--- title: "Conductor selection, 100 MW 70 km 132 kV" subject: "Transmission and Distribution System Design" chapter: 4 key: "semester_8/transmission_and_distribution_system_design:conductor-selection-100mw-70km-132kv" source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/conductor-selection-100mw-70km-132kv site: BCT Engineering --- # Conductor selection, 100 MW 70 km 132 kV Transmission and Distribution System Design · Chapter 4: Conductor and Support Selection - Asked in: 2078 Kartik, 16 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/conductor-selection-100mw-70km-132kv - Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-4 ## Question For 3 phase 50 Hz transmission line to deliver 100 MW of power over 70 km, 132 kV single circuit line has been decided to design. Suggest the suitable conductor which meets following technical criterion. (i) Satisfy the thermal limit. (ii) Efficiency of line not to be less than 94% (iii) Voltage regulation of line not to be greater than 12%. Use conductor table attached. Assume the ambient temperature and maximum allowable temperature same as mentioned in conductor table. [Given ACSR conductor table:] | Code name | Aluminium No./mm | Steel No./mm | Approx. overall diameter (mm) | Aluminium area (mm²) | Steel area (mm²) | Total area (mm²) | Approx. weight (kg/km) | Nominal breaking load (kN) | Nominal DC resistance at 20°C (Ω/km) | Current rating (A) | |---|---|---|---|---|---|---|---|---|---|---| | Mole | 6/1.50 | 1/1.50 | 4.50 | 10.6 | 1.77 | 12.4 | 42.8 | 4.14 | 2.7027 | 66 | | Squirrel | 6/2.11 | 1/2.11 | 6.33 | 21.0 | 3.50 | 24.5 | 84.7 | 7.87 | 1.3659 | 101 | | Fox | 6/2.79 | 1/2.79 | 8.37 | 36.7 | 6.11 | 42.8 | 148.1 | 13.21 | 0.7812 | 142 | | Mink | 6/3.66 | 1/3.66 | 10.98 | 63.1 | 10.50 | 73.6 | 254.9 | 21.87 | 0.4540 | 199 | | Skunk | 12/2.59 | 7/2.59 | 12.95 | 63.2 | 36.90 | 100.1 | 463.0 | 52.79 | 0.4568 | 206 | | Beaver | 6/3.99 | 1/3.99 | 11.97 | 75.0 | 12.50 | 87.5 | 302.9 | 25.76 | 0.3820 | 221 | | Racoon | 6/4.09 | 1/4.09 | 12.27 | 78.8 | 13.10 | 91.9 | 318.3 | 27.06 | 0.3635 | 228 | | Otter | 6/4.22 | 1/4.22 | 12.66 | 83.9 | 14.00 | 97.9 | 338.8 | 28.81 | 0.3415 | 237 | | Cat | 6/4.50 | 1/4.50 | 13.50 | 95.4 | 15.90 | 111.3 | 385.3 | 32.76 | 0.3003 | 256 | | Hare | 6/4.72 | 1/4.72 | 14.16 | 105.0 | 17.50 | 122.5 | 423.8 | 36.04 | 0.2730 | 271 | | Coyote | 26/2.54 | 7/1.91 | 15.89 | 131.7 | 20.10 | 151.8 | 520.7 | 45.88 | 0.2192 | 311 | | Cougar | 18/3.05 | 1/3.05 | 15.25 | 131.5 | 7.31 | 138.8 | 418.8 | 29.74 | 0.2188 | 308 | | Tiger | 30/2.36 | 7/2.36 | 16.52 | 131.2 | 30.60 | 161.8 | 602.2 | 57.87 | 0.2202 | 313 | | Lion | 30/3.18 | 7/3.18 | 22.26 | 238.3 | 55.60 | 293.9 | 1093.4 | 100.47 | 0.1213 | 450 | | Bear | 30/3.35 | 7/3.35 | 23.45 | 264.4 | 61.70 | 326.1 | 1213.4 | 111.50 | 0.1093 | 480 | | Goat | 30/3.71 | 7/3.71 | 25.97 | 324.3 | 75.70 | 400.0 | 1488.2 | 135.13 | 0.0891 | 543 | | Sheep | 30/3.99 | 7/3.99 | 27.93 | 375.1 | 87.50 | 462.6 | 1721.3 | 156.30 | 0.0771 | 592 | | Antelope | 54/2.97 | 7/2.97 | 26.73 | 374.1 | 48.50 | 422.6 | 1413.8 | 118.88 | 0.0773 | 586 | | Bison | 54/3.00 | 7/3.00 | 27.00 | 381.7 | 49.50 | 431.2 | 1442.5 | 121.30 | 0.0758 | 593 | | Deer | 30/4.27 | 7/4.27 | 29.89 | 429.6 | 100.20 | 529.8 | 1971.4 | 179.00 | 0.0673 | 643 | | Elk | 30/4.50 | 7/4.50 | 31.50 | 477.1 | 111.30 | 588.4 | 2189.5 | 198.80 | 0.0606 | 684 | | Camel | 54/3.35 | 7/3.35 | 30.15 | 476.0 | 61.70 | 537.7 | 1798.8 | 146.40 | 0.0608 | 677 | | Moose | 54/3.53 | 7/3.53 | 31.77 | 528.5 | 69.50 | 597.0 | 1997.3 | 159.92 | 0.0547 | 720 | Note: current ratings are based on wind velocity of 0.6 m/s, solar heat radiation of 1200 W/m², ambient temperature of 50°C and conductor temperature of 80°C. ## Short answer The line requires a minimum 486 A thermal rating, ≥94% efficiency, and ≤12% regulation. ACSR Goat meets thermal limit but fails regulation; Sheep and Bison are marginal. ACSR Deer (30/4.27+7/4.27 mm) satisfies all criteria with 643 A rating, 96.08% efficiency, and 11.65% regulation. ## Answer 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 $VR = (V_S/|A| - V_R)/V_R$ | Conductor | $I_{rated}$ (A) | Thermal OK? | $R_{80}$ (Ω/km) | $X$ (Ω/km) | η (%) | VR (%) | |---|---|---|---|---|---|---| | Bear | 480 | No | 0.1355 | 0.3962 | 93.78 | 13.98 | | Goat | 543 | Yes | 0.1105 | 0.3898 | 94.87 | 12.88 | | Sheep | 592 | Yes | 0.0956 | 0.3852 | 95.53 | 12.21 | | Bison | 593 | Yes | 0.0940 | 0.3873 | 95.60 | 12.20 | | Deer | 643 | Yes | 0.0835 | 0.3809 | 96.08 | 11.65 | 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the current used for the thermal check found for 100 MW at 132 kV? A. I = P/(V cosφ) = 100e6/(132e3 x 0.9) B. I = P/(sqrt(3) V cosφ), about 486 A C. I = P/(3 V cosφ), about 281 A D. I = P/(sqrt(3) V), about 437 A Answer: B. For a 3-phase line the line current is P/(sqrt(3) V cosφ), giving about 486 A at 0.9 pf. The tabulated rating must be at least this. (Key point: Thermal limit current) 2. Which conductors pass the thermal limit of 486 A? A. Bear (480 A) and larger B. Goat (543 A) and larger; Bear is rejected C. Only Deer and larger D. Any conductor, as thermal limit is irrelevant for 132 kV Answer: B. Bear at 480 A is below 486 A, so the smallest passing conductor is Goat at 543 A. (Key point: Thermal screening) 3. Why is the tabulated 20 °C resistance multiplied by about 1.24? A. To allow for corona loss B. To correct for conductor resistance at 80 °C using R20[1 + 0.004(80 - 20)] C. To account for the steel core D. To convert from Ω/km to Ω per phase Answer: B. Resistance rises with temperature, and the table's rating assumes 80 °C, so R80 = 1.24 R20 is used. (Key point: Resistance at operating temperature) 4. Why is Deer chosen rather than Goat? A. Goat fails the thermal limit B. Goat fails efficiency (below 94%) C. Goat has regulation 12.88%, above the 12% limit, while Deer gives 11.65% D. Deer is the cheapest conductor Answer: C. Goat passes thermal and efficiency (94.87%) but fails the 12% regulation limit. Deer passes all three checks. 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