GATE EE 2024 Set 1 — Question 40
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Electrical Machines → Synchronous Machines → Synchronous Reactance & Regulation
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Question
A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor via a lossless line with a per-phase inductive reactance of 5 . The per-phase synchronous reactance of the generator is 30 with negligible armature resistance. If the generator is producing the rated current at the rated voltage, then the power factor at the terminal of the generator is
Correct answer
(A) 0.63 lagging.
Solution
Given: kV, MVA, per phase, load pf lagging, so . The synchronous reactance () lies inside the machine, behind its terminals, so it does not affect the terminal power factor.1. Impedance seen from the generator terminals (per phase, star-connected):2. Load impedance. Let . Then and . The terminals see :3. Components:4. Terminal power factor:The net reactance seen from the terminals is inductive, so the power factor is lagging.Answer: (A) 0.63 lagging
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