GATE EE 2020 Set 1 — Question 53
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Electrical Machines → Synchronous Machines → Synchronous Reactance & Regulation
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Question
The figure below shows the per-phase Open Circuit Characteristics (measured in V) and Short Circuit Characteristics (measured in A) of a 14 kVA, 400 V, 50 Hz, 4-pole, 3-phase, delta connected alternator, driven at 1500 rpm. The field current, is measured in A. Readings taken are marked as respective coordinates in the figure. Ratio of the unsaturated and saturated synchronous impedances of the alternator is closest to:
Correct answer
(A) 2.100
Solution
1.Identify Synchronous Impedance Definitions:
- Unsaturated synchronous impedance () is calculated from the air-gap line (linear portion of the OCC).
- Saturated synchronous impedance () is calculated at the rated voltage using the actual OCC curve.
- From the SCC, the characteristic is a straight line passing through and . Thus, .
- From the linear part of the OCC (air-gap line), it passes through . Thus, V_{oc(linear)} = rac{210}{2} I_f = 105 I_f.
- .
- The alternator is delta-connected, so the phase voltage equals the line voltage V.
- From the OCC curve, V occurs at A (point ).
- At A, the short-circuit current is A.
- .
- Ratio .
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