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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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The relation between the receiving end voltage and the reactive power in terms of short circuit strength is
E 1 + Q S s c
E 1 - Q S s c
E 1 + 2 Q S s c
E Q S s c
E1-QSsc
Quick Summary: The relationship between receiving end voltage and reactive power is derived from the power flow equations in a transmission line. For a lossless line, the change in voltage magnitude is inversely proportional to the short-circuit capacity of the system, reflecting the sensitivity of the bus voltage to reactive power injection.
The relationship between receiving end voltage and reactive power is derived from the power flow equations in a transmission line. For a lossless line, the change in voltage magnitude is inversely proportional to the short-circuit capacity of the system, reflecting the sensitivity of the bus voltage to reactive power injection.
VR≈E(1−SscQ) — Voltage magnitude approximation
Ssc=XthV2 — Short circuit capacity definition
In a power system, the voltage drop across a line is primarily dependent on the reactance of the line and the reactive power flow (Q). The short-circuit strength (S_{sc}) is defined as the product of the rated voltage and the fault current. As Q increases, the drop in voltage is scaled by the ratio of Q to S_{sc}, which represents the system's stiffness. The negative sign in the expression indicates that supplying reactive power increases the receiving end voltage, while consuming reactive power decreases it relative to the no-load condition.
A higher Ssc implies a 'stiffer' bus with lower voltage sensitivity to reactive power changes.
Injecting positive reactive power (+Q) raises the bus voltage.
Absorbing reactive power (−Q) lowers the bus voltage.
This linear approximation is valid for small variations in reactive power near the nominal operating point.
Simplifies voltage control studies in radial networks
Allows quick estimation of voltage stability
Linear approximation ignores non-linear line resistance effects
Valid only for small deviations around nominal voltage
Power system load flow analysis
Voltage stability margin assessment
Placement of reactive power compensation devices
The factor Q/Ssc is often referred to as the voltage sensitivity factor.
Option A represents the incorrect sign, which would imply increasing reactive power demand decreases voltage excessively.
B is correct — The receiving end voltage is given by E(1−SscQ), showing how reactive power consumption influences the voltage drop relative to the system's short-circuit capacity.
Always remember that Ssc acts as the 'stiffness' constant of your node; a larger Ssc makes the node more robust against voltage fluctuations.