## 3 Case Study  
The case study aims to illustrate the capabilities and performance of the proposed optimal planning models and it considers the design of hundreds of microgrids for different numbers of residential clients (1, 10, 20 and 100 clients) (i.e., by solving the optimization models developed), assuming their implementation in the city of Santiago de Chile. This exercise was also repeated for various reliability requirements. The graphic representation of the configuration alternatives for the microgrids is presented in Figures 2 and 3. The microgrid alternatives include the following main assets: PV generator, inverters and batteries. In addition, the participation of the power grid is considered during the connected operational mode (a fundamental characteristic of an urban microgrid). It should be noted that given the characteristics of the clients in each microgrid (diversity of energy consumption and number of clustered clients), the proposed models optimally determine which configuration to use and what sizing to carry out of the assets that build up each microgrid (by minimizing investment and operational cost together). On the other hand, the microgrid models that are proposed in this work require a set of input data, which must be collected and processed for the analysis. Regarding load demand, hourly residential household load profiles are based on the CREST Demand Model, which incorporates a stochastic model for generating electricity demand profiles [42]. The model produces demand data broken down by end use. For this, it uses a bottom-up modeling approach, which is based on active occupation patterns and daily activity profiles derived from user surveys. Among its many characteristics, the CREST Demand Model includes a representation for each household appliance and lighting, with which the aggregations of the household loads are simulated, so that the diversity of these is appropriately represented and the demand for end use is adequately correlated. Hence, parameter adjustments were carried out in the CREST tool, related to the nominal power and type of electrical appliances, to adequately represent the demand of low-consumption urban areas. Various load profiles of residential households were obtained, which present an average of 135 kWh per month [43]. Critical load profiles were also considered, which for residential households typically averaged 55 kWh per month. The critical load in this work consists of lighting, a television, a fridge, and a personal computer. This choice is made to ensure that in an emergency people feel safe, their home is illuminated, their food is kept in a good condition and they stay informed or entertained with the television  
Figure 3: Alternative 2, configuration for microgrids of a residential household. Figure 2: Alternative 1, configuration for microgrids of a residential household. and/or personal computer. The electrical appliances included in the CREST model for this study are presented in Table 2.  
The load profiles obtained by CREST (after the modification), for any one week of the study year, and from different groups of 1 and 100 clients, are presented in Figure 4, where it can be noted that although the individual profiles are quite different, their aggregate behavior is similar, as is the case in practice. As for the annual hourly profile of solar generation (Figure 5), it was obtained from the Solar Explorer of the Ministry of Energy of Chile [44]. Daily solar generation profiles with an installed power of 1 kW are considered for the city of Santiago de Chile (Latitude: \(-33.4372\), Longitude: \(-70.6506\)), with solar radiation values between 4 and 6 kWh/m\({}^{2}\) day.