## Efficency

**
The
per-unit efficiency
h of an electrical machine with input power P _{in}, output power P_{out}
and power loss P_{loss} is:**

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} /
h
**

For an
electrical machine with output power P_{out} (proportional to
current) and power loss P_{loss} comprising a fixed loss P_{fix}
(independent of current) plus a variable loss P_{var} (proportional
to square of current) the efficiency is a maximum when P_{var} is
equal to P_{fix}.

For a
transformer, P_{fix} is the iron loss and P_{var} is the
copper loss plus the stray loss.

For an
induction machine, P_{fix} is the iron loss plus the mechanical loss
and P_{var} 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.