# Relation between power and energy

If I have an expression for the 'rated generator power' of a wind turbine, call it $P(t)$ how is the energy, that the wind turbine generator generate, related to the power $P(t)$?

So:

$$E(t)=\dots$$

• Power can be interpreted as energy consumed per second. So if a device consumes energy 'E' in 't' seconds then the energy consumed per unit time ,i.e $\frac{E}{t}$, will give us the power. – Mitchell May 17 '17 at 11:09
• Why not just $E(t) = \int_0^t P(t) dt$ ? – Cheeku May 17 '17 at 11:11

From the Wikipedia article on power it states that

power is the rate of doing work. It is the amount of energy consumed per unit time.

Therefore: $$P = \frac {dE}{dt}$$ and therefore (assume we start at $t = 0$) you can integrate to get: $$E(t) = \int_0^t P (t)\ dt$$