Question

On a base of 132 kV, 100 MVA, a transmission line has 0.2 per unit impedance. On a base of 220 kV, 50 MVA, it will have a per unit impedance of:

1. \(0.2*\frac{{50}}{{100}}*{\left( {\frac{{220}}{{132}}} \right)^2}\)
2. \(0.2*\frac{{100}}{{50}}*{\left( {\frac{{132}}{{220}}} \right)^2}\)
3. \(0.2*\frac{{50}}{{100}}*{\left( {\frac{{132}}{{220}}} \right)^2}\)
4. \(0.2*\frac{{100}}{{50}}*{\left( {\frac{{220}}{{132}}} \right)^2}\)

Answer 1

Correct Answer - Option 3 : \(0.2*\frac{{50}}{{100}}*{\left( {\frac{{132}}{{220}}} \right)^2}\)

Concept:

Per unit quantity:

Per unit quantity = Actual quantity in the units / Base (or) reference quantity in the same units

⇒ Per unit impedance Zpu = Zactual / Zbase

⇒ Zpu = ZΩ × MVAb / (kVb)2

Conversion of one per unit impedance into another per unit impedance is given by

\({{\bf{Z}}_{{\bf{pu}}}}\left( {{\bf{new}}} \right) = {{\bf{Z}}_{{\bf{pu}}}}\left( {{\bf{old}}} \right)\left( {\frac{{{\bf{MV}}{{\bf{A}}_{{\bf{new}}}}}}{{{\bf{MV}}{{\bf{A}}_{{\bf{old}}}}}}} \right){\left( {\frac{{{\bf{k}}{{\bf{V}}_{\bf{b}}}_{{\bf{old}}}}}{{{\bf{k}}{{\bf{V}}_{\bf{b}}}_{{\bf{new}}}}}} \right)^2}\)

Calculation:

Given that

Zpu old = 0.2

MVAold = 100 MVA

kVb old = 132 kV

MVAnew = 50 MVA

kVb new = 220 kV

\({{\bf{Z}}_{{\bf{pu}}}}\left( {{\bf{new}}} \right) = {{\bf{Z}}_{{\bf{pu}}}}\left( {{\bf{old}}} \right)\left( {\frac{{{\bf{MV}}{{\bf{A}}_{{\bf{new}}}}}}{{{\bf{MV}}{{\bf{A}}_{{\bf{old}}}}}}} \right){\left( {\frac{{{\bf{k}}{{\bf{V}}_{\bf{b}}}_{{\bf{old}}}}}{{{\bf{k}}{{\bf{V}}_{\bf{b}}}_{{\bf{new}}}}}} \right)^2}\)

\(Z_{pu}(new)=0.2*\frac{{50}}{{100}}*{\left( {\frac{{132}}{{220}}} \right)^2}\)