Identical series capacitors are installed at both ends of the line in Problem 5.14, providing \(40 \%\) total series compensation. Determine the equivalent \(A B C D\) parameters of this compensated line. Also calculate the impedance of each series capacitor.

Problem 5.14

A \(500-\mathrm{km}, 500-\mathrm{kV}, 60-\mathrm{Hz}\), uncompensated three-phase line has a positivesequence series impedance \(z=0.03+j 0.35 \Omega / \mathrm{km}\) and a positivesequence shunt admittance \(y=j 4.4 \times 10^{-6} \mathrm{~S} / \mathrm{km}\). Calculate:

(a) \(Z_{c}\),

(b) \((\gamma l)\), and

(c) the exact \(A B C D\) parameters for this line.