# Smart Grid Architecture for Rural Distribution Networks: Application to a Spanish Pilot Network
## 5 Study Case
### The Dimensioning of IDPRs  
This subsection presents the methodology to size the IDPRs, according to the magnitude of the existing power flows in the network and addressing the new operation modes for the grid, as previously defined in Section 4. The PN currently feeds 25 consumers, who have an overall contracted power of 150 kW [39]. Figure 10 presents the total apparent power fed by each secondary substation and the network. However, the total consumption peak of the whole PN does not exceed 30 kVA, as can be \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Scenario** & **Phase A** & **Phase B** & **Phase C** \\ \hline \multirow{4}{*}{Voltage} & (1) & 137.38 V & 137.60 V & 135.75 V \\  & (2) & 137.54 V & 137.96 V & 135.97 V \\  & (3) & 138.10 V & 137.14 V & 136.48 V \\  & (4) & 140.05 V & 140.54 V & 138.32 V \\ \hline \multirow{4}{*}{Current} & (1) & 19.25 A & 21.31 A & 19.87 A \\  & (2) & 18.51 A & 20.55 A & 18.07 A \\ \cline{1-1}  & (3) & 19.32 A & 25.25 A & 9.95 A \\ \cline{1-1}  & (4) & 31.78 A & 32.20 A & 30.64 A \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Voltage and current Root Mean Square (RMS) values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **IDPR Contribution** & **Phase A** & **Phase B** & **Phase C** \\ \hline \multirow{2}{*}{THD of voltage} & No contributing & 1.66\% & 2.52\% & 2.09\% \\  & Contributing & 1.46\% & 1.50\% & 1.50\% \\ \hline \multirow{2}{*}{THD of current} & No contributing & 12.42\% & 17.09\% & 15.83\% \\  & Contributing & 6.44\% & 6.54\% & 6.77\% \\ \hline \multirow{2}{*}{Power factor} & No contributing & 0.9949 & 0.8380 & 0.6005 \\  & Contributing & 0.9999 & 0.9982 & 0.9910 \\ \hline \multirow{2}{*}{Degree of unbalance} & No contributing & 35.5\% & 46.3\% & 18.2\% \\  & Contributing & 33.6\% & 34.0\% & 32.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Real measurements for proving the IDPR contributions. seen in Figures 10 and 19. Furthermore, as introduced in Section 2.2, the MV grid of the PN distributes at 5 kV and the step down transformers in each SS permits interfacing to the final users at 230 V or 400 V. Such characteristics will be translated into the modelling of the PN in the following section. While assessing the introduction of IDPRs into the PN, one should consider that these back-up resources could be eventually operated in master mode. Such operation mode greatly influences the required power and energy storage capacities for IDPRs, as in such circumstances an IDPR could even ensure the supply for the whole PN. Accordingly, even the proposed computational scenarios consider the operation of the IDPRs in slave mode, and their sizing should be a function of the requirements while in master mode. The minimum power capacity for an IDPR in isolated mode is defined from the analysis of the demand patterns presented in Figure 10. A probabilistic analysis of the above-mentioned profiles shows that the PN value does not exceed 18.7 kVA (see the maximum value of the last box-plot representation in Figure 19). Therefore, 18.7 kVA is determined as a threshold level for the minimum power capacity for an IDPR, which is required for isolating the whole system. Note that, from this minimum sizing, a 50% security factor has been applied, in order to ensure the right operation of the power electronics under electrical transients, e.g., transformer and load inrush currents. As a result, the rated power should be set at 30 kVA. Thus, a 30 kVA IDPR is able to energise and maintain balanced the whole PN. Despite a 30 kVA IDPR could energise the whole PN at the same time, a good strategy for reducing the electrical transients during the energisation process is to energise step by step the network, starting with the biggest SS. According to Figure 19, it is also possible to size IDPRs for different autonomous sectors. For example, the required power should be about 20 kVA for S1, 30 kVA for S1 and S2, 5 kVA for S3, and 15 kVA for S2 and S3.