## 1 Introduction
[16] investigated the possibility of integrating energy and water supply systems so that excess wind power production could be used in desalination units to supply the freshwater demand on Cape Verde Island. The main idea was to use desalinated water in a pumped hydro system in order to store the extra produced power from wind and to fulfill the gap between intermittent RES production and the island energy demand. Despite the recognized RES potentiality within small islands, the current share of installed RES plants with respect to the total electricity production is generally very low, even if a high potential of exploitation is available within the territory [17, 18]. In this regard, [PERSON] et al. [19] identified some critical barriers against a significant penetration of renewable energy on Sicilian islands, which are mainly related to local regulations and landscape management that usually forbid RES large-scale plant installations. It was also observed that an interactive strengths, weaknesses, opportunities, and threats (SWOT) analysis on the energy system could contribute to a collective and social learning process facing institutional, organizational, or common problems that usually inhibit the application of sustainable strategies on small islands [20]. Even though RES large-scale plants could undergo economic and administrative barriers, retrofit actions at the building level could, in turn, be diffusively proposed. Indeed, it was largely proven that they could lead to a substantial reduction in the energy demand toward a Net Zero Energy Building target [21]. Moreover, the extensive use of renewable energy sources could strongly influence the load curve of the community, as demonstrated by [PERSON] et al. [22] for the island of Northern Cyprus where the use of solar thermal water heater was intensely encouraged by the local government, leading to a maximum yearly saving about 72 GWh [23]. Indeed, solar thermal technologies can be a very good solution to decrease the electricity demand by domestic hot water [24], because a great amount of energy consumption also takes place during the operational period, in order to satisfy the demand of domestic hot water (DHW) [25]. Moreover, the use of active and smart systems at the building level, enabling the possibility of implementing demand-side management (DSM) policies, could be easily applied in a typical building on Lampedusa Island (Italy), controlling the effect of flexible electrical loads on the load curve of the island. Among flexible loads, the one most influencing the peak and the energy consumption of a typical house in Lampedusa is the electrical storage water heater (ESWH). For example, [PERSON] et al. [26] studied how photovoltaic systems interact with the heat pump water heater (HPWH) for domestic hot water (DHW) production without relying on batteries but only on a thermal storage tank. It is then reasonable to suppose that better results could be achieved if both strategies (use of RES source with high efficiency of water heater and demand response strategies) were applied. The present work relies on energy-retrofit strategies on Lampedusa Island (Italy, 35\({}^{\circ}\)30\({}^{\prime}\)56\({}^{\prime\prime}\) north (N) 12\({}^{\circ}\)34\({}^{\prime}\)23\({}^{\prime\prime}\) east (E), 568 degree-days). Lampedusa is one of the Italian small islands not connected to the mainland electric grid, for which the Italian Government established financial support to avoid a local inhabitant fee for extra costs in electricity production, according to a social equity principle. Since 2014, the government proposed to gradually abolish the support mechanism while promoting the use of RES. Specifically, in 2017, it introduced a legislative decree aimed at financing different energy-retrofit strategies, including the installation of solar thermal plants or heat pumps for domestic hot water (DHW) production.