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*Answer can only contain numeric values

QUESTION: 1

A synchronous generator has synchronous reactance of 1.5 PU. It is connected to an infinite bus voltage 1 PU, equivalent reactance of 0.4 PU. If the maximum output is 2 PU, the load angle for an output of 1 PU is _______ degrees.

Solution:

P = P_{max} sin δ

1 = 2 sin δ

δ = 30°

*Answer can only contain numeric values

QUESTION: 2

A 12 pole 3ϕ alternator driven at speed of 500 rpm supplies power to an 8 pole, 3ϕ I.M. If the slip of the motor at full load is 3%. Calculate full load speed of the motor.

Solution:

For alternator

F = 50 Hz

For I.M

N_{r} = (1 - S) Ns = (1 - .03) × 750

∴ N_{r} = 727.5 RPM

QUESTION: 3

At a location in India, it is necessary to supply 300 kW of 60 Hz power. The only power source available operate at 50 Hz. It is decide to generate the power by means of a motor-generator set consisting of a synchronous motor driving synchronous generator. How many pole should each of the two machine have in order to convert 50 Hz power to 60-Hz power?

Solution:

∴ A 10-pole synchronous motor must be coupled to a 12-pole synchronous generator to accomplish this frequency conversion.

QUESTION: 4

A synchronous generator connected to an Infinite bus is under excited. Considering only the reactive power, from the point of the system the machine act as

Solution:

For generator

When E_{f} cosδ < V, i.e under excited generator, then reactive power (Q_{out}) is negative i.e supplying leading VARs and therefore operating at leading power factor, thus behaving like a capacitor.

*Answer can only contain numeric values

QUESTION: 5

A 30 KVA, 230 V, Y connected, 3 phase salient pale synchronous generator supplies rated load at 0.707 lagging power factor. The reactance per phase are X_{d} = 2X_{q} = 4 Ω. Neglect the armature resistance determine the power angle (in degree).

Solution:

QUESTION: 6

A 3 phase alternator has generated emf per phase of 300 V with 15% third harmonic and 10% fifth harmonic content. If the alternator is star connected, what is the value of rms line voltage?

Solution:

In star connection, the third harmonic component of the three phases cancel out at the line terminals because they are co phased.

∴ the line emf will be consisting of the fundamental and fifth harmonic only

Fundamental component E_{1} = 300 V

5^{th} harmonic component, E_{5} = 0.1 × 300 = 30 V

Emf per phase,

= 301.5 V

rms line voltage,

*Answer can only contain numeric values

QUESTION: 7

A salient pole synchronous generator has X_{d }of 0.90 PU and X_{q} of 0.6 PU. The armature resistance is negligible and generator delivers rated KVA at unity P.F and rated terminal voltage. What is the value of excitation voltage?

Solution:

Generated voltage of salient pole synchronous generator

Direct component of current

I_{d} = I_{a} sin 30.96 = 0.5145 PU

∴ |E_{F}| = 1.17 + .5145 × 0.3 = 1.324 PU

*Answer can only contain numeric values

QUESTION: 8

A 4 pole 50 Hz star connected alternator has 8 slots/pole/phase, conductor per slot being 8 and flux per pale 0.28 wb. If the winding coil span is 150°, the inductor phase voltage is ________ V.

Solution:

Given

Slots/pole/phase m = 8

Conductor/slot = 9

Coil/pole = 24

Slot = 24 × 4 = 96

Total no. of conductor z = 96 × 8 = 768

Conductor/phase = 256

Number of turn = 128

= 0.9556

E_{ph} = 4.44 × 0.9556 × 0.965 × 0.28 × 50 × 128 = 7337.09 V

QUESTION: 9

An alternator has 18 slots/pole and first coil lies in slots 1 and 16. What is the ratio of pitch factor for 3^{rd} harmonic and 5^{th} harmonic

Solution:

Coil span is 16 – 1 = 15 slots

Number of empty slots = 18 – 15 = 3 slots

Pitch factor for 3^{rd} harmonic,

= 0.707

Pitch factor for 5^{th} harmonic

= 0.259

*Answer can only contain numeric values

QUESTION: 10

A 30 KVA, 230 V, Y connected, 3 phase salient pale synchronous generator supplies rated load at 0.707 lagging power factor. The reactance per phase are X_{d} = 2X_{q} = 4 Ω. Neglect the armature resistance determine The percentage voltage regulation__________

Solution:

= 132.79 × 0.9136 + 75.307 × 4 sin (24 + 45°)

= 121.316 + 281.19

= 402.506

Percentage voltage regulation

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