--- title: "Long line by short model and vice versa" subject: "Power System Analysis I" chapter: 5 key: "semester_4/power_system_analysis_i:long-line-short-model-vice-versa" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/long-line-short-model-vice-versa site: BCT Engineering --- # Long line by short model and vice versa Power System Analysis I · Chapter 5: Transmission Line Modeling - Asked in: 2073 Bhadra, 4 marks; 2068 Magh, 6 marks (asked 2 times) - 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/long-line-short-model-vice-versa - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-5 ## Question What will happen if a long line is modelled by the short line model and vice versa? ## Short answer Modelling a long line with the short-line model ignores shunt capacitance, giving incorrect sending-end voltage, missing the Ferranti effect, wrong current and power factor, and unsafe design. Conversely, using the exact long-line model for a short line gives correct results because hyperbolic terms simplify to short-line parameters, but requires more computation. ## Answer The **long-line model** (distributed parameters) is exact for any length. The **short-line model** keeps only the series impedance $Z$ and ignores the shunt capacitance ($A = D = 1$, $B = Z$, $C = 0$). #### Long line modelled by the short-line model A long line (above about 250 km) has a large shunt capacitance and large charging current, and the parameters are distributed. Using the short model: - **Charging current is ignored.** The sending-end current is taken equal to the receiving-end current, which is wrong; at light load the real $I_S$ is mostly charging current. - **Sending-end voltage is wrong.** With a lagging load the short model overestimates $V_S$ (no capacitive rise), so the voltage regulation comes out too high. - **Ferranti effect cannot be predicted.** At no load the short model gives $V_R = V_S$, whereas a long line actually has $V_R > V_S$. - **Losses and efficiency are wrong**, since the true current varies along the line. - **Power factor at the sending end is wrong**; the reactive power generated by the line is missing. - Reactive compensation, insulation and protection design based on these results would be unsafe. Example: for a 300 km, 220 kV line delivering 50 MW at 0.8 lag (Z = 40 + j125 Ω, Y = j10⁻³ S), the short model gives $V_S \approx 251$ kV at p.f. 0.75 lag, whereas the Π model gives about 238 kV at p.f. 0.99 lead. #### Short line modelled by the long-line model - The long-line equations are exact for all lengths, so the results are **correct**. - For a short line, $\gamma l$ is very small, so $\cosh\gamma l \approx 1$, $Z_c\sinh\gamma l \approx Z$ and $\sinh\gamma l / Z_c \approx 0$. The answers become practically the same as the short-line model. - The only drawback is **more calculation** (complex hyperbolic functions) for no real gain in accuracy. #### Summary | Case | Accuracy | Effect | |---|---|---| | Long line, short model | Poor | Wrong $V_S$, $I_S$, p.f., regulation; Ferranti effect missed | | Short line, long model | Exact | Correct, only more work | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which set of ABCD constants does the short-line model use? A. A = D = 1 + ZY/2, B = Z, C = Y(1 + ZY/4) B. A = D = 1, B = Z, C = 0 C. A = D = cosh(γl), B = Zc sinh(γl), C = sinh(γl)/Zc D. A = 0, B = Z, C = 1, D = 0 Answer: B. The short model keeps only series impedance, so A = D = 1, B = Z, C = 0. (Key point: Short model assumptions) 2. At no load, a long line is modelled by the short-line model. The model predicts: A. VR greater than VS B. VR equal to VS, so the Ferranti rise is missed C. VR much less than VS D. Infinite voltage at the receiving end Answer: B. With C = 0 the short model gives VR = VS at no load, while a real long line has VR > VS. (Key point: Ferranti effect missed) 3. What is the main reason a short model is inaccurate for a long line? A. It ignores charging current from the large shunt capacitance, so IS = IR B. It ignores series resistance C. It uses line-to-line instead of phase voltage D. It includes too many hyperbolic terms Answer: A. A long line has large charging current, which the short model neglects, giving wrong VS, IS, power factor and regulation. (Key point: Main error in long line on short model) 4. A short line is analysed with the exact long-line model. The result is: A. Wildly inaccurate because the model is for long lines only B. Correct, essentially the same as the short model, but with more calculation C. Impossible because γl is zero D. Correct only if shunt capacitance is added by hand Answer: B. The long-line model is exact for any length; for small γl it reduces to A = 1, B = Z, C ≈ 0. (Key point: Short line on long model) 5. For a long line with lagging load, the short model compared with the real line gives: A. An underestimated VS and negative regulation B. An overestimated VS since capacitive rise is absent, so regulation looks too high C. Exactly the same VS D. A leading power factor at the sending end Answer: B. Without the capacitive voltage rise, the short model overestimates VS (e.g. 251 kV vs about 238 kV in the example). (Key point: Effect on sending voltage) ## Related in Power System Analysis I - [Equivalent-π model of a long line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aequivalent-pi-long-line) — Power System Analysis I, chapter 5 - [Equivalent-T of 300 km long line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Along-line-equivalent-t-300km) — Power System Analysis I, chapter 5 - [Modelling 500 km as medium, 50 km as long](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Awrong-model-500km-50km) — Power System Analysis I, chapter 5 - [150 km line by T-model, 60 MW](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3A150km-t-model-60mw) — Power System Analysis I, chapter 5 - [Voltages and currents vary along a long line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Along-line-voltage-varies-along) — Power System Analysis I, chapter 5, asked 2× - [280 km, 60 Hz line: nominal-π vs long line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3A280km-60hz-nominal-pi-long) — Power System Analysis I, chapter 5, asked 2× ## Related in other subjects - [Ybus with nominal π model, line lengths](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aybus-km-lines-pi-model) — Power System Analysis II, chapter 1, asked 2× - [Incremental model of a transmission line](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atransmission-line-incremental-model) — Telecommunications, chapter 2 - [HR trickling filter, 2.5 MLD; change if standard](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Atrickling-hr-2p5mld-std-compare) — Sanitary Engineering, chapter 7 - [True length: tape found 2.5 cm too long](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-825-plus-750-m) — Surveying I, chapter 2