### Formulas

The per-unit efficiency **h** of an electrical machine with input power **P _{in}**, output power

**P**and power loss

_{out}**P**is:

_{loss}**h = P**

_{out}/ P_{in}= P_{out}/ (P_{out}+ P_{loss}) = (P_{in}– P_{loss}) / P_{in}Rearranging the efficiency equations:

**P _{in} = P_{out} + P_{loss} = P_{out} / h = P_{loss} / (1 – h)**

**P**

_{out}= P_{in}– P_{loss}= hP_{in}= hP_{loss}/ (1 – h)**P**

_{loss}= P_{in}– P_{out}= (1 – h)P_{in}= (1 – h)P_{out}/ hFor an electrical machine with output power **P _{out}** (proportional to current) and power loss

**P**comprising a fixed loss

_{loss}**P**(independent of current) plus a variable loss

_{fix}**P**(proportional to square of current) the efficiency is a maximum when

_{var}**P**is equal to

_{var}**P**.

_{fix}For a transformer, **P _{fix}** is the iron loss and

**P**is the copper loss plus the stray loss.

_{var}For an induction machine, **P _{fix}** is the iron loss plus the mechanical loss and

**P**is the copper loss plus the stray loss.

_{var}*Energy Conversion*

Comparing megawatt-hours and gigajoules, 1 MWh is equivalent to 3.6 GJ. For an energy conversion process with a per-unit efficiency **h**, 1 MWh of energy output is obtained from (3.6 / **h**) GJ of energy input.

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. | ||||||

BE f G I j k m N n P p R | susceptance induced voltage frequency conductance current j-operator coefficient number of phases number of turns rotational speed power pole pairs resistance | [siemens, S] [volts, V] [hertz, Hz] [siemens, S] [amps, A] [1Ð90°] [number] [number] [number] [revs/min] [watts, W] [number] [ohms, W] | SsTVXYZdFfhqw | voltamperes slip torque terminal voltage reactance admittance impedance loss angle magnetic flux phase angle efficiency temperature angular speed | [volt-amps, VA] [per-unit] [newton-metres, Nm] [volts, V] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [webers, Wb] [degrees, °] [per-unit] [centigrade, °C] [radians/sec] |