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For a fixed receiving end and sending end voltages in a transmission system, what is the locus of the constant power
A straight line
An ellipse
A parabola
A circle
A straight line
Quick Summary: In a transmission system represented by the general ABCD network constant equation, the locus of constant power at the receiving end is a circle in the complex power plane ($P + jQ$). However, for a fixed sending end voltage ($V_s$) and receiving end voltage ($V_r$), the power circle diagram relates active and reactive power, resulting in a circle.
In a transmission system represented by the general ABCD network constant equation, the locus of constant power at the receiving end is a circle in the complex power plane (P+jQ). However, for a fixed sending end voltage (VsтАЛ) and receiving end voltage (VrтАЛ), the power circle diagram relates active and reactive power, resulting in a circle.
PrтАЛ+jQrтАЛ=BAтАЛVr2тАЛтИа(╬▓тИТ╬▒)тИТBVsтАЛVrтАЛтАЛтИа(╬▓+╬┤) тАФ Receiving end power equation
R=BVsтАЛVrтАЛтАЛ тАФ Radius of the receiving end power circle
The receiving end power PrтАЛ+jQrтАЛ is determined by the equation SrтАЛ=VrтАЛIrтИЧтАЛ. Substituting the transmission line equation IrтАЛ=BAтАЛVrтАЛтИТB1тАЛVsтАЛ, the locus equation takes the form (PrтАЛтИТP0тАЛ)2+(QrтАЛтИТQ0тАЛ)2=R2, which defines a circle in the PтИТQ plane.
The power circle diagram is a graphical representation of the power flow in a transmission line.
For a fixed VsтАЛ and VrтАЛ, the receiving end power locus is a circle.
The radius is proportional to the product of VsтАЛ and VrтАЛ and inversely proportional to the magnitude of the B parameter.
Allows visual determination of power limits.
Easily identifies stability margins under variable load conditions.
Assumes constant voltage magnitudes which may not hold under severe faults.
Requires complex mapping for non-linear loads.
Power system stability analysis.
Transmission line capacity planning.
The question text provided suggests a 'straight line' which is technically incorrect for power circles; it is a circle. The correct locus is a circle.
The A and B constants represent the generalized circuit constants of the transmission line.
A is technically incorrect as the locus of constant receiving end power for fixed VsтАЛ and VrтАЛ is a circle, not a straight line.
Always remember that in power flow analysis, power-voltage relations typically yield circular loci due to the squared terms in the voltage and current relationships.