## 4 Results and Analysis
### Solution of the Deterministic Planning Problem
#### 4.1.2 Results for the Cases with Reliability Requirements  
In order to plan microgrids that can operate in islanded mode whilst considering the diversity of energy consumption in each group of 1, 10, 20 and 100 clients, three fault durations (4, 8 and 12 h) were simulated for the two case studies. The above means that 2400 microgrids were designed with reliability requirements, that is, 100 optimization exercises for each group of \(n\) clients for each duration fault and each case study were determined, where in each iteration \(n\) corresponding clients were chosen randomly from the CREST Demand Model in order to mimic the diversity of residential customers. In this sense, the models sought to evaluate the effect of different energy requirements to support the sizing of each microgrid, as well as to compare results with different numbers of residential households. Results for Microgrids Planning with Reliability Requirements (Case 1)  
In order to perform statistical analyses from hundreds of deterministic simulations in Case 1 (100 faults per microgrid), Figure 8 shows graphs of the investment costs per household, according to the level of protection (referred to the percentage of faults that are covered by installing the indicated number of panels and batteries), and the duration of the fault. It is important to notice that the standard deviation for each level of protection is included in the graph, for the various groups of microgrids. All results for deterministic planning consider the sensitivity (EoS) for the investment costs (Table 4). Figure 7: Distribution of investment costs per client for different microgrids, without reliability requirements. The effect on investment costs per household, as the level of protection increases, is shown in Figure 8a. A protection level of 90% refers to the percentage of fault (lasting 8 h) that can be covered by the microgrid configuration alternative used, for example, in one-client groups the investment costs incurred to guarantee protection against 90% of faults is around USD 300 per year. Clustering clients helps to reduce the investment costs of each microgrid: if a protection level is taken as a reference, for example, 90%, in the case of microgrids with 10, 20 and 100 households, a saving of 16.3%, 18.5% and 23.0% with respect to the average investment cost for one-client microgrids with the same level of protection can be achieved. On the other hand, costs increase as the level of protection required by the community also increases. This behavior is as expected, since protecting oneself from a greater number of faults implies higher investment costs per household. In the case of a protection level close to 100%, the user or the community would be protecting themselves from a fault that could occur at any time during the day, which implies that they must have a considerable storage capacity. Figure 8b represents a cut made at the 90% protection level which enabled the investment costs to be compared according to the duration of the faults. It is observed that protecting oneself from a more extensive contingency has a higher investment cost for  
Figure 8: Investment cost per household as a function of (**a**) protection level for faults of 8 h duration and (**b**) duration of faults with 90% protection level (Case 1). all household groups, and this is due to the fact that more storage capacity is required if the fault occurs during hours of no sunlight. When taking as a reference the cost curve of microgrids for 100 residential households, the increase in the investment average cost, which is the result of preparing the microgrids for longer hours of operation in islanded mode, is 25.6% for faults from 4 to 12 h.  
As an example, Table 6 presents results of the deterministic planning approach (Case 1), for four groups of 1, 10, 20 and 100 residential clients. A specific fault of 8 h duration (starting time 906 h, that is 06:00 pm on the 37 th day of the year) is considered, from which the type of assets and size of four microgrids are determined.