---
title: "Classification of lines by length and model validity"
subject: "Power System Analysis I"
chapter: 5
key: "semester_4/power_system_analysis_i:line-classification-by-length"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/line-classification-by-length
site: BCT Engineering
---

# Classification of lines by length and model validity

Power System Analysis I · Chapter 5: Transmission Line Modeling

- Asked in: 2073 Bhadra, 4 marks
- Video: [The REAL Reason to Classify Transmission Lines as Short Medium or Long](https://www.youtube.com/watch?v=PYKM6XBLx2s) — 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/line-classification-by-length
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-5

## Question

How are transmission lines classified according to their lengths? Explain why all lines can be represented by the long transmission line model whereas all the lines cannot be represented by the short transmission line model.

## Short answer

Lines are classified by length: short (<80 km, capacitance neglected), medium (80–250 km, nominal-π or T), long (>250 km, distributed parameters). The long-line model uses exact hyperbolic equations valid for any length. The short-line model omits shunt capacitance, giving incorrect results for medium and long lines where charging current is significant.

## Answer

Transmission lines are classified by length because the effect of shunt capacitance (charging current) grows with length. The usual limits for 50 Hz lines are:

| Type | Length | Model used |
|---|---|---|
| Short | up to 80 km (below about 20 kV) | Series $R + jX$; capacitance neglected |
| Medium | 80–250 km (20–100 kV) | Lumped: nominal-Π or nominal-T |
| Long | above 250 km (above 100 kV) | Distributed parameters (exact) |

#### Why every line can use the long-line model
- The long-line model solves the line's differential equations exactly with distributed $r$, $L$, $C$ ($A = \cosh\gamma l$, $B = Z_c\sinh\gamma l$, $C = \sinh\gamma l/Z_c$). It makes no approximation, so it is valid for any length.
- For a short line, $\gamma l$ is small, so $\cosh\gamma l \approx 1$, $Z_c\sinh\gamma l \approx Z$ and $\sinh\gamma l/Z_c \approx 0$. The model reduces to the short-line result. For a medium line, $A \approx 1 + ZY/2$ and $B \approx Z$, which are the nominal-model values.
- So the result is always correct; only the calculation is longer.

#### Why the short-line model cannot be used for all lines
- It assumes $C = 0$, so the charging current and the reactive power generated by the line are ignored, and $I_S = I_R$.
- For medium and long lines the charging current is a large part of the line current. Ignoring it gives wrong sending-end voltage, current, power factor, regulation and efficiency.
- It cannot show the Ferranti effect (no-load $V_R > V_S$) or the variation of voltage and current along the line.
- So it is valid only where the charging current is negligible, that is, for short lines.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Medium transmission lines (50 Hz) are those of length:
   A. Up to 80 km
   B. 80 to 250 km
   C. Above 250 km
   D. 250 to 500 km
   Answer: B. Short up to 80 km, medium 80-250 km, long above 250 km. (Key point: Classification limits)

2. Why does the long-line model work for every length?
   A. It ignores capacitance
   B. It is an approximation designed for average lengths
   C. It is exact, with no approximation, and reduces to short or medium forms for small γl
   D. It uses lumped parameters
   Answer: C. It solves the distributed differential equations exactly. (Key point: Why long model works for all)

3. The short-line model cannot be used for all lines because it:
   A. Ignores charging current (C = 0, IS = IR)
   B. Ignores resistance
   C. Needs hyperbolic functions
   D. Is only for DC
   Answer: A. For medium and long lines charging current is large, so results become wrong. (Key point: Limitation of short model)

4. Which effect does the short-line model fail to show?
   A. Voltage drop due to resistance
   B. Ferranti effect, no-load VR greater than VS
   C. Power loss in R
   D. Phase shift due to X
   Answer: B. With no shunt capacitance the model gives VR = VS at no load. (Key point: Ferranti effect)

## Related in Power System Analysis I

- [Model validity and nominal-π ABCD with phasor](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Along-model-validity-nominal-pi) — Power System Analysis I, chapter 5
- [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
- [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×
- [Distributed parameters and current along a long line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Adistributed-parameters-long-line-current) — Power System Analysis I, chapter 5
- [Typical ABCD values of long lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Along-line-abcd-typical-values) — Power System Analysis I, chapter 5
- [Line model classification and short-line ABCD](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aclassify-models-short-line-abcd) — Power System Analysis I, chapter 5

## 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
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- [G-S one iteration with π-model lines](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Ags-one-iteration-pi-lines-2069) — Power System Analysis II, chapter 2