# Mdp1 _sciences_
## 3 Results & Discussion
### Forecast-Based Curtailment  
Now that the capability of the different forecast approaches to predict wind speed changes two time steps into the future has been documented at some detail, it can be explored how these results translate into the mitigation of incompliance events through forecast-based curtailment (FBC). Two metrics will be discussed: (1) The FBC efficiency (Equation (8)), and (2) the relative energy cost \(\Delta E/E\), where \(\Delta E\) is the curtailed amount of energy, and \(E\) is the uncurtailed energy production for the observation period (\(\sim\)1a). Both quantities depend on the critical or tolerable slope \(a\) introduced before.  
The results can be inspected in Figure 10, together with those of the ideal case, i.e., for perfect forecasts. The ideal FBC efficiency curve can seen to be nearly flat, with an average value of around 80% and a slight nearly linear increase towards higher critical slope values. While not all incompliance events can be mitigated with the FBC method, it is certainly encouraging to see that a method relying solely on the self-regulation capabilities of a wind turbine should be able to mitigate most of the events that might be of concern to the operator of the electric grid. The associated energy penalty for the ideal case is very small, about 0.2% for a critical slope \(a\) of 1 m/s and practically zero for slopes of 2 m/s or higher. (It should be remembered that \(a\) is always taken as a positive quantity, and all incompliance events correspond to \(y<-a\).) This is particularly noteworthy in the light of the common practice of utilities or independent system operators to require a _flat_ curtailment of wind power plants during periods of low regulation reserves (i.e., a restriction to a maximum power output below rated power, or reduction by a constant factor), which may result in very substantial energy penalties. (See Reference [14] for an introduction to the subject and Reference [20] for a systematic comparison between the energy cost of FBC and flat curtailment.)  
Not unexpectedly, the practical forecast methods implemented in this work do not quite live up to the expectations of the ideal method, but their contributions are still fairly substantial. As before, the ensemble methods constructed from the methods using exogenous data fare best, with an FBC efficiency of around 35%, as shown in Figure 10. The FBC efficiency is nearly independent of the critical slope \(a\), with only a slight increase towards larger \(a\)-values. Interestingly, the reference method (KF4), based on measurement data from the target tower alone, not only fails to improve compliance but even decreases it, as demonstrated by its negative FBC efficiency in Figure 10. This is readily explained in terms of the unfavorable ratio between false and true positives of the method; see Figures 9 and 11. Given that the rate for false positives is about one order of magnitude higher than the rate of true positives (which is only about 10%), there are many events that lead to overcorrection. This stresses the need for exogenous data, as successfully demonstrated in this work.  
Figure 10: FBC results for all methods. Left: FBC efficiency, right: curtailment cost.