## 4 Case Study  
Although Chile has a high electrification rate (99.8% for 2017 [38]), it is estimated that 25,000 families are not connected to the electricity grid, while another 5000 only have a partial supply for a few hours a day [39]. Indeed, many isolated rural dwellings that are connected to the electricity grid do not have a reliable supply throughout the year because of both voltage drops due to the considerable distances from electrical substations and the corrosive characteristics of coastal areas. This limits the opportunities to develop these rural regions. Many of these rural communities depend on agriculture for their livelihoods; however, the effects of climate change are having negative impacts on traditional agriculture. Historically, artificial irrigation has not been required in southern Chile because rainfall is distributed throughout the year, but the 2010-2018 period broke this trend, being the driest on record with a rainfall deficit of 20-40% [26]. As a case study, we evaluate the proposed EWMS strategy using data extracted from the Jose Painecura Huenalihuen community located in the municipality of Carahue, Chile. The local hydrogeology indicates the presence of limited aquifer potential due to the high variability of sediments and rocks [40]. Groundwater is poorly understood in the region and has only been monitored since 2013. The authorities have reported a significant increase in water rights used primarily for human and animal consumption (55%), water for irrigation (33%), water for industrial use (10%), and other uses (2%). Two principal aquifer levels have been identified: one is superficial (less than 20 m depth) and the other is deeper (more than 20 m). The wells in the shallow aquifer tend to dry out in summer or during periods of drought. Thus, groundwater is closely related to river flows (especially the shallow aquifer, where decreases in precipitation directly affect the river flow), which are the most accessible groundwater type [41]. Figure 3 shows the location of the community, with a mountainous coastal terrain in which the crops grow on the hills and the water must be pumped from the aquifers for irrigation. This community has an inadequate electricity supply, which is reflected in a _System Average Interruption Duration Index_ of 69.51 [h]. The average interruption in Chile is 12.17 [h][42]. In the future, we hope to setup a microgrid (connected to the main grid) to benefit 44 families. This microgrid will have the following characteristics:  
* Photovoltaic Power Plant, 90 kWp. * Lead-acid Battery Bank, 43.2 kWh. * 0.25 kW and 1.1 m\({}^{3}\)/h centrifugal pumps at a hydraulic height of 14 m. One pump is assumed per farmer. Figure 4 shows the microgrid topology. The controllable loads (\(L_{\text{C}}\)), non-controllable loads (\(L_{\text{NC}}\)), and the grid are identified in the AC bus, and the photovoltaic power plant (\(PV\)) and lead-acid battery bank (\(BB\)) are on the DC bus. The crops present in the community are potatoes, peas, and tomatoes, whose main characteristics are expressed in Table 1. In the table, \(K_{y}\) is the sensitivity to the lack of water at each stage, \(K_{c}\) is a crop coefficient related to the growth stage, \(P_{c}\) is a factor that relates the total water available in the root zone to the water that can be absorbed by the crop, and \(CN\) is the relative impermeability of the soil/vegetation. The sale price received by the farmers in Table 1 is approximated as half the final market price. Figure 3: Location of the José Painecura Huefälihuen community [40]. For the simulation, we considered ten farmers whose irrigation and pumping systems were managed by the EWMS system. Table 2 summarizes the two dominant parameters related to the three main crops cultivated by the farmers, which are the cultivated area and the minimum expected relative yield, \(Y_{min}\) (related to the expected self-consumption).