--- title: "Modelling 500 km as medium, 50 km as long" subject: "Power System Analysis I" chapter: 5 key: "semester_4/power_system_analysis_i:wrong-model-500km-50km" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/wrong-model-500km-50km site: BCT Engineering --- # Modelling 500 km as medium, 50 km as long Power System Analysis I · Chapter 5: Transmission Line Modeling - Asked in: 2078 Chaitra, 2+2 marks - 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/wrong-model-500km-50km - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-5 ## Question What will happen if a 500 km long transmission line is modeled using the medium length transmission line model and a 50 km long line is represented by the long length model? ## Short answer Modeling a500 km line with medium-line model yields inaccurate voltage, regulation, and Ferranti rise because distributed capacitance is ignored; the exact long-line model must be used. Modeling a50 km line with the long-line model gives correct but unnecessarily complex results; short-line approximation suffices. ## Answer #### 500 km line modelled as a medium line (nominal-Π or T) - A 500 km line is a **long line**. Its parameters are distributed, and $\gamma l$ is large (about 0.5 rad at 50 Hz), so $\cosh\gamma l$ and $\sinh\gamma l$ are no longer close to $1 + ZY/2$ and $\gamma l$. - The nominal model lumps all capacitance at one or two points. This gives errors in $A$, $B$, $C$ and hence in the sending-end voltage, current, power factor, regulation and losses. The error grows rapidly with length. - The Ferranti rise at light load and the reactive power generated by the line are wrongly estimated, so the size of shunt reactors and the insulation level may be chosen wrongly. - The results are therefore **inaccurate and unsafe** for design. The exact long-line model (or its equivalent-Π) must be used. #### 50 km line modelled by the long-line model - The long-line equations are **exact for any length**, so the results will be **correct**. - For 50 km, $\gamma l$ is very small, so $\cosh\gamma l \approx 1$, $Z_c\sinh\gamma l \approx Z$, $\sinh\gamma l/Z_c \approx Y \approx 0$. The answers become almost the same as the short-line model ($A = 1$, $B = Z$, $C = 0$). - The only cost is **unnecessary calculation** with complex hyperbolic functions, for no practical gain. | Case | Accuracy | Practical effect | |---|---|---| | 500 km on medium model | Poor | Wrong $V_S$, $I_S$, regulation | | 50 km on long model | Exact | Correct but more effort | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A 500 km line is represented by a nominal medium model. The main problem is: A. The model has too many parameters B. The nominal model is exact but slow C. Distributed parameters are lumped, giving errors in A, B, C that grow with length D. It cannot use per-phase analysis Answer: C. Lumping capacitance at one or two points is a poor approximation when γl is large. (Key point: Parameters of 500 km line) 2. Using the medium model for a 500 km line can lead to: A. Correct reactor sizing B. Wrong Ferranti rise and reactive power estimates, so reactors/insulation may be wrongly chosen C. Lower cost with no loss of accuracy D. Only errors in frequency Answer: B. Errors in voltage rise and reactive generation make design unsafe. (Key point: Consequences of the error) 3. A 50 km line analysed with the long-line model gives: A. Poor accuracy since the line is short B. Results that fail because γl is too small C. Correct results, almost identical to the short model, with extra calculation D. Results needing a nominal-T correction Answer: C. The long model is exact; for small γl, cosh ≈ 1, Zc sinh ≈ Z, sinh/Zc ≈ 0. (Key point: 50 km line on long model) 4. For a 50 km line, the long-line constants reduce to: A. A = 1, B = Z, C ≈ 0 B. A = 0, B = 1, C = Z C. A = 1 + ZY/2, B = Z, C = Y D. A = Z, B = Y, C = 1 Answer: A. Small γl gives the short-line constants A = D = 1, B = Z, C = 0. (Key point: Short-length limit) ## Related in Power System Analysis I - [Long line by short model and vice versa](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Along-line-short-model-vice-versa) — Power System Analysis I, chapter 5, asked 2× - [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 - [Nominal-T 100 km line, 50 MVA at 132 kV](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Anominal-t-100km-50mva) — Power System Analysis I, chapter 6 - [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× - [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 - [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 ## Related in other subjects - [Incremental model of a transmission line](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atransmission-line-incremental-model) — Telecommunications, chapter 2 - [Design: 230 m head plant, 20 km line](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2070-230m-20km) — Power Plant Design, chapter 4, asked 14× - [Design: 230 m head plant, 55 km line](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2074-230m-55km) — Power Plant Design, chapter 4, asked 12× - [6° phase shift per 100 km of lossless line](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aphase-shift-6-degree-100km) — High Voltage Engineering, chapter 3