## 3 Results and Analysis
### Case Study I: 69-Bus Test System  
First, the 69-bus and 12.66 kV distribution network [34] is simulated for a generalized analysis of the model and solution method. Table 1 presents the number of generation modules and power capacity of each DG plant, as well as the buses at which DG projects can be installed. Aiming to enlarge the search and solution spaces, a higher than usual 30-40% maximum penetration index \(Pl_{max}\) = 70% is considered in this case-study. The Pareto frontier obtained by the proposed multi-objective solution method based on Genetic Algorithm and Maximin metric (MOHGA) is presented in Figure 3, where y1, y2 and y3 are the normalized total installation cost of DG plants (\(C_{instal}\)), daily active power losses (\(LAE_{daily}\)), and daily amount of equivalent CO\({}_{2}\) emission (\(EqCO_{2}E\)), respectively. Good scattering of Pareto frontier points (3.4%) certify the Maximin metric efficiency to aid multi-objective solution methods in the searching of diversity of solution alternatives. The scale of values for the axes in Figure 3 is related to the proposed normalization factors (value of objective functions referring to the solution obtained by miminization \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & & **DG Insertion Buses** & & \(\mathbf{NDG^{max}_{u}}\) & \(\mathbf{P^{DG}_{n}}\) **(kW)** \\ \hline Photovoltaic (PV) & 13 & 29 & 32 & — & 20 & 100 \\ Wind Turbine (W) & 3 & 38 & 47 & 68 & 10 & 150 \\ Hydro (H) & 24 & 36 & 58 & 62 & 8 & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Case study I: insertion buses, maximum number of DG modules and unity capacity. Figure 3: Three-dimensional plot of Pareto frontier—case-study I.  
of daily active power losses considered as a mono-objective problem). Minimum power loss solution implies that normalized power losses of any alternative of solution achieve a range higher than 1.0, as observed in y2 axis. As minimization of daily active power losses seeks to maximum generation, the normalized values for the other two objective functions correspond to the maximum installation cost of DG plants and maximum daily amount of equivalent CO2 emission, so that y1 and y3 axes attain values lower than 1.0. Analysis of results identifies that the obtained Pareto-set presents 81% of individuals with photovoltaic in bus 13 with an average power of 272 kWe, 84% of individuals with wind source in bus 68 with an average power of 511 kWe, and 83% of its individuals with hydro source in bus 62 with an average power of 1.07 MWe. The Pareto-set also presents the set of buses 13 (PV)-68 (wind)-62 (hydro) in 60% of the individuals. Thus, analysis of Pareto-sets can also identify better locations for DG installations in distribution networks. Figure 4 presents the normalized objective functions plotted two by two aiming to verify conflict among them. It can be observed that the curvature in y1-y2 and y2-y3 planes indicates that, as mentioned, minimization of installation costs and minimization of CO2 emissions are conflicting with minimization of network power losses. The solution based on the minimum losses of active power criterion attains comparatively larger quantities of DG generation modules, which reflects the DisCo viewpoint seeking to improve system efficiency by power loss reductions. Despite of higher installation costs of hydro and wind plants, the comparatively low capacity factor of photovoltaic plants may explain the absence of generation units from this primary energy source ob