In a 750KVAR capacitor bank operating at 13.8kV and 60Hz, what is the calculated capacitive reactance (Xc)?

To calculate the capacitive reactance (Xc) of a capacitor bank, the formula used is:

[ X_c = \frac{V^2}{Q} ]

where ( V ) is the voltage in volts and ( Q ) is the reactive power in VARs. First, the voltage must be converted from kilovolts to volts. Since the operating voltage is 13.8 kV, we convert it as follows:

[ V = 13.8 , kV \times 1000 = 13800 , V ]

Next, the reactive power is given as 750 KVAR, which also needs to be converted to VARs:

[ Q = 750 , kVAR \times 1000 = 750000 , VAR ]

Now we can plug these values into the formula for ( X_c ):

[ X_c = \frac{(13800)^2}{750000} ]

Calculating the squared voltage:

[ (13800)^2 = 190440000 ]

Now substituting this value into the formula:

[ X_c = \frac{190440000}{750000} \approx 254.25 , \Omega ]

R