## 3 Results and Analysis
### Case Study II: 918-Bus Test System  
The 918-bus/13.8 kV distribution network corresponds to a Brazilian urban feeder from Goiania, State of Goias. The data for this system can be requested to the authors. Network buses on which DG projects can be inserted, as well as the number of generation modules and power capacity of each module are presented in Table 3. Only photovoltaic types were allowed since it is a downtown urban feeder. The maximum penetration index is fixed in \(PI_{max}=120\%\), so that power flow from the substation to the grid is possible. In PV-02 was given a higher efficiency and higher cost in comparison to previous cases, simulating a technological advance: \(cf\) = 20% and CO\({}_{instal}\) = 1500 USD/kWe, respectively. Figure 5 shows the feeder picture (on Google Earth) and current during a typical day. Figure 5: Feeder picture (on Google Earth) and feeder current during a day for case II. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & \multicolumn{3}{c}{**DG Insertion Buses**} & \multicolumn{3}{c}{\(\text{NDG}_{n}^{\text{max}}\)} & \(\text{P}_{n}^{DG}\) (\(\text{kW}\)) \\ \hline PV-01 & 129 & 248 & 367 & 565 & 666 & 15 & 150 \\ PV-02 & 138 & 301 & 468 & 737 & 811 & 20 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Case study II: insertion buses, maximum number of DG modules and unity capacity. Figure 6 depicts the Pareto frontier obtained by the proposed approach. In this case, y1, y2, and y3 are the normalized total installation cost, daily power losses and amount of equivalent CO2 emission, respectively. A well scattering of Pareto frontier points (1.3%) proves over again the efficiency of the Maximin metric to tackle multi-objective solution methods in searching diversity of solution alternatives. The obtained Pareto-set presents two prevailing buses for installation of photovoltaic plants: for PV-01 type, 47% of the individuals propose bus 565 with 440 kVe of average power and 42% suggest bus 666 with 1440 kWe of average power; for PV-02 type, predominance is in bus 468 (95% of individuals) with an average power of 1265 kWe. Complementarily, the pair of buses 565-468 is in 47% of individuals and the pair 666-468 in 38%, totalizing 85% of solution alternatives from Pareto-set. Normalized objective functions plotted two by two in Figure 7 and observation of curvature in y1-y2 and y2-y3 planes indicate over again that minimization of installation costs and of CO2 emissions are conflicting with minimization of network power losses. Figure 6: Three-dimensional plot of Pareto frontier—case-study II. Figure 7: Graphic comparison among objective functions for conflict checking—case-study II. The comparatively larger quantities of generation modules observed in the solution based on minimum losses and maximum net present value criteria reflects an agreement of goals to both DisCo and DG owner, since higher production of energy implies in lower losses to the DisCo seeking of efficiency while it results in higher sales and shorter payback time to the DG owner. The comparatively lower number of generation modules regarding the solution for the Max-Min approximation criterion reflects again the need for tradeoffs among conflicting goals in such a way as to ensure success in the decision-making process. The solution based on both minimum losses and maximum NPV criteria presents daily active power losses \(LAE_{daily}\) = 3.42 MWh at an installation cost of 5.57 \(\times\) 10\({}^{6}\) USD and net benefit of 0.99 \(\times\) 10\({}^{6}\) USD, resulting in a power loss reduction of 17.8% in comparison to the case with no dispersed generation (\(LAE_{daily}\) = 4.16 MWh). When DG is owned by the DisCo, \(LAE_{daily}\) can also be converted in USD based on the same energy price and MAR as interest rate, which would result in savings of 4.88 \(\times\) 10\({}^{6}\) USD to the DisCo. MMA decision criterion results in daily active power losses (\(LAE_{daily}\)) of 3.72 MWh, corresponding with 10.6% of power loss reduction.