I have the following problem:
- a wind farm
- uncontrolled input: time and location-dependent wind speed
- control input: time-dependent induction factor
- set values: time-dependent power demand
- output: total power
For simplicity, let’s assume that all turbines use the same control input, so the input and the output are scalar.
I want to use feed-forward control; the control signal depends on the time and location-dependent wind speed, multiplied by a time-dependent correction factor that is a spline with 6 control points.
Each of these control point values has a strong correlation with the power output in distinct time intervals, so we can say:
y_i \approx f(u_i)
And we try to minimize the error
e_i = r_i - y_i
where r(t) is the time-dependent demand, and r(i) the demand in the i-th time segment.
Running the simulation once is costly, like 2 to 3 seconds. Furthermore, the output is noisy. If I minimize the integral of the error over the simulation time, I need 500 to 1000 black box evaluations to find a solution. However, due to the strong correlation between u_i and y_i, I believe that a different algorithm might be faster.
Any suggestions?
Perhaps a stochastic root-finding method could be used?