If a 50 MVAR shunt capacitor is energized at a 100 kV bus when the bus is at 90 kV, what is the MVAR output?

To determine the output of a shunt capacitor when it is energized at a voltage lower than its rated voltage, you need to consider how capacitors behave with respect to voltage changes. The MVAR output of a capacitor is proportional to the square of the voltage across it.

In this case, the shunt capacitor is rated for 50 MVAR at 100 kV. When the bus voltage drops to 90 kV, the output can be calculated using the ratio of the voltage squared at 90 kV to the voltage squared at 100 kV:

1. Calculate the voltage ratio:

• The voltage ratio is ( \frac{V_{new}}{V_{rated}} = \frac{90}{100} = 0.9 ).

2. Since the output is proportional to the square of the voltage, you need to square this ratio:

• ( (0.9)^2 = 0.81 ).

3. Multiply the rated MVAR by this squared ratio to find the output at the lower voltage:

• Output MVAR = 50 MVAR * 0.81 = 40.5 MVAR.

This calculation shows that when the bus is at 90 kV, the