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I need to know why capacitor banks are rated in KVAr rather than Farads?
Suppose I have one capacitor bank of 10kVAr which is for a rated voltage of 400V. Will this bank provide the same reactive power of 10KVAr at 200V? Ir will it change? If yes, how can I calculate how much reactive power it will provide at 200V?
Capacitor banks designed for power factor correction are rated in kVAr (kilo-volt-ampere reactive) because it's convenient. One will typically know the reactive power required by some load, then it's simply a matter of selecting a capacitor of the equal but negative reactive power to improve the power factor.
Reactive power \$Q\$ for a purely reactive load (such as a capacitor) is calculated by:
$$ Q = {|V|^2 \over X} $$
Where \$V\$ is the voltage, and \$X\$ is the reactance which can be calculated by:
$$ X = {-1 \over 2 \pi f C} $$
where \$C\$ is the capacitance. Putting those together, the relationship between reactive power (kilo-volt-ampere reactive, \$Q\$) and capacitance (farad, \$C\$) is:
$$ Q = - 2 \pi\, f C\, |V|^2 $$
Since the frequency and voltage of a power distribution system are typically fixed, specifying the capacity in kVAr instead of F eliminates some of the mundane calculation required.
Since the reactive power is proportional to the square of the voltages, converting to kVAr at one voltage can be converted to another voltage by examining the ratio of the squares of the voltages. For example:
$$ {208^2 \over 240^2} = 0.7511 $$
So to convert a kVAr rating for 240 VAC to one for 208 VAC, multiply by 0.75.
Similarly adjustment is required if the frequency is other than specified.
It's like measuring water volume in acre-feet instead of gallons or m3, if you have a reservoir with a catchment of known area that needs to be filled by rainfall. It's a convenient application-specific version of the same unit.
At a given voltage and frequency, which are always nominally constant in the context of correcting power factor, Farads and kVAr are related by a simple constant of proportionality. Work it out once for your location, then you can label your capacitors in an application-specific way, rather than a physics oriented way.
[10kvar x (200x200)]/(400x400)=2.5kvar.
So, the 10kvar capacitor bank rated at 400v will provide 2.5kvar at 200v.
