ME – 092

*ME092*

I Semester M.E. (PES) Degree Examination, June/July 2015 (2K8 Scheme) ELECTRICAL MACHINE DYNAMICS Time : 3 Hours

Max. Marks : 100

Instruction : Answer any five full questions. 1. a) Derive the expression for mechanical force, in an electromechanical energy conversion system having electro static field as coupling media.

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b) In an electromagnetic relay shown in Fig. 1 the exciting coil has 1500 turns. The cross sectional area of core is 50 cm2. Reluctance of magnetic circuit is negligible. Neglect fringing effect. i) Find the inductance for an air gap of X = 0.1 cm what is the field energy ? When the coil carries a current of 3A ? What is the force on the armature under these conditions ? ii) Find the mechanical energy output when the armature moves from Xa = 1 cm to Xb = 0.5 cm assuming coil current = 3A.

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2. a) Show that a polyphase machine can be reduced to an equivalent 2 φ machine or d-q axis machine.

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b) The self and mutual inductances of a doubly excited magnetic system are LS = (0.6 + 0.2cos θ )H Lr = (0.75 + 0.3 cos2 θ )H Msr = cos θ H P.T.O.

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The winding resistances are negligible i) For θ = 60° find the magnitude and direction of torque when current is is = 20A and Ir = –10A. ii) The rotor winding is shorted and sinusoidal current of 20A rms flows in the stator winding. Find the direction and magnitude of torque at θ = 60°. 10 3. a) A plunger is working inside a magnetic circuit excited by a coil and moves against the tension of the spring. Obtain the differential equation for the motion of the plunger and emf induced in the coil.

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b) Using generalised machine theory, obtain the impedance matrix of a DC shunt motor for steady state operation. Obtain the characteristics of i) Speed Vs torque and ii) Torque Vs armature current.

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4. a) A cumulatively compound generator with its shunt field separately excited has the following parameters. rf = 100 Ω Lf = 50H ra = 0.6 Ω La = 0.03H rs = 0.4 Ω

Ls = 0.02H

Md = mutual inductance b/w series and shunt field = 1 H Kg = 100 at 100 rad/sec Ks = 0.5 at 100 rad/sec. a) The generator is running at constant speed of 100 rad/sec. and is open ckted. Shunt field is switched a/c 200 V. Find the rise in armature voltage. b) After steady state has reached in part (a) the armature is suddenly short circuited. Find an expression for the armature short ckt current.

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b) Using generalised machine theory, obtain the equivalent circuit for steady state operation of 3 φ induction motor.

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5. a) How do you classify the transients in an induction motor. Obtain expression for speed as a function of time for transients under normal working condition such as a sudden change in voltage and a sudden change in applied load torque on the shaft of the motor.

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b) A 400V 3 φ , 50Hz 4 pole induction motor has the following constants on per phase basis Rs = 0 Xs = Xr = 1.20 hm Xm = 38.8 Ω . Determine the resistance of the rotor such that the motor can be bought to a slip of 10% from standstill in minimum time. Find also the minimum time.

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6. a) Show that for a salient pole synchronous machine power as a function of power angle is given by P=

VE′f V2 ⎡ 1 1⎤ Sin δ + − ⎢ ⎥ Sin2δ under transients. X′d 2 ⎢⎣ X′q X′d ⎥⎦

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b) A 3 phase short circuit occurs at the terminals of an unloaded synchronous machine. Deduce the expression for the fault current taking into account the filed resistance. 10 7. a) For a synchronous m/c show that ψ f = L ffif +

3 Mafid 2

ψ d = Ma fif + L did

ψ q = L qiq ψ o = L oio

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b) A 3 φ alternator has per phase Xd = 1.15 pu and Xq = 0.75 pu. Draw the phasor diagram for the machine when operating at full load 0.85 p.f. lag and estimate. i) load angle ii) the regulation Neglect the effect of armature reaction and effect of saturation. _______________________

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