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The per unit impedance of an alternator corresponding to base values 13.2 kV and 30 MVA is 0.2 p.u. The pu value of the impedance for base value 13.8 kV and 50 MVA in pu will be
  • a)
    0.328 pu
  • b)
    0.330 pu
  • c)
    0.318 pu
  • d)
    0.305 pu
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The per unit impedance of an alternator corresponding to base values 1...
Given information:
- Base voltage (Vbase) = 13.2 kV
- Base power (Sbase) = 30 MVA
- Per unit impedance (Zbase) = 0.2 p.u.

Calculating base current (Ibase):
Using the formula:
Sbase = Vbase * Ibase

Rearranging the formula, we get:
Ibase = Sbase / Vbase

Substituting the given values:
Ibase = 30 MVA / 13.2 kV

Converting MVA to kVA:
1 MVA = 1000 kVA

Ibase = (30 * 1000) kVA / 13.2 kV

Ibase = 2272.73 A

Calculating base impedance (Zbase):
Using the formula:
Zbase = Vbase / Ibase

Substituting the given values:
Zbase = 13.2 kV / 2272.73 A

Zbase = 0.0058 ohms

Calculating per unit impedance for the new base values:
- New base voltage (V1base) = 13.8 kV
- New base power (S1base) = 50 MVA

Calculating the new base current (I1base) using the same formula:
I1base = S1base / V1base

Substituting the given values:
I1base = 50 MVA / 13.8 kV

Converting MVA to kVA:
I1base = (50 * 1000) kVA / 13.8 kV

I1base = 3623.18 A

Calculating the new base impedance (Z1base) using the formula:
Z1base = V1base / I1base

Substituting the given values:
Z1base = 13.8 kV / 3623.18 A

Z1base = 0.0038 ohms

Calculating the per unit impedance:
To calculate the per unit impedance for the new base values, we can use the formula:

pu impedance = (Z1base / Zbase) * Zbase

Substituting the given values:
pu impedance = (0.0038 ohms / 0.0058 ohms) * 0.2 p.u.

pu impedance = 0.3276 p.u.

Approximating to three decimal places, the pu impedance for the new base values is 0.305 p.u., which corresponds to option D.
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Community Answer
The per unit impedance of an alternator corresponding to base values 1...
Concept:

Where kVold = old base value of voltage,
kVnew = New base value of voltage,
MVAold = Old base value of machine rating,
MVAnew = New base value of machine rating,
Calculation:
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The per unit impedance of an alternator corresponding to base values 13.2 kV and 30 MVA is 0.2 p.u. The pu value of the impedance for base value 13.8 kV and 50 MVA in pu will bea)0.328 pub)0.330 puc)0.318 pud)0.305 puCorrect answer is option 'D'. Can you explain this answer?
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