Three Phase Power

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Formulas

For a balanced star connected load with line voltage V_line and line current I_line:

V_star = V_line / Ö3

I_star = I_line

Z_star = V_star / I_star = V_line / Ö3I_line

S_star = 3V_starI_star = Ö3V_lineI_line = V_line² / Z_star = 3I_line²Z_star

For a balanced delta connected load with line voltage V_line and line current I_line:

V_delta = V_line

I_delta = I_line / Ö3

Z_delta = V_delta / I_delta = Ö3V_line / I_line

S_delta = 3V_deltaI_delta = Ö3V_lineI_line = 3V_line² / Z_delta = I_line²Z_delta

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:

Z_delta = 3Z_star

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]

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