BUNDLED CONDUCTORS INVOLVING CAPACITANCE

The equivalent circuit of a short transmission line is shown in Fig. 5.4,where

Is- sending-end current
Ir- receiving-end current
Vs- sending-end line-to-neutral voltage
Vr- receiving-end line-to-neutral voltage

The circuit is solved as a simple series ac circuit. Since there are no shunt arms, the current is the same at the sending and receiving ends of the line and


The voltage at the sending end is


where Z is zl, the total series impedance of the line.

The effect of the variation of the power factor of the load on the voltage regulation of a line is most easily understood for the short line and therefore will be considered at this time. Voltage regulation of a transmission line is the rise in voltage at the receiving end, expressed in percent of full-load voltage when full load at a specified power factor is removed while the sending-end voltage is held constant. In the form of an equation


where is the magnitude of receiving-end voltage at no load and is the magnitude of receiving-end voltage at full load with constant. After the load on the short transmission line represented by the circuit of Fig. 5.4, is removed, the voltage at the receiving-end is equal to the voltage at the sending-end. In Fig. 5.4, with the load connected, the receiving-end voltage is designated by and . The sending-end voltage is and The phasor diagrams of Fig. 5.5 are drawn for the same magnitudes of receiving-end voltage and current and show that a larger value of sending-end voltage is required to maintain a given receiving-end voltage when the receiving-end current is lagging the voltage than when the same current and voltage are in phase. A still smaller sending-end voltage is required to to maintain the given receiving-end voltage when the receiving-end current leads the voltage. The voltage drop is the same in the series impedance of of the line in all cases, but because of the different power factors the voltage drop is added to the to the receiving-end voltage at a different angle in each case. The regulation is greatest for lagging power factors. The inductive reactance of a transmission line is larger than the resistance, and the principle of regulation illustrated in Fig. 5.5 is true for any load supplied by a predominantly inductive circuit. The magnitude of the voltage drop for a short line have been exaggerated with respect to in drawing the phasor diagrams in order to illustrate the point more clearly. The relation between the power factor and regulations for longer line is similar to that for short lines but is not visualized so easily.