### 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_{star}I_{star} = Ö3V_{line}I_{line} = V_{line}^{2} / Z_{star} = 3I_{line}^{2}Z_{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_{delta}I_{delta} = Ö3V_{line}I_{line} = 3V_{line}^{2} / Z_{delta} = I_{line}^{2}Z_{delta}**

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

**S**

^{2}= P^{2}+ Q^{2}**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 |
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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. |
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BCEfGhIjLPQ |
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] |
QRStVWXYZfw |
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] |