# A Learning-Based Methodology to Optimally Fit Short-Term Wind-Energy Bands
## 3 Optimization of Wind-Energy Bands
### Experimental Evaluation
Figure 11: Average width of bands found for the training set as \(\theta\) changes while \(\lambda\) is fixed in 1 [leftmost], relative deviation between average widths register for training and testing sets [middle], and violations of off-band energy limits over testing set. [red samples correspond to Garrad Hassan, blue ones to Meteologica and green to PSF44]. Figure 10: Wind-energy bands for the same days when \(\theta=\) 0.01 instead of \(\theta=\) 0.05 [\(\lambda=1\)]. Regarding off-band energy violations to the limit \(\theta\) when computed over the test-set (they do not happen in the training-set because of (2)(\(ii\))), the rightmost of Figure 11 shows the fraction of those violations, i.e., the fraction of samples where the off-band energy surpasses \(T\theta\). They are also low for all forecasts and are particularly lower as values of \(\theta\) get apart from zero. The previous exercise experimentally justifies the persistence hypothesis this technique is based on. The goal of this work is providing stochastic short-term optimal power dispatch schedulers, with accurate wind-energy bands, in the context of the Uruguayan Electricity Market. In particular, our interest is keeping off-band energy below 10% of the average PLF, which is around 0.35; so we consider \(\theta=0.035\). In Uruguay, 35% of electricity comes from wind-power sources, thus that value of \(\theta\) corresponds to 1.23% of the average energy consumed, what is ambitious. That value is used as reference during this work. The other parameter to consider is \(\lambda\) which attends to the fact that, whatever accurate a family of forecasts may be, there will always be samples that degrade the overall quality of the whole. Table 2 shows how some attributes of the bands change as \(\lambda\) decreases from 1 to 0.6, while \(\theta\) remains fixed in 0.035 (our target off-band violation). The first three four columns correspond to Meteologica forecasts, the second part does to [PERSON]'s and the last one to PSF44 forecasts. These metrics were computed over the test-set by using optimal \(x\) coefficients for each \(\lambda\) over the samples in the training-set. Columns labeled as %_anomalous_ indicate the percentage of the samples, in each case, whose off-band energies surpasses the 0.035 of the total plant factor (\(T\theta\)). We decided to use different adjectives to distinguish between _atypical days_: samples intentionally excluded from the training-set, and _anomalous days_: samples in the testing-set that by chance surpass the off-band energy limit. The columns \(\overline{BW}\) and %\(\overline{BW}\) respectively show the average absolute and relative areas of the wind-power bands over the test set, using 72 as the full plant factor for the time horizon. Finally, the number of seconds spent by the solver to find the optimal solution for each case appears in the column labeled as \(t\)(s). Observe that as \(\lambda\) decreases so it does the expected width for energy bands, because the solver is allowed to select down to \(\lambda D\) days during the training, and the optimization ends up by crafting bands for the best subset with a \(\lambda\) fraction of the original number of days. Computation times ascend, because (2) becomes combinatorial for \(\lambda<1\). Conversely, the percentage of _anomalous days_ (i.e., those whose off-band energy falls outside the limit) increases, since the calibration performed over a partial/elite training-set is no longer representative over the complement (i.e., the test-set). A second goal of this work is keeping the percentage of _anomalous days_ below 10%, which translates into attaining the target \(\theta\) at least 90% of the times. The final goal is over the allowed variance for wind-power. Until now, we have focused upon energy rather than power. Keeping the process within narrower bands