For a distribution line rated at 50 MVA, with 50 MW and -50 Mvar, is the line overloaded?

To determine if a distribution line rated at 50 MVA is overloaded when it carries 50 MW and -50 Mvar, it’s essential to understand how power ratings work in terms of real power (MW) and reactive power (Mvar).

The apparent power (S) for a line can be calculated using the formula:

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

where P is the real power in MW and Q is the reactive power in Mvar. In this case:

• P = 50 MW

• Q = -50 Mvar (negative indicates that it's capacitive reactive power)

By inserting these values into the equation:

[ S = \sqrt{(50)^2 + (-50)^2} ]

[ S = \sqrt{2500 + 2500} ]

[ S = \sqrt{5000} ]

[ S \approx 70.71 \text{ MVA} ]

The calculated apparent power is approximately 70.71 MVA, which exceeds the line's rating of 50 MVA. This indicates that the line is indeed overloaded, as it is carrying more apparent power than it is designed to handle.

The option stating that the line