## 1 Introduction  
Investments in solar photovoltaic (PV) technologies have experienced stable growth supported by the many policies and incentives to increase the installation of renewable energy sources (RES) [1]. For example, an additional 70 GW was reported in 2016 alone [2]. After that, the global investment declined due to the accentuate decrease in the PV system costs and increase of electricity prices, which has allowed many countries to reach grid parity, which refers to the point at which the cost of generating PV electricity equals the cost of buying it from the grid [2, 3]. Consequently, in such countries, directly consuming the solar PV generation (i.e., self-consumption, SC) became more attractive than feeding the PV production into the grid and, in return, receiving a subsidy (i.e., feed-in tariff) [2]. Furthermore, many countries have developed policies favoring SC over feed-in tariffs. For example, in Germany, the PV owner has a premium paid per kWh of SC from PV. China, the largest solar PV technology manufacturer, also favors SC with a bonus on top of the saved retail price [4]. In Portugal, SC has only been allowed since 2014, with a feed-in tariff for the surplus PV production. Before that, only feed-in tariffs were allowed. However, in the domestic sector, the periods of PV generation and electricity demand rarely coincide, implying that only a limited share of solar PV energy can be used directly for SC. Someworks have reported shares of direct SC around 30% [5]. In this context, battery energy storage systems (BESS) offer the opportunity to increase SC levels by storing excess solar PV production to be used later (i.e., indirect SC). For example, in [5], the authors claimed that it was possible to increase the relative SC between 13% and 24% using a BESS with a capacity of 0.5-1 kWh per installed kW of solar PV. Nevertheless, as with standalone solar PV, the financial viability of PV coupled BESS (PV-BESS) for SC is affected by the different regulation schemes [6]. Hence, it is crucial to study the impact of local legislation on the profitability of PV-BESS investors. Against this background, in this paper, we present an economic assessment of solar-powered residential BESS on Madeira Island (Portugal), where, since 2014, only self-consumption is allowed, and any excess PV production must be curtailed [7; 8]. This last restriction happens in part due to the isolated nature of the island electric grid (i.e., not interconnected to continental Europe), which can be significantly affected by the intermittent and uncertain nature of renewable production [9]. In the specific case of Madeira Island, the residential consumers' electricity bill consists of two components, a fixed component that depends on the contracted power (kVA) and a dynamic part governed by the actual energy consumption (kWh) [8]. In this scenario, PV-BESS can directly reduce the energy bill by minimizing the dynamic component, achieved by increasing the self-consumption, and by enabling energy arbitrage (i.e., charge the BESS from the grid when the buying prices are lower and discharge when prices are higher). In previous work that considered the Madeira Island case [10], it was shown through year-long simulations that, in the current scenario of no feed-in tariff, BESS will improve the value of solar PV installations by considerably increasing the rates of SC (between 10% and 30% depending on the BESS capacity). However, in line with much of the existing literature (see Section 2), it was found that the resulting reductions in the energy bill are not sufficient to pay the initial investment during the lifetime of the BESS. While this works sheds some light on the present situation on Madeira Island, it suffered from several short-comings now addressed in this paper. First, it only considered a flat-rate power tariff, which also excluded the possibility of assessing energy arbitrage potential. The BESS sizing did not consider the installation characteristics (i.e., size of PV and load demand).