## 3 Results
### Optimistic and Pessimistic Forecasts: The Versatility of Quantile Forecasting  
At the heart of a scheduling strategy, there is always a PV production forecast. An EMS that performs scheduling of distributed energy resources, for a given window of time in the future, requires forecasts as inputs. But forecasts are never 100% accurate, then, their intrinsic uncertainty becomes an important subject to be studied as presumably, this will have an effect on the final performance obtained from a given scheduling strategy. Recalling the statistical definition of quantile, what the deterministic quantile forecasts say is: if a given quantile \(\tau\) with probability level \(x\) is used as a prediction (i.e., \(x_{fcast}=\tau_{x}\)), then there will be \(x\)% of probability that the bias (i.e., the forecasting error) is positive, being the bias computed as the difference between the forecast value and observation (i.e., \(B=x_{fcast}-x_{obs}\)). This is an interesting characteristic of the quantile forecasting method, as it allows for the decomposition of the bias or forecasting error \(E_{fcast}\) in two components, namely: the -absolute- magnitude and a the sense or direction. Quantile forecasting allows us to choose (to some extent) between the absolute magnitude and the sense or direction of the forecasting error, which can be beneficial in an application where \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Proposed Strategy** & \multicolumn{3}{c}{**Reference Strategy**} & **Performance** \\ \hline  & **NO MG** & \(\text{PVB}_{\text{max}}\) & \(\text{PVB}_{\text{max}}\)– & **Indicator** \\ \hline \(\text{EC}_{\text{min}}\)-\(\text{AnEn}_{\tau=0.5}\) & \(-14.5\%\) & \(-10.3\%\) & \(-8.8\%\) (\(\text{AnEn}_{\tau=0:1:0.2}\)) & \(\text{EC}\) (\(\text{\#}\) /kWh) \\ \(\text{CO}_{\text{2 min}}\)-\(\text{AnEn}_{\tau=0.3}\) & \(+3.3\%\) & \(-6.0\%\) & \(-1.6\%\) (\(\text{AnEn}_{\tau=0.1}\)) & \(\text{CO}_{2}\) (\(\text{gCO}_{2}\)/kWh) \\ \(\text{GPP}_{\text{min}}\)-\(\text{AnEn}_{\tau=0.4}\) & \(-36.5\%\) & \(-9.0\%\) & \(-36.5\%\) (\(\text{AnEn}_{\tau=0.1:0.9}\)) & \(\text{GPP}\) (\(\text{\#}\) ) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of the optimization-based scheduling strategies with respect to the reference cases. The best-suited forecasting method for each strategy is used. having a bias in a given direction is more beneficial than having it in the other direction (or not having it at all). The results are obtained for the entire test period and they are summarized in Table 3. In this table, the GC indicator is also included, as grid-commitment is a common service to all of the scheduling strategies (EC\({}_{\text{min}}\), CO\({}_{\text{2 min}}\) and GPP\({}_{\text{min}}\)), assured by the balancing module (BAL). Here, we show the results of using a very pessimistic forecast (AnEn\({}_{\tau=0.1}\); rMBE = \(-\)0.354, rMAE = 0.384), a very optimistic forecast (AnEn\({}_{\tau=0.9}\); rMBE = 0.316, rMAE = 0.329), a quasi-unbiased forecast (PE; rMBE = \(-\)0.001, rMAE = 0.372), a low-bias high-accuracy forecast (NWP; rMBE = \(-\)0.002, rMAE = 0.219), and a perfect forecast (PF; rMBE = rMAE = 0). The best results (bold values) for all indicators are obtained with the perfect forecast (PF), with a 100% of GC for the three scheduling strategies as well as the smallest values for EC, CO\({}_{2}\), and GPP, as stated in Table 3. This is consequent, as the optimal strategies found during scheduling are being strictly followed when a perfect forecast is used (the most accurate forecast possible), hence the optimal performance is achieved. However, this scenario is unrealistic, as having a perfect PV-power forecast is most likely unachievable. Regarding the EC\({}_{\text{min}}\) strategy, we observe some correlation with the bias of the forecasting error, as EC presents its highest (worst) value with the most pessimistic forecast (AnEn\({}_{\tau=0.1}\)), followed by the most optimistic forecast (AnEn\({}_{\tau=0.9}\)) and the persistence forecast (PE), which has low-bias and high-absolute-error.