--- title: "Short line 40 km, 381 MVA: regulation and efficiency" subject: "Power System Analysis I" chapter: 6 key: "semester_4/power_system_analysis_i:short-line-40km-381mva" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/short-line-40km-381mva site: BCT Engineering --- # Short line 40 km, 381 MVA: regulation and efficiency Power System Analysis I · Chapter 6: Performance Analysis - Asked in: 2075 Baisakh, 6 marks - Video: [Three Phase Short Transmission Line Explained | Voltage Regulation, Efficiency & Numerical](https://www.youtube.com/watch?v=GKOllJ9gurw) — Electrology - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/short-line-40km-381mva - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-6 ## Question A 220 kV, three phase transmission line is 40 km long. The resistance per phase is 0.15 Ω per km and the inductance per phase is 1.3263 mH per km. The shunt capacitance is negligible. Use the short line model to find the voltage and power at the sending end and the voltage regulation and efficiency when the line is supplying a three phase load of 381 MVA at 0.8 power factor lagging at 220 kV. ## Short answer Sending end line voltage is 246.2 kV, three-phase power 322.8 MW + j278.6 MVAr. Voltage regulation is 11.91% and efficiency 94.43%, based on short-line model with Z=6+j16.667 Ω. ## Answer Short-line model: shunt capacitance neglected, $I_S = I_R$. #### Line impedance $$ \begin{aligned} R &= 0.15\times40 = 6\ \Omega \\ X &= 2\pi(50)(1.3263\times10^{-3})(40) = 16.667\ \Omega \\ Z &= 6 + j16.667\ \Omega \end{aligned} $$ #### Receiving end $$ \begin{aligned} V_R &= \frac{220}{\sqrt3} = 127.02\angle0^\circ\ \text{kV} \\ I_R &= \frac{381\times10^6}{\sqrt3\times220\times10^3} = 999.87\angle-36.87^\circ\ \text{A} \end{aligned} $$ #### Sending-end voltage $$ \begin{aligned} V_S &= V_R + I_R Z = 127.02 + (0.99987\angle-36.87^\circ)(17.71\angle70.20^\circ) \\ &= 127.02 + 17.71\angle33.33^\circ \\ &= 142.15\angle3.93^\circ\ \text{kV (phase)} \end{aligned} $$ Line value $= \sqrt3\times142.15 = 246.21$ kV. #### Sending-end power $$ \begin{aligned} S_S &= 3V_S I_S^* = 3(142.15\angle3.93^\circ)(0.99987\angle36.87^\circ) \\ &= 322.80 + j278.59\ \text{MVA} \end{aligned} $$ Sending-end pf $= \cos(40.80^\circ) = 0.757$ lagging. #### Regulation $$ \%VR = \frac{246.21 - 220}{220}\times100 = 11.91\% $$ #### Efficiency Receiving power $P_R = 381\times0.8 = 304.8$ MW. $$ \eta = \frac{304.8}{322.80}\times100 = 94.43\% $$ (Check: loss $= 3I^2R = 3(999.87)^2(6) = 18.0$ MW.) **Answer: $V_S$ = 246.2 kV (line), $S_S$ = 322.8 MW + j278.6 MVAr, regulation 11.91 %, efficiency 94.43 %.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the short-line model assume here? A. Resistance neglected B. Shunt capacitance neglected, so I_S = I_R C. Half the capacitance at each end D. Capacitance at the middle only Answer: B. With shunt capacitance negligible, the sending current equals the receiving current and V_S = V_R + I_R Z. (Key point: Short line model) 2. How is the sending-end voltage obtained? A. V_S = V_R - I_R Z using line voltage B. V_S = V_R + I_R Z per phase (142.15 kV phase, 246.21 kV line) C. V_S = I_R Z only D. V_S = V_R / (1 + Z) Answer: B. Per phase V_S = 127.02 + 17.71 angle 33.33 deg = 142.15 angle 3.93 deg kV; multiply by sqrt(3) for the line value. (Key point: Sending voltage) 3. How is voltage regulation calculated for this short line? A. (142.15 - 246.21)/142.15 B. I R / V_S C. (246.21 - 220)/220 x 100 = 11.91 % D. (220 - 246.21)/246.21 x 100 Answer: C. Short line has A = 1, so regulation = (V_S - V_R)/V_R using consistent (line) values. (Key point: Regulation) 4. How is efficiency found? A. 304.8 MW / 381 MW B. P_R / P_S = 304.8/322.8 = 94.43 %, with P_R = 381 x 0.8 C. 381 / 322.8 D. Q_S / Q_R Answer: B. Output is the real power 381 x 0.8 = 304.8 MW and input is P_S = 322.8 MW; the difference 18 MW equals 3I^2R. 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