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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 = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(3)
and I = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (4)
P=I * V (5)
gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia From (4)

This becomes gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia V = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (6)
Let P = VAR
Then Z =gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(7)
or Z =gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(8)
Or Z = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (9)
Letting Z = XC Or XL (10)
We have XC (Or XL) = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (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 = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 259.168 Ohms

A three-phase shunt reactor of 150KVAR, at 13.8KV will yield

Xc = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia =  gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 1269.6 Ohms


2. Capacitance

XC = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(12)
But, as stated VAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (6)

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia VAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (13)
Or = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (14)
Then VAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(15)
KVAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (16)

Example:

From above 600KVAR at 12.47KV equals 259.168 Ohms and from (12)

XC = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia. Then C = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Let f = 60 Hertz gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Then C = 0.000010235 farads or 10.235 microfarads.

From (16) KVAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

KVAR = 600


3. Inductance

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(17)
VAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia from (6) = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(18)
KVAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (19)

From above 150KVAR at 13.8KV equals 1269.6 Ohms and from (17)

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia. Let f = 60 Hertz gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Then L = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 3.36773 Henries

Or 3367.73 millihenries.

From (19) KVAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

KVAR = 150

  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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