If a radial line delivers 60 MVAR with a total loading of 100 MVA, what is the active power delivered?

To determine the active power delivered in this scenario, we can use the relationship between active power (P), reactive power (Q), and apparent power (S) in a power system. This relationship is defined by the equation:

[ S^2 = P^2 + Q^2 ]

Where:

• ( S ) is the apparent power in MVA,

• ( P ) is the active power in MW,

• ( Q ) is the reactive power in MVAR.

In this case, we are provided with:

• ( S = 100 ) MVA (the total loading),

• ( Q = 60 ) MVAR (the reactive power delivered).

Now, substituting the known values into the equation:

[ (100)^2 = P^2 + (60)^2 ]

Calculating these squares, we have:

[ 10000 = P^2 + 3600 ]

To find ( P^2 ), we rearrange the equation:

[ P^2 = 10000 - 3600 = 6400 ]

Taking the square root of both sides gives us:

[ P = \sqrt{6400} = 80 \text{ MW} ]

Hence