*EJM152*

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I Semester M.E. (PE) Degree Examination, March 2013 (2K8 Scheme) Power Electronics PE-113 : GENERALIZED MACHINE THEORY Time : 3 Hours

Max. Marks : 100

Instruction : Answer any five full questions. 1. a) An electromagnetic relay is existed from a voltage source, the current and the flux linkages are related as i = 3 λ 3(1 – x) 3 where x < 1. Find the force as a function of time.

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b) Two windings one mounted on the stater and the other on the rotor have the following self and mutual inductances Ls = 2.2H, LR = 1.2H, MSR = 1.212, cos θ H where θ is the angle between the axes of windings. The rotor winding is short circuited and the current in the stater windings is Is = 12.12 sin ωt. 14 i) If the rotor is stationary derive an expression for the instantaneous torque on the rotor in terms of angle θ . ii) Determine the average torque when θ = 45°. iii) If the rotor is allowed to move will it rotate continuously or will it tend to come to rest ? If it comes to rest at what value of θ rotor comes to rest ? 2. a) A plunger is working inside a magnetic circuit existed by a coil and moves against the tension of the spring. Obtain the differential equation for motion of the plunger and emf induced in the coil. 10 b) Derive an expression for the average torque in a variable capacitance single phase electrostatic machine. 10 3. a) Derive the voltage equations for a KRON’s primitive machine.

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b) Obtain parks transformation (d, q, o) matrix of a 3-phase balanced system.

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4. With usual notations, obtain frequency response of an electrostatic microphone.

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5. a) For a single axis D.C. machine get the simplified block diagram (linearized) representation, involving field control, the machine being treated as a shunt motor using usual notations. 10 b) Show that separately existed motor with armature control driving inertia load can be treated as capacitive loading. Also obtain the simplified block diagram of armature control. 10 P.T.O.

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*EJM152*

6. a) Using generalized machine theory obtain the impedance matrix and the equivalent circuit of a 3 φ induction motor.

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b) Show that for the stator and rotor equations of an n-m symmetrical machine can be expressed as V = R I + T = Jθ + Dθ + Kθ −








d LI dt

d ⎤ (LI)⎥ with usual notations. ⎣ dθ ⎦

1 ⎡I 2⎢

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7. a) For a single axis dc machine with ‘M’ field windings derive an expression for the single voltage VK for the K th field winding with normal assumption. Also draw the block diagram representation. 14 b) Enumerate the steps involved in the analysis of N-M symmetrical machine along with the assumptions.

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