J Fitó

N Dimri

J Ramousse

Competitiveness of renewable energies for heat production in individual housing: A multicriteria assessment in a low-carbon energy market

Keywords: 1) Renewable energy, 2) Multicriteria analysis, 3) Techno-economic assessment, 4) Environmental assessment, 5) Space heating, 6) Domestic Hot Water, 7) Solar energy

The French energy market is highly reliant on nuclear power. Several factors pressure for a phase-out of this technology, but finding an environmentally and economically competitive substitute is not easy.

Renewable sources are a candidate, and a full deployment in the residential sector could significantly reduce nuclear-based electricity production in France. In this paper, we assess multicriteria competitiveness of renewable energies for residential heat production in a French dwelling. A total of 9 solutions combining the following systems are compared: boilers (electric, biomass or gas-fired), heat pumps (air-source or ground-source) and solar panels (solar thermal or photovoltaic). Global performance is analyzed for each solution through energy, exergy, economic, exergoeconomic and environmental (5E) multi-criteria analysis considering energy efficiency, exergy efficiency, Levelized Cost Of Energy, exergy destruction cost and CO2 mitigation. Sensitivity of selected indicators is analyzed with respect to the heat load, the investment cost and the fuel cost. The ground-source heat pump and the biomass boiler are found to be the most competitive solutions. It is also found that temporal mismatch between production and consumption is the major drawback of solar-driven solutions, especially for solar thermal collectors. One of the innovations of this study is comparing various residential heat production systems through various performance criteria. The other innovation is applying the study in the French context, which has a very high share of non-carbon electricity. Results from this study can be generalized to other OECD countries in future conditions, i.e. when their shares of non-carbon electricity become very high.

ε Exergy efficiency (-) η Energy efficiency (-) .

Exergy factor of chemical fuels input to the grid (-)

Maintenance cost factor (-) / CO2 emissions (tCO2/year)

℘ 1
Thermal or electrical peak power produced by the unit (kWpeak)

INTRODUCTION

Nuclear power covers around 11% of global electricity production [1] and roughly 71% of electricity production in France [START_REF] Rte | Données en énergie en France[END_REF]. As a matter of fact, France has the world's highest share of nuclear power in electricity generation [START_REF] Malischek | The future of nuclear power in France: an analysis of the costs of phasing-out[END_REF]. Out of France's 58 nuclear power plants, 37 of them will start ageing within the next 15 years [START_REF] Malischek | The future of nuclear power in France: an analysis of the costs of phasing-out[END_REF]. Retrofitting these plants can prolong their lifetime, but this is only a short-term solution. Moreover, the public's negative opinion on nuclear power [START_REF] Abdulla | Limits to deployment of nuclear power for decarbonization: Insights from public opinion[END_REF][START_REF] Bird | Nuclear power in australia: A comparative analysis of public opinion regarding climate change and the fukushima disaster[END_REF] and issues related to waste disposal [START_REF] Yano | Investing in a permanent and sustainable nuclear waste disposal solution[END_REF] heat up the debates on a gradual phase-out of this technology.

For a country that relies on nuclear power as strongly as France, a phase-out is a very complex decision.

Like many other countries, France is committed to keeping CO2 emissions as low as possible, and this is enforced by political pressure and carbon taxes. Typical efficiencies of nuclear power plants are comparable to those of fossil fueled power plants (33-37% [START_REF]Nuclear power reactors[END_REF]), and their carbon emissions are lower. As a matter of fact, the inclusion of nuclear in the energy mix has been proposed in some countries that are heavily reliant on fossil fuels [START_REF] Devitt | Nuclear frames in the Irish media: Implications for conversations on nuclear power generation in the age of climate change[END_REF][START_REF] Jewell | Introducing nuclear power in Turkey: A historic state strategy and future prospects[END_REF]. From the viewpoint of carbon emissions, it can be tricky to phase out a technology that outperforms other technologies. Renewable sources should be the candidate. But even renewables have their own issues, if they are to cover high shares of energy production. Due to their intermittency, hundreds of GWh of storage batteries would be necessary to match the demands.

Their construction would have a non-negligible ecological impact that is yet to be assessed [START_REF] Percebois | Storage cost induced by a large substitution of nuclear by intermittent renewable energies: The French case[END_REF].

Moreover, a very high economic cost is estimated for substituting nuclear power with renewables.

Percebois and Pommeret estimated marginal costs between 5.5 and 16.6 billion euros per year, only to reduce France's nuclear generation from its current 71% to 50% by means of solar-PV and wind power production [START_REF] Percebois | Storage cost induced by a large substitution of nuclear by intermittent renewable energies: The French case[END_REF]. They pointed out that a fair share of those costs would come from the need for storage units. Malischek and Trüby estimated marginal costs of 76 billion €2010 for a complete phase-out of nuclear power in France [START_REF] Malischek | The future of nuclear power in France: an analysis of the costs of phasing-out[END_REF], which after scale adjustment is very similar to the estimation from Percebois and Pommeret. Therefore, a large scale substitution of nuclear generation by renewables seems a costly decision, and other opportunities should be explored.

In 2019, the residential sector was responsible for roughly 36% (170 TWh) of the final electricity consumption in France, the second highest share in the country [START_REF] Rte | Bilan électrique de[END_REF]. Of those 170 TWh consumed, space heating and domestic hot water accounted for 28% and 12% respectively, i.e. the highest and third highest shares among the different residential usages. This means that residential heat needs totaled 68 TWh of electricity consumed in France in 2019. Thus, it could be stated that if the entire residential heat needs in France were covered by renewable sources, the share of nuclear power in the French energy mix could drop from 380 TWh (70.6%) to 312 TWh (57.9%).

Based on the data above, it can be affirmed that the residential sector has a relevant weight for cutting back the French dependence on nuclear power. A massive introduction of renewables in this sector would also reduce the use of other non-renewable systems. According to the French ADEME, in 2014 about 57% of residential heating systems in France were gas-fired, while 42% were grid-driven electric boilers [START_REF]Les avis de l'ADEME : Modes de chauffage dans l'habitat individuel[END_REF]. Besides, the residential sector may be the most appropriate for a small scale phase-out. As suggested by Busic-Sontic and Fuerst [START_REF] Busic-Sontic | Does your personality shape your reaction to your neighbours' behaviour? A spatial study of the diffusion of solar panels[END_REF], the diffusion of solar panels in residential districts can be fast, thanks mainly to peer effects. They pointed out that peer effects are stronger in districts where homeowners have a higher conscientiousness and openness to the experience of installing solar panels.

Performance of renewable energies in domestic thermal applications depends on several intrinsic and extrinsic factors. For instance, these sources are intermittent and typically mismatched with residential thermal demands. Weather conditions are usually a limiting factor too, tightly bound to the location.

The crucial extrinsic factor is the market in which renewable solutions must compete. The high efficiency of nuclear power leads to low revenue requirements on the electricity produced, making any grid-driven solution economically competitive in this country. A comparative assessment between renewable and non-renewable solutions needs to account for several criteria.

In the literature, the advantages of renewable sources have been proven in front of fossil-fueled national energy grids. However, the French grid has a high share of non-carbon electricity. The main novelty of this study is evaluating the potential competitiveness of renewable-driven solutions against a highly decarbonized national energy grid. Since many countries are evolving towards low-carbon electricity, the case of France is relevant to future conditions for those countries.

Many existing studies in the literature investigate different types of heat production systems which could be used in residential heating applications. Esen et al. [START_REF] Esen | Technoeconomic appraisal of a ground source heat pump system for a heating season in eastern Turkey[END_REF] evaluated and compared a groundsource heat pump (GSHP) system to conventional heating mechanisms such as electric resistance, fuel oil, liquid petrol gas, coal, diesel oil and natural gas for space heating. The GSHP system was reported to have a lower annualized lifecycle cost, i.e. economically favorable, when compared to all the considered systems except natural gas heating. Furthermore, GSHP systems were found preferable to air-source heat pump (ASHP) systems, as a result of a higher coefficient of performance (COP) and lower annualized lifecycle cost [START_REF] Esen | A techno-economic comparison of ground-coupled and air-coupled heat pump system for space cooling[END_REF].

Ayadi and Al-Dahidi [START_REF] Ayadi | Comparison of solar thermal and solar electric space heating and cooling systems for buildings in different climatic regions[END_REF] compared the performance of solar thermal and solar PV systems for space heating, space cooling and domestic hot water production in 5 different climatic regions. The study proposed a systematic methodology for comparing the solar systems with multiple combinations of conventional systems: a reversible heat pump, an air-to-water heat pump, a diesel-fired hot water boiler, an electrically-driven vapour compression chiller, and combined cooling heat and power (CCHP).

The comparison was done in terms of primary energy savings and Levelized Cost Of Energy (LCOE). Their results showed that both the solar thermal solution and the solar PV solution reduce primary energy consumption and the LCOE with respect to the most efficient reference system. Nevertheless, the solar PV solution outperformed the solar thermal solution. They also point out that DHW demands represent a significant share of total energy consumption of buildings (7% -15%). They state that a solar thermal system designed to meet both heating and DHW demands maximizes the utilization of the collected solar energy and improves the non-renewable primary energy ratio.

Sustar et al [START_REF] Sustar | Performance modeling comparison of a solar combisystem and solar water heater[END_REF] compared the performance of a solar combisystem (for heating and DHW) and a solar water heater. It was found that the combisystem led to more savings than the solar water heater, thanks to providing space heating in addition to DHW production. It was also found that the incremental savings supplied by the combisystem as compared to the solar water heater were 0.5%, 7% and 18.6% for collector areas of 3 m², 6 m² and 9 m² respectively, i.e. they increased with collector area. The study also found out that the incremental savings were highly sensitive to the shares of DHW loads and space heating loads. Highest savings occurred when the shares of DHW demands were low.

Lohani and Schmidt [START_REF] Lohani | Comparison of energy and exergy analysis of fossil plant, ground and air source heat pump building heating system[END_REF] compared the energy and exergy performances of a fossil plant heating system, an air source heat pump heating system and a ground source heat pump heating system. In their results, the ground source heat pump outperformed the two other systems. Specifically, the ground source heat pump had roughly 25% less demand of absolute primary energy and exergy, and about 50% higher overall primary COP than the conventional system. The study also found that, although the energy flow in the building was the biggest of the energy chain, the biggest exergy losses occurred in the energy conversion systems, rather than in the building itself. This shows why exergy analysis is very important to get more insight of these processes.

Saloux et al [START_REF] Saloux | Exergo-economic analyses of two building integrated energy systems using an exergy diagram[END_REF] compared a solar assisted heat pump and a PV-driven ambient air heat pump through energy, economic and exergoeconomic analysis. It was found that the ambient air heat pump is optimal from energy and economic perspectives, while the solar assisted heat pump provided the best exergy performance. The study puts a special focus on the exergoeconomic analysis, by differentiating between renewable and non-renewable exergy flows/destructions. The optimization led to different optimal solutions if the energy or the exergy criteria were followed. Moreover, different optimal solutions were found if exergy destruction of non-renewable energy flows was used as criteria instead of total exergy destruction. The authors concluded that the choice of performance indicators is important and can change the configuration of the optimal system, especially with exergy indicators.

Tolga Balta [START_REF] Balta | Exergetic cost analysis and sustainability assessment of various low exergy heating systems[END_REF] carried out an exergetic cost and sustainability assessment of 3 different low exergy heating systems. The options were a standard boiler driven by fuel-oil, a condensing boiler driven by natural gas, and an air heat pump driven by electricity. Results from the study pointed out that the condensing boiler driven by natural gas was the most cost-effective system, due to the low costs of natural gas with respect to fuel-oil and electricity.

Most of the studies in the literature cover either a large range of different solutions, or a large range of performance criteria. In order to enrich the discussion, we propose here a multicriteria study on a total of 9 different solutions for heating and DHW production, based on 5 different performance criteria. Six heat production units were considered: gas-fired boilers, electric boilers, biomass boilers, solar thermal collectors, air source heat pumps and ground source heat pumps. We also consider the possibility of running the heat pumps and the electric boiler with either the grid or PV panels. This gave a total of 9 different solutions under study.

A few other multicriteria studies exist in literature for renewable-based domestic heating. Some of them focus on a specific system, like the study from Chen et al [START_REF] Chen | Multicriteria performance investigations of a hybrid ground source heat pump system integrated with concentrated photovoltaic thermal solar collectors[END_REF], which focuses on a hybrid ground source heat pump system integrated with concentrated photovoltaic thermal solar collectors. Other multicriteria analyses use a comparative approach like ours, typically focusing on technical, economic and environmental indicators, like the study from Yang et al on several renewable energy home heating technologies, including boilers, heat pumps and solar collectors among others [START_REF] Yang | Using multi-criteria analysis to prioritize renewable energy home heating technologies[END_REF]. Other multicriteria comparative studies use the aforementioned criteria and include social and usability criteria, too, like the study from Kontu et al [START_REF] Kontu | Multicriteria evaluation of heating choices for a new sustainable residential area[END_REF] on several systems, including electric heating, biomass boilers, pellet boilers and ground source heat pumps, among others. In addition to energy, economy and environment, our study includes the exergy and exergoeconomic criteria, in order to assess thermodynamic irreversibilities and the associated costs. We also analyze the influence of extrinsic factors, such as production/consumption mismatch, market prices or the possibility of selling excess PV-electricity to the national grid. After the 5-criteria and sensitivity analyses, we discuss other factors qualitatively (technical, operational, climatic…), and opportunities for further breakthrough of renewable-based solutions.

The first stage of this study consisted in determining the self-production and self-consumption indices of solar thermal collectors and photovoltaic panels. To this end, annual profiles were defined (Section 2.2)

for space heating and domestic hot water needs of a single dwelling in the city of Chambéry (France).

Based on the maximum instantaneous demands, the sizing was determined for each type of panel, taking into account the use of an electric boiler or a heat pump for PV-driven solutions. Along with all this information, relevant economic data were retrieved for the different systems in the French energy market. After this stage of modeling and data gathering, performance analyses were applied solution by solution through 5 different criteria (Section 2.3): energy, exergy, economy, exergoeconomy and environment. This allowed to compare the solutions quantitatively in the nominal scenario (Section 3.1).

That comparison was explored further for the economic and exergoeconomic criteria, by the mean of a sensitivity analysis with respect to investment costs and fuel costs (Section 3.2). This allowed to compare the solutions in other favorable/unfavorable scenarios, all of them relevant to the French energy market. At this point, and to close the study as comprehensively as possible, a qualitative discussion was pursued (Section 4) covering several parameters, factors and constraints not accounted for in the quantitative analysis. Finally, the major conclusions of this study were reported qualitatively (Section 5).

MATERIALS AND METHOD

This study assesses and compares yearly performance of several solutions that aim to satisfy space heating and domestic hot water production in a residential dwelling. Some of the proposed solutions consist in a single unit that produces heat directly, while others are an assembly of a power production unit with a power-to-heat conversion unit. For the sake of a fair comparison, all solutions were evaluated against exactly the same heat load. Then, the required energy inputs for each system were determined upstream, by means of their operating parameters. As stated in the Introduction, a multicriteria comparison was deemed appropriate to compare the systems. Five indicators were used: energy efficiency, exergy efficiency, Levelized Cost Of Energy, exergy destruction cost and CO2 mitigation. The following subsections offer details on how the scenario was modeled.

Systems

The study includes the most commonly used heat production systems for individual residential dwellings (Table 1). The most common types of boilers in the French residential sector are gas-fired boilers and electric boilers (the latter connected to the electric grid). Biomass boilers were considered as direct competitors. In addition, air source and ground source heat pumps were considered as competitors to the electric boiler. For every electric-driven heat production system, PV panels were evaluated as competitors to the electric grid. Lastly, solar thermal collectors (ST) were also considered. This led to a total of 9 different solutions, encompassing both renewable and non-renewable sources. Due to temporal mismatch, the systems driven by the solar resource use the electric grid as a backup. Further, the amount of CO2 emitted (kg/kWh) from the grid was evaluated considering the shares of gas, coal and fuel oil in the French energy mix (7.7%, 1.8% and 0.7%, respectively [START_REF]Total. France's overall energy mix[END_REF]) and the respective carbon emissions from each of these sectors [START_REF]Les emissions de CO2 par kWh produit en France [CO2 emissions by kWh produced in France[END_REF]. The dead state temperature (T0) for exergy analysis is set to the reference temperature for Chambéry [START_REF]Centre Scientifique et Technique du Bâtiment (CSTB): ANNEXE -Méthode de calcul Th-BCE 2012[END_REF].

Load profiles and solar matching indices

A dwelling of 120 m² and built after 2012 was assumed in the H1 Zone, i.e. the RT2012 climatic zone for Chambéry (France). The dwelling's profiles of thermal demand were calculated through data from the PHEBUS investigation [START_REF] Sdes | Enquête Performance de l'Habitat, Équipements, Besoins et Usages de l'énergie[END_REF] and from the French ADEME's report on the topic [START_REF] Ademe | Les besoin d'eau chaude sanitaire en habitat individuel et collectif[END_REF]. An hourly profile of solar irradiation was retrieved from the PVGIS-SARAH database [START_REF]PVGIS tool[END_REF] for the year 2016. The latitude and longitude were 45,567 and 5,922 decimal degrees, respectively. The elevation was 282 m, the slope was 35 degrees (optimum) and the azimuth was 1 degree (optimum).

Figures 1a and1b present samples of the resulting hourly profiles for one winter day and one summer day, respectively. The total yearly demand was quantified at 2872 kWh for DHW production, and 2232 kWh for space heating. The peak thermal demand (heating + DHW production) was quantified at 1.35 kW. Production/consumption temporal mismatch is a classic issue in systems driven by renewable energies.

To account for this phenomenon properly, hourly profiles were used in the assessment. It is visible on the profiles given in Figure 1 that the production of solar systems will be partially mismatched with the dwelling's needs. In order to quantify solar matching, the Self-Production Index (SPI) and the Self-Consumption Index (SCI) were used. Both indicators assess the energy demands covered by the renewable system (% ), but the SPI (eq. 1) compares them to the total demands (% $ $ ) while the SCI (eq. 2) compares them to the system's total production (% $ ).

2!3 7 8 9:;<= 8 >?9:@> (1)

2 3 7 8 9:;<= 8 ABC> (2)
Figure 2 shows the evolution of the solar self-production and self-consumption indices as a function of the annual thermal energy generation ratio. The annual thermal energy generation ratio is defined as a ratio of the panels' yearly energy production to the total annual heating demand (in percent). The value 100% does not mean that the system is selfsufficient since it leads to overproduction in summers and during peak sunshine hours and underproduction during winters and non-sunshine hours. Moreover, as the annual thermal generation ratio increases, the required solar panel area, peak power and the cost would also increase. Therefore, the aim of a good solar panel sizing is to achieve the maximum possible self-production and selfconsumption, without significantly escalating the investment cost. It is interesting to note that for a given annual thermal energy generation ratio, the required panel area (and consequently, peak power) would be the highest for PV + electric boiler, followed by PV + ASHP and PV + GSHP. This is due to the difference in COPs, wherein the GSHP has the highest COP. Further, the ST panels require the lowest area, among all the solar panel-based systems, owing to the highest energy efficiency (i.e. 80%). For the sake of analysis, the indices are dissociated into space heating and domestic hot water production.

Low energy production ensures that most of it is consumed, granting high self-consumption indices.

Such high self-consumption can in fact make PV systems profitable [START_REF] Escobar | Profitability of self-consumption solar PV system in Spanish households: A perspective based on European regulations[END_REF][START_REF] Tongsopit | The economics of solar PV self-consumption in Thailand[END_REF], even in the absence of regulatory support policies for them [START_REF] Lang | Profitability in absence of subsidies: A techno-economic analysis of rooftop photovoltaic selfconsumption in residential and commercial buildings[END_REF]. On the other hand, it causes low self-production indices with respect to the dwelling's needs. Increasing the self-production only comes at the cost of a high drop in self-consumption. It can also be observed that indices for domestic hot water production are better than for space heating. The reason is simple: space heating is needed mostly in the evening/night and more predominantly in winters, when solar irradiation is not available. On the other hand, domestic hot water may be needed at any time of the day, in any season of the year. Hence, the demand profile of domestic hot water facilitates solar matching. In the present study, peak power sizing method has been utilized to determine the required area of solar panels (in order to meet the dwelling's peak hourly demand over the year) and consequently, the self-production and self-consumption indices. The selfproduction and self-consumption indices, thus obtained, for both PV (marked as ×) and ST (marked as +) panels are highlighted in Figure 2. With the sizing rules used, the peak electric productions of the solar PV panels were estimated at: 1.78 kWp to run the electric boiler; 0.76 kWp to run the air source heat pump; and 0.53 kWp to run the ground source heat pump. The peak thermal production of the ST collectors was estimated at 3.2 kWp. These values are used for the nominal scenario presented below.

Performance criteria

For each system, 5 criteria were assessed: overall energy efficiency (η), overall exergy efficiency (ε), Levelized Cost Of Energy (LCOE), cost of exergy destruction (CD) and CO2 mitigation (∆ 62 ). The evaluation of each criterion is developed in the following paragraphs.

Energy criteria

All solutions were evaluated with respect to the same residential demands, i.e. space heating (Q SH ) and domestic hot water (Q DHW ) demands. The overall energy input ( ) was determined for every system through an overall energy balance (eq. 3a). The balance accounted for the inlets, outlets and losses. The losses (∑ ) were determined (eq. 3b) through the system overall efficiency (F).

7 % (& + % &' + ∑ (3a) With 7 • 41 -F5 (3b)
The system's energy efficiency (F, eq. 4) is the ratio of its useful output to its total energy input. For the biomass and gas-driven boilers, this first criterion is straightforward and presented in Table 2.

F 7 8 KL M8 NLO P Q@ (4)
The energy input ( , eq. 5) may include a solar contribution if the system includes solar panels ( , ), a primary energy contribution if the system is connected to the electric grid ( , ),

and an environmental, low-temperature heat input if the system includes a heat pump (

Calculation of the solar contribution proceeds only if the solution includes solar panels. In the rest of cases, the solar contribution is null. The solar contribution ( , , eq. 6a) depends on the energy issued by the panels for the purposes of heating ( ,(& , eq. 6b) and DHW production ( , &' , eq. 6c). It also depends on the solar panels efficiency (F ). The energy issued by the panels depends on their self-production index (SPI) and their self-consumption index (SCI

All solutions in this study require some input of primary energy, even solar-driven solutions (due to temporal mismatch). The primary energy input ( , , eq. 8a) refers to the grid's energy inlet in order to produce electricity. This input depends on the electricity issued by the Grid for the purposes of space heating (e # $,(& , eq. 8b) and domestic hot water production (e # $, &' , eq. 8c). The primary energy input evolves conversely to the solar self-production index (SPI), because the Grid is a backup for solar-driven systems. It also depends on the COP of the electricity-to-heat conversion system.

, 7 ! " # $ • ge # $,(& + e # $, &' h (8a) e # $,(& 7 8 KL W KL • 41 -2!3 (& 5 (8b) e # $, &' 7 8 NLO W NLO • 41 -2!3 &' 5 (8c)
Calculation of the low-temperature heat input ( , , eq. 9a) proceeds only if the solution includes a heat pump. The heat pump's heat input was assessed for the purposes of space heating (% &W ,(& , eq. 9b)

and domestic hot water production (% &W , &' , eq. 9c). Each input depends on the heat pump's COP for that application. (9a)

% &W ,(& 7 % (& • i1 - R W KL j (9b) % &W , &' 7 % &' • i1 - R W NLO j (9c)
It was assumed that the GSHP runs in reverse mode whenever heat is not needed, in order to regenerate the ground's heat. Since there are summer periods where neither heating nor DHW are needed, the GSHP can cover domestic hot water demands even in summer.

Exergy criteria

An overall exergy balance (eq. 10a) was applied to each solution by accounting for exergy inlets ( ), outlets ( ) and overall destructions (∑ ). Overall destructions were assessed through the inlets and the system exergy efficiency (eq. 10b). The main utility of the overall exergy balance was to determine exergy destruction. It was required for calculating the exergy destruction costs in the exergoeconomic assessment (refer to subsection 2.3.4).

7 + ∑ (10a) With ∑ 7 • 41 -k5 (10b)
Exergy efficiency (ε) was assessed similarly to energy efficiency (eqs. 11 and 13a), by previously converting every energy flow to an exergy flow. Thus, every heat flow was multiplied by its exergy factor (eq. 12), which depends on its temperature (i.e. 1 -) * ) ⁄ ). The solar input was treated as a heat flow too (eq. 13b), although coming from a source at such high temperature (Tsun) that its exergy factor nears 1 (refer to Table 2). In order to keep thermodynamic consistency, the same dead state temperature (T0)

21
was assumed for every flow, and its value was kept constant throughout the year [START_REF] Pons | On the reference state for exergy when ambient temperature fluctuates[END_REF]. The selected value was -11 °C, which corresponds to the reference temperature used in the French building code RT2012 [START_REF]Centre Scientifique et Technique du Bâtiment (CSTB): ANNEXE -Méthode de calcul Th-BCE 2012[END_REF]. Primary energy was assumed as chemical energy, thus with an exergy factor set to . 7

1. k 7

P Cm; P Q@ (11) 7 % (& • i1 - n o n KL j + % &' • i1 - n o n NLO j (12) 7 , + , + , (13a) , 7 ,
• i1 -

n o n Km@ j (13b) , 7 , (13c) , 7 , • i1 - n o n
=?:; j (13d)
Including the exergy efficiency as criteria helps choose the system that implies less degradation of the available energy. The interest of this criterion is to account for the thermodynamic value of energy flows, independently of other factors like their availability or their costs.

Economic criteria

Total costs of each solution were determined through a techno-economic balance (eq. 14). It comprises capital expenditures (CAPEX) and operating expenses (OPEX). The CAPEX (eq. 15a) are the sum of investment costs of all units, transformed into annuities by means of the Capital Recovery Factor (CRF, eq. 15b). The investment cost of a unit is a function of the peak power ℘ 1 (thermal or electric) to be produced by the unit. The OPEX (eq. 16a) considers fuel costs (eq. 16b), and operation and maintenance costs (6&q), expressed as a fraction (φ) of the CAPEX (eq. 16c). If the system includes PV panels, the revenues from selling excess electricity to the grid ( , eq. 16d) are discounted from the operating expenses.

n n 7 r! s + 6! s (14)

r! s 7 ∑ + , • ℘ 1 • "t (15a)
"t 7

• 4RM 5 @ 4RM 5 @ uR (15b)

6! s 7 v + 6&q - (16a) v 7 • 4% (& + % &' 5 F ⁄ (16b) 6&q 7 w • r! s (16c) 7 • e Wf (16d)
The Levelized Cost Of Energy (LCOE, eq. 17) was used as economic indicator. This indicator determines the product's price (heat in this case) in order to recover the overall system costs.

x 6 7

XyX

8 KL M 8 NLO (17)

Exergoeconomic criteria

The overall exergoeconomic balance on a system is the same as the techno-economic balance, but expressed on an exergy costing basis (eq. 18). Exergy costing means that the inputs and outputs are computed in exergy ( and ), with their specific exergy costs ( ̅ , and ̅ W, ). The rest of the components are the same as in the techno-economic balance. The main utility of the exergoeconomic balance is to determine product costs of each component, which become the fuel costs of other downstream components.

̅ W, • 7 r! s + ̅ , • + 6&q - (18)
The exergy destruction cost C D was used as exergoeconomic indicator (eq. [START_REF] Saloux | Exergo-economic analyses of two building integrated energy systems using an exergy diagram[END_REF]. This indicator determines the operating expenditures related to the system's thermodynamic inefficiencies. For each system, equation 15 was applied unit by unit and C D was assessed for each unit and then for the global system (the sum of all units).

7 ̅ , • (19)
For each unit, the specific exergy cost of fuel ( ̅ , ) was derived from the total fuel costs C F and the total exergy input Ex in (eq. 20). For those units that receive several inputs of energy, the average fuel cost is the weighted average of the costs of all inputs, following the F-Principle described in the SPECO method (SPecific Exergy COsting) [START_REF] Lazzaretto | SPECO: A systematic and general methodology for calculating efficiencies and costs in thermal systems[END_REF]. It is also affected indirectly by the systems' exergy efficiencies.

Note that investment costs are taken into account implicitly, since investment on a unit increases the price of its product, and that product is the fuel of other units downstream in the process. Accordingly, the C D of solar panels is 0 because their fuel (solar irradiation) is cost-free.

̅ , 7 ∑ z ∑ P Q@ (20)
Accounting for exergy destruction costs helps choose the system that implies less economic losses due to degradation of the available energy. Since this criterion focuses on the costs of sources (eq. 15), solardriven systems have a theoretical advantage (cost-free source). Still, overall performance in this criterion depends on other factors like source availability, or the intrinsic efficiency of the production/conversion systems. Thus, it is difficult to predict whether solar-driven systems will outperform grid-driven systems straightforwardly.

Environmental criteria

For the environmental assessment, the net CO2 mitigation (∆ 62 ) for each of the 9 considered solutions was evaluated compared to a gas-fired boiler, i.e. the solution with the highest CO2 emissions.

∆ 7 / # { -/ (21)
where, / # { and / 62 represent the CO2 emissions from the gas-fired boiler and the analyzed system, respectively.

The CO2 emissions (/ 62 ) were obtained as (in tonnes):

/ 7 | } R Ru~; > • } R Ru~: • €y R*** • P Q@,ABQ9:B• WP' ƒBQ> 4grid, including backup requirements5 €y R*** . -% (& + % &' - 4gas -fired/biomass boiler 5 (22)
where, x Z› and x d are the transmission and distribution losses, and appliance losses, respectively, and 6 2 (in kg/kWh) is the amount of CO2 emitted per kWh of energy produced (Table 2) [START_REF] Uk Parliament | Carbon footprint of heat generation[END_REF]. x Z› and x d were assumed to be 40% and 20%, respectively [START_REF] Rajoria | Exergetic and enviroeconomic analysis of novel hybrid PVT array[END_REF][START_REF] Joshi | Energy matrices, exergo-economic and enviro-economic analysis of an active single slope solar still integrated with a heat exchanger: A comparative study[END_REF]. It should be noted that

P Q@,ABQ9:B• ! " oe_ ›
represents the total electricity produced by the grid (in kWh).

Subsequently, the carbon credits earned (€/year) can be computed, as an enviro-economic indicator, from the CO2 mitigation using the relation given below.

7

• ∆

where, represents the environmental cost (€/tCO2). The value of can range from 13$/tCO2 to 16$/tCO2 [START_REF] Elzen | The Copenhagen Accord: Abatement costs and carbon prices resulting from the submissions[END_REF]. Mostly, an average value of 14.5 $/tCO2 is adopted by researchers [START_REF] Rajoria | Exergetic and enviroeconomic analysis of novel hybrid PVT array[END_REF][START_REF] Joshi | Energy matrices, exergo-economic and enviro-economic analysis of an active single slope solar still integrated with a heat exchanger: A comparative study[END_REF][START_REF] Caliskan | Exergoeconomic, enviroeconomic and sustainability analyses of a novel air cooler[END_REF]. In the present study, we do not consider the enviro-economic aspect ( ) and focus on the environmental indicator i.e. CO2 mitigation (∆ 62 ).

RESULTS

This section includes analytic descriptions of results in this study. Any further discussions on the implications of these results are presented in Section 4 (Discussion).

Nominal scenario

Table 3 presents monocriterion performances for each system, with optimal values highlighted with bold font. For the sake of analysis, some major intermediate results are also included: the CAPEX, the OPEX, the exergy destruction costs within the grid (C D,grid ) and within the heat production unit (C D,HeatUnit ), the fuel specific costs for the heat production unit (c F,HeatUnit ) and the product specific costs for the solar panels (c In order to support the analysis, Figure 3 displays, for each solution, the energy and exergy efficiencies as well as CO2 mitigation. Energy-wise, the biomass and gas-fired boilers are the best solutions thanks to their high efficiencies (90 %), and because they do not need intermediate conversion units. The energy efficiencies of Grid + GSHP and Grid + ASHP are lower by 21.9% and 30.3%, respectively. These solutions cannot take full advantage of the heat pumps' good COPs because of the grid's comparatively low energy efficiency (i.e. 38.8%). PV + electric boiler is the worst solution energy-wise, with an energy efficiency of 20.0%, performing 48.1%

worse than the Grid + GSHP and 39.7% worse than the Grid +ASHP. Moreover, replacing the Grid with the PV panels as the power source for the heat pumps reduces the energy efficiency by about 22%.

Global efficiency of the ST solution is lower than expected. The collectors themselves have pretty good energy efficiency (80 %), and do not suffer from chained inefficiencies like other solutions. Thus, the only explanation is temporal mismatch: 1) A high share of the demands is covered by the backup (Grid + Elec boiler), which has comparatively low efficiency; 2) A high share of heat produced by ST collectors is dumped, thus penalizing performance (refer to Table 3).

Exergy-wise, the Grid + GSHP solution dominates clearly, which is understandable since these subsystems have the two highest individual efficiencies (57.1% and 38.8%, respectively). The GSHP, despite converting electricity to a lower-grade energy (i.e. heat), does so with a very high COP. The Grid in France is rather efficient energetically, and it does not underperform exergy-wise because it converts chemical energy to electric energy (which have the same exergy factors). The Grid + ASHP solution is second-best, but from afar already (by 5.7%), because of the COP difference between GSHPs and ASHPs.

The Grid + ASHP solution is almost matched by the biomass and gas-fired boilers, which benefit from high energy efficiencies in spite of converting chemical exergy to low-grade heat. Solutions based on solar panels exhibit medium-to-low exergy efficiencies ranging from 4% (PV + electric boiler) to 12.8% (PV + GSHP). Solar thermal collectors, despite their high energy efficiencies, transform solar irradiation (θ ≈ 0.93) into low grade heat (θ ≈ 0.20). Moreover, they suffer from temporal mismatch as already discussed. PV panels, despite transforming irradiation into electricity (θ = 1), have low energy efficiency themselves.

The environmental indicator prioritizes the PV + GSHP, closely followed by the Grid + GSHP, the Biomass boiler, the PV + ASHP and the Grid + ASHP. The environmental attractiveness of the HPs is clear, even when the grid is involved. This is certainly due to their high COPs and low carbon emissions from the French national grid. It is important to note that the French national grid is quite environment friendly with merely 56 g/kWh of CO2 emissions ( 6 2 ) when compared to a conventional coal-fired power plant ( 6 2 7 986 g/kWh). This is because the French national grid primarily produces about 72% of its electricity from nuclear energy, while relying on fossil sources for only 1.8% (coal), 7.7% (gas) and 0.7% (fuel) [START_REF]Total. France's overall energy mix[END_REF]. The CO2 mitigation (∆ ) of the French national grid + electric boiler is calculated to be 9.87 tCO2/year (with reference to a coal-based power plant + electric boiler). Therefore, most grid-driven solutions have good environmental performances anyway. The higher ∆ in case of biomass boiler is as expected, since it does not run on fossil fuels and has very low carbon emissions. The ST collectors perform decently, and both the solutions involving an electric boiler are clearly worse than their HPbased counterparts. This results from the COP difference between the HPs and the electric boiler leading to higher electricity requirements, and consequently higher CO2 emissions, in the electric boilerbased solutions. As expected, any solution involving solar panels performs quite well environmentally.

Also, as expected, the least attractive system is the gas-fired boiler.

It can also be seen on Fig. 3 that the energy, exergy and environmental criteria suggest different solutions. This illustrates the interest of exergy as an independent criterion. Exergy analysis accounts for both the quantity and quality or energy flows, while energy analysis only focuses on the quantity.

Besides, exergy optimality is sometimes associated to environmental optimality, but that is not necessarily the case. While a CO2 emissions analysis focuses on the energy source, an exergy analysis covers the whole energy chain. In this study, that difference was relevant because intermediate conversion units are involved.

Figure 4 presents the economic and exergoeconomic performances of every solution. From an economic standpoint, the grid-driven ground-source heat pump (GSHP) seems the best option (LCOE = 0.071 €/kWh), thanks to its high COP. The PV-driven GSHP is second-best (0.081 €/kWh) for the same reason. It is followed by solutions involving either a biomass boiler (0.085 €/kWh) or an air-source heat pump (ASHP). In fact, the ASHP is almost as competitive when run by the grid (0.087 €/kWh) as by PV panels (0.088 €/kWh). This is remarkable, because the PV-driven ASHP needs investment on two units instead of one, and yet the LCOE remains the same. The reason for this is that excess electricity produced by the panels can be sold to the grid, generating some additional revenues. The gas boiler is decent (0.102 €/kWh), but not quite at the top. While its CAPEX is among the lowest (92 €/year), its OPEX is among the highest (427 €/year). The ST collectors and both solutions involving an electric boiler are at the low end, by a large difference (around 4 c€/kWh higher than the gas-fired boiler). For the Grid + electric boiler system, the issue is a combination of the grid's high operating costs and the boiler's poor COP. With PV + electric boiler the explanation is similar, because the boiler's poor COP forces the system to back up with the grid more often. Due to temporal mismatch, the ST collectors can only utilize some of the heat produced. This forces a frequent use of the grid backup. Besides, ST collectors have the second highest investment costs. This is in agreement with the results in [START_REF] Ayadi | Comparison of solar thermal and solar electric space heating and cooling systems for buildings in different climatic regions[END_REF], where the solar thermal system had a high initial cost compared to reference systems.

Exergoeconomics-wise, the grid-driven ground source heat pump is dominant again (213 €/year). Even when PV-driven, it outperforms all other types of heat production systems (257 €/year). The main reason is its high COP, as mentioned in the preceding paragraphs. In addition, the PV-driven GSHP implies lower exergy destruction costs at the grid (77 €/year) than an entirely grid-driven GSHP (121 €/year), thanks to solar irradiation being a cost-free source. The solar thermal collectors (526 €/year) are efficient and run on solar energy, too, but they cannot fully benefit from these advantages due to temporal mismatch. Thus, their backup costs are simply too high. None of the other solutions benefits from the two advantages at the same time (high efficiency and solar energy).

The PV-driven GSHP should outperform the Grid-driven GSHP thanks to the solar input, which is costfree. However, Figure 4 shows that it is not quite the case. This is due to the exergoeconomic balance for the PV panels. Since the GSHP is efficient, it consumes little electricity. Little electricity consumed means fewer opportunities to amortize investment on PV panels. This leads to a higher LCOE for electricity produced by PV panels. As a result, average fuel costs for the GSHP (c F,HeatUnit ) are higher if partially PV-driven (0.209 €/kWhex) than if entirely Grid-driven (0.130 €/kWhex). Consequently, exergy destruction costs within the GSHP itself are also higher (180 €/year, in front of 92 €/year if entirely griddriven). In the end, global exergy destruction costs are higher for the PV-driven GSHP (257 €/year) than for the grid-driven GSHP (213 €/year). Note how this difference is smaller if we compare the PV-driven and Grid-driven ASHP instead: 341 €/year versus 330 €/year, because the ASHP consumes more electricity. If the heating unit is as low-efficient as an electric boiler, the PV-driven solution finally becomes preferable (813 €/year) to the Grid-driven solution (942 €/year). This leads to a counter-intuitive conclusion: exergoeconomics-wise, a more efficient heat pumping unit is detrimental to the PV panels in comparison to the grid.

The exergoeconomic criterion proved to diverge from the economic criterion. For instance, notice how the LCOE of Grid + EB (143 €/MWh) is twice that of Grid + GSHP (71 €/MWh), but their exergy destruction costs are more than a quadruple (942 €/y versus 213 €/y). Investment costs are not the cause of this divergence: those of the electric boiler (50 €/y) are one third of those of the GSHP (150 €/y). Fuel costs are not the cause either, because both systems are grid-driven. The cause lies on the poor exergy performance of the electric boiler. Notice how exergy destruction costs within the boiler (536 €/y) are roughly 6 times those of the GSHP (92 €/y). Indirectly, grid exergy destruction costs are also higher with the boiler (406 €/y) than with the GSHP (121 €/y), because more electricity is consumed. This illustrates how exergoeconomics diverge from techno-economics. They can also diverge from exergy. Although exergy and exergoeconomics recommend the same solution (Grid + GSHP) in this study, this was purely coincidental.

After mono-criterion performances have been analyzed, a discussion is offered below on multicriteria optimality. To facilitate a visual comparison, Figure 5 presents multicriteria relative optimality in the form of a radar chart. In each criterion, the value of 1 represents the best solution(s). Thus, the promising systems are those closest to the radar's outermost vertices. Polygons with the greatest areas point out the solutions with the best multicriteria performances. If all criteria are given the same importance, the Grid-driven GSHP is the most promising solution. It outperforms all other solutions exergy-wise, economy-wise and exergoeconomics-wise. Only the PVdriven GSHP or the Biomass Boiler can compete in some aspects. The Grid + GSHP and PV + GSHP take advantage of the GSHP's high COP. In addition, the grid-driven GSHP takes full advantage of the grid's better efficiency compared to PV panels. In contrast, a PV-driven GSHP is more environmentallyfriendly, but solar mismatch hinders it from being more promising in any of the other criteria. The biomass boiler is the most competitive energy-wise, and the second-most environmentally-friendly one.

It outperforms the GSHP energy-wise because the GSHP requires a fair input of low-temperature heat.

Exergy-wise, however, that low-temperature heat has very little value, allowing the Grid + GSHP solution Specific fuel cost ( ) 0.130 (Grid-driven) [0.117, 0.143] €/kWh Figure 6a shows sensitivity of the LCOE with respect to the abovementioned parameters. For each system, the high-end values correspond to maximum investment cost and fuel cost, and vice versa. The biomass boiler is clearly the most sensitive solution. Depending on the economic context, its LCOE may drop from 5.7 c€/kWh (giving the most promising solution) to 11.2 c€/kWh (setting this solution as the 6 th in the list). Meanwhile, the heat pumps (all types and all electricity sources) show the lowest sensitivities to economic uncertainties. These solutions stay in the range of 6.3-9.8 c€/kWh, with the Grid + GSHP solution being the most promising (as low as 6.3 c€/kWh). As explained in the analysis of Fig. 3, the cases with the grid and with a GSHP are more favorable than those with PV panels and an ASHP, respectively. Anyway, outside of the Grid + GSHP, the other heat pump solutions are almost equivalent economy-wise. The gas boiler (9.2 -11.2 c€/kWh) may become competitive with the biomass boiler, but not with the heat pumps. The solar thermal collectors and both solutions involving an electric boiler are the least promising ones, all comprised in the tranche of 11.5 -16 c€/kWh. These 3 systems are moderately sensitive to the parameters (wherein LCOE varies by approximately 2 c€/kWh), but not even in the best case can they look economically interesting. Overall, the heat pumps seem like the safest bet in the French residential sector, although higher economic sensitivities have been reported

for electric boilers and heat pumps [START_REF] Nielsen | Economic valuation of heat pumps and electric boilers in the Danish energy system[END_REF].

Figure 6b shows sensitiveness of the indicator CD. In terms of this indicator, the Grid + GSHP system (192 -234 €/year) is the most promising and stable solution. The PV + GSHP is close (232 -282 €/year), but suffers from the abovementioned drawbacks of running PV panels. The biomass boiler (192 -352 €/year) can actually become competitive with the Grid + GSHP, but again, this is subject to great uncertainty. The explanation to this is the high variations of both the investment and fuel costs for this type of boiler. As a result, its exergoeconomic indicator registers variations up to +/-29% (80 €/year) with respect to the nominal scenario. In the most unfavorable of the cases, it can even be outperformed by the gas-fired boiler (311 -380 €/year). It is also noticeable that ASHP solutions (296 -374 €/year) are inferior to GSHP solutions, because electricity prices are the same for both but the GSHP has better COP.

This implies less electricity consumption, exergy destruction and fuel expenses. Since the LCOE of these solutions is more sensitive than the CD, one might conclude that investment costs are currently the most influential economic parameter on heat pumps. The solar thermal collectors (473 -578 €/year) perform decently in this criterion, but not quite enough to be promising. Again, the cause is a lack of a solid compensation method for temporal mismatch. Nevertheless, they manage to largely outperform all solutions involving electric boilers (which are in the range of 730 -1040 €/year). This happens because both types of solar panels benefit from the costless solar source and similar SPI and SCI (refer to Table 2), but solar thermal collectors are way more efficient than PV panels, individually. It can also be seen that PV-driven solutions perform worse than their grid-driven counterparts, except when they are connected to an electric boiler.

DISCUSSION

This section discusses qualitatively several key factors to increase competitiveness of renewables in a wider context. The discussion includes operating parameters that were not considered in the quantitative study.

Discussion on the boilers depending on the fuel used

The reference scenario for this study is using either a gas-fired boiler or an electrically grid-driven boiler to satisfy the dwelling's heat demands. In our results, the biomass boiler outperforms those types of boilers in several criteria. In addition, they avoid other technical issues, such as the risks of leakage or even explosion of a gas-fired boiler. They are not susceptible to grid cut-offs like electric boilers, either.

However, a few operational drawbacks of biomass boilers have not been accounted for in this study.

First of all, moisture is an issue. As pointed out in the conclusions by Costa et al [START_REF] Costa | Mass, energy and exergy analysis of a biomass boiler: A portuguese representative case of the pulp and paper industry[END_REF], the main potential for improvement is on the decrease of the residual biomass moisture content. The conclusion from Las-Heras-Casas et al [START_REF] Las-Heras-Casas | Implementation of biomass boilers for heating and domestic hot water in multi-family buildings in Spain: Energy, environmental, and economic assessment[END_REF] pointed out that climate is another factor. In their study, the savings were greater with the increasing severity of winter weather, with a substantial reduction in energy costs.

Another drawback not considered in our study is the storage of biomass. If instantaneous availability of the fuel (wood) is to be guaranteed, it must be stored. That storage can take up much space in the dwelling.

Economics-wise and exergoeconomics-wise, fuel costs appear to be the key parameter according to literature. For example, in [START_REF] Balta | Exergetic cost analysis and sustainability assessment of various low exergy heating systems[END_REF] the boiler run by natural gas outperformed the other systems, which were run by either fuel-oil or electricity. The main reason for this result were the costs of natural gas, which were around 70% lower than those of the other fuels. The author of that study concluded that fuel costs are highly significant parameter, especially when the compared systems have similar performances [START_REF] Balta | Exergetic cost analysis and sustainability assessment of various low exergy heating systems[END_REF]. In our study, performances are indeed very similar between the gas-fired boiler (90%), the biomass boiler (90%) and the electric boiler (100%). This justifies the interest of running sensitivity analyses on fuel costs. It also means that fuel costs differences must be taken into account before generalizing the results of this study to other countries.

Discussion on the heat pumps

Electrically-driven heat pumps are direct competitors of electric boilers and have proven strictly better in the multicriteria analysis. Nevertheless, electric boilers have two relative advantages. First, they do not require an external heat source, so they are not susceptible to frosting , a typical limitation of heat pumps [START_REF] Chung | Prediction of the frost growth and performance change of air source heat pump system under various frosting conditions[END_REF]. Frosting is such a drawback that it can delimitate the areas in which heat pumps are feasible [START_REF] Xu | Climatic division based on frosting characteristics of air source heat pumps[END_REF]. Second, their output temperature can be adjusted by selecting the material, virtually reaching pretty high temperatures. Heat pumps can only reach the same temperatures through a heat source of accordingly high temperature.

The results from this study show that the LCOEs of the GSHP-based solutions (both GSHP+PV and GSHP+grid) are higher than that of gas-fired boiler (GFB). Furthermore, the solutions based on electric boiler (driven by PV/grid) have higher LCOEs when compared to the GSHP solutions (refer to Table 3 or Fig. 4). This is in accordance with the results reported in [START_REF] Esen | Technoeconomic appraisal of a ground source heat pump system for a heating season in eastern Turkey[END_REF], wherein the natural gas heating system is found to be more economical, while electric resistance heating is reported to be economically inferior to a GSHP system (grid-driven). However, it is worthwhile to note that the GSHP systems (PV/grid-driven) outperform the gas-fired boiler from an exergoeconomic standpoint, exhibiting lower costs of exergy destruction.

Ground source heat pumps (GSHP) outperformed air source heat pumps (ASHP) in this study. This tendency is in agreement with those reported in other studies from the literature. For instance, in [START_REF] Lohani | Comparison of energy and exergy analysis of fossil plant, ground and air source heat pump building heating system[END_REF] the GSHP showed at least 50% higher exergy efficiency than the ASHP. In our study, the GSHP has 36% higher exergy efficiency than the ASHP if PV-driven, or 32% higher if Grid-driven (refer to the exergy efficiencies in Table 3). The deviation with respect to [START_REF] Lohani | Comparison of energy and exergy analysis of fossil plant, ground and air source heat pump building heating system[END_REF] is explained by the diversity of applications in our study, which leads to a diversity of temperature levels. In [START_REF] Lohani | Comparison of energy and exergy analysis of fossil plant, ground and air source heat pump building heating system[END_REF], condenser temperatures were 30-40 °C because only space heating was considered. In our study we assumed a condenser temperature of 35 °C for space heating (which is essentially the same), but we considered domestic hot water production too. DHW production requires condenser temperatures of at least 65 °C. Therefore, the heat pumps are forced to operate with greater temperature lifts. And with greater temperature lifts, the same increase in evaporator inlet temperature leads to smaller relative increases in COP. That explains why in our study the GSHP outperforms the ASHP by a smaller margin exergy-wise. Note also that exergy efficiencies reported in [START_REF] Lohani | Comparison of energy and exergy analysis of fossil plant, ground and air source heat pump building heating system[END_REF] are smaller than those in our study, because that other study considered building and distribution losses, which were not in the scope of our study.

The heat source of ground source heat pump is at a higher temperature in winter, granting them a better COP when most of the needs take place. Besides, that temperature remains quite stable throughout the year, in contrast to air's. However, air temperature may surpass ground temperature and grant air source heat pumps a better COP for DHW production in summer, or space heating in early spring or late autumn. Furthermore, in summer the ground source heat pump is forced to operate in reverse mode (cooling mode) to regenerate the ground source [START_REF] Huttrer | Geothermal heat pumps: An increasingly successful technology[END_REF][START_REF] Sanner | Current status of ground source heat pumps and underground thermal energy storage in Europe[END_REF]. The CAPEX of ASHPs is lower than that of GSHPs, however the OPEX is higher for ASHPs (Table 3). The GSHPs are economically more favourable (lower LCOE) than ASHPs (in concurrence with the results given in [START_REF] Esen | A techno-economic comparison of ground-coupled and air-coupled heat pump system for space cooling[END_REF]). Furthermore, the costs of exergy destruction are also lower for GSHPs and thus, the GSHPs perform better than ASHPs exergoeconomically as well. Besides, technical implementation of air source heat pumps is arguably simpler. Furthermore, they take up less ground surface.

Discussion on solar PV panels and concurrence with the grid

Given the same electricity-to-heat conversion unit, the grid proved better energy-, exergy-and economy-wise. On the other hand, PV panels were better environment-wise and exergoeconomics-wise.

It seems unthinkable that PV panels would surpass the grid energy-or exergy-wise in the future. Solar PV panels are a developed technology, not likely to undergo an efficiency breakthrough in the next years. Besides, this study did not account for some extrinsic operational issues that reduce their effective production. According to literature, partial shading [START_REF] Winston | Performance improvement of solar PV array topologies during various partial shading conditions[END_REF] can cause power output losses between 10% and 70% [START_REF] Winston | Performance improvement of solar PV array topologies during various partial shading conditions[END_REF][START_REF] Hajighorbani | Evaluation of fuzzy logic subsets effects on maximum power point tracking for photovoltaic system[END_REF]. Moreover, soiling [START_REF] Pulipaka | Analysis of irradiance losses on a soiled photovoltaic panel using contours[END_REF][START_REF] Maghami | Power loss due to soiling on solar panel: A review[END_REF] can reduce power output between 10% and 40% [START_REF] Ullah | Investigation of optimal tilt angles and effects of soiling on PV energy production in Pakistan[END_REF]. On the other hand, large areas are available for implementation of PV panels, perhaps compensating for the low performance of this kind of energy harvesting.

The economic competitiveness of solar PV panels has several layers to discuss about. First of all, they require an additional investment with respect to the grid. Moreover, if the dwelling does not run electrically-driven heating, the investment cost increases. This may dissuade many residential users from installing a PV array in their dwellings. On the other hand, solar irradiation is costless, and the low maintenance costs of PV panels may compensate for the investment cost in the long run. In fact, this study has found that PV-driven heat pumps are among the most interesting solutions, despite the double investment. It has also been found that grid-driven solutions are more competitive, but from a small margin. This margin varies depending on two factors: efficiency of the electricity-to-heat conversion system, and temporal mismatch.

In the case of PV panels, there exists a trade-off between exergy efficiency and investment cost. As Saloux et al [START_REF] Saloux | Exergo-economic analyses of two building integrated energy systems using an exergy diagram[END_REF] discussed in their study, solar energy cannot be recovered without an appropriate investment on solar panels. With a substantial capital cost, irreversibilities can be reduced and system performance increases. Therefore, real systems should be balanced between investment and exergy losses [START_REF] Saloux | Exergo-economic analyses of two building integrated energy systems using an exergy diagram[END_REF]. These trade-offs exist for many units, and they can affect decision-making in these case studies. Accounting for these kinds of trade-offs is a future work envisaged by the authors of the present study.

The conversion system's efficiency affects indirectly the economic attractiveness of PV panels. As observed in Fig. 3, the panels are almost as competitive as the grid if connected to an electric boiler (COP = 1) or an air source heat pump (COP = 2-3). However, with a ground source heat pump (COP = 3-4) they are clearly less attractive. A very efficient conversion system consumes less electricity; this gives less opportunities of amortizing the PV panels investment cost. Thus, it seems that switching from the grid to PV panels is more viable economically if the conversion system is not very efficient. A user who has a ground source heat pump and ponders on installing PV panels may be discouraged by these counter-intuitive findings. Nevertheless, excess PV electricity can still be utilized for the electric needs of the dwelling (which were not considered in this study).

The economic impact of temporal mismatch on PV-driven solutions is less than expected. The main reason is that excess electricity is sold to the grid. In some contexts, this or other forms of mismatch compensation might be preferable to electric batteries. For instance, it has been suggested in literature that collective load aggregation between different prosumers equipped with PV panels can reach 90% self-consumption rates, without needing any storage at all [START_REF] Reis | Demand aggregation for photovoltaic self-consumption[END_REF]. On the other hand, the self-production remains limited without storage. A detailed study comparing the economic performance of these two strategies could be interesting.

Although the French energy market is economically very competitive, subsidies can further support deployment of solar panels and other renewable sources. Such subsidies are typically state-led, but the convenience of voluntary markets is discussed in literature too [START_REF] Herbes | Are voluntary markets effective in replacing state-led support for the expansion of renewables? -A comparative analysis of voluntary green electricity markets in the UK, Germany, France and Italy[END_REF].

The environmental indicator shows an advantage for the PV panels, but by a lesser margin than expected. This has two main causes: lower self-production in the absence of storage, and the French grid's relatively low CO2 emissions. Besides, the environmental advantage of solar panels may be less attractive if their embodied energy was considered [START_REF] Mousa | Comparative energy and greenhouse gas assessment of industrial rooftop-integrated PV and solar thermal collectors[END_REF].

Discussion on the Solar Thermal collectors

Results for the ST solution are the most underwhelming in this study. Temporal mismatch (an extrinsic issue) denies the ST collectors' intrinsic advantages, namely their high energy efficiency (up to 80%) and the matching of energy type (they produce heat in adequacy to the demand). As a result, they are outclassed by most of the other solutions in most of the criteria. Note how the biomass and gas-fired boilers have similar energy efficiencies (90% each), but their situational efficiencies are 51% higher than that of the ST solution with grid backup. Most of this difference comes from temporal mismatch.

ST collectors and PV panels suffer from just the same temporal mismatch, and that is visible if both are given the same backup system. Note in Table 3 how the ST solution (with Grid + EB as backup) almost doubles the energy and exergy performances of the PV + EB solution (with Grid + EB as backup).

However, note how their LCOE are almost the same (0.144 €/kWh for PV + EB and 0.140 €/kWh for ST).

This has one clear explanation: excess electricity is sellable to the national grid, contrary to excess heat.

In addition, note how the PV panels can outperform the ST collectors if they are given a more efficient conversion unit, such as a Heat Pump. It may be concluded that PV panels can compensate temporal mismatch better than ST collectors.

This uncovers another relative disadvantage of ST collectors: there exists no convincing thermal equivalent for selling electricity to the grid. The closest equivalent would be selling excess heat to a nearby district heating substation. However, district heating networks are not yet as generalized as electric networks are. Other ways to compensate for solar thermal mismatch may include, but not limited to: (i) storage, which can reduce mismatch at the expense of investment cost, reaching a tradeoff; (ii) using the dwelling's thermal inertia, which is a typical problem in space cooling [START_REF] Kuczyński | Experimental study of the influence of thermal mass on thermal comfort and cooling energy demand in residential buildings[END_REF] but an advantage in space heating, granting thermal flexibility [START_REF] Toradmal | Boosting the share of onsite PV-electricity utilization by optimized scheduling of a heat pump using buildings thermal inertia[END_REF]; (iii) at a district scale, collective selfconsumption may allow to cumulate the thermal profiles of residential and tertiary buildings, which are complementary in time.

In the present study, the energy efficiency of ST collectors was evaluated as 39% (refer to Table 3 or Fig. 3). It should be noted that this value represents the annual energy efficiency in the absence of any storage unit. The maximum collector efficiency in [START_REF] Esen | Experimental investigation of a two-phase closed thermosyphon solar water heater[END_REF] was found to vary between 47-59% for a solar water heating system consisting of solar collector, heat pipes (with different refrigerants) and storage tank (condenser section). These values were obtained for the days with different weather conditions in April and May (summer months) while considering a water storage tank. Hence, a lower energy efficiency value than that reported in [START_REF] Esen | Experimental investigation of a two-phase closed thermosyphon solar water heater[END_REF] seems quite reasonable.

Environment-wise, ST collectors and PV panels are almost equivalent (refer to the ST and PV + EB solutions on Fig. 2). Like PV panels, ST collectors may look less environmentally friendly if their embodied energy is considered. However, it has been stated in literature that solar thermal collectors' embodied energy is less than that of PV panels [START_REF] Mousa | Comparative energy and greenhouse gas assessment of industrial rooftop-integrated PV and solar thermal collectors[END_REF].

CONCLUSIONS AND PERSPECTIVES

This study aimed to evaluate competitiveness of renewable sources for heat production in individual housing. The novelty of this work is to compare several renewable-based solutions with their grid-based counterparts, thanks to a multicriteria analysis (energy, exergy, economy, environment and exergoeconomics -5E). The quantitative analysis was followed by a qualitative discussion on additional performance parameters, and the possibility to solve the drawbacks of each renewable-based system.

Since quantitative results may depend strongly on the context, only qualitative conclusions are presented:

• For the specific context of an individual residence in France, a ground-source heat pump driven by the electric grid is the most appealing solution exergy-wise, economy-wise and exergoeconomics-wise.

• Nevertheless, a biomass boiler performs better energy-wise and is equivalent environment-wise, and can therefore be a competitor. In addition, it does not depend on a low-temperature heat input like heat pumps do. Economy-wise, it may become the most promising too, but this is subject to great uncertainty.

• Given the same heat production unit, PV panels outperform the French electric grid from an environmental standpoint, with a PV-driven ground-source heat pump being the best solution.

Nevertheless, the differences are rather small. Meanwhile, the grid usually outperforms the PV panels in all other criteria.

• Economy-wise and exergoeconomics-wise, switching from the grid to PV panels may only be interesting if the heat production unit is low-efficient, such as an electric boiler.

• Heat pumps outperform electric boilers in all criteria considered. This collides with the fact that electric boilers are widespread.

• The biomass boiler is better than, or at least equal to, the gas-driven boiler with regards to all the criteria considered. However, some parameters were not taken into account, such as the need for storage space, or humidity issues.

• Adding storage batteries should improve PV panel's competitiveness from the environmental and exergy standpoints strictly, and from the economic and exergoeconomic standpoints to some extent.

• Solar thermal collectors are strongly hindered by production/consumption temporal mismatch.

Without a thermal storage, this solution is simply not promising.

• On the other hand, PV panels are submitted to just the same mismatch, but dispose of more compensation mechanisms (aside of storage). Excess electricity can be sold to the grid, while excess heat is complicated to manage. And while this study considered heat production only, electricity produced by the PV panels can be consumed for the residence's appliances, too, increasing matching indices. If properly investigated, this variety of solutions can seriously boost competitiveness of PV-driven solutions with respect to their grid-driven counterparts, even in the French energy market.

It is important to keep in mind that this study was applied on the specific context of France. The French national electric grid is energy-efficient as well as cost-efficient, and has low CO2 emissions thanks to the high share of nuclear power. With such advantages, it is less of a counter-intuitive finding that some grid-driven solutions are still competitive with renewable-driven solutions. Chances are that all griddriven solutions explored here would not be competitive enough in other energy markets, more reliant on coal and other CO2-heavy sources, or less efficient grids. Results from this study can be generalized to other OECD countries in future conditions, i.e. when their shares of non-carbon electricity become very high.

This study opened up two main perspectives. One of them is to perform a dynamic analysis considering advanced strategies for improving efficiency of renewable-driven systems. Such strategies would include thermal storage (sensible or latent) and electric storage. It would be worth investigating whether selling excess electricity can be better than electric storage economy-wise. Such question depends on the context, mainly on the prices of the energy market. Another advanced strategy would be to use the dwelling's inertia, i.e. heating it before heating is actually needed. Such strategy can mitigate temporal mismatch at the expense of the users' thermal comfort. Finally, accounting for the dwelling's cooling and electric needs may yield a more comprehensive analysis.

The other perspective is to apply a similar study at district scale, where needs are much greater. This allows to think of solutions that are not applicable to individual housing, such as concentrating solar thermal plants or geothermal plants, for example. These kinds of plants can reach higher temperatures than residential systems, allowing for cogeneration eventually. Even other types of renewable or recovery sources could be considered: wind-powered electricity production, waste-to-energy power plants, sewer heat recovery, wave energy if the district is close to the shore… Finally, a district has complementary profiles of energy needs. One prime example is office and residential buildings, which have essentially opposite profiles. This enables advanced management through collective selfconsumption, via district energy networks.

Figure 1 .

 1 Figure 1. (a) Hourly solar irradiation and thermal needs in one winter day (15 th of January). (b) Hourly solar irradiation and thermal needs in one summer day (15 th of July).

Figure 2 .

 2 Figure 2. Sensitivity analysis of self-production and self-consumption indices.

Figure 3 .

 3 Figure 3. Energy, exergy and environmental performance of each solution.

Figure 4 .

 4 Figure 4. Economic and exergoeconomic performance of each solution.

Figure 5 .

 5 Figure 5. Multi-criteria comparison through relative optimality (nominal scenario).

Figure 6 .

 6 Figure 6. Sensitivity analysis of economy-related indicators: a) Levelized Cost Of Energy (LCOE); b) Cost of exergy destruction (CD).

Table 1 . Systems considered in this study. Heating solution (acronym) System(s) Temporal mismatch Backup

 1

	GFB	Gas-Fired Boiler (GFB)	No	-
	BB	Biomass Boiler (BB)	No	-
	Grid + EB	National electric grid (Grid) + Electric Boiler (EB)	No	-
	PV + EB	Photovoltaic panels (PV) + Electric Boiler (EB)	Yes	Grid + EB
	Grid + ASHP	National electric grid (Grid) + Air Source Heat Pump (ASHP)	No	-
	PV + ASHP	Photovoltaic panels (PV) + Air Source Heat Pump (ASHP)	Yes	Grid + ASHP
	Grid + GSHP	National electric grid (Grid) + Ground Source Heat Pump (GSHP)	No	-
	PV + GSHP	Photovoltaic panels (PV) + Ground Source Heat Pump (GSHP)	Yes	Grid + GSHP
	ST	Solar Thermal collectors (ST)	Yes	Grid + EB

Table 2

 2 presents the technical and economic parameters considered for each system. The selfproduction indices (SPI) and the self-consumption indices (SCI) were estimated from the area of panels, solar irradiation data for the city of Chambéry (France), and the demand profiles (refer to section 2.2).

Table 2 .

 2 Technical and economic parameters unit by unit.

	Unit	Parameter		Value	Units	Source
	Gas-fired boiler (GFB)	Energy efficiency (η)	90	%	[12,27]
		Maintenance factor (φ)	10	%	[28]
		Economic lifespan (n)	15	years	[12,28]
		Specific investment cost (+ , )	344	€/kWpeak	[12,29]
		Specific fuel cost ( )	0.074	€/kWh	[12,29]
		CO2 emitted (	)	0.38	kg/kWh	[30]
	Biomass boiler (BB)	Energy efficiency (η)	90	%	[12,27]
		Maintenance factor (φ)	10	%	[12,28]
		Economic lifespan (n)	15	years	[12,28]
		Specific investment cost (+ , )	350	€/kWpeak	[12,29]
		Specific fuel cost ( )	0.058	€/kWh	[12,29]
		CO2 emitted (	)	0.035	kg/kWh	[30]
	National electric grid (Grid)	Primary energy ratio (PERGrid)	2.58	kWprimary/kWfinal	[31]
		Maintenance factor (φ)	10	%	[28]
		Economic lifespan (n)	25	years	[28]
		Specific investment cost (+ , )	0	€/kWpeak	Assumed
		Specific fuel cost ( )	0.050	€/kWh	[12,29,32]
		CO2 emitted (	)	0.056	kg/kWh	[24,25]
	Solar photovoltaic panels (PV)	Specific peak production (℘ 1 )	0.15	kW_elec_peak/m²	Section 2.2
		Energy efficiency (η)	15	%	[33]
		Self-consumption, heating (2 3 (& ) Self-consumption, DHW (2 3 &' )	49 87	% %	Section 2.2 Section 2.2

  ). Refer to subsection 2.2 for the calculation of the SPI and the SCI. If solar thermal collectors are used, the energy issued is heat. If PV panels are used, the energy issued is electricity and the calculation requires the COP of the electricity-to-heat conversion unit. Different COP values were assumed for the purposes of space heating ( 6! (& ) and DHW production ( 6! &' ). Note that for the electric boiler, the COP is 1. No thermal storage or electric batteries were assumed in this study.

		,(& 7 V % (& • 8 KL W KL • (W, KX KL ( , KX KL (W, ab ( , ab KL KL	4Y Zℎ 2) \]]^ Z\_`5 4Y Zℎ !c d ^]`5	(6b)
		, &' 7 V	% &' • 8 NLO W NLO • (W, KX NLO ( , KX NLO (W, ab ( , ab NLO NLO	4Y Zℎ 2) \]]^ Z\_`5 4Y Zℎ !c d ^]`5	(6c)
	Excess electricity produced by PV panels was also assessed (e Wf	, eq. 7). It increases if the self-
	consumption indexes decrease. Determining this excess electricity is relevant for the economic analysis.
	Indeed, excess electricity is sold to the national Grid, generating some additional revenues (refer to
	subsection 2.3.3).
	e Wf	7 Wf	,(& • 41 -2 3 Wf (& 5 + Wf	, &' • 41 -2 3 Wf &' 5
	,	7	R S A:@?TU • 4	,(& +	, &' 5	(6a)

Table 3 .

 3 Multicriteria performance of different systems for residential heat production.

	η	ε	LCOE	CAPEX	OPEX	C D	C
	Solution

D,grid C D,HeatUnit c F,HeatUnit c P,panels ∆ [%] [%] [€/kWh] [€/year] [€/year] [€/year] [€/year] [€/year] [€/kWhex] [€/kWhex] [tCO2/year] Gas-fired boiler (GFB)

		90.0 17.3	0.102	92	427	346	0	346	0.074	-	0.00
	Biomass boiler (BB)	90.0 17.3	0.085	94	338	272	0	272	0.058	-	1.76
	Grid + Elec boiler (Grid + EB) 38.8	7.4	0.143	50	678	942	406	536	0.130	-	1.34
	PV panels + Elec boiler	20.0	4.0	0.144	367	443	813	264	549	0.133	0.139	1.55
	Grid + ASHP	59.7 17.4	0.087	144	298	330	174	156	0.130	-	1.68
	PV + ASHP	37.2	9.4	0.088	279	200	341	110	231	0.192	0.368	1.75
	Grid + GSHP	68.1 23.1	0.071	150	212	213	121	92	0.130	-	1.76
	PV + GSHP	45.9 12.8	0.081	285	147	257	77	180	0.209	0.551	1.81
	ST collectors	39.0	7.6	0.140	335	381	526	227	299	0.130	0.129	1.61

ACKNOWLEDGEMENTS

The authors are grateful to the ADEME (the French Agency for Environment and Energy Management) for their financial support through the RETHINE project (Réseaux Electriques et THermiques InterconNEctés). This work was also supported by the Université Savoie Mont Blanc.

to outperform the biomass boiler. Since exergy and exergoeconomics have yet a limited presence in benchmarking, the biomass boiler may still be a commercially-appealing competitor.

Sensitivity analysis on economic parameters

The economic analysis has pointed out the most and least promising systems based on average costs for each unit. However, costs may vary depending on location and other techno-economic factors. This subsection analyzes potential competitiveness of each system based on variations of investment and fuel costs between the boundaries provided by the French ADEME (the French Agency for Environment and Energy Management) [START_REF]Les avis de l'ADEME : Modes de chauffage dans l'habitat individuel[END_REF][START_REF] Amorce/Ademe | Comparatif des modes de chauffage & prix de vente de la chaleur en[END_REF][START_REF] Guillerminet | Coûts des énergies renouvelables en France[END_REF][START_REF] Ademe | Les besoin d'eau chaude sanitaire en habitat individuel et collectif[END_REF]. Those boundaries are shown in Table 4. Note that no variation is proposed for the grid's investment cost or the solar panels' fuel costs, because those costs are null.

Complete amortization was assumed for the grid, and solar irradiation is cost-free.