Conductor selection, 100 MW 70 km 132 kV

The conductor must pass three checks: the thermal limit, efficiency ≥ 94% and regulation ≤ 12%. The smallest standard ACSR that passes all three is chosen.

Assumptions (not given in the question):

• Power factor 0.9 lagging.
• Equivalent spacing $D_{eq} = 5.0$ m, typical for a 132 kV single-circuit tower.
• Resistance at 80 °C: $R_{80} = R_{20}[1 + 0.004(80 - 20)] = 1.24R_{20}$.
• GMR $= 0.7788r$.
• 70 km is treated as a medium line using the nominal-π model.
• Ambient 50 °C and conductor 80 °C, as in the table, so the tabulated current rating is used directly.

(i) Thermal limit

$$I = \frac{P}{\sqrt{3}V\cos\phi} = \frac{100\times10^6}{\sqrt{3}\times132\times10^3\times0.9} = 486.0\ \text{A}$$

The rating must be at least 486 A. Bear (480 A) and smaller conductors are rejected. Goat (543 A) is the smallest conductor that passes.

Line constants (per km)

$$\begin{aligned} X &= 2\pi f\left(2\times10^{-7}\ln\frac{D}{0.7788r}\right)\times1000\ \Omega/\text{km} \\ B &= 2\pi f\,\frac{2\pi\varepsilon_0}{\ln(D/r)}\times1000\ \text{S/km} \end{aligned}$$

For Deer ($d = 29.89$ mm, $r = 1.4945$ cm):

• $R_{80} = 0.0673 \times 1.24 = 0.0835\ \Omega$/km
• $X = 0.3809\ \Omega$/km
• $B = 3.007\ \mu$S/km

(ii) and (iii) Efficiency and regulation

For each conductor:

• $Z = (R + jX)\times70$, $Y = jB\times70$, $A = 1 + ZY/2$
• $V_S = AV_R + ZI_R$, $I_S = CV_R + AI_R$, with $V_R = 132/\sqrt{3}$ kV
• $\eta = P_R/P_S$ and $VR = (V_S/|A| - V_R)/V_R$

For Deer: $V_S = 146.96$ kV (line), loss = 4.081 MW, so $\eta = 100/(100 + 4.081) = 96.08\%$ and $VR = 11.65\%$.

Selection

• Goat passes the thermal and efficiency checks but fails regulation (12.88% > 12%).
• Sheep and Bison are marginal, at about 12.2%.
• Deer passes all three: rating 643 A > 486 A, η = 96.08% > 94%, VR = 11.65% < 12%.

Answer: ACSR Deer (30/4.27 + 7/4.27 mm) is the suitable conductor.

If a smaller spacing (about 4 m) is used, Sheep and Bison would just meet the 12% limit (VR about 11.9%), and they could be compared with Deer on cost.