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Three synchronous generators, each of which is rated to 100 MVA, 11 KV, have an impedance per unit of 0.15. If all three generators are replaced by a single equivalent generator, what will be the effective per unit impedance of each generator?
- a)0.45
- b)0.15
- c)0.025
- d)0.05
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Three synchronous generators, each of which is rated to 100 MVA, 11 KV...
Using Thevenin's Theorem, Vth = V all the three impedances will be in parallel.
Single line diagram:
So, equivalent p.u. impedance of each generator is
Zth = Zn / 3 = 0.15 / 3 = 0.05 pu
Key Points
Zth = Zn / 3 = 0.15 / 3 = 0.05 pu
Key Points
- All generators are connected in parallel to increase current going to the line because all generators are at equal voltages.
- Generators are shown with their impedances in a single line diagram.
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Community Answer
Three synchronous generators, each of which is rated to 100 MVA, 11 KV...
Calculation:
Given data:
- Number of generators: 3
- Rating of each generator: 100 MVA
- Voltage rating: 11 kV
- Impedance per unit: 0.15
To find:
- Effective per unit impedance of each generator when replaced by a single equivalent generator
Step 1: Calculation of equivalent impedance
The total impedance of the three generators connected in parallel can be calculated as follows:
Zeq = Zg / N
Where,
Zeq = Equivalent impedance
Zg = Impedance of a single generator
N = Number of generators
Given that Zg = 0.15, and N = 3, we can substitute these values into the equation:
Zeq = 0.15 / 3
Zeq = 0.05
Therefore, the equivalent impedance of the three generators connected in parallel is 0.05 per unit.
Step 2: Calculation of effective per unit impedance
To find the effective per unit impedance of each generator, we need to divide the equivalent impedance by the number of generators:
Effective per unit impedance = Zeq / N
Given that Zeq = 0.05 and N = 3, we can substitute these values into the equation:
Effective per unit impedance = 0.05 / 3
Effective per unit impedance = 0.0167
Therefore, the effective per unit impedance of each generator when replaced by a single equivalent generator is 0.0167.
Step 3: Comparing the options
a) 0.45 - This is not the correct answer.
b) 0.15 - This is not the correct answer.
c) 0.025 - This is not the correct answer.
d) 0.05 - This is the correct answer.
Therefore, option D, 0.05, is the correct answer.
Conclusion:
When three synchronous generators with an impedance per unit of 0.15 are replaced by a single equivalent generator, the effective per unit impedance of each generator becomes 0.05.
Given data:
- Number of generators: 3
- Rating of each generator: 100 MVA
- Voltage rating: 11 kV
- Impedance per unit: 0.15
To find:
- Effective per unit impedance of each generator when replaced by a single equivalent generator
Step 1: Calculation of equivalent impedance
The total impedance of the three generators connected in parallel can be calculated as follows:
Zeq = Zg / N
Where,
Zeq = Equivalent impedance
Zg = Impedance of a single generator
N = Number of generators
Given that Zg = 0.15, and N = 3, we can substitute these values into the equation:
Zeq = 0.15 / 3
Zeq = 0.05
Therefore, the equivalent impedance of the three generators connected in parallel is 0.05 per unit.
Step 2: Calculation of effective per unit impedance
To find the effective per unit impedance of each generator, we need to divide the equivalent impedance by the number of generators:
Effective per unit impedance = Zeq / N
Given that Zeq = 0.05 and N = 3, we can substitute these values into the equation:
Effective per unit impedance = 0.05 / 3
Effective per unit impedance = 0.0167
Therefore, the effective per unit impedance of each generator when replaced by a single equivalent generator is 0.0167.
Step 3: Comparing the options
a) 0.45 - This is not the correct answer.
b) 0.15 - This is not the correct answer.
c) 0.025 - This is not the correct answer.
d) 0.05 - This is the correct answer.
Therefore, option D, 0.05, is the correct answer.
Conclusion:
When three synchronous generators with an impedance per unit of 0.15 are replaced by a single equivalent generator, the effective per unit impedance of each generator becomes 0.05.
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Three synchronous generators, each of which is rated to 100 MVA, 11 KV, have an impedance per unit of 0.15. If all three generators are replaced by a single equivalent generator, what will be the effective per unit impedance of each generator?a)0.45b)0.15c)0.025d)0.05Correct answer is option 'D'. Can you explain this answer?
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