---
title: "Line as source and sink of reactive power"
subject: "Power System Analysis I"
chapter: 6
key: "semester_4/power_system_analysis_i:line-source-sink-reactive"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/line-source-sink-reactive
site: BCT Engineering
---

# Line as source and sink of reactive power

Power System Analysis I · Chapter 6: Performance Analysis

- Asked in: 2071 Magh, 4 marks
- Video: [Source and Load for Reactive Power - Voltage Profile Control - GATE Power System](https://www.youtube.com/watch?v=YU5V-PAwTqE) — Ekeeda GATE & ESE
- 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-source-sink-reactive
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-6

## Question

Explain how a transmission line behaves as a source and sink of reactive power.

## Short answer

At loads below the surge impedance loading (SIL), the line’s shunt capacitance generates more reactive power than its series inductance absorbs, making it a net source. Above SIL, the inductance dominates, so the line becomes a sink. At SIL, net reactive power is zero.

## Answer

A transmission line has **series inductance** (which absorbs reactive power) and **shunt capacitance** (which generates reactive power). Whether the line as a whole is a source or a sink of VArs depends on which of the two is larger, and that depends on the load.

#### Reactive power generated and absorbed
For a line of length $l$ with reactance $x$ and susceptance $b$ per unit length, at voltage $V$ carrying current $I$:
$$
Q_{gen} \approx V^2 b\,l,\qquad Q_{abs} = I^2 x\,l
$$
- $Q_{gen}$ depends on voltage, which is nearly constant, so it is almost **fixed**.
- $Q_{abs}$ depends on $I^2$, so it **rises with load**.

#### Three cases
Using the surge impedance $Z_c = \sqrt{L/C}$ and surge impedance loading $SIL = V^2/Z_c$:

| Loading | Condition | Line behaves as |
|---|---|---|
| Light load ($P < SIL$) | $V^2\omega C > I^2\omega L$ | **Source** of VAr (capacitive); voltage rises along the line (Ferranti effect) |
| $P = SIL$ (natural load) | $V^2\omega C = I^2\omega L$ | Neither; flat voltage profile, no net Q |
| Heavy load ($P > SIL$) | $I^2\omega L > V^2\omega C$ | **Sink** of VAr (inductive); voltage drops along the line |

```text
 Q net from line
   + |\
     |  \   source (light load)
   0 +----*------------- P
     |    SIL  \
   - |           \  sink (heavy load)
```

#### Consequences
- At light load, excess VArs raise receiving-end voltage; **shunt reactors** are switched in to absorb them.
- At heavy load, the line absorbs VArs and voltage falls; **shunt capacitors, SVCs or series capacitors** supply VArs.
- Long EHV lines and cables (high $C$) are strong VAr sources at light load; short, heavily loaded lines are VAr sinks.

**Example:** a 400 kV line with $Z_c = 400\ \Omega$ has SIL = 400 MW. At 200 MW it supplies VArs to the system; at 600 MW it absorbs VArs.

## Check yourself

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

1. Which element absorbs and which generates reactive power?
   A. Inductance generates; capacitance absorbs
   B. Both absorb
   C. Both generate
   D. Series inductance absorbs I^2 X; shunt capacitance generates V^2 b
   Answer: D. Q_abs = I^2 x l, Q_gen = V^2 b l. (Key point: Elements)

2. At light load (P < SIL) the line behaves as:
   A. Sink of VAr
   B. Source of VAr, with voltage rise (Ferranti)
   C. Neither
   D. Resistor
   Answer: B. Charging VAr exceeds I^2X absorbed. (Key point: Light load)

3. At natural loading (P = SIL):
   A. Voltage collapse
   B. Net Q zero and flat voltage profile
   C. Maximum VAr absorbed
   D. Maximum VAr generated
   Answer: B. V^2 omega C = I^2 omega L so they balance. (Key point: At SIL)

4. Which is the correct remedy?
   A. Series resistors
   B. None
   C. Shunt reactors at light load; capacitors/SVC at heavy load
   D. Capacitors at light load; reactors at heavy load
   Answer: C. Reactors absorb surplus VAr at light load; capacitors supply VAr at heavy load. (Key point: Remedies)

## Related in Power System Analysis I

- [Line as source and sink of reactive power, effects](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aline-source-sink-reactive-effects) — Power System Analysis I, chapter 6
- [Need and methods of reactive power compensation](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Areactive-compensation-need-methods) — Power System Analysis I, chapter 6, asked 2×
- [Reactive power proportional to voltage drop](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Areactive-power-voltage-drop) — Power System Analysis I, chapter 6

## Related in other subjects

- [Charging reactive power of line at no load](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Acharging-reactive-power-no-load) — High Voltage Engineering, chapter 3, asked 2×