What is the power factor of the Roxboro-Milburnie Black 230kV line with energy flows of 80 MW and 60 MVAR?

To determine the power factor of the Roxboro-Milburnie Black 230kV line, you need to analyze both the real power (MW) and the reactive power (MVAR). The power factor is defined as the ratio of real power flowing to the load, to the apparent power in the circuit.

In this case, the real power is 80 MW, and the reactive power is 60 MVAR. The apparent power (S) can be calculated using the Pythagorean theorem because apparent power is the vector sum of real and reactive power.

The formula is:

[ S = \sqrt{P^2 + Q^2} ]

where:

• ( P ) = real power (in MW)

• ( Q ) = reactive power (in MVAR)

Substituting the given values:

[ S = \sqrt{(80)^2 + (60)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \text{ MVA} ]

The power factor (PF) can then be calculated using the formula:

[ PF = \frac{P}{S} = \frac{80 \text{ MW}}{100 \