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# Three Phase Power

### Formulas

For a balanced star connected load with line voltage Vline and line current Iline:

Vstar = Vline / Ö3

Istar = Iline

Zstar = Vstar / Istar = Vline / Ö3Iline

Sstar = 3VstarIstar = Ö3VlineIline = Vline2 / Zstar = 3Iline2Zstar

For a balanced delta connected load with line voltage Vline and line current Iline:

Vdelta = Vline

Idelta = Iline / Ö3

Zdelta = Vdelta / Idelta = Ö3Vline / Iline

Sdelta = 3VdeltaIdelta = Ö3VlineIline = 3Vline2 / Zdelta = Iline2Zdelta

The apparent power S, active power P and reactive power Q are related by:

S2 = P2 + Q2

P = Scosf

Q = Ssinf

where cosf is the power factor and sinf is the reactive factor

Note that for equivalence between balanced star and delta connected loads:

Zdelta = 3Zstar

 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]