Economic-Engineering Modelling of the Buildings Sector to Study the Transition towards Deep Decarbonisation in the EU

: The paper presents a newly developed economic-engineering model of the buildings sector and its implementation for all the European Union (EU) Member States (MS), designed to study in detail ambitious energy e ﬃ ciency strategies and policies, in the context of deep decarbonisation in the long term. The model has been used to support the impact assessment study that accompanied the European Commission’s communication “A Clear Planet for All”, in November 2018. The model covers all EU countries with a ﬁne resolution of building types, and represents agent decision-making in a complex and dynamic economic-engineering mathematical framework. Emphasis is given to behaviours driving the energy renovation of buildings and the ensuing choice of equipment for heating and cooling. The model represents several market and non-market policies that can inﬂuence energy decisions in buildings and promote deep energy renovation. Moreover, the paper presents key applications for supporting policies targeting ambitious reduction of energy consumption and carbon emissions in buildings across Europe. The results illustrate that the achievement of ambitious energy-e ﬃ ciency targets in the long-term heavily depends on pursuing a fast and extensive renovation of existing buildings, at annual rates between 1.21% and 1.77% for the residential sector and between 0.92% to 1.35% for the services sector. In both cases, the renovation rates are far higher past trends. Strong policies aimed at removing non-market barriers are deemed necessary. Electriﬁcation constitutes a reasonable choice for deeply renovated buildings and, as a result, almost 50% of households chooses electric heating over gas heating in the long term. However, heat pumps need to exploit further their learning potential to be economical and implementable for the various climatic conditions in Europe. The results also show that the cost impacts are modest even if renovation and decarbonisation in buildings develop ambitiously in the EU. The reduced energy bills due to energy savings can almost o ﬀ set the increasing capital expenditures. Fundraising di ﬃ culties and the cost of capital are, however, of concern.


Introduction
As one of the signing parties in the Paris agreement, the European Union (EU) has undertaken the commitment to pursue best efforts in order to limit the global average temperature rise to 1.5 • C. Consequently, the energy system should become carbon-neutral by mid-century while all sectors undergo substantial transformations to achieve strong energy savings and switch to low-carbon technologies and fuels. The main pillars of this transformation are energy efficiency, electrification of end-uses and decarbonisation of power generation through a wide penetration of variable renewables.
Barriers can be divided into market and non-market barriers [14], with market barriers being related to "true" costs (which consumers actually pay), termed hidden up-front investment costs and factors related to the accessibility to capital resources. Non-market barriers refer to elements which do not have a direct payable or "true" cost. The model, however, monetises non-market barriers as "perceived costs" and by raising risk premium factors, as others also did in the literature [15]. The non-market barriers can be broadly categorised in three groups: (a) (lack of) information and knowledge, (b) uncertainty about economic and technical performance, and (c) poor access to funding and limited cash flow by individuals (e.g., high opportunity cost of equity and debt).
Even within a group of consumers with similar attributes, the individuals do not have homogeneous preferences when deciding on efficiency and heating investment, but they rather exhibit idiosyncratic behaviours. Also, the engineering peculiarities of the building stock regarding age, technical constraints and geographical location vary to such an extent that the technical and costing circumstances differ even within groups of buildings with similar attributes.
Consequently, modelling economic-engineering decision-making to project the energy demand in the buildings sector into the future is a complex endeavour the main difficulties being behaviours and variety. It is difficult to capture behavioural factors in the modelling because of the large variety of idiosyncratic behaviours and decision circumstances. Despite relying on statistical evidence, econometric modelling fails to incorporate the complex engineering constraints and possibilities of building renovation.
PRIMES-BuiMo opts for a hybrid economic-engineering approach, covering the dynamics of stock evolution and placing great emphasis on modelling behaviours, as well as on policies influencing behaviours (see Figure 1). Hence, the model represents idiosyncratic behaviours and (non-) market barriers, while also providing a high-resolution disaggregation of the building stock. Furthermore, it classifies the building stock in many different categories (termed "building classes") based on house/building type, geographic location, age of construction, income class or services sub-sector. Thereby, the model projects into the future energy demand, using a dynamic simulation of the renovation of the buildings' shell, together with the choice of technology and fuel types for the different uses of energy.
Following [18] the mathematical models for energy in buildings can be classified in a) top-down approaches, b) bottom-up (accounting) approaches, c) approaches based on building physics, d) statistical models, and e) hybrid models. The top-down models investigate the inter-relationships of energy demand in buildings and the economy at large and are aggregate approaches [19]. The categorisation of energy models into bottom-up, top-down and hybrid is established in the literature reviewing modelling, [20].
The bottom-up methods apply a fine segmentation of buildings in categories, calculate an engineering-based cost optimisation on a single representative building type per category to derive energy demand and energy savings, and finally multiply the results by the number of similar buildings in the same category to calculate totals, [21][22][23]. The approaches based on physics also consider individual typical buildings and apply engineering calculations [24]. In contrast, the statistical approaches are aggregate, usually reduced-form, models on which regression methods estimate parameters statistically, [25][26][27][28][29]. These models cannot handle assessment of restructuring policies directly. The literature of statistical aggregated models of energy demand in buildings is vast and its review is out of the scope of the present paper.
Hybrid models are the largest and more complex of the modelling techniques classified in the paper, and are the only ones that combine economic, behavioural and engineering approaches. The hybrid models formulate the decisions as derived from utility and cost optimisation, subject to constraints part of which represent engineering aspects. The presence of utility functions allows for the incorporation of preferences and other parameters capturing behaviours and imperfections. The hybrid approaches usually calculate the frequency of choices at different levels based on distribution functions, which reflect the discrete choice theory, [30]. Historically, some of the largest energy models applied to Energies 2019, 12, 2745 5 of 28 the buildings sector following the physical bottom-up approach are among others Building Research Establishment Housing Model for Energy Studies (BREHOMES) [31], Building Research Establishment Domestic Energy Model (BREDEM) [32], Domestic Energy and Carbon Model (DeCARB) [33], and National Nondomestic Buildings Energy and Emissions Model (N-DEEM) [34]. There exist several other physical bottom-up modelling approaches developed recently to support the EU policy for the buildings sector, [35][36][37][38]. Several recent physical models are mentioned in other places in this paper, as our modelling has drawn on data and some engineering functions developed for these models. Modèle d'Evolution de la Demande d'Energie (MEDEE) [39], Model for Analysis of Energy Demand (MAED) [40] and the demand sub-models of Long-range Energy Alternatives Planning System (LEAP) [41] are examples of bottom-up accounting models, lacking representation of price-driven substitutions and economic or behavioural choices. exhibit idiosyncratic behaviours. Also, the engineering peculiarities of the building stock regarding 158 age, technical constraints and geographical location vary to such an extent that the technical and 159 costing circumstances differ even within groups of buildings with similar attributes.

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Consequently, modelling economic-engineering decision-making to project the energy demand 161 in the buildings sector into the future is a complex endeavour the main difficulties being behaviours 162 and variety. It is difficult to capture behavioural factors in the modelling because of the large variety 163 of idiosyncratic behaviours and decision circumstances. Despite relying on statistical evidence, 164 econometric modelling fails to incorporate the complex engineering constraints and possibilities of 165 building renovation. evolution and placing great emphasis on modelling behaviours, as well as on policies influencing 168 behaviours (see Figure 1). Hence, the model represents idiosyncratic behaviours and (non-) market 169 barriers, while also providing a high-resolution disaggregation of the building stock. Furthermore, it 170 classifies the building stock in many different categories (termed "building classes") based on 171 house/building type, geographic location, age of construction, income class or services sub-sector.
172 Thereby, the model projects into the future energy demand, using a dynamic simulation of the renovation 173 of the buildings' shell, together with the choice of technology and fuel types for the different uses of 174 energy. Our model, PRIMES-BuiMo is in the category of hybrid economic-engineering models. Due to the complexity of the mathematical problem and the data intensiveness, hybrid models of full-scale are very rare in the literature. Examples are the Canadian Hybrid Residential End-Use Energy and Emission model (CHREM) [42][43][44], the residential and services sector sub-models of the National Energy System Model (NEMS) [45] and the Canadian Integrated Modelling System (CIMS) model in Canada, [46,47]. Several model applications for the buildings sector have been performed using linear programming models that cover the entire energy system and represent energy equipment choices as part of the overall optimisation. Examples are MARKet and Allocation (MARKAL), The Integrated MARKAL-EFOM (Energy Flow Optimization Model) System (TIMES) and several others [48,49]. The linear programming approaches do not model idiosyncratic behaviours, based on the discrete choice theory, and non-linear cost-potential relations, as in the hybrid models mentioned in the beginning of this paragraph. This is a major drawback of the linear programming modelling approach.
Regarding the modelling of buildings renovation, the literature according to [50] can be divided in two main streams: (a) the models that evaluate technical options of renovation economically mainly based on present value calculations combined with physical modelling of buildings and (b) behavioural models that capture homeowners' decision making for renovation. The literature on modelling renovation is expanding [51][52][53][54] but it lacks comprehensive modelling of renovation of buildings for the purpose of projections for the entire stock and for assessing policy measures. The PRIMES-BuiMo has the ambition to cover this gap in the literature, as it incorporates a fully-fledged economic-engineering model of renovation decisions within the energy model. Also, the application of the model for many countries with very fine segmentation of buildings is also novel in the literature of modelling renovation decisions. Other large-scale models, such as NEMS, CIMS, CHREM and TIMES, that we mentioned above, do not include endogenous economic modelling of renovation of buildings, and instead use simple accounting equations based on exogenous parameters. A further novelty of PRIMES-BuiMo is the combination of discrete choice theory with dynamic programming in the modelling of renovation decisions; such a mathematical formulation cannot be found in the literature according to our knowledge.
A vast literature deals with non-market barriers and subjective factors (including subjective discount rates), which hinder energy efficiency investment, [55]. The present modelling approach has drawn on this literature extensively, regarding the conceptual framework and numerical data that have been estimated statistically (the references are included in the corresponding sections of the paper). To our knowledge, however, there exist no full-scale model that incorporates the non-market barriers and their removal thanks to policies in a systematic manner. PRIMES-BuiMo is a novel modelling approach to this respect.
Finally, PRIMES-BuiMo is by far the largest model ever built for the buildings sector of the EUMS, as it uses a fine segmentation of the building stock and the agents acting as decision-makers. The model builds on this fine segmentation to represent idiosyncratic behaviours and the influence of subjective factors and imperfections, which are considered as non-market barriers. Thanks to the segmentation and the explicit modelling of behaviours, PRIMES-BuiMo is able to assess individual policy measures of market and non-market nature, a feature which is very important for policymaking as the distributional effects are of great policy significance.

The Mathematical Framework
Decision-making for energy-related investment in the buildings sector includes: demolition and construction of new buildings, renovation of the building's shell, purchasing of new energy-using equipment and appliances (e.g., washing machines, lighting and many others) and scrappage of old equipment and appliances, including possible premature replacement of equipment. The consumer considers different time horizons for these investment decisions; renovation has a long lifetime, but lighting equipment may last for only a few years. Also, there is an inherent hierarchy among the investment decisions; renovation of a building is prior to the choice of heating system, and this, in turn, influences the choice of a water heating system.
For every investment decision, the decision-maker is invited to choose among various technologies, which may, in turn, vary in terms of capital costs and energy consumption (or energy savings) performance. Capital costs are generally higher when energy efficiency increases. The eco-design policy framework, which is part of the formulation, bans certain technologies based on poor energy efficiency and promotes the most efficient ones via the labelling system, which generally induces lower technical risks.
The equipment using energy also differ according to the type of fuel they use; the model spans a wide variety of options, including liquid fuels (notably diesel oil), liquefied petroleum gas (LPG), distributed gas (with different possible blends of natural gas, hydrogen, biogas and synthetic e-gas), electricity, distributed heat, biomass (wood, pellets and waste), solar and geothermal energy. The availability of a fuel type depends on the distribution infrastructure. The various building categories, belonging to different geographic areas, have differentiated access to fuel distribution infrastructure.
Investment decisions also rely on the interdependence between the deepness of a building's energy insulation and the choice of heating equipment and fuel. A highly insulated building has low Energies 2019, 12, 2745 7 of 28 energy consumption, and in the case of passive buildings, it may only occasionally use energy for heating or cooling. The power size and the rate of use are important factors for the economics of the candidate heating systems, and thus the thermal performance of a building influences the rational choice of heating equipment. Oversized equipment for a highly insulated building is less cost-effective compared to other types of appropriate size, even if the unit cost of purchasing is higher for the latter than for the former. For example, an electric heat pump would be more suitable for a well-insulated house rather than a boiler, which would inevitably be oversized. The choice also depends on the power sizes available in the market, as well as the flexibility of its use. The model captures this complexity by considering the entire typical building, including the thermal performance of the shell, for the calculation of the technical size of the candidate heating and cooling systems and the evaluation of the economic performance of equipment and fuel types. An assessment per sqm and not per building would be unable to capture the influence of power sizes and the thermal performance of buildings on the choice of heating equipment. The model includes the possibility of revising the choice of equipment and fuel for heating and cooling after a deep renovation of the building, even if the previously installed heating equipment has not reached the end of their lifetime.
In reality, decisions regarding equipment and fuel types are nested choices. The choice of heating equipment and fuel type reasonably takes place prior to the choice of water heating and cooking system. The decision hierarchy is due to the high cost of installation and operation of heating compared to the cost of other heat uses. The model reflects the nested choices as a tree of interdependent choices. Not all combinations of choices are fully compatible with each other, and the model applies penalty factors to unusual combinations, as such cases involve additional or hidden costs also in reality. The compatibility of choices differs between various building categories, especially concerning the geographical area, the size of the building, the availability of energy supply infrastructure, and others.
It is well known that the models based on engineering-economic optimisation suffer from the representative-agent hypothesis. Even if the building and agent characteristics are highly segmented, as far as data availability allows, the limitations arising from the representative-agent hypothesis are still valid. In reality, the individual decision-maker makes only discrete choices. Models producing a single discrete choice for each class of building, based on the representative-agent hypothesis oversimplify and are unacceptable, even if the segmentation of building classes is very fine.
An approach based on discrete choice theory, as described in [56], is more appropriate for addressing the representative-agent hypothesis. Discrete choice theory postulates that the frequencies of candidate choices in the population within a segment of buildings follow a given probability distribution function and thus discrete variables transform into continuous ones. The frequencies of candidate choices derive from a comparison of their performance according to a cost or utility function, which is the same as that the individuals use to derive their discrete choice. The cost of utility comparisons may involve elasticity, maturity and risk-reflecting parameters to capture preferences and behaviours. In this way, the model represents the heterogeneity of idiosyncratic behaviours and the varying decision-making circumstances within each class of building, thus addressing the representative-agent hypothesis.
Based on the above considerations, PRIMES-BuiMo formulates nested discrete choices based on discrete choice theory and embeds said choices into a dynamic programming framework, subject to constraints representing sources with a limited potential. Mathematically, the model solves a nonlinear complementarity problem within a dynamic programming problem (see Table 1 for the nomenclature of PRIMES-BuiMo).
The first part of the model projects useful energy demand into the future, using econometric functions which relate demand for useful energy services to macroeconomic, demographic and price variables that are exogenous projections. The useful energy categories comprise space heating, cooling, water heating, cooking, lighting, black appliances and white appliances, as well as other similar categories for the services sector.
Net annual cost (operating and capital costs, inclusive of investment for building insulation) for the useful energy demand U t,h ϕ t,h ln ϕ t,h = β 0h + β 1h ln M t,h + β 2h ln C t,h Log-linear function for the steady-state relationship between the useful energy U t,h and the explanatory factors The functions (1) to (3) project useful energy into the future as follows: Index t denotes time (years) and h spans the building categories, which are defined as a combination of building type categories (geographic location, age, single or multi-family) and agent classes (income classes for households and sectors for the services). The formula represents the influence of macroeconomic (income for households and gross value added for the services sector) and demographic (or number of employees for the services sector) factors denoted by the symbol M t,h and the net annual cost of the useful energy service by C t,h , which adds operating and capital costs, inclusive of investment in building insulation. A log-linear function φ combines these factors and influences the projection of useful energy along a logistic curve with a varying upper bound u d t,h , also expressed as a function of macroeconomic growth and demographics.
In the next step, the model projects into the future the buildings stock, based on historical trends and the influence of the rate of growth of macroeconomic and demographic factors, A dynamic econometric Equation (4) projects the annual growth rate of new buildings, . N t,h for replacing demolished buildings, based on an exogenous rate of demolition τ t,h , and for increasing the stock of buildings S t,h , which tends dynamically to an optimal stock at a pace θ h . The optimal stock is a latent, non-observable variable. The transfer of population or activity between categories of buildings, denoted by T t,h ,h , follows a logistic growth curve using an exogenous rhythm r h ,h and a maximum growth limit λ h ,h . . .
At this stage, the model formulates how the decision-maker meets the useful energy requirements. The building shell covers part of the heating and cooling useful energy depending on the degree of insulation. The model applies building codes (i.e., standards for heat losses) for new constructions and considers an exogenous rate of compliance to the codes. Innovation in old buildings to improve insulation is endogenous in the model, as explained below.
The measurement of heat losses of buildings follows the EN 13790:2008 [57], which considers the U-values, external temperatures and internal thermostat settings, which is an exogenous parameter. Renovation of buildings has various purposes, but the model only considers renovation for energy savings, which derive from the thermal performance driven by investment in insulation and other interventions.
The model classifies the various possible renovation plans in a discrete set of interventions sorted (denoted by k) in ascending order of thermal performance. Investment costs are also increasing following this order. The model aims to first calculate the timing and the degree or deepness of renovation (i.e., the choice of a renovation plan) for each building category. As the amount of investment and the burden of the renovation works are considerable, it is unlikely that a particular building undergoes renovation in a stepwise manner during its lifetime.
Consequently, a decision-maker has to choose a particular dynamic strategy with specific timing and deepness of renovation among a large variety of possibilities. Strategies with stepwise renovation interventions are by construction costlier than others that deliver the same degree of renovation but invest only once or twice during the building's lifetime. The decision-maker needs to calculate the present value of cost streams to compare alternative dynamic strategies of renovation. The costs include investment expenditures for renovation, the cost of purchasing energy after the energy savings and other operating and maintenance costs.
The approach of modelling behaviours consists of including additional cost items to represent barriers. Hidden costs include costs to avoid disturbance to neighbouring flats, reflect complicated waste removal, expenditures due to architectural restrictions, etc. Other costs account for non-market barriers (e.g., subjective cost of capital, perceived costs due to lack of information or to uncertainties regarding the energy savings performance, lack of economies of scale, and others). Additional costs may apply in relation to the specificities of the building category (e.g., related to the geographic area, single or multi-family building, and others). Subsidies may also apply directly as an investment subsidy and reduction of debt interest rates, and indirectly as a penalty on the fuel prices for the consumption remaining after the savings. The penalty factor may represent non-identified policies that promote energy efficiency in buildings or apply required energy savings. White certificate systems also act as indirect penalties on fuel costs.
The model generates a large number of dynamic renovation strategies (denoted by i or ii) for each building type and calculates the present value of cost streams over a long period using a discount rate that reflects the subjective cost of equity and the cost of debt, eventually including risk premium factors which differ by income class [58].
In Equation (7) I t,h,i represents investment expenditures for renovation, which occur sporadically and include all kinds of indirect hidden costs and subsidies, whereas C t,h,i represents all kinds of annual costs of heating and cooling (including all cost items mentioned above and cost penalties).
A decision-maker would select a single renovation strategy based on the minimum value of v h,i . However, the model retains a number of the most economic renovation strategies, assigns different frequencies to them, and performs the calculation for each building and consumer class. In this way, the model captures idiosyncratic behaviours and heterogeneous building characteristics. The model assumes that the frequencies of renovation strategies per building category follow a Gumbel distribution function, [59][60][61][62], from which the shares of each renovation strategy derive, as in Equation (8).
The decision about renovation precedes the choice of heating and cooling equipment, while the optimal choice depends on the thermal performance of the building shell. Also, whenever a deep renovation takes place, the model requires the revision of the choice of heating and cooling equipment, irrespective of its age.
To determine economic optimality, the model calculates costs for the entire building (and not per unit, for example per sqm) and considers discrete power sizes of candidate equipment types as available in the market. A highly insulated building will need equipment of smaller power size than a poorly insulated one.
The model uses total costs inclusive of capital and hidden costs, as well as operating costs, to select among alternative heating and cooling equipment types. The hidden and perceived costs also relate to the conditions of the building category (e.g., the conditions of fuel supply in a geographical area, among others). Also, climatic conditions influence the costs, as electric heat pumps need burning gas as a complement in cold climate areas. To compare alternatives, the model calculates the present value of cost streams of candidate strategies, j, which involve the choice of a particular equipment type and the timing of investment and scrappage. The cost stream includes capital costs and operating costs for purchasing energy and maintaining the equipment; the calculation of present value uses a discount rate distinctly defined for decision-maker classes, notably for distinguishing between income classes, as opportunity costs of cash flow differ by income class [58].
The choice also depends on technology maturity factors, µ h,j , expressing uncertainty perceived by the decision-maker for not yet mature technologies. As already explained, the cost of equipment in a strategy j is conditional (denoted by j|i ) on the choice of a renovation strategy i. The model then applies a discrete choice formulation to calculate the frequency of choices of dynamic strategies referring to equipment.
The choice of equipment depends in the model on nested hierarchical choices of equipment types, on technology types (varying by energy efficiency performance, hence by purchasing cost) and on fuel types to be used by the equipment. All nesting levels calculate frequencies of selected options following a discrete choice formulation, which includes the relevant costs, inclusive of hidden and perceived cost components, as well as maturity factors. The cost of fuels depends on market prices, conditions of supply prevailing for the building category (availability of infrastructure and costs of distribution) and policy options that influence costs, such as taxes, subsidies, penalty or promotion factors related to policy targets concerning renewables, among others. Furthermore, the model formulates cost impacts stemming from resources subject to an exhaustible potential. Examples are the construction industry capacities for renovation works, the availability of certain fuels, e.g., biomass, and the distribution system capacity. The case of non-availability of a particular distribution system such as district heating or gas in a given region implies non-availability of the corresponding option in the model. The formulation of resource constraints is explicit in the model, and the dual values of the constraints add to the cost variables (with a positive sign).
The model can handle system-wide policy targets in the same way. The model outcomes (i.e., the choices) will have to have implications, measured in policy target terms, that are equal or higher to the defined target; in this way, the model can handle system-wide energy efficiency, targets for renewables and other policies. The dual values of the policy target constraints add to cost variables in the form of benefits (i.e., with a negative sign). Finally, cost variables, adjusted by the positive or negative dual values of the resource or policy constraints, influence the choice of strategies, equipment types and fuels, until reaching an equilibrium in the sense of a mixed-complementarity problem. Being a fully dynamic model, PRIMES-BuiMo keeps track of all vintages of equipment and appliances.
The formulation of equipment choice and energy consumption is much simpler for lighting and electric appliances. The model emphasises the choice of technology type, by representing distinct classes depending on energy efficiency performance based on the eco-design regulations.

The Dataset
As far as the residential sector is concerned, the dataset classifies the households into 270 building categories, defined by: In the current model version, discount rates range between 10% and 14.1% for the residential sector and are in line with the lower-end of statistically-estimated discount rates for households [17,63,64].
The model distinguishes services sector into segments and formulates them separately, as shown below: The buildings stock splits into classes following the age of construction, divided into nine age bands covering the period 1920-2015. Furthermore, the building classes distinguish among ventilation techniques, notably mechanically and naturally ventilated buildings.
Regarding the engineering information for the renovation sets, the model defines eight distinct renovation packages and draws data from [74]. The lightest package includes replacement of windows, and the deepest renovation package involves the installation of a thick insulation layer to reduce air permeability levels.
The dataset includes around 50 different types of equipment for space heating, air cooling and other heat uses (see Tables A1 and A2), as well as 11 types of electric appliances. Data availability was not enough to represent full correspondence with the eco-design segmentation of appliances. The technology categories per type of equipment are defined according to energy efficiency and range from currently available technology to Best Not Available Technology (BNAT). The data on the technical-economic characteristics of equipment technologies (efficiency rate, technical and economic lifetime, investment cost, operation and maintenance costs and other variable non-fuel costs) draw on a large number of sources, as well as on a recent study, which reports on an extensive consultation with industrial stakeholders [74]. All technologies are supposed to follow a learning-by-doing process, which is exogenous to the model, and the learning achievement can vary by scenario.

Illustrative Model Applications
A structural model like PRIMES-BuiMo is suitable for projections and not for forecasts, as it lacks evidence based on statistical inference. The purpose of such models is to compare projections based on different policy options and draw policy recommendations from the comparison thereof. To this end, the model firstly quantifies a Baseline scenario which includes the policies aiming at achieving the EU targets for 2030 and does not include additional policies for the period after 2030. Contrasting scenarios, also quantified, include additional policies for the period after 2030 in an aim to achieve ambitious carbon emissions reduction targets until 2050. The comparison of projections based on the model is useful, as it illustrates whether the policies for 2030 are sufficient to achieve the targets for The baseline scenario includes the following targets for 2030, as proposed by the European Commission in the "Clean Energy for All Europeans" policy package [75]: (a) at least 40% reduction in GHG emissions (from 1990 levels), (b) at least 32% share for renewable energy in gross final energy consumption and (c) at least 32.5% lower primary and final energy consumption compared to a projection performed in 2007. The policy package foresees energy efficiency improvement of buildings as one of the major pillars, and for this reason, it includes several legislative initiatives, which mainly encompass:

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The Energy Performance of Buildings Directive (Directive (EU) 2018/844), which entered into force on 9 July 2018 [76], and according to which new buildings are assumed to be nearly zero-energy buildings as of 2020.
The directives mentioned above cover only the period until 2030 and include provisions for monitoring and enforcing energy consumption reductions in the MS. The energy efficiency improvement in the buildings sector, foreseen by the directives, is ambitious. Article 7 of the EED mandates a 1.5% reduction in final energy consumption per year, applicable as a compound rate until 2030. It is at the discretion of the MS to put in place policies promoting efficiency investment.
However, the directive provides a mandatory menu of options, which include the promotion of energy service companies, the obligation of utilities to support energy savings at the premises of the customers and financial supporting schemes with a particular focus on consumer classes with poor fund-raising possibilities. The modelling of these legal provisions is straightforward in the PRIMES-BuiMo model, thanks to the representation of a large variety of policies and the high segmentation of building and consumer categories. The modelling of the obligation to reduce energy consumption relies on a penalty factor applying to the cost of energy in buildings. An increase in the value of penalty implies additional and deeper renovation of buildings to pay-off eventually. The value of the penalty coincides with the dual variable of the constraint representing the annual energy efficiency target until 2030. At the same time, several policies prescribed in the directive induce a reduction in perceived costs and technical uncertainties, and increase access to funding. In the modelling, reducing perceived cost factors and discount rates increases the deepness and frequency of building renovation.
Based on different cost structures and possibilities, the model results may suggest different energy-efficiency efforts by building class and MS. The country-specific models run iteratively until the energy efficiency performance for the entire EU reaches the desired target. In this way, the model can suggest how to allocate the energy efficiency effort to the MS optimally and respectfully of the specific potential and possibilities of the MS. To capture eventually limited capacity of the construction industry and avoid concentration of renovation investment in a short period, for example close to 2030, the model represents a feedback from the dual variable of the construction industry capacity potential to the cost of renovation, hence to the choice of timing of renovation within the candidate renovation strategies. In this manner, the model projects an escalation of renovation investment over time. The resulting renovation rates are, as expected, significantly above historical rates, but not excessively high yearly, thanks to the feedback of the construction industry capacity.
Energy efficiency improvement does not rely on renovation solely but also derives from the market uptake of advanced equipment and appliances. The modelling accommodates the provisions of the eco-design directive by raising penalty factors, discouraging adoption of non-compliant technology varieties and reducing perceived cost factors applied on advanced technology varieties. Electric heat pumps are among the preferred technology options. Consumers increasingly adopt heat pumps for heating and cooling following the growing trend of building renovation, while the magnification of the heat pump market induces cost and performance improvements. Thus, electrification develops, while energy efficiency improves.
Despite the ambitious development of energy efficiency in buildings until 2030, the projections based on the model show that the policies until 2030 are not in themselves sufficient to enhance the energy efficiency improvement post-2030, as needed to reach the ambitious emission reduction targets for 2050. The efficiency policies put in place until 2030 have long-lasting effects in the period after 2030, but the implied energy savings are not enough as the targets are also more ambitious for 2050 than for 2030. Table 2 shows that the strong pace of renovation and energy savings until 2030 slows down considerably after 2030. However, the electrification trend continues without any disruptions and produces a relatively small slowdown of direct emission reduction post-2030. The design of the alternative policy scenarios focuses on the period 2030-2050 and aim to achieve GHG emissions reduction above 80% by 2050 compared to emissions in the EU in 1990. The European Commission communicated in November 2018 a long-term strategy for the period 2030-2050 and compared various scenarios achieving the emission targets by 2050, see [75]. The strategy foresees, in all scenarios, a significant contribution of the buildings sector to the overall emissions reduction. The energy efficiency improvement is a major pillar of the strategy and an autonomous policy objective, as in the policy package until 2030. The reduction of energy consumption is a cost-effective way of reducing emissions and, via a rational use of electricity and fuels, it facilitates the energy supply sectors to address the risk of a shortage of low carbon resource possibilities. The power sector, in all scenarios of the strategy, achieves zero-carbon intensity by developing renewables, and in particular solar and wind, as other options, such as nuclear and carbon capture and storage (CCS), have limited potentials for several reasons. Also, electricity becomes the carrier of preference to reduce emissions in otherwise inflexible sectors, such as mobility and heat, and in some of the scenarios serves as a feedstock to the production of carbon-neutral hydrogen and hydrocarbons. Without strong energy efficiency improvement, electricity demand would increase excessively challenging the development of renewables and the balancing of stochastic variability.
The modelling analysis of the long-term strategy, based on the PRIMES model [75], quantified several scenarios for the EU until 2050 and used the PRIMES-BuiMo model for the buildings sector. The paper includes three of the scenarios of the strategy, which follow different assumptions while achieving ambitious carbon emissions reduction by 2050. All three scenarios share the policy assumptions of the baseline scenario for the period until 2030 and apply additional, but different policies during the period 2030-2050. More specifically:

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The Energy-Efficiency scenario involves policies that deliver very ambitious energy savings in the buildings sector and at the same time, projects further electrification of heat. The scenario does not include the development of carbon-neutral hydrogen and hydrocarbons.

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The Hydrogen and E-fuels scenario focuses on the supply-side of the energy system and assumes the development of climate-neutral fuels that can replace natural gas in distribution systems. The scenario assumes that ambitious energy savings take place to avoid the excessive increase in the volume of electricity needed to produce hydrogen and e-fuels. However, energy efficiency ambition is lower than in the previous scenario.

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The Combined scenario assumes a more ambitious emissions reduction target for 2050 compared to the previous two scenarios, aiming at carbon-neutrality by 2050. To this end, the scenario assumes development of very ambitious energy savings together with carbon-neutral hydrogen and e-fuels.
Climate-neutrality of a fuel, hydrogen or hydrocarbon, is meant for the entire chain of production and use, including for the energy inputs to the production of the fuel. Climate-neutral electricity producing hydrogen and CO 2 captured from the air and biogenic sources can form climate-neutral methane and liquid hydrocarbons. Using CO 2 captured from fossil-fuel combustion does not ensure carbon-neutrality as the CO 2 is released into the air when combusting the synthetic hydrocarbon.
All three scenarios include energy-efficiency promoting policies that are of higher intensity in the period 2030-2050 than in 2020-2030, thus contrasting the policy assumptions of the Baseline Scenario. The policies include incentives to accelerate the pace and enhance the depth of energy renovation of buildings, stringent building codes accompanied by higher enforcement, and strict eco-design standards for equipment and appliances. The ambitious policy induces higher awareness about possibilities and benefits of energy efficiency, as well as financial and implementation facilitation of investment.
Consequently, perceived costs, risk premiums and other barriers reduce and are reflected onto the assumptions of the modelling. They imply a faster pace and enhanced deepness of investment in renovation, construction of passive buildings and uptake of highly efficient equipment. However, the Hydrogen and E-fuels scenario includes somehow less ambitious policies for energy efficiency, than the other two scenarios, as the carbon-neutral fuels present an attractive option for emissions reduction and thus consumers can afford moderating the energy efficiency ambition.
The rate of renovation of buildings is significantly higher in the strategy scenarios compared to the baseline scenario during the same period. By construction, the renovation rate is higher in the Energy Efficiency scenario, than in the other strategy scenarios and, similarly, the deepness of renovation is higher. The renovation effort of the strategy scenarios is slightly less intensive in the period 2030-2050 than in the period 2020-2030 (see Table 3) due to saturation effects, as the building stock becomes increasingly well-insulated and stringent building codes apply to new constructions. The penetration of electricity in the heat market tends to increase in the long-term, in all scenarios, as heat pumps are an economically rational choice for highly insulated buildings. Another driver to the benefit of heat pumps consists of promotional policies aiming at the renewables targets, given that beyond a certain value of the COP (coefficient of performance) the heat pumps are considered as renewables. Also, the positive anticipation of the increasing market size for heat pumps enables higher learning achievements and cost reductions leading to a further facilitation of their success in the heat market. However, the electrification is lower in the Hydrogen and E-fuels scenario as the carbon-neutral fuels can compete with electricity in this scenario. Figure 2 illustrates trade-offs between electric heating and gas heating when for the latter carbon-neutral gaseous fuels are available. It is worth noticing that the Hydrogen and E-fuels scenario needs to exploit all options to achieve carbon neutrality in the buildings sector.
Because of the additional policies, the strategy scenarios succeed to reduce emissions by 2050 much below the levels in the baseline. The combined scenario is more ambitious than the other two scenarios and reaches almost full carbon neutrality by 2050 in the buildings sector. The scenario of Hydrogen and E-fuels achieves much lower emissions in 2050 than the Energy efficiency scenario because the former includes the carbon-neutral gaseous fuels in addition to other options. The energy efficiency scenario, having electricity as practically the only carbon-neutral carrier, cannot fully substitute gas and cannot abate emissions as much as when carbon-neutral gas is available. Limited potentials, inconveniences, as well as air pollution, of using biomass in buildings do not allow renewables to expand beyond certain limits and be alternative to carbon-neutral gas. The combined scenario reaches carbon-neutrality by blending hydrogen up to 20%vol, biomethane up to 30%vol and e-methane in gas distribution, combined with very ambitious renovation of buildings and large market penetration of electricity.

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The combined scenario reaches carbon-neutrality by blending hydrogen up to 20%vol, 641 biomethane up to 30%vol and e-methane in gas distribution, combined with very ambitious 642 renovation of buildings and large market penetration of electricity.

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The model is able to handle energy efficiency targets in the buildings sector defined by   The model is able to handle energy efficiency targets in the buildings sector defined by policymaking. The target is included as an overall constraint in the mixed complementarity formulation of the model and influences the choices regarding renovation, equipment and appliances. Mathematically, the choices are influenced by the dual variable of the target constraint, which acts as a cost penalty on the consumption of final energy. In this manner, deep renovation options become attractive as the penalty reduces their pay back period. However, higher the uptake of deep renovation option, higher is the unit cost of renovation as the nonlinear cost-potential curves have increasing slopes. Figure 3 illustrates the relationship between the value of the penalty, hence the stringency of the energy efficiency target (denoted by EE constraint) and the average annual renovation rate calculated by the model.   Total final energy consumption in buildings is well below Baseline levels in 2050, in all three scenarios, and the demand for electricity is also lower despite the significant increase in the share of electricity in total energy consumption in buildings. The energy efficiency improvement implying a rational use of electricity helps maintaining demand for electricity at reasonable levels to the benefit of sustainability in the power sector. Figure 4 illustrates the dependence of final energy consumption for heating in houses on the climate policy for 2050 in the EU. The figure plots the model results from several scenario applications for various energy efficiency supporting policies and climate policy targets for 2050. Part of these scenarios foresee reaching 80% emission reduction in the EU by 2050; this target is considered to be compatible with a climate strategy limiting temperature rise to 2 • C. Other scenarios, which are compatible with a 1.5 • C climate strategy, adopt a target of reducing GHG emissions by more than 95% in 2050 compared to 1990 levels. Energy efficiency improvement is a major pillar in all these scenarios; however, the scenarios also differ regarding the intensity of energy efficiency policy for the buildings sector.     The model performs a detailed accounting of costs, which include capital expenditures (CAPEX) for insulating the building, and the purchasing of equipment and appliances, and operating expenditures (OPEX) for purchasing energy products and maintaining the equipment. In this way the model calculates total costs incurring to procure the useful energy services, with total costs being inclusive of expenditures for building insulation. The "total cost of energy services" can be used to compare the scenarios from a cost-effectiveness perspective, see [79].
The policies of the baseline scenario aiming at achieving the targets in 2030 imply significant increases in investment expenditures in the period 2020-2030, compared to historical trends, both for the intense insulation of buildings and the purchasing of efficiency equipment and appliances (see Table 4). The achievement of the 2030 targets implies that individuals and firms need to raise funding at a considerable extent, compared to common practices. The implementation policies will have to address the issue of affordability, and the ensuing adverse social impacts, for the consumer classes in the buildings sector that have poor access to debt and have limited cash flow. Sensitivity analysis using the model showed that increasing the discount rate to represent high opportunity costs of cash flow is significantly detrimental to the energy efficiency improvement pace. The financing barrier is sufficient to jeopardise the achievement of the targets. Although the increase in the renovation of buildings saves energy and tends to reduce the bill of purchasing fuels, the results show an increase in OPEX, on average, in the period 2020-2030, compared to the period 2011-2020. The causes are primarily the shift of fuel mix towards electricity, which is more expensive than gas per unit of useful energy, and at a lesser extent the trend towards a slight increase in the gas prices after 2020, compared to the previous period. Table 5 summarises the evaluation of costs for the long-term policy scenarios and the comparison to the baseline scenario for the period 2031-2050.
It is worth noticing that the Energy Efficiency scenario implies the same or slightly higher total costs of energy services in the buildings sector compared to the Baseline scenario, although the former scenario achieves very significant emissions reduction in 2050 (50% less in the long-term scenario). The significantly higher investment in the Energy Efficiency scenario succeeds to reduce costs of purchasing fuels compared to the Baseline, and the savings in the energy bill offsets the additional CAPEX. From a cost perspective, the Energy Efficiency scenario is the best among the three long-term scenarios. However, the implementation of such an ambitious renovation program is questionable.
The Hydrogen and E-fuels scenario relies less on energy efficiency and more on the possibility of using carbon-neutral distributed methane. Regarding convenience for consumers and avoidance of disruptions in the way energy is used and distributed in the buildings sector, the Hydrogen and E-fuels scenario is more reliable than the Energy Efficiency scenario. However, the total costs of energy are significantly higher. The main reason is that the distributed carbon-neutral methane is significantly costlier than the conventional fuels used in the Energy Efficiency scenario. The unit cost of purchasing energy products in the Energy Efficiency scenario in 2050 is 12% higher than in the Baseline, due to the higher use of electricity, but the unit cost of energy products in the Hydrogen and E-fuels scenario is close to 30% in 2050 more expensive than in the Baseline. The spending of lower amounts in CAPEX dedicated to efficiency does not fully compensate the increase in OPEX due to the expensive fuel mix, and thus total energy costs in the Hydrogen & E-fuels scenario are higher than in the Energy Efficiency scenario.
Nonetheless, the Hydrogen and E-fuels scenario is affordable if one considers the very significant drop of carbon emissions relative to the Baseline, as the former scenario implies only 4% higher total energy costs in the residential sector and 11% higher costs in the services sector (5% for the buildings sector as a whole) in cumulative terms in the period 2031-2050, compared to the costs in the Baseline Scenario. It is worth noticing that the CAPEX, hence the investment expenditures, do not increase in the Hydrogen & E-fuels scenario in the period 2031-2050, compared to the Baseline. The increase in costs is entire due to the increase in OPEX. In other words, the former scenario is robust regarding implementation, compared to scenarios with a significant increase in the investment effort, as the Energy Efficiency scenario, which needs 18% higher CAPEX than the Baseline. However, it should be noted that the scenario assumes tapping on the entire learning-by-doing potential of e-fuels. The cost structure of e-fuels is heavily dependent on the cost of electricity, as the cost shares of methanation (for gas) and Fischer-Troops (for liquids) become relatively small after exploiting the learning potential. However, significant uncertainty surrounds the costs of CO 2 capture from the air and, to a lesser extent, from biogenic resources. The scenario assumptions are optimistic about these costs. The Combined scenario is much more ambitious than the other two, for emissions reduction and is reasonably more expensive. Given the larger magnitude of emissions reduction, the scenario is also affordable as it implies only a 11%-12% increase in cumulative total energy costs in the period 2031-2050 compared to the Baseline for achieving carbon-neutrality. The Combined scenario is costlier both in investment expenditures and operating costs. High costs derive from the maximum use of all options as the scenario needs to reach carbon-neutrality. Both ambitious efficiency and large amounts of carbon-neutral gas are necessary to achieve drastic emissions reduction. The increase in CAPEX, compared to the Baseline, is significant (15% in the period 2031-2050), and is slightly below the levels in the Energy Efficiency scenario. The increase in OPEX, compared to the Baseline, is also significant (19% in the period 2031-2050) and is due to two factors: the gas for distribution is entirely free of natural gas, and the e-gas has a much higher share than hydrogen. By assumption, the gas mix in the Hydrogen and E-fuels scenario includes natural gas, a small share of e-gas and a high share of hydrogen. The gas mix in this scenario is significantly less expensive than the gas mix in the Combined scenario, as the e-gas is more expensive than hydrogen. Sensitivity analysis using the model has explored several other configurations for the scenarios that aim to achieve carbon-neutrality, as the Combined scenario, but lack of space does not allow presenting them in this paper. Table 6 provides another perspective of the way the long-term scenarios achieve emissions reduction, compared to the baseline. The table compares cumulative figures in the period 2031-2050 and decomposes the emissions reduction relative to the baseline in a contribution due to the improvement of energy intensity and to the improvement of carbon intensity. The energy intensity is the ratio of final energy consumption over useful energy (including energy savings due to the thermal performance of the building shell). The carbon intensity is the ratio of direct CO 2 emissions in the buildings sector over final energy consumption. The contribution of the former represents the effect of energy efficiency improvement, and the contribution of the latter represents the effect of decarbonising the fuel mix. Table 6. Structure of emissions reduction in the long-term policy scenarios.

Energy Efficiency Scenario
Hydrogen and E-fuels Scenario Combined Scenario capturing the heterogeneity of consumer behaviours and building conditions constitute the complexity of the model. The design also emphasised the representation of a multitude of policies, market and non-market based, as well as targets, and the inclusion of several barriers to rational choices in a monetised form. The numerical implementation of the model concerns all European countries, covers the residential and the services sector buildings, all split on many classes, and the time horizon until 2070, divided into five-year steps. The model has already a record of successful applications in the assessment of European policy options in the buildings sector regarding energy efficiency improvement, via renovation of old buildings and advanced equipment driven by eco-design standards, decarbonisation targets and fuel mix restructuring towards e-fuels. The complex mathematics, the high granularity and the policy richness proved to be of great value in the assessment of the European policies because they aim to be specific by MS and able to evaluate specific policy instruments regarding cost-effectiveness and the possible social adverse effects. It would have been impossible to capture all the aspects required by the policy assessment without the complexity implemented in the model.
To improve the accuracy of the data and reduce computer time are among the priorities of the research in the short term. The model is highly data-intensive. However, new databases for the building stock of Europe are in preparation by Eurostat and the Joint Research Centre (JRC). Although the model runs on a cluster of high-end computers, the computer time is not satisfactory and has obliged us simplifying some parts of the model. Research is underway to linearise the nonlinear Logit and Weibull functions by delimiting the set of feasible choices via the tangents of the indifference curves. The approach underway also transforms the resource and learning functions in linear stepwise expressions. The aim is to run a large inter-temporal linear complementarity problem with continuous and binary variables, instead of the current nonlinear formulation. It is expected to improve computer time substantially, remove simplifications and be able to further increase the segmentation granularity, including time-of-use accounting of all energy forms and uses, without computer time penalisation.
The scenario analysis shows that very ambitious energy efficiency improvement and carbon emissions reduction are possible in the building sector of the EU at affordable costs both for 2030 and 2050. Key in the transition is the acceleration of the pace of renovation of old buildings and the enhancement of the deepness of insulation. Obstacles exist preventing rational exploitation of the cost-effective potential of buildings' renovation. Removing barriers, mobilising investment funding and helping less endowed consumers are the main challenges that the policy needs to address. The potential of energy savings via the uptake of advanced equipment and appliances is also significant, and the eco-design policies need an enhancement to enable the progress further. Heat pumps are of particular interest in the transition, as they are the preferential option for highly insulated buildings, consume electricity very efficiently and can also contribute to the targets for renewables. The scenario projections confirm that ambitious energy-efficiency improvement pays-off and go together with increasing electrification of heat. However, achieving full carbon-neutrality in the building sector seems difficult with recourse to carbon-neutral fuels, such as hydrogen and e-gas, that replace natural gas in the distribution. The scenarios studied a trade-off between a strategy based on extreme energy efficiency, accompanied by electrification, and a strategy where the carbon-neutral distributed gas complements energy efficiency and electrification, which are less extreme but still high. The former strategy is overall less costly than the latter, but the latter has the merit of maintaining current infrastructure and convenience for consumers. The energy-efficiency strategy is particularly capital-intensive, and the e-fuels strategy is less capital-intensive but implies higher operating costs. The fuel mix in the e-fuels strategy remains costlier in the long-term than the conventional fuel mix, despite assuming full exploitation of the learning potential for hydrogen, methanation and CO 2 capture from the air and biogenic sources. Implementation feasibility is the main uncertainty of the energy efficiency and electrification strategy, while high fuel cost is the main uncertainty of the strategy that complements energy efficiency and electrification with carbon-neutral gas. More detailed focus on technologies, implementation and learning potentials are objectives for further research concerning policy applications of the model. Author Contributions: Conceptualization, T.F. and P.C.; Data curation, T.F., A.d.V. and P.C.; Methodology, T.F. and P.C.; Supervision, P.C.; Validation, T.F. and P.C.; Writing-original draft, T.F.; Writing-review & editing, A.d.V. and P.C.

Funding:
The European Commission partially funded this research within a Long-Range Energy Modelling Framework contract.