When the voltage is at 207 kV, how many MVARs does a 230 kV, 50 MVAR capacitor bank provide?

To determine the number of MVARs that a 230 kV, 50 MVAR capacitor bank provides at a voltage of 207 kV, it is essential to understand the relationship between voltage and reactive power (MVAR). Capacitor banks provide reactive power that is dependent on the voltage level at which they operate. The relationship is roughly proportional to the square of the voltage.

Given that the capacitor bank is rated at 50 MVAR at its base voltage of 230 kV, we can calculate the MVAR output at a lower voltage, which is 207 kV, using the formula:

MVAR_output = MVAR_rated * (V_actual^2/V_rated^2)

Substituting the known values into the formula:

MVAR_output = 50 * (207^2 / 230^2)

Calculating the squares:

207^2 = 42849

230^2 = 52900

Now, substituting these values in:

MVAR_output = 50 * (42849 / 52900)

MVAR_output = 50 * 0.8109 ≈ 40.54

Since reactive power outputs are usually rounded to the nearest whole number, this rounds to approximately