## 1 Introduction  
In recent years, the excessive global increment of energy consumption and the issue of environmental pollution has led to the shift towards a green economy. The scientific community has put a significant amount of effort into improving the manufacturing quality and performance of the devices which are utilized in renewable energy systems (such as photovoltaics, wind generators and batteries). Nevertheless, the implementation of control strategies in order to guarantee the optimization of the system's performance remains crucial. In that context, battery energy storage systems (BESS) are going to play a key role in the future in many sectors [1]. However, BESSs have not proven yet notable performances in the household sector [1]. In [2, 3] it is analyzed that the application of a photovoltaic (PV) battery system in a household is a significantly challenging issue regarding its sustainability. This is mainly due to the high investment costs for the development of a BESS. Furthermore, in most countries single rate (SR) energy tariffs and time-of-use (ToU) energy tariffs are used. This implies that applying a BESS without renewable energy sources (RES) is at the first case (SR) infeasible and at the second case (ToU) extremely challenging. Additionally, despite the continuous decrease of the lithium-ion battery costs and the consecutive improvement of the batteries' performance, the value for money relation still cannot be considered ideal. In order to overcome these difficulties, various economic and technical studies [4; 5] have been performed over the past years which have proved that it remains unclear whether a residential PV battery system can operate profitably. Moreover, in [6] it is proved that achieving 100% autonomy in a household with a PV battery system is not a realistic scenario in most countries in Europe without oversizing the PV or the BESS. In addition, in [7] the importance of developing management strategies for analyzing the performance of the PV battery system is highlighted. Various scenarios are analyzed such as operation of the system without PV and operation without BESS. Another remarkable example of techno-economic studies is the work presented in [8], where a decision support tool for a BESS with integrated photovoltaic is presented. This tool aims to define the optimal sizing of BESS and optimal operation scheduling by taking under consideration various parameters such as weather data, electricity pricing environment and BESS specifications/costs. In addition, plenty methodologies for calculating the levelized cost of energy (LCOE) have been developed. A methodology which intends to minimize the LCOE by defining optimal photovoltaic (PV) rated power and BESS capacity is analyzed in [9]. Methodologies for calculating LCOE, economic and technical studies are implemented so as to define the optimal PV rated power and BESS capacity by taking into account specific conditions like building dimensions, geographical location, climate, energy consumption per season and energy market. Therefore, they cannot be considered suitable for universal use. All the aforementioned factors prove the difficulty of ensuring sustainability of BESSs in building applications and hence they evince the requirement of applying efficient energy management strategies (EMS). A BESS can be used in a residential building with RES or without in case of the existence of a ToU tariff or real time pricing (RTP) tariff. Nonetheless, efficient control of BESSs plays a significant role in achieving sustainability regardless the existence of RES [10; 11]. A non-constrained operation will result in a long operation time for the BESS and/or high operating currents and thus to significant degradation effects. In [12] the economic impact of battery ageing in a residential PV battery system is highlighted. Moreover, in [13] a methodology is presented for preventing battery degradation in a residential BESS by using forecast-based operating strategies.