## 3 Simulation Results
### Simulation Results  
The LVC algorithm was run in preventive control mode, for a planning horizon of 24 h and a frequency of 4 plans per hour (i.e., every 15 min). All of the consumers with HEMS were considered to be available to participate in grid operation, as well as the DSO-owned storage device located at node 117. The simulation was run for the Autumn day (Figure 10), the most recent data available. The voltage magnitude limits considered were \(\pm\)10% of the distribution transformer nominal voltage, \(V_{\text{N}}\). It is important to note that although the voltage magnitude limits are considered to be \(\pm\)10% \(V_{\text{N}}\), the LVC algorithm establishes stricter limits in order to compensate for the errors associated with the forecasts and state estimation, as well as the uncertainty associated with the behaviour of the flexibility-providing consumers. By doing this, fewer corrections are required in real-time operation, at the expense of a higher flexibility usage, but the grid is operated in a safer manner. In Figure 11 a detail of the section of the network's single-line diagram is shown where the voltage constraints are forecasted to occur. As it can be seen, the voltage violations are forecasted to occur towards the end of the feeder, that is, the nodes electrically more distant from the MV/LV distribution transformer. In Figures 12 and 13 the forecasted voltage profiles are shown for every customer in the LV network for a 24-h control horizon, before and after the application of the LVC tool, respectively. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**MAPE, \%**} & \multicolumn{4}{c}{**RMSE, p.u.**} \\ \cline{2-9}  & **Phase R** & **Phase S** & **Phase T** & **Average** & **Phase R** & **Phase S** & **Phase T** & **Average** \\ \hline Winter & 0.47\% & 2.40\% & 2.21\% & 1.70\% & 0.00003 & 0.00074 & 0.00069 & 0.00049 \\ Spring & 0.42\% & 0.18\% & 0.41\% & 0.34\% & 0.00003 & 0.00000 & 0.00003 & 0.00002 \\ Summer & 0.36\% & 0.11\% & 0.32\% & 0.26\% & 0.00002 & 0.00000 & 0.00002 & 0.00001 \\ Autumn & 0.40\% & 0.23\% & 0.17\% & 0.27\% & 0.00002 & 0.00001 & 0.00000 & 0.00001 \\ \hline Average & 0.41\% & 0.73\% & 0.78\% & 0.64\% & 0.00003 & 0.00019 & 0.00018 & 0.00013 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model validation. Mean Absolute Percentage Error (MAPE) and the Root-Mean-Square Error (RMSE) values obtained for the electrically furthest node. Figure 11: Simulation results. Single-line diagram of the network section where voltage violations are forecasted to occur. In yellow, nodes that violate the LVC’s limits; in red, nodes that violate the EN-50160 limit. As shown in Figure 12, the voltage profiles, without the application of the LVC preventive control algorithm, surpass the predefined voltage magnitude upper limit during the solar peak production period of the day. Furthermore, it can also be seen that the voltage magnitude profiles tend to follow a curve similar to the solar PV production curve. This can be explained from the analysis of Figure 6. Since the consumption is low during the peak solar production period of the day, the excessive microgeneration leads to reverse power flows, thus resulting in a voltage rise. Figure 14 shows in greater detail the voltage rise effect for the feeder and time instant where the worst voltage violation is registered, with and without the application of the LVC algorithm. In Figure 15 the control action established to the DSO-owned storage device is shown. In Figures 16-21 the control actions established to the consumers with HEMS are presented. In Table 5 a summary of the total flexibility provided by the HEMS is provided, together with the flexibility that is effectively requested by the LVC algorithm to the private consumers with HEMS. Figure 14: Worst voltage deviation. Comparison of the voltage profiles forecasted for the feeder and time instant where the worst voltage violation is forecasted to occur, with and without the application of the LVC. Figure 12: Simulation results.