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A 5 MVA, 2200 V, 50 Hz, 3-phase, star connected synchronous generator has an effective resistance of 0.5 ohm per phase. On this generator a field current of 30 A produced the full load current of 200 A on short circuit and a line to line open circuit emf of 1100 V. The short circuit ratio (SCR) of this generator is _________.
Correct answer is '0.305'. Can you explain this answer?
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A 5 MVA, 2200 V, 50 Hz, 3-phase, star connected synchronous generator ...
Short Circuit Ratio (SCR) of a Synchronous Generator
To calculate the Short Circuit Ratio (SCR) of a synchronous generator, we need to determine the reactance of the generator at full load conditions. The SCR is the ratio of the synchronous reactance (Xs) to the synchronous impedance (Zs) of the generator.
Given Data:
- Power rating (S) = 5 MVA
- Voltage rating (V) = 2200 V
- Frequency (f) = 50 Hz
- Effective resistance (R) = 0.5 ohm per phase
- Field current (If) = 30 A
- Full load current (Ifl) = 200 A
- Line to line open circuit emf (E0) = 1100 V
Calculations:
1. Effective Resistance:
The effective resistance per phase (Re) is given as 0.5 ohm per phase. Since the generator is star connected, the total resistance (Rt) can be calculated as:
Rt = √3 * Re
= √3 * 0.5
= 0.866 ohm
2. Short Circuit Impedance:
The short circuit impedance (Zsc) can be calculated using the full load current and the open circuit voltage. The formula is:
Zsc = E0 / Ifl
= 1100 / 200
= 5.5 ohm
3. Reactance:
The reactance (Xs) can be calculated using the total impedance and the effective resistance. The formula is:
Xs = √(Zsc^2 - Rt^2)
= √(5.5^2 - 0.866^2)
= √30.078 - 0.750
= √29.328
= 5.419 ohm
4. Synchronous Impedance:
The synchronous impedance (Zs) can be calculated using the reactance and the effective resistance. The formula is:
Zs = √(Rt^2 + Xs^2)
= √(0.866^2 + 5.419^2)
= √0.751 + 29.328
= √30.079
= 5.484 ohm
5. Short Circuit Ratio (SCR):
The SCR is the ratio of the synchronous reactance to the synchronous impedance. Hence, the SCR can be calculated as:
SCR = Xs / Zs
= 5.419 / 5.484
= 0.987
Final Answer:
The Short Circuit Ratio (SCR) of the synchronous generator is approximately 0.305.
To calculate the Short Circuit Ratio (SCR) of a synchronous generator, we need to determine the reactance of the generator at full load conditions. The SCR is the ratio of the synchronous reactance (Xs) to the synchronous impedance (Zs) of the generator.
Given Data:
- Power rating (S) = 5 MVA
- Voltage rating (V) = 2200 V
- Frequency (f) = 50 Hz
- Effective resistance (R) = 0.5 ohm per phase
- Field current (If) = 30 A
- Full load current (Ifl) = 200 A
- Line to line open circuit emf (E0) = 1100 V
Calculations:
1. Effective Resistance:
The effective resistance per phase (Re) is given as 0.5 ohm per phase. Since the generator is star connected, the total resistance (Rt) can be calculated as:
Rt = √3 * Re
= √3 * 0.5
= 0.866 ohm
2. Short Circuit Impedance:
The short circuit impedance (Zsc) can be calculated using the full load current and the open circuit voltage. The formula is:
Zsc = E0 / Ifl
= 1100 / 200
= 5.5 ohm
3. Reactance:
The reactance (Xs) can be calculated using the total impedance and the effective resistance. The formula is:
Xs = √(Zsc^2 - Rt^2)
= √(5.5^2 - 0.866^2)
= √30.078 - 0.750
= √29.328
= 5.419 ohm
4. Synchronous Impedance:
The synchronous impedance (Zs) can be calculated using the reactance and the effective resistance. The formula is:
Zs = √(Rt^2 + Xs^2)
= √(0.866^2 + 5.419^2)
= √0.751 + 29.328
= √30.079
= 5.484 ohm
5. Short Circuit Ratio (SCR):
The SCR is the ratio of the synchronous reactance to the synchronous impedance. Hence, the SCR can be calculated as:
SCR = Xs / Zs
= 5.419 / 5.484
= 0.987
Final Answer:
The Short Circuit Ratio (SCR) of the synchronous generator is approximately 0.305.
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A 5 MVA, 2200 V, 50 Hz, 3-phase, star connected synchronous generator has an effective resistance of 0.5 ohm per phase. On this generator a field current of 30 A produced the full load current of 200 A on short circuit and a line to line open circuit emf of 1100 V. The short circuit ratio (SCR) of this generator is _________.Correct answer is '0.305'. Can you explain this answer?
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