# Overhead Lines and Transformers

When fully loaded, overhead lines absorb reactive power. With a current *I* amperes flowing in a line of reactance per phase X(V) the VArs absorbed are I^{2}X per phase. On light loads the shunt capacitances of longer lines may become dominant and high voltage overhead lines then become VAr generators.

Transformers always absorb reactive power. A useful expression for the quantity may be obtained for a transformer of reactance *X _{T}* p.u. and a full load rating of

^{3}*V**f*^{I}*rated*

The ohmic reactance Therefore the VArs absorbed

# Cables

Cables are generators of reactive power owing to their high shunt capacitance.

A 275 kV, 240 MVA cable produces 6.25-7.5 MVAr per km; a 132 kV cable roughly 1.9 MVAr per km; and a 33 kV cable, 0.125 MVAr per km.

# Loads

A load at 0.95 power factor implies a reactive power demand of 0.33 kVAr per kW of power, which is more appreciable than the mere quoting of the power factor would suggest. In planning a network it is desirable to assess the reactive power requirements to ascertain whether the generators are able to operate at the required power factors for the extremes of load to be expected. An example of this is shown in Figure 5.2, where the reactive losses are added for each item until the generator power factor is obtained.

Example 5.1

In the radial transmission system shown in Figure 5.2, all p.u. values are referred to the voltage bases shown and 100 MVA. Determine the power factor at which the generator must operate.

**Solution**

Voltage drops in the circuits will be neglected and the nominal voltages assumed.

Starting with the consumer load, the VArs for each section of the circuit are added in turn to obtain the total Busbar A,

**Figure 5.2 **Radial transmission system with intermediate loads. Calculation of reactive-power requirement

I^{2} * x* loss in 132 kV lines and transformers
Busbar C,

* I^{2}X* loss in 275 kV lines and transformers

If the I^{2}X loss in the large generator-transformer is ignored, the generator must deliver * P* — 2.5 and Q = 2.125 p.u. and operate at a power factor of 0.76 lagging.