Can average power be non zero, but instantaneous power be zero Q. A wind-powered generator converts wind energy into electric energy, Assume that the generator converts a fixed fraction of wind energy intercepted by its blades into electrical energy. For wind speed v, the electric power output will be proportional to:
In this problem my teacher told me that the power is non zero since the mass of the fluid changes with time (it's proportional to the velocity)
Which got me thinking about a similar problem, for example a person is cycling with a constant velocity for 30 min and the machine is connected to a generator which converts mechanical energy into electrical. The average power over the duration the person cycles is obviously (30 min) non zero since work is being performed over a duration, but what about the instantaneous power? Will it be zero, for instance in an infinitesimally small time when he's cycling with constant velocity.
 A: 
The average power is obviously non zero since work is being performed over a duration.

Being more specific, for average power you must specify the time interval you are considering. There isn't just "average power"; you have to say something like "the average power from $2$ to $4$ seconds" or something like that. From there it completely depends on the energy input/output at the start and end of the interval: $P_\text{avg}=\Delta E/\Delta t$. Note that even if work is being done over the entire interval, if $\Delta E=0$ (i.e. if the energy didn't change) then the average power is still $0$.

but what about the instantaneous power? Will it be zero, for instance in between?

You have described a constant, non-zero power process, so the instantaneous power is also constant and non-zero. Just because it happens over an instant doesn't mean it is $0$.
Hitting the title then

Can average power be non zero, but instantaneous power be zero

Yes! Just as stated above, for average power you need to specify a time interval. For instantaneous power you just specify an instant in time. So you can certainly have an interval where over it the average power is non-zero but there is an instant in time within that interval where the instantaneous power is $0$. e.g. if on that interval the instantaneous power switches from positive to negative then at some point it will need to be $0$, assuming the power as a function of time is continuous.
Side note: if things still aren't making sense, just think about average vs. instantaneous velocity; the differences between average and instantaneous are exactly the same, but it might be easier to grasp velocity instead of power.
