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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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Constant power locus of a transmission line at a particular sending end and receiving end voltage is
Straight line
Circle
Parabola
Ellipse
Circle
The constant power locus represents all possible combinations of active (P) and reactive (Q) power that a transmission line can deliver for fixed sending-end (VS) and receiving-end (VR) voltages. This locus manifests as a circle in the complex power plane, centered at a point determined by the transmission line parameters (A,B constants).
The constant power locus represents all possible combinations of active (P) and reactive (Q) power that a transmission line can deliver for fixed sending-end (VS) and receiving-end (VR) voltages. This locus manifests as a circle in the complex power plane, centered at a point determined by the transmission line parameters (A,B constants).
PR+jQR=∣B∣∣VS∣∣VR∣∠(β−δ)−∣B∣∣A∣∣VR∣2∠(β−α)
(PR−P0)2+(QR−Q0)2=(∣B∣∣VS∣∣VR∣)2
The relationship between VS and VR is given by the transmission equation VS=AVR+BIR. The receiving end complex power SR=PR+jQR=VRIR∗. Substituting IR into the transmission equation yields a quadratic form in PR and QR with equal coefficients for PR2 and QR2, which mathematically defines the equation of a circle.
The radius of the constant power circle is determined by ∣B∣∣VS∣∣VR∣.
The circle center depends on the line constants A=∣A∣∠α and B=∣B∣∠β.
These loci are vital for determining power flow limits and stability regions in power systems.
A change in VS or VR shifts the center or changes the radius, resulting in a family of concentric or overlapping circles.
Provides a clear graphical representation of power delivery limits.
Essential for calculating the stability margin of transmission lines.
Complex calculation for long lines requiring distributed parameter modeling.
Assumes constant voltage magnitudes which may not hold during disturbances.
Power system stability analysis.
Design of reactive power compensation devices (SVC/STATCOM).
Load flow analysis at the planning stage.
The locus is specifically a circle in the P-Q plane.
Option A (Straight line) represents the locus of power at constant current, not constant voltage.
The circle is often referred to as the 'Receiving End Power Circle Diagram'.
B is correct — The constant power locus of a transmission line for fixed terminal voltages is a circle in the complex P-Q plane.
Always remember that in the complex power plane (P vs Q), any equation of the form (P−P0)2+(Q−Q0)2=R2 signifies a circle, which frequently appears in power system stability questions.