## 1 Introduction
### Energy Storage Options for Small-Scale PV Systems  
Short-term energy buffering has been introduced to PV-membrane systems via the addition of supercapacitors (SCs) with a suitable charge controller. SCs have proven to be good candidates for short-term energy buffering [33; 34; 35; 36], with the technology being chosen due to its ability to endure hundreds of thousands of charge/discharge cycles, as well as being able to provide a large amount of instantaneous power. For example, [PERSON] et al. developed a regulator with the use of relays and a 250-F supercapacitor (maximum voltage of 32 V) to stabilize the solar power supply to the pump in a PV-membrane desalination system [36]. The system exhibited a SEC of 2.9-4.3 kWh/m\({}^{3}\) when treating brackish water, synthesized using 8-22 g/L of sodium chloride (NaCl). Further advantages of SCs are the high efficiency (85-98%) of energy storage [37] and the relatively long lifetime (8-12 years) [38; 39], significantly longer than classical lead-acid (LA) batteries. However, the disadvantage of SCs are, firstly, the high self-discharging rate, which was calculated to be 1.5% per day in a previous work [40]. This is significantly higher than that encountered with either LA or lithium-ion (Li-ion) batteries, which achieve 5% per month and 1% to 2% per month, respectively [37]. Secondly, the amount of electrical energy that can be stored in SCs is much more limited than that in batteries, typically only providing energy buffering for a period of minutes [34]. For long-term electrical energy storage, LA batteries remain the most common solution applied to PV systems due to their global availability and relatively low cost [37; 41]. There are several studies of the successful operation of RE-membrane systems that incorporate LA batteries. A seawater desalination plant equipped with a 4.8-kW\({}_{\text{p}}\) PV array and 60 kWh of LA battery storage was installed on the island of Gran Canaria, Spain, being capable of providing 0.8-3 m\({}^{3}\)/d of drinking water [42]. The lower limit of the amount of energy stored in the batteries remained ~19 kWh. This corresponds to a depth of discharge (DoD) of 32%, a value that should be remained above in order to prevent damage and extend the lifetime of the batteries. The batteries enabled an improvement of water production by ~15% compared to the daily water production of 800 L without batteries being present. A small-scale PV-membrane pilot plant that was installed at a vocational training center in Northern Tanzania [43] was equipped with 2.25-kW\({}_{\text{P}}\) PV power and 2.2-kWh batteries (battery technology not stated), which allowed for two hours of an additional operation when no PV power was available. The system was operated successfully over a nine-month period, with a water production of 2.4 m\({}^{3}\)/d at a SEC of 4.4 kWh/m\({}^{3}\) when treating feedwater with an electrical conductivity (EC) of 3000 \(\upmu\)S/cm [43]. Another small-scale PV-membrane desalination system was designed with 2 kW\({}_{\text{P}}\) of PV power and 2.4-kWh LA batteries in Malaysia [44]. The system was capable of producing 5.1 m\({}^{3}\) of clean water per day (10 h) at a SEC of 1.1 kWh/m\({}^{3}\) while treating brackish water at a salinity of 2000 mg/L. Batteries were used to provide a stable current supply and store energy during cloudy weather. The total hours of autonomy via the addition of batteries during the daytime and nighttime operation modes (10 h of operation per day) were tested to be ~22 h and 24 h, respectively; however, the number of hours of autonomy afforded by the battery bank declined to 11 h after one year of operation during the daytime due to the high ambient temperature (exceeding 35 \({}^{\circ}\)C). The overall disadvantages of LA batteries are their low roundtrip efficiency of 75-84%, limited number of charging/discharging cycles (~2000) [45], reduced operational lifetime (three-five years) and DoD of higher than 50% [37].