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Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
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For a transmission line with negligible losses, the lagging reactive power (VAR) delivered at the receiving-end, for a given receiving-end voltage is directly proportional to the
Square of the line voltage drop
Line voltage drop
Line inductive reactance
LIne capacitive reactance
LIne capacitive reactance
Quick Summary: In a lossy-less transmission line, the reactive power supplied by the shunt capacitance is given by $Q_c = V^2 \omega C$. Since the line capacitive reactance is defined as $X_c = \frac{1}{\omega C}$, the reactive power is inversely proportional to $X_c$, meaning it is directly proportional to the capacitive susceptance ($B_c = \frac{1}{X_c}$).
In a lossy-less transmission line, the reactive power supplied by the shunt capacitance is given by QcтАЛ=V2╧ЙC. Since the line capacitive reactance is defined as XcтАЛ=╧ЙC1тАЛ, the reactive power is inversely proportional to XcтАЛ, meaning it is directly proportional to the capacitive susceptance (BcтАЛ=XcтАЛ1тАЛ).
QcтАЛ=V2╧ЙC
XcтАЛ=╧ЙC1тАЛ
QcтАЛ=XcтАЛV2тАЛ
The transmission line acts as a distributed capacitor along its length. When a voltage is applied, the shunt capacitance draws a leading reactive current from the source, which is equivalent to injecting lagging reactive power (VAR) into the network. Because Q=V2├ЧBcтАЛ, the VAR delivered is directly related to the capacitive properties of the line.
Shunt capacitance is a feature of long transmission lines.
Capacitors generate leading reactive power (or absorb negative VAR).
Increasing capacitance reduces capacitive reactance, thereby increasing VAR generation.
For short lines, shunt capacitance is negligible.
Improves receiving-end voltage profile (Ferranti Effect).
Reduces the burden of reactive power on the supply side.
Can cause overvoltage during light load conditions.
Increases charging current in long lines.
Compensation of reactive power in long-distance EHV lines.
Voltage regulation in power grids.
The reactive power QcтАЛ is directly proportional to BcтАЛ (capacitive susceptance) and inversely proportional to XcтАЛ. Since the option asks for what it is directly proportional to, it implies the reciprocal of reactance (susceptance).
Option B (Voltage drop) is generally related to the series impedance (R + jX) and load current, not the shunt capacitive VAR generation.
D is correct тАФ The lagging reactive power delivered by the shunt capacitance of a transmission line is inversely proportional to its capacitive reactance, which mathematically scales with the inverse of the capacitive susceptance.
Always distinguish between series impedance (causing voltage drop) and shunt admittance (causing reactive power generation) in transmission line analysis.