## 3 Results
### Optimistic and Pessimistic Forecasts: The Versatility of Quantile Forecasting
This suggests that this service requires low-bias and low-absolute-error forecasts to yield the best performance, as is the case when using the NWP and PF. The difference between the best and the worst strategies (EC\({}_{\text{min}}\)-PF and EC\({}_{\text{min}}\)-AnEn\({}_{\tau=0.1}\) respectively) are as high as 92.8%, which represent an increase in the price of the electricity of 0.14 E /kWh. However, it must be remarked that the smallest cost obtained (using EC\({}_{\text{min}}\)-PF) is approximately 0.154 E /kWh, which is competitive with the tempo tariff only in the peak hours of the white and red days, where the electricity price is higher than this value. This remarks the importance of optimally deciding when to store/use energy from the battery, and when is better to buy the energy directly from the utility grid, in order to optimize this service. Regarding the CO\({}_{2}\) indicator, the highest value is obtained with the most optimistic forecast (AnEn\({}_{\tau=0.9}\)) forecast, which is 41.2% higher than the reference PF case, followed by the AnEn\({}_{\tau=0.1}\) approach (+15.9%), the persistence approach (+3.2%) closing with the NWP forecasting method that only presents an increase of +1.6% with respect to the reference PF approach. There is a clear difference here between the results of the quantile forecasts (AnEn\({}_{\tau=0.1}\), AnEn\({}_{\tau=0.9}\)) and the other two forecasting methods (PE, NWP), which suggests that this service is favored by low-bias forecasts. The carbon footprint when using the CO\({}_{\text{2 min}}\)-PF strategy is 63 gCO\({}_{2}\)/kWh, which is higher than the mean and mode of the carbon footprint that is associated to the electricity coming from the utility grid. This fact helps to explain the results that were obtained in Table 2, that show that the average CO\({}_{2}\) content is higher when a MG is deployed, due to the high embedded CO\({}_{2}\) emissions of the battery and the solar panels. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scheduling** & **Performance** & **AnEn\({}_{\tau=0.1}\)** & **AnEn\({}_{\tau=0.9}\)** & **PE** & **NWP** & **PF** \\
**Strategy** & **Indicator** & **(Pessimistic** & **Forecast**)** & **(Optimistic Forecast**)** & **(Unbiased Forecast 1)** & **(Reference & **(Most Accurate** \\  & & & & & & & **Forecast**) \\ \hline \multirow{2}{*}{\(EC_{\text{min}}\)} & EC (€ /kWh) & 0.297 & 0.217 & 0.176 & 0.169 & **0.154** \\  & GC (\%) & 99.9 & 92.1 & 96.2 & 99.1 & 100 \\ \hline \multirow{2}{*}{CO\({}_{\text{2 min}}\)} & CO\({}_{\text{2}}\) (gCO\({}_{2}\)/kWh) & 73 & 89 & 65 & 64 & **63** \\  & GC (\%) & 99.9 & 88.1 & 94.3 & 98.5 & 100 \\ \hline \multirow{2}{*}{\(GPP_{\text{min}}\)} & GPP (kW) & 15 & 18 & 15 & 18 & **15** \\  & GC (\%) & 99.7 & 90.8 & 95.3 & 99.1 & 100 \\ \hline \hline \end{tabular}  
* Aside from the perfect forecast (PF).  
\end{table} 
Table 3: Impact in performance of different types of forecasts. Regarding the GPP\({}_{\text{min}}\) strategy, the behaviour is a little bit different. In this case, the smallest contracted power (i.e., the best performance) is obtained with the most pessimistic (AnEn\({}_{\tau=0.1}\)), most unbiased (PE), and most accurate (PF) forecasts, at the same time. From this fact, it could be concluded that optimistic forecasts such as AnEn\({}_{\tau=0.9}\), are not favorable for the grid-peak-power service. The reason behind is the fact that, under-estimative (or unbiased) forecasts, are more likely to have errors that result in battery getting fully charged, hence promoting the PV curtailment. When this happens, the scheduled--smooth--grid profile produced by the GPP\({}_{\text{min}}\) strategy remains less modified. A similar situation happens when the PF is used, as it does not produce changes to the scheduled grid profile. This is not the case when using the NWP forecasts, as it has a more over-estimative tendency when compared to PE or AnEn\({}_{\tau=0.1}\). For this indicator, the use of the AnEn\({}_{\tau=0.9}\) and NWP forecasts, leads to an increase of 9.8% in the annual fee.