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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]

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