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# Efficiency

### Formulas

The per-unit efficiency h of an electrical machine with input power Pin, output power Pout and power loss Ploss is:
h = Pout / Pin = Pout / (Pout + Ploss) = (Pin – Ploss) / Pin

Rearranging the efficiency equations:
Pin = Pout + Ploss = Pout / h = Ploss / (1 – h)
Pout = Pin – Ploss = hPin = hPloss / (1 – h)
Ploss = Pin – Pout = (1 – h)Pin = (1 – h)Pout / h

For an electrical machine with output power Pout (proportional to current) and power loss Ploss comprising a fixed loss Pfix (independent of current) plus a variable loss Pvar (proportional to square of current) the efficiency is a maximum when Pvar is equal to Pfix.

For a transformer, Pfix is the iron loss and Pvar is the copper loss plus the stray loss.

For an induction machine, Pfix is the iron loss plus the mechanical loss and Pvar is the copper loss plus the stray loss.

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. B E 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] S s T V X Y Z d F f h q w 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]