Conductor selection, 100 MW 80 km, no corona

The conductor is chosen as the smallest standard ACSR that passes all three checks.

Assumptions: power factor 0.9 lagging; the standard ACSR table supplied with IOE papers (DC resistance at 20°C, current rating at 80°C conductor temperature); fair weather with $\delta = 1$ and irregularity factor $m = 0.85$; maximum system voltage for 132 kV is 145 kV.

Spacing (GMD) from the figure

The middle conductor is 9 m horizontally and 2.5 m vertically from the top and bottom conductors. The top and bottom conductors are 5 m apart vertically.

$$\begin{aligned} D_{12} &= D_{23} = \sqrt{9^2+2.5^2} = 9.341\ \text{m}, \quad D_{13} = 5\ \text{m}\\ GMD &= \sqrt[3]{9.341\times 9.341\times 5} = 7.584\ \text{m} \end{aligned}$$

(i) Thermal limit

$$I = \frac{P}{\sqrt3\, V\cos\phi} = \frac{100\times10^6}{\sqrt3\times132\times10^3\times0.9} = 485.99\ \text{A}$$

• Bear is rated 480 A, which is less than 486 A, so Bear is not acceptable.
• Goat is rated 543 A, which is more than 486 A, so Goat passes. Goat is the smallest conductor that does.

(ii) Efficiency of at least 94%

$$\begin{aligned} P_{loss,max} &= P\left(\frac{1}{0.94}-1\right) = 6.383\ \text{MW}\\ R_{max} &= \frac{6.383\times10^6}{3\times485.99^2} = 9.009\ \Omega \;\Rightarrow\; 0.1126\ \Omega/\text{km} \end{aligned}$$

Here $\eta = P/(P+P_{loss})$ and $P_{loss} = 3I^2R$. Goat meets the target with a margin. Even if its resistance is raised by 10% for temperature and skin effect, η is still about 94.7%.

(iii) No corona in fair weather

The disruptive critical voltage (phase, rms) for Goat, with $r = 25.97/2 = 1.2985$ cm, is:

$$\begin{aligned} V_c &= 21.1\, m\,\delta\, r \ln\frac{GMD}{r}\\ &= 21.1\times0.85\times1\times1.2985\times\ln\frac{758.4}{1.2985}\\ &= 148.3\ \text{kV (phase)} \end{aligned}$$

The highest operating phase voltage is $145/\sqrt3 = 83.7$ kV. Since 148.3 kV is greater than 83.7 kV, there is no corona in fair weather. This also holds for Bear, whose $V_c = 136.1$ kV.

Selection

Answer: ACSR "Goat" (30/7/3.71 mm, 400 mm² total area) is the most suitable conductor. It carries 486 A within its 543 A rating, gives an efficiency of 95.2%, and has a corona voltage of 148 kV per phase against 83.7 kV operating.