Basic Formulas
The following pages of formulas, some derivations and discussions are intended to assist in designing and applying capacitor banks properly. Also, refer to Capacitor Bank Inrush Calculations for additional information.
1. Ohm’s Law
RI = V
or
V = IZ
|
(1)
(2)
|
Then Z = 
|
(3) |
and I =  |
(4) |
| P=I * V |
(5) |
From (4)
|
|
This becomes  V =  |
(6) |
| Let P = VAR |
|
Then Z =
|
(7)
|
or Z =
|
(8) |
Or Z =  |
(9) |
| Letting Z = XC Or XL |
(10) |
We have XC (Or XL) =  |
(11) |
This will allow you to determine the reactance of a capacitor or reactor when voltage and KVAR is given.
Example:
A three-phase 600KVAR capacitor bank at 12,470 will yield
Xc = =  = 259.168 Ohms
A three-phase shunt reactor of 150KVAR, at 13.8KV will yield
Xc = =  = 1269.6 Ohms
2. Capacitance
XC = 
|
(12)
|
But, as stated VAR = (6)
|
|
 VAR =  |
(13) |
Or =  |
(14) |
Then VAR = 
|
(15)
|
KVAR =  |
(16) |
Example:
From above 600KVAR at 12.47KV equals 259.168 Ohms and from (12)
XC = . Then C = 
Let f = 60 Hertz 
Then C = 0.000010235 farads or 10.235 microfarads.
From (16) KVAR = 
KVAR = 600
3. Inductance
|
(17)
|
VAR = from (6) = 
|
(18) |
KVAR =  |
(19) |
From above 150KVAR at 13.8KV equals 1269.6 Ohms and from (17)
. Let f = 60 Hertz
Then L =  =  = 3.36773 Henries
Or 3367.73 millihenries.
From (19) KVAR =  = 
KVAR = 150
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LEGEND |
| R |
Resistance |
| I |
Amps |
| V |
Volts |
| Z |
Impedance |
| P |
Power (in Watts and/or Vars) |
| VAR |
Reactive Power |
| K |
Kilo (103) |
| XC |
Capacitive Reactance |
| XL |
Inductive Reactance |
| M |
Mega (10>6) |
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