The relation between the receiving end voltage and the reactive power in terms of short circuit strength is
A
E1+QSsc
B
E1-QSsc
C
E1+2QSsc
D
EQSsc

Question

The relation between the receiving end voltage and the reactive power in terms of short circuit strength is

Examoogle · Accepted Answer

E (1 - \frac{Q}{S_{s c}})

Explanation: 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. Working Principle: 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. Key Formulas: $V_R \approx E (1 - \frac{Q}{S_{sc}})$ — Voltage magnitude approximation; $S_{sc} = \frac{V^2}{X_{th}}$ — Short circuit capacity definition Key Points: A higher $S_{sc}$ 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. Advantages: Simplifies voltage control studies in radial networks; Allows quick estimation of voltage stability Disadvantages: Linear approximation ignores non-linear line resistance effects; Valid only for small deviations around nominal voltage Applications: Power system load flow analysis; Voltage stability margin assessment; Placement of reactive power compensation devices Additional Info: The factor $Q/S_{sc}$ 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. Answer: B is correct — The receiving end voltage is given by $E(1 - \frac{Q}{S_{sc}})$, showing how reactive power consumption influences the voltage drop relative to the system's short-circuit capacity. Exam Tip: Always remember that $S_{sc}$ acts as the 'stiffness' constant of your node; a larger $S_{sc}$ makes the node more robust against voltage fluctuations.

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