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GATE 2020 EE – Question 53

Electrical Machines · Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors · 2 marks · Multiple choice

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, $I_f$ is measured in A. Readings taken are marked as respective $(x,y)$ coordinates in the figure. Ratio of the unsaturated and saturated synchronous impedances $(Z_{s(unsat)}/Z_{s(sat)})$ of the alternator is closest to:

Diagram for GATE 2020 EE question 53
  1. 2.100
  2. 2.025
  3. 2.000
  4. 1.000

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Show answer and explanation

Correct answer: (A) 2.100

Explanation

The short-circuit characteristic is linear, with 20 A at $I_f=4$ A, i.e. 5 A per field amp. The unsaturated impedance comes from the linear part of the OCC: at $I_f=2$ A, $Z_{s(unsat)}=\frac{210}{10}=21\ \Omega$. The saturated impedance is taken at rated voltage, $I_f=8$ A, where $I_{sc}=40$ A, so $Z_{s(sat)}=\frac{400}{40}=10\ \Omega$. The ratio is $\frac{21}{10}=2.1$.