If a transmission line carries 400 MW and 300 MVAR, what is the total MVA?

To find the total MVA (megavolt-amperes), you need to consider both the active power (MW) and the reactive power (MVAR) in the transmission line. The relationship between these powers and the total apparent power (MVA) can be described using the Pythagorean theorem as the active and reactive powers are orthogonal components.

The formula to calculate the total MVA is:

[

\text{Total MVA} = \sqrt{(\text{MW})^2 + (\text{MVAR})^2}

]

In this case, you have 400 MW of active power and 300 MVAR of reactive power. Plugging in the values:

[

\text{Total MVA} = \sqrt{(400)^2 + (300)^2} = \sqrt{160000 + 90000} = \sqrt{250000} = 500 \text{ MVA}

]

This calculation shows that the total apparent power in the transmission line is indeed 500 MVA, representing the combined effect of both the real and reactive power. Thus, the answer indicating that total MVA is 500 is accurate, reflecting the correct use of the power calculations in electric