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An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.
Q.
If a 3 phase fault takes place at motor terminals, the subtransient fault current is
- a)9.71 kA
- b)11.25kA
- c)1.79 kA
- d)17.25 kA
Correct answer is option 'D'. Can you explain this answer?
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An alternator and synchronous motor each rated for 50 MVA, 13.2 kV hav...
Calculation of Subtransient Fault Current in a Transmission Link
Given data:
- Alternator and synchronous motor ratings: 50 MVA, 13.2 kV
- Subtransient reactance: 20%
- Transmission link: 10% on the base of machine ratings
- Motor load: 35 MW, 0.9 p.f. lag, 12.5 kV
To calculate the subtransient fault current in the transmission link during a 3-phase fault at the motor terminals, we can follow these steps:
Step 1: Calculate the base impedance of the system
The base impedance of the system can be calculated using the alternator rating as follows:
Zbase = Vbase^2 / Sbase
where Vbase = 13.2 kV / √3 = 7.63 kV (phase voltage) and Sbase = 50 MVA
Therefore, Zbase = 7.63^2 / 50 = 1.16 Ω
Step 2: Calculate the subtransient reactance of the system
The subtransient reactance of the system can be calculated using the given data as follows:
X"d = 20% of the synchronous reactance (Xs) = 0.2 * Xs
The synchronous reactance can be calculated as:
Xs = V^2 / (3 * S)
where V is the rated voltage and S is the rated power
For the alternator and motor, Xs = 13.2^2 / (3 * 50) = 1.452 Ω
Therefore, X"d = 0.2 * 1.452 = 0.2904 Ω
Step 3: Calculate the equivalent impedance of the motor
The equivalent impedance of the motor can be calculated using the given data as follows:
Zeq = V^2 / (3 * P * cosθ)
where P is the active power (35 MW) and cosθ is the power factor (0.9 lag)
For the motor, Zeq = 12.5^2 / (3 * 35 * 0.9) = 0.149 Ω
Step 4: Calculate the fault current
The fault current can be calculated using the following formula:
I fault = V / (Zeq + Zlink + Zd)
where Zlink is the impedance of the transmission link and Zd is the subtransient reactance of the system
Zlink = 10% * Zbase = 0.1 * 1.16 = 0.116 Ω
Therefore, I fault = 12.5 / (0.149 + 0.116 + 0.2904) = 17.25 kA
Therefore, the subtransient fault current in the transmission link during a 3-phase fault at the motor terminals is 17.25 kA.
Answer: (d) 17.25 kA
Given data:
- Alternator and synchronous motor ratings: 50 MVA, 13.2 kV
- Subtransient reactance: 20%
- Transmission link: 10% on the base of machine ratings
- Motor load: 35 MW, 0.9 p.f. lag, 12.5 kV
To calculate the subtransient fault current in the transmission link during a 3-phase fault at the motor terminals, we can follow these steps:
Step 1: Calculate the base impedance of the system
The base impedance of the system can be calculated using the alternator rating as follows:
Zbase = Vbase^2 / Sbase
where Vbase = 13.2 kV / √3 = 7.63 kV (phase voltage) and Sbase = 50 MVA
Therefore, Zbase = 7.63^2 / 50 = 1.16 Ω
Step 2: Calculate the subtransient reactance of the system
The subtransient reactance of the system can be calculated using the given data as follows:
X"d = 20% of the synchronous reactance (Xs) = 0.2 * Xs
The synchronous reactance can be calculated as:
Xs = V^2 / (3 * S)
where V is the rated voltage and S is the rated power
For the alternator and motor, Xs = 13.2^2 / (3 * 50) = 1.452 Ω
Therefore, X"d = 0.2 * 1.452 = 0.2904 Ω
Step 3: Calculate the equivalent impedance of the motor
The equivalent impedance of the motor can be calculated using the given data as follows:
Zeq = V^2 / (3 * P * cosθ)
where P is the active power (35 MW) and cosθ is the power factor (0.9 lag)
For the motor, Zeq = 12.5^2 / (3 * 35 * 0.9) = 0.149 Ω
Step 4: Calculate the fault current
The fault current can be calculated using the following formula:
I fault = V / (Zeq + Zlink + Zd)
where Zlink is the impedance of the transmission link and Zd is the subtransient reactance of the system
Zlink = 10% * Zbase = 0.1 * 1.16 = 0.116 Ω
Therefore, I fault = 12.5 / (0.149 + 0.116 + 0.2904) = 17.25 kA
Therefore, the subtransient fault current in the transmission link during a 3-phase fault at the motor terminals is 17.25 kA.
Answer: (d) 17.25 kA
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An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer?
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An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. 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 An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer?.
An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. 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 An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer?.
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An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer?, a detailed solution for An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of An alternator and synchronous motor each rated for 50 MVA, 13.2 kV having subtransient reactance of 20% are connected through a transmission link of 10% on the base of machine ratings. The motor acting as a load of 35 MW at 0.9 p.f. lag and the terminal voltage is 12.5 kV.Q.If a 3 phase fault takes place at motor terminals, the subtransient fault current isa) 9.71 kAb) 11.25kAc) 1.79 kAd) 17.25 kACorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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