs armature current. 10 b) An electromagnetic relay is excited from a voltage source, the current and flux linkages are related as i = 3λ3 (1 − x )3 where x < 1. Find the force as a function of time. 5. a) Using generalized machine theory, obtain d, q, o equations for 3 phase synchronous motor for steady state operation.
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b) Starting from the impedance matrix of a 3 phase non salient pole synchronous machine without damper winding. Derive the phasor voltage equations under balanced steady state operations. Hence draw the phasor diagram for both motor and generator. 10 6. a) Derive an expression for accelerating time of a 3 φ induction motor during starting. 12 b) A 400 V, 3 phase, 50 Hz, 4 pole induction motor has the following per phase constants Rs = 0 Xs = Xr = 1.2 Xm = 38.8 Ω . Determine the resistance of the rotor such that the motor can be brought to a step of 0.05 from standstill in minimum time. Find also the time of acceleration.
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7. a) A synchronous generator has the following constants xd = 1.0 p.u, xq = 0.5 p.u. and is delivering 1 p.u current at 0.9 p.f lag to an infinite bus of voltage 1 p.u. Find d, q, o components of current and the excitation voltage. 10 b) A 400V, 3 phase 50 Hz, 15A, 0.8 p.f squirrel cage induction motor has full load rated speed of 1450 rpm. The stator losses total 150W. Total inertia of rotating parts is 0.05 kgm2. Calculate the number of starts (by direct starting) and stops (by plugging) per minute that the motor can make without exceeding the permissible temperature. 10 —————
