It is desired to transmit \(2000 \mathrm{MW}\) from a power plant to a load center located \(300 \mathrm{~km}\) from the plant. Determine the number of \(60 \mathrm{~Hz}\), threephase, uncompensated transmission lines required to transmit this power with one line out of service for the following cases:

(a) \(345 \mathrm{kV}\) lines, \(Z_{c}=\) \(300 \Omega\),

(b) \(500 \mathrm{kV}\) lines, \(Z_{c}=275 \Omega\),

(c) \(765 \mathrm{kV}\) lines, \(Z_{c}=260 \Omega\). Assume that \(\mathrm{V}_{\mathrm{S}}=1.0\) per unit, \(\mathrm{V}_{\mathrm{R}}=0.95\) per unit, and \(\delta_{\max }=35^{\circ}\).