Exam 3: Transmission Line Parameters

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$\begin{aligned}& R_{d c, 20^{\circ} \mathrm{C}}=\frac{P_{20^{\circ} \mathrm{C}} l}{A}=\frac{(17.00)(1000 \times 1.016)}{1113 \times 10^{3}}=\underline{\underline{0.01552}} \frac{\Omega}{1000^{1}} \\& R_{d c, 50^{\circ} \mathrm{C}}=R_{d c, 20^{\circ} \mathrm{C}}\left(\frac{50+T}{20+T}\right)=0.01552\left(\frac{50+228.1}{20+228.1}\right) \\& R_{d c, 50^{\circ} \mathrm{C}}=(0.01552)(1.1209)=\underline{0.01739} \frac{\Omega}{1000^{1}} \\& \frac{R_{60 \mathrm{HƵ}, 50^{\circ} \mathrm{C}}}{R_{d c, 50^{\circ} \mathrm{C}}}=\frac{0.0951 \Omega / \mathrm{mi}}{\left(0.01739 \frac{\Omega}{1000^{1}}\right)\left(5.28 \frac{1000^{1}}{\mathrm{mi}}\right)}=\frac{0.0951}{0.0918}=\underline{\underline{1.035}}\end{aligned}$
The $60 \mathrm{HƵ}$ resistance is $3.5 \%$ larger than the dc resistance, due to skin effect.

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(a) $954 \mathrm{MCM}=\left(954 \times 10^{3} \mathrm{cmil}\right)\left(\frac{\frac{\pi}{4} \text { sqmil }}{1 \mathrm{cmil}}\right)\left(\frac{1 \mathrm{in}}{1000 \mathrm{mil}}\right)^{2}\left(\frac{.0254 \mathrm{~m}}{\text { in }}\right)^{2}$
$=\underline{\underline{4.834 \times 10^{-4}} \mathrm{~m}^{2}}$
(b) $R_{60 \mathrm{~HƵ}, 45^{\circ}}=R_{60 \mathrm{~Hz}, 75^{\circ}}\left(\frac{45+T}{75+T}\right)$
$\begin{aligned}& =(0.0740)\left(\frac{45+228.1}{75+228.1}\right)=(0.0740)(0.9010) \\& =\underline{\underline{0.0667} \Omega / \mathrm{km}}\end{aligned}$

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From Table A. 4
$R_{60 \mathrm{~HƵ}, 50^{\circ} \mathrm{C}}=\left(0.0969 \frac{\Omega}{\mathrm{mi}}\right)\left(\frac{1 \mathrm{mi}}{1.609 \mathrm{~km}}\right)=0.0602 \frac{\Omega}{\mathrm{km}} \text { per conductor (at } 75 \% \text { current capacity) }$
For 4 conductors per phase:
$R_{60 \mathrm{~HƵ}, 50^{\circ} \mathrm{C}}=\frac{0.0602}{4}=\underline{\underline{0.0151}} \frac{\Omega}{\mathrm{km}} \text { per phase }$