Formulas
If an inductive load with an active power demand P has an uncorrected power factor of cosf1 lagging, and is required to have a corrected power factor of cosf2 lagging, the uncorrected and corrected reactive power demands, Q1 and Q2, are:
Q1 = P tanf1
Q2 = P tanf2
where tanfn = (1 / cos2fn – 1)½
The leading (capacitive) reactive power demand QC which must be connected across the load is:
QC = Q1 – Q2 = P (tanf1 – tanf2)
The uncorrected and corrected apparent power demands, S1 and S2, are related by:
S1cosf1 = P = S2cosf2
Comparing corrected and uncorrected load currents and apparent power demands:
I2 / I1 = S2 / S1 = cosf1 / cosf2
If the load is required to have a corrected power factor of unity, Q2 is zero and:
QC = Q1 = P tanf1
I2 / I1 = S2 / S1 = cosf1 = P / S1
Shunt Capacitors
For star-connected shunt capacitors each of capacitance Cstar on a three phase system of line voltage Vline and frequency f, the leading reactive power demand QCstar and the leading reactive line current Iline are:
QCstar = Vline2 / XCstar = 2pfCstarVline2
Iline = QCstar / Ö3Vline = Vline / Ö3XCstar
Cstar = QCstar / 2pfVline2
For delta-connected shunt capacitors each of capacitance Cdelta on a three phase system of line voltage Vline and frequency f, the leading reactive power demand QCdelta and the leading reactive line current Iline are:
QCdelta = 3Vline2 / XCdelta = 6pfCdeltaVline2
Iline = QCdelta / Ö3Vline = Ö3Vline / XCdelta
Cdelta = QCdelta / 6pfVline2
Note that for the same leading reactive power QC:
XCdelta = 3XCstar
Cdelta = Cstar / 3
Series Capacitors
For series line capacitors each of capacitance Cseries carrying line current Iline on a three phase system of frequency f, the voltage drop Vdrop across each line capacitor and the total leading reactive power demand QCseries of the set of three line capacitors are:
Vdrop = IlineXCseries = Iline / 2pfCseries
QCseries = 3Vdrop2 / XCseries = 3VdropIline = 3Iline2XCseries = 3Iline2 / 2pfCseries
Cseries = 3Iline2 / 2pfQCseries
Note that the apparent power rating Srating of the set of three series line capacitors is based on the line voltage Vline and not the voltage drop Vdrop:
Srating = Ö3VlineIline
| NOTATION | ||||||
| The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. | ||||||
| B C E f G h I j L P Q | susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power | [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] | Q R S t V W X Y Z f w | quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency | [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec] | |
Subscribe to Monthly Download Updates
Don't miss anything!
Get EEP's updates without having to keep checking up on the portal to see if there is anything new. New FREE technical articles, electrical books, guides, software and other exclusive content you will receive via email. Pretty simple!
ahmad
we have a 420 kva transformer and the load is about 380kva help me to find the best capasitor bank
for this specification
thank