What is the expected output if a capacitor bank rated at 100 MVAR operates at a system voltage of 0.9 PU?

The expected output of the capacitor bank operating at 0.9 per unit (PU) voltage can be understood by considering the relationship between the reactive power output of a capacitor and the operating voltage.

Capacitor banks are rated based on their reactive power output at a nominal system voltage. When the system voltage deviates from the nominal value, the output reactive power changes in proportion to the square of the voltage. The formula that relates reactive power (Q) to voltage (V) and rated capacity (Q_rated) is given by:

[ Q = Q_{rated} \times \left( \frac{V}{V_{rated}} \right)^2 ]

Given that the capacitor bank is rated at 100 MVAR, and the operating voltage is 0.9 PU, it can be plugged into the formula:

[ Q = 100 , \text{MVAR} \times (0.9)^2 ]

Calculating this gives:

[ Q = 100 , \text{MVAR} \times 0.81 = 81 , \text{MVAR} ]

This shows that when the operating voltage is at 0.9 PU, the output of the capacitor bank reduces to