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

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

• A. 30 MW
• B. 40 MW
• C. 100 MW
• D. 80 MW

Answer: (D)

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

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