Gujarat Power Engineering and Research Institute

 B.E. SEM. VI (ELECTRICAL).

PRESENTED BY: HARSH SONI

Circle Diagram

Circle Diagram

1.Receiving-end Circle Diagram

2.Sending-end Circle Diagram

It has been shown above that-the flow of active and reactive power over a Transmission line can be handled computationally.

It will now be shown that the Locus of complex sending- and receiving-end power is a circle.

Since circles are convenient to draw, the circle diagrams are a useful aid to visualize the load flow problem over a single transmission.

1. Receiving-end circle diagram

The expressions for complex number receiving-and sending-end powers are Reproduced below from above Equations.

…(1)

…(2)

As per the above equations, and are each composed of two phasor components-one a constant phasor and the other a phasor of fixed magnitude but variable angle.

Rs Ss

The loci for Sr and Ss would therefore be circles drawn from the tip of constant phasors as centres

It follows from Eq. (1) that the centre of receiving-end circle is located at the tip of the phasor.

Horizontal coordinate of the centre

The radius of the receiving-end circle is

Vertical coordinate of the centre

Fig.1 Receiving-end circle diagram

As per fig.1 the operating point ‘M’ indicates the receiving end values of , and .For constant the centre remains fixed. For varying and constant centre of circles move along the line

RP RQ RV RC

RV SV

ROC

In polar coordinates

Similarly for Eq. (2) the centre of sending-end circle is located at the of the phasor

2. Sending-end circle diagram

Horizontal coordinate of the centre

Vertical coordinate of the centre

The radius of the sending-end circle is

Fig.2 Sending-end circle diagram

The operating point N is located by measuring the torque angle in the direction indicated fromthe reference line.

SV SC

SV RVSOC

For constant the centre remains fixed. For varying and constant centre of circles move along the line

Thank You