# On the Determination of Meshed Distribution Networks Operational Points after Reinforcement
## 3 Results and Discussion  
Simulation results have shown that in order to achieve the maximum possible total loading without substantially compromising voltages across the line, the transformer that feed the low voltage distribution system has to have the calculated load. Table 5 and Figure 3 show the calculated values for the objective function for each case; the values are increasing when the production from the renewables also increasing, since more load is able to be fed to the low voltage network distribution transformers without decreasing voltage at all points. The production is able to feed nearby loads; hence, the total load served is increasing without severely affecting voltage drop. The higher increase is observed when voltage drop has higher weighting factor for the case 1 and lower for case 4. The graphical representation of this interrelation shall normally provide perfect curves; however, due to the probabilistic approach applied, there could be minor rounding errors that do not substantially affect the results. The source code for this publication has been written on Matpower 6.0 [36; 37] and Mathworks Matlab 2017a [38]. The Monte Carlo simulation was run on Aris high performance computing [39]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & \(\mathbf{w_{1}}\) & \(\mathbf{w_{2}}\) \\ \hline
1 & 0.5 & 0.5 \\
2 & 0.6 & 0.4 \\
3 & 0.7 & 0.3 \\
4 & 0.8 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Examined cases. Tables 6-9 and their graphical representations Figures 4-6 present the recommended loading per node for each examined case, according to the outcomes of the developed calculation procedures. For the case 1 (Table 6 and Figure 4), the obtained results indicate that most of the transformers can be fed near their installed capacity. However, there are connection points that when energy production from renewables is high, they need to keep their load low and vice versa. Other transformers, such as 49 and 15, need to be downscaled if these operational patterns are to be applied. In all cases, its proposed loading does not exceed 60% of their installed capacity. Another solution could be to further reinforce the line at these points. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline
**without DG** & 0.7683 & 0.7611 & 0.7611 & 0.7689 \\
**10\% of DG prod** & 0.7872 & 0.7772 & 0.7759 & 0.7795 \\
**20\% of DG prod** & 0.7997 & 0.7918 & 0.7871 & 0.7879 \\
**30\% of DG prod** & 0.8097 & 0.8045 & 0.7966 & 0.7949 \\
**40\% of DG prod** & 0.8175 & 0.8155 & 0.8048 & 0.8009 \\
**50\% of DG prod** & 0.8261 & 0.8251 & 0.8124 & 0.8061 \\
**60\% of DG prod** & 0.8351 & 0.8303 & 0.8194 & 0.8107 \\
**70\% of DG prod** & 0.843 & 0.8361 & 0.8255 & 0.8148 \\
**80\% of DG prod** & 0.8499 & 0.8434 & 0.8309 & 0.8117 \\
**90\% of DG prod** & 0.8521 & 0.8483 & 0.8346 & 0.8143 \\
**full DG prod** & 0.8537 & 0.8496 & 0.8356 & 0.8166 \\ \hline \end{tabular}
\end{table} 
Table 5: Calculated value of the objective function. DG: distribution generation. Figure 3: Graphical representation of the calculated values. Figure 5: Loading per node according for case 2. Figure 6: Loading per node for cases 3 and 4.