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A 3-phase salient pole alternator has direct axis reactance as 0.4 p.u. and quadrature axis reactance as 0.2 p.u. The excitation voltage is 1.3 p.u. and terminal voltage is held at 1 p.u. For the maximum power output, the rotor angle should be _______.
- a)40.8⁰
- b)90⁰
- c)63.06⁰
- d)50.86⁰
Correct answer is option 'C'. Can you explain this answer?
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A 3-phase salient pole alternator has direct axis reactance as 0.4 p....
For a salient pale alternator, the output power is
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P=3.25sinδ+1.25sin2δ
Far maximum power output,
=3.25cosδ+2.5cos2δ=0
=3.25cosδ+2.5cos2δ=02.5cos28+3.25cosδ=0
2.5[2cos2δ−1]+3.25cosδ=0
⇒5cos2δ−2.5+3.25cosδ=0
Let cos δ=x 5x2 + 3.25x - 2.5 = 0
x=0.453,−1.103( rejected )
cosδ=0.453
δ=cos−1[0.453]
δ = 63.06⁰
Most Upvoted Answer
A 3-phase salient pole alternator has direct axis reactance as 0.4 p....
Solution:
Given data:
Xd = 0.4 p.u.
Xq = 0.2 p.u.
E = 1.3 p.u.
Vt = 1 p.u.
The maximum power output of a salient pole alternator is obtained when the rotor angle (δ) is equal to the load angle (θ). The load angle is the angle between the terminal voltage (Vt) and the internal generated voltage (E) in the q-axis.
The expression for the load angle is given by:
θ = tan⁻¹((Esinδ)/(Vt – Ecosδ))
For maximum power transfer, dP/dδ = 0.
The expression for dP/dδ is given by:
dP/dδ = (E²Vt/Xd)sin2δ – (E²/Xd)sinδcosδ
Equating dP/dδ to zero, we get:
(E²Vt/Xd)sin2δ – (E²/Xd)sinδcosδ = 0
sinδ(cosδ – (Vt/Xd)sinδ) = 0
sinδ = 0 or cosδ = (Vt/Xd)sinδ
If sinδ = 0, then δ = 0⁰ or 180⁰, which corresponds to no power transfer.
Therefore, cosδ = (Vt/Xd)sinδ
cosδ = (1/0.4) × 0.2 = 0.5
δ = cos⁻¹(0.5) = 60.06⁰
Hence, the correct option is (C) 63.06⁰.
Given data:
Xd = 0.4 p.u.
Xq = 0.2 p.u.
E = 1.3 p.u.
Vt = 1 p.u.
The maximum power output of a salient pole alternator is obtained when the rotor angle (δ) is equal to the load angle (θ). The load angle is the angle between the terminal voltage (Vt) and the internal generated voltage (E) in the q-axis.
The expression for the load angle is given by:
θ = tan⁻¹((Esinδ)/(Vt – Ecosδ))
For maximum power transfer, dP/dδ = 0.
The expression for dP/dδ is given by:
dP/dδ = (E²Vt/Xd)sin2δ – (E²/Xd)sinδcosδ
Equating dP/dδ to zero, we get:
(E²Vt/Xd)sin2δ – (E²/Xd)sinδcosδ = 0
sinδ(cosδ – (Vt/Xd)sinδ) = 0
sinδ = 0 or cosδ = (Vt/Xd)sinδ
If sinδ = 0, then δ = 0⁰ or 180⁰, which corresponds to no power transfer.
Therefore, cosδ = (Vt/Xd)sinδ
cosδ = (1/0.4) × 0.2 = 0.5
δ = cos⁻¹(0.5) = 60.06⁰
Hence, the correct option is (C) 63.06⁰.
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A 3-phase salient pole alternator has direct axis reactance as 0.4 p.u. and quadrature axis reactance as 0.2 p.u. The excitation voltage is 1.3 p.u. and terminal voltage is held at 1 p.u. For the maximum power output, the rotor angle should be _______.a)40.8⁰b)90⁰c)63.06⁰d)50.86⁰Correct answer is option 'C'. Can you explain this answer?
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A 3-phase salient pole alternator has direct axis reactance as 0.4 p.u. and quadrature axis reactance as 0.2 p.u. The excitation voltage is 1.3 p.u. and terminal voltage is held at 1 p.u. For the maximum power output, the rotor angle should be _______.a)40.8⁰b)90⁰c)63.06⁰d)50.86⁰Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 3-phase salient pole alternator has direct axis reactance as 0.4 p.u. and quadrature axis reactance as 0.2 p.u. The excitation voltage is 1.3 p.u. and terminal voltage is held at 1 p.u. For the maximum power output, the rotor angle should be _______.a)40.8⁰b)90⁰c)63.06⁰d)50.86⁰Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3-phase salient pole alternator has direct axis reactance as 0.4 p.u. and quadrature axis reactance as 0.2 p.u. The excitation voltage is 1.3 p.u. and terminal voltage is held at 1 p.u. For the maximum power output, the rotor angle should be _______.a)40.8⁰b)90⁰c)63.06⁰d)50.86⁰Correct answer is option 'C'. Can you explain this answer?.
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