### Formulas

For each system parameter, per-unit value is equal to the actual value divided by a base value:

**E _{pu} = E / E_{base}**

**I _{pu} = I / I_{base}**

**Z _{pu} = Z / Z_{base}**

Select rated values as base values, usually rated power in MVA and rated phase voltage in kV:

**S _{base} = S_{rated} = Ö3E_{line}I_{line}**

**E _{base} = E_{phase} = E_{line}/ Ö3**

The base values for line current in kA and per-phase star impedance in ohms/phase are:

**I _{base} = S_{base} / 3E_{base} ( = S_{base} / Ö3E_{line})**

**Z _{base} = E_{base} / I_{base} = 3E_{base}^{2} / S_{base} ( = E_{line}^{2} / S_{base})**

Note that selecting the base values for any two of **S _{base}**,

**E**,

_{base}**I**or

_{base}**Z**fixes the base values of all four. Note also that Ohm’s Law is satisfied by each of the sets of actual, base and per-unit values for voltage, current and impedance.

_{base}#### Transformers

The primary and secondary MVA ratings of a transformer are equal, but the voltages and currents in the primary (subscript ** _{1}**) and the secondary (subscript

**) are usually different:**

_{2}**Ö3E _{1line}I_{1line} = S = Ö3E_{2line}I_{2line}**

Converting to base (per-phase star) values:

**3E _{1base}I_{1base} = S_{base} = 3E_{2base}I_{2base}**

**E _{1base} / E_{2base} = I_{2base} / I_{1base}**

**Z _{1base} / Z_{2base} = (E_{1base} / E_{2base})^{2}**

The impedance **Z _{21pu}** referred to the primary side, equivalent to an impedance

**Z**on the secondary side, is:

_{2pu}**Z _{21pu} = Z_{2pu}(E_{1base} / E_{2base})^{2}**

The impedance **Z _{12pu}** referred to the secondary side, equivalent to an impedance

**Z**on the primary side, is:

_{1pu}**Z _{12pu} = Z_{1pu}(E_{2base} / E_{1base})^{2}**

Note that per-unit and percentage values are related by:

**Z _{pu} = Z_{%} / 100**

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. | ||||||

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] |

What the hell is “Ö3”? I never heard of it!

It is root(3)