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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?
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
  • 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.
Free Test
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.
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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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