A transformer rated at 50 MVA is currently carrying 30 MW of load. At this load, what is the maximum allowable MVAR flow through the transformer?

• A. 50 MVAR
• B. 30 MVAR
• C. 40 MVAR
• D. 0 MVAR

Answer: (C)

To determine the maximum allowable MVAR flow through a transformer rated at 50 MVA while it is carrying a load of 30 MW, it is essential to understand the relationship between real power (MW), reactive power (MVAR), and apparent power (MVA).

The apparent power (S) in a transformer can be expressed as the vector sum of its real power (P) and reactive power (Q):

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

In this case, the transformer is rated for 50 MVA, which is the maximum level of apparent power it can handle. The real power load is given as 30 MW, and we want to find out how much reactive power can flow through the transformer without exceeding its rated capacity.

Given that S = 50 MVA and P = 30 MW, we can rearrange the formula to solve for Q (reactive power):

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

[ Q = \sqrt{50^2 - 30^2} ]

[ Q = \sqrt{2500 - 900} ]

[ Q = \sqrt{1600} ]

[ Q = 40 ,