## 1 Introduction  
Collectively, buildings in the EU are responsible for 40% of our energy consumption and 36% of greenhouse gas emissions, which mainly stem from construction, usage, renovation, and demolition [1]. Improving energy efficiency in buildings therefore has a key role to play in achieving the ambitious goal of carbon-neutrality by 2050, set out in the European Green Deal. Renovating existing buildings could reduce the EU's total energy consumption by 5-6% and lower carbon dioxide emissions by about 5%. Yet, on average, less than 1% of the national building stock is renovated each year. (Member State rates vary from 0.4% to 1.2%). In order to meet our climate and energy objectives, the current rates of renovations should at least double [1]. In fact, the strategy of the \"Renovation Wave for Europe-Greening our buildings, creating jobs, improving lives\" aims to double annual energy renovation rates by 2030 and to foster deep energy renovations of both residential and non-residentialbuildings [2]. The increased rate and depth of renovation will have to be maintained also post 2030, in order to reach EU-wide climate neutrality by 2050 [3]. Different studies have been carried out to assess the energy efficiency of different type of buildings by using different methodologies and focusing on different renovation strategies. [PERSON] et al. performed the cost optimal analysis of energy retrofit alternatives in the case of a large housing stock owned by a semi-public real estate company, with the goal of meeting nearly zero energy building standards according to Italian regulations. The proposed method focuses on major energy renovation alternatives, given the assumption that interventions take place only when social and political conditions are favourable [4]. The thermal systems are considered in the renovation of three buildings. The result of this study was a design support system (DSS) providing the annual savings in terms of (\(\mathbf{\ell}\)/m\({}^{2}\)). In the present study, the methodology used also considers the cost-optimal analysis [5]; however, the total primary energy savings per year (MW/h) of the social dwelling stock for three scenarios according to three renovation rates were assessed, and the thermal systems were not included as possible renovation solutions [6; 7], as explained in Section 4. Energy simulations supported by a cost-optimal methodology have been used to design the renovation of historic buildings [8], which is a methodology that has been proved to be needed when involving in-depth renovation of buildings [9; 10]. This study reinforces the goodness of the cost-optimal methodology; however, the present paper is not focused on historic buildings. It is focused just on residential buildings, given that some of the renovation measures, such as external insulation on the facade, could be applied. [PERSON] et al. [11] analysed the renovation of a pilot office building in a warm climate following an LCA methodology. The main difference with the present study is that the building was for office use rather than residential. [PERSON] et al. have evaluated the potential of energetic savings of the dwellings in Catalonia and its economic impact, according to different scenarios of efficiency that have been defined according to their current regulations at state and autonomic level [12]. Passive and active measures have been considered for the refurbishment of residential buildings following the cost-optimal methodology of the European Directives. However, this paper describes a cost-optimal analysis of a residential building of Catalonia and proposes a cost-effective evaluation divided in two steps: first a passive evaluation, where the envelope performance is improved using thermal comfort and initial investment costs as a criteria of decision; and a second step, active evaluation, where the passive and actives measures are combined and evaluated using the global cost and the non-primary energy consumption to find the cost-optimal scenario.