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A 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu is
- a)0.673 p.u.
- b)0.166 p.u.
- c)0.115 p.u.
- d)0.217 p.u.
Correct answer is option ''. Can you explain this answer?
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Calculation of Saturated Synchronous Impedance
Given parameters:
- Rated power (S) = 100 kVA
- Rated voltage (V) = 415V
- Open-circuit voltage (Voc) at If = 15A = 415V
- Armature current (Ia) at If = 10A = Rated armature current
- Armature resistance (Ra) = 0.1 pu
Step 1: Calculation of synchronous reactance (Xs)
The open-circuit voltage is given by the equation:
Voc = V + jIXs
where I is the excitation current and Xs is the synchronous reactance.
At If = 15A, Voc = 415V
415 = 415 + j15Xs
Xs = 0
Therefore, Xs at If = 15A is 0.
Step 2: Calculation of armature leakage reactance (Xl)
The armature leakage reactance (Xl) is given by the equation:
Xl = Ra / (Ia^2)
At If = 10A, Ia = Rated armature current
Xl = 0.1 / (Rated armature current)^2
Step 3: Calculation of saturated synchronous impedance (Zs)
The saturated synchronous impedance (Zs) is given by the equation:
Zs = Voc / (sqrt(3) * Ia)
At If = 10A, Ia = Rated armature current
Zs = 415 / (sqrt(3) * Rated armature current)
Substituting the value of Xl in the above equation, we get:
Zs = (415 / sqrt(3)) * (1 + jXl * sqrt(3))
Zs = 0.115 p.u. + j0.198 p.u.
Therefore, the saturated synchronous impedance in p.u. is 0.115 p.u. (Option C).
Given parameters:
- Rated power (S) = 100 kVA
- Rated voltage (V) = 415V
- Open-circuit voltage (Voc) at If = 15A = 415V
- Armature current (Ia) at If = 10A = Rated armature current
- Armature resistance (Ra) = 0.1 pu
Step 1: Calculation of synchronous reactance (Xs)
The open-circuit voltage is given by the equation:
Voc = V + jIXs
where I is the excitation current and Xs is the synchronous reactance.
At If = 15A, Voc = 415V
415 = 415 + j15Xs
Xs = 0
Therefore, Xs at If = 15A is 0.
Step 2: Calculation of armature leakage reactance (Xl)
The armature leakage reactance (Xl) is given by the equation:
Xl = Ra / (Ia^2)
At If = 10A, Ia = Rated armature current
Xl = 0.1 / (Rated armature current)^2
Step 3: Calculation of saturated synchronous impedance (Zs)
The saturated synchronous impedance (Zs) is given by the equation:
Zs = Voc / (sqrt(3) * Ia)
At If = 10A, Ia = Rated armature current
Zs = 415 / (sqrt(3) * Rated armature current)
Substituting the value of Xl in the above equation, we get:
Zs = (415 / sqrt(3)) * (1 + jXl * sqrt(3))
Zs = 0.115 p.u. + j0.198 p.u.
Therefore, the saturated synchronous impedance in p.u. is 0.115 p.u. (Option C).
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A 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu isa)0.673 p.u.b)0.166 p.u.c)0.115 p.u.d)0.217 p.u.Correct answer is option ''. Can you explain this answer?
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A 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu isa)0.673 p.u.b)0.166 p.u.c)0.115 p.u.d)0.217 p.u.Correct answer is option ''. 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 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu isa)0.673 p.u.b)0.166 p.u.c)0.115 p.u.d)0.217 p.u.Correct answer is option ''. 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 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu isa)0.673 p.u.b)0.166 p.u.c)0.115 p.u.d)0.217 p.u.Correct answer is option ''. Can you explain this answer?.
A 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu isa)0.673 p.u.b)0.166 p.u.c)0.115 p.u.d)0.217 p.u.Correct answer is option ''. 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 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu isa)0.673 p.u.b)0.166 p.u.c)0.115 p.u.d)0.217 p.u.Correct answer is option ''. 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 100kVA, 415V, Y-connected synchronous machine generates rated open-circuit voltage of 415V at a field current of 15A. The short circuit armature current at a field current of 10A is equal to its rated armature current. The saturated synchronous impedance in p.u., if armature resistance is 0.1pu isa)0.673 p.u.b)0.166 p.u.c)0.115 p.u.d)0.217 p.u.Correct answer is option ''. Can you explain this answer?.
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