## 3 Results
### Optimizing the Services: Finding the Best-Suited Quantile Forecasts  
It must be recalled that an optimization-based EMS, such as the ones that are proposed in this work, require deterministic forecasts of PV production. Therefore, quantile forecasts are a way to provide the EMS with a deterministic forecast that has intrinsic probabilistic information embedded. More specifically, the most valuable information that we can extract from a quantile forecast is the probability of the error being either over or under estimative. By knowing this information in advance, we can deliberately use the forecasts that are best suited for the service being targeted during the scheduling. The results that are presented in Figure 7 include the PV costs, reduction in the expected Through-Output-Energy (TOE) of the PV array due to curtailment, as well as the correction in battery cycling life. The TOE is the total energy that is expected to be delivered by an element (i.e., PV panels, battery) throughout its working lifetime in an specific place. In other words, the electricity cost and CO\({}_{2}\) content for the battery and PV energy is affected by the profile of use, following Equations (A3), (A6), (A9), and (A10). The results that are shown in Figure 7a are obtained with the EC\({}_{\text{min}}\) scheduling strategy, while the ones of Figure 7b are obtained with the CO\({}_{\text{2 min}}\) scheduling strategy. In both plots, the battery life is presented as a gray curve that represents the battery cycling life as a percentage of the nominal cycling life (i.e., the maximum possible cycling life). In both cases, the reduction in battery life plays a major role in the behaviour of both EC and CO\({}_{\text{2}}\) indicators, as they find its minimum value, where the battery life is maximum. In both cases, the quantile forecasts permit obtaining a better performance (however marginal) than NWP, being EC and CO\({}_{\text{2}}\) 2.4% and 0.7% less than the values that were obtained using NWP, respectively. It is important to remark than the best performance for the EC is obtained while using the AnEn\({}_{\tau=0.5}\) forecast, while the lowest carbon footprint is found using the AnEn\({}_{\tau=0.3}\) quantile forecast. This is important because it remarks the fact that the most accurate forecast (i.e., the one presenting the smallest rMAE or rRMSE) does not always yield the best performance in every service. Regarding the minimization of the contracted power that was observed in Figure 7c, quantiles forecasts below AnEn\({}_{\tau=0.4}\) allow for a reduction of 16.6% with respect to the NWP forecasts. Above AnEn\({}_{\tau=0.5}\), the performance is the same for both quantile forecasts and NWP, which allow a contracted power of 18 kW, according to the tempo tariff. This fact can be explained as for higher quantiles there is over-estimation of the PV production, which would lead to a situation where the system will empty the battery and make use of the grid in order to compensate for the over-estimations of PV production. If we look at the grid-commitment in Figure 7d (GC-orange curve), it presents a pseudo-parabolic decrease with the increase of the quantile. In contrast, we observe that the self-consumption (SC-gray curve) increases, also following a pseudo-parabolic pattern. This can be simply explained, as follows: over-estimative forecasts (i.e., high quantiles) provoke errors that have to be counteracted by the grid, as it foresees more PV production than the actual. Therefore, all of the PV power available is used  
Figure 7: Impact of probabilistic forecasts in: (**a**) the energy cost (EC) using the EC\({}_{\text{min}}\) scheduling strategy; (**b**) the carbon footprint (CO\({}_{\text{2}}\)) using the CO\({}_{\text{2}}\)min scheduling strategy; (**c**) the grid peak-power (GPP) using the GPP\({}_{\text{min}}\) strategy and (**d**) the grid-commitment (GC) and self-consumption rate (SC) using the CO\({}_{\text{2}}\)min scheduling strategy.