What is the actual VARS delivered by a 60 MVAR shunt capacitor bank at 0.9 p.u. voltage?

To determine the actual VARs delivered by a shunt capacitor bank, we need to consider the impact of the system voltage on the capacity of the capacitor bank. Capacitors are designed to deliver a certain amount of reactive power, measured in VARs, under specific conditions, typically at a rated voltage.

In this case, the shunt capacitor bank is rated at 60 MVAR, which means under nominal conditions (1 per unit voltage), it would indeed deliver 60 MVAR of reactive power. However, because the voltage is stated to be at 0.9 p.u., we need to calculate the actual reactive power delivered at this reduced voltage level.

Reactive power delivered by a capacitor bank is proportional to the square of the voltage. Therefore, if the voltage is at 90% of the nominal level, the delivered VARs will be calculated using the formula:

Actual VARs = Rated VARs × (Voltage in p.u.)²

Substituting the values:

Actual VARs = 60 MVAR × (0.9)²

Actual VARs = 60 MVAR × 0.81

Actual VARs = 48.6 MVAR

Since we're often dealing with rounded figures in such questions, we can