How the Energy Price Variability in Italy Affects the Cost of Building Heating: A Trnsys-Guided Comparison between Air-Source Heat Pumps and Gas Boilers

: The paper investigates the variation in building thermal energy demand for different indoor air set-point temperature and presents an economic analysis comparing the cost of a heating generation system based on an air-to-water heat pump and a gas boiler. Dynamic simulations were performed considering three different residential building characteristics of the Italian building stock placed in different Italian municipalities: Milan, Rome and Naples. An economic analysis was carried out considering the gas and electricity prices related to the years 2019–2022 provided by Italian Regulatory Authority for Energy, Networks and Environment (ARERA). The analysis showed the competitiveness of the heat pump compared with the gas boiler as a heating generation system in terms of annual costs for heating in almost all the scenarios considered and also showed an important reduction in building thermal energy demand if the set-point temperature was reduced, even by 1 ◦ C.


Introduction
The 2018/844/EU directive [1] reports that 50% of the Union's final energy consumption is employed for heating and cooling, of which 80% is used in buildings. Moreover, the directive promotes renovation strategies to reach the 2050 EU climate targets. In the European Union, in fact, buildings are responsible for approximately 36% of carbon dioxide emissions. Several studies propose different energy retrofitting strategies and the estimation of considered investments [2,3], mostly considering heat pumps as generation systems for heating and cooling buildings.
Wang et al. [4] proposed a systematic literature review of heat pumps applied in the residential sector and their roles in achieving the nearly Zero Energy Buildings (nZEB) target and decarbonizing the energy sector. For cost savings and increased photovoltaic self-consumption, they also analyzed heat pumps paired with thermal storage systems and heat pumps integrated with solar PV systems. With the aim of reducing carbon dioxide emissions by deciding the utilization strategies of a heat pump for heating a building, a recent study by Valdiserri et al. [5,6] proposed a method to evaluate the CO 2 emissions generated when a common electric device is connected to the grid. In the context of reducing carbon dioxide emissions, it is also important to consider that the energy price has risen since 2021, and for this reason, European countries impose measures to reduce primary energy consumption. For instance, in Italy, the minister of ecological transition recently signed a new decree [7] that imposes (i) the reduction of 1 • C in buildings and (ii) a reduction in the period when heating systems can be switched on. As mentioned, most studies on this topic focus on the primary energy saving in buildings using ground-or air-source heat pumps as generation systems, replacing old boilers or employing hybrid systems. Beccali et al. [8] reviewed hybrid systems using electrical heat pumps assisted by gas boilers for heating and domestic hot water production. Their comprehensive review focused on the importance of control strategies; different studies showed that hybrid systems could be very advantageous if the integration or switch of the two generators is well managed. In this context, a recent case study in southern Italy [9], where a rule-based control algorithm was applied, showed energy flexibility's importance in the building design and retrofit process. Moreover, Beccali et al. [8] remarked that climate can influence the performance of a heat pump. As demonstrated by many researchers [10][11][12], the climatic and installation conditions affect the entire system's performance. Carrol et al. [10] found three main areas of focus within this framework: defrosting management, ASHP system management and ASHPs as smart grid demand response components. Rossi di Schio et al. [13] performed a Trnsys analysis of three different Italian municipalities to evaluate how experimental climate data affect defrosting cycles in air-source heat pumps. Their study showed that neglecting the effect of defrosting yields the tendency to underestimate the electric energy consumption of heat pumps by up to 10%.
In the literature, some works focus mainly on the economic relevance of a heat pump as an alternative to a gas boiler for residential building heating. The study by Ruffino et al. [14] showed that heat pumps are competitive against gas boilers, but also that they are heavily dependent on refurbishment incentives and penalized by the high electricity prices in Italy. Ala et al.,in [15], presented an energetic and economic analysis of using heat pumps instead of gas boilers in the south of Italy; the results showed that the competitiveness of the heat pump with respect to a gas boiler is mainly influenced by the amount of thermal energy demand of the building. In 2020, Barnes and Bhagavathy [16] asserted that in the UK scene, there is weak economic competitiveness of the heat pump compared with the gas boiler due to the taxes and levies that are heavily applied to domestic electricity bills compared with gas bills. As discussed in [4], heat pumps associated with a photovoltaic system could be an interesting alternative in nZEBs. Moreover, as highlighted in [17], a step-by-step approach to achieving nZEB status must be carried out with a perspective on the cost to identify a better energy solution.
In a few papers, attention is paid to the analysis of costs [18][19][20]. In particular, in [18], two cost estimation methods, i.e., the Levelized Cost of Energy (LCOE) and the Energy System Analysis (ESA) methods, were introduced and were compared for electricity, decentralized heating and district heating technologies, with reference to two system configurations of the German energy system. Fakhri et al. [19] referred to Sweden, and Busato et al., to Italy [20].
In the authors' opinion, it can be useful to characterize the effectiveness of the two different heating generation systems, determining the cost-effective management of heat pumps compared with gas boilers, in a situation globally characterized by an energy crisis and an increase in energy prices. In the present paper, indeed, a comparison is presented, referring to the Italian scenario and considering the gas and electricity prices related to the years 2019-2022 provided by Italian Regulatory Authority for Energy, Networks and Environment (ARERA). In detail, a single-family house was investigated, with three different envelope components and placed in three different municipalities, i.e., climatic conditions. The energy requirement was numerically evaluated, for all the considered cases, using a dynamic simulation performed with Trnsys. For all the considered cases, a comparison between an air-to-water heat pump and a gas boiler was conducted with special regard to the costs of energy consumption, evaluated using the official prices provided by ARERA.

Energy Analysis
This paper investigated the behavior of a single-family house with three different building envelope components, in three different climates. The choice of three different envelope components corresponded to three different building typologies, referring to different construction period habits. Moreover, in order to present general results that can be applied to approximately the entire Italian territory, the building's behavior modeled in three different climates was investigated.

Building
In Figure 1, the layout of the considered residential building is shown. We investigated a single-family house characterized by a floor area of 80 m 2 and a volume of 240 m 3 . The building considered displays six different thermal zones: two rooms (R1 and R2), a living room (LR), a kitchen (K), a bathroom (BA) and a corridor (CO). The total window surfaces are reported in Table 1. Three different sets of building envelope components, reported in Tables 2 and 3, were investigated to better fit the real characteristics of an important part of buildings built in Italy in the last decades. The envelope elements of building B1 in Tables 2 and 3 are typical of Italian buildings built in years 1970-1990; conversely, the envelope components of buildings B2 and B3 are characteristics of more recent Italian residential constructions. envelope components corresponded to three different building typologies, referring to different construction period habits. Moreover, in order to present general results that can be applied to approximately the entire Italian territory, the building's behavior modeled in three different climates was investigated.

Building
In Figure 1, the layout of the considered residential building is shown. We investigated a single-family house characterized by a floor area of 80 m 2 and a volume of 240 m 3 . The building considered displays six different thermal zones: two rooms (R1 and R2), a living room (LR), a kitchen (K), a bathroom (BA) and a corridor (CO). The total window surfaces are reported in Table 1. Three different sets of building envelope components, reported in Tables 2 and 3, were investigated to better fit the real characteristics of an important part of buildings built in Italy in the last decades. The envelope elements of building B1 in Tables 2 and 3 are typical of Italian buildings built in years 1970-1990; conversely, the envelope components of buildings B2 and B3 are characteristics of more recent Italian residential constructions.    Internal gains related to occupation and electric equipment according to IEA SHC Task 44 [21] were considered, and the hourly profiles (the same for each day of the simulation performed) are shown in Figure 2; task 44, in fact, provides common boundary conditions for the dynamic simulations of heating and cooling systems coupled with buildings.
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Figure 2.
Internal gains related to occupation and electric equipment. The hourly profile was the same for all days of the heating season. A power of 60 W per person was considered, given by 40 W radiative and 20 W convective gains.

Heating System
The building presented five fan-coils as emitters for the thermal abovementioned zones, LR, K, R1, R2 and BA, while the corridor (CO) had no terminal emitter. In Figure   Figure 2. Internal gains related to occupation and electric equipment. The hourly profile was the same for all days of the heating season. A power of 60 W per person was considered, given by 40 W radiative and 20 W convective gains. The behavior of the three buildings (B1, B2 and B3) was modeled by virtually placing them in three different Italian municipalities: Milan (45 • 28 N, 9 • 11 E), Rome (41 • 54 N, 12 • 29 E) and Naples (40 • 21 N, 14 • 15 E). The three municipalities are characterized by different climates; therefore, each of them presents different winter design temperatures (t des ), different heating degree days (HDD) and different standard periods for the operation of the heating system, as reported in Table 4. In Table 4, the thermal power requested by the three buildings (P th,des ) at the corresponding winter design temperature of the respective municipality is also reported.

Heating System
The building presented five fan-coils as emitters for the thermal abovementioned zones, LR, K, R1, R2 and BA, while the corridor (CO) had no terminal emitter. In Figure 3, the layout of the heating system is sketched; there was a thermal storage tank of 0.1 m 3 connected to the fan-coils and to the generator, which was an electric air-to-water inverter heat pump.

Figure 2.
Internal gains related to occupation and electric equipment. The hourly profile was t same for all days of the heating season. A power of 60 W per person was considered, given by 40 radiative and 20 W convective gains.

Heating System
The building presented five fan-coils as emitters for the thermal abovemention zones, LR, K, R1, R2 and BA, while the corridor (CO) had no terminal emitter. In Figu 3, the layout of the heating system is sketched; there was a thermal storage tank of 0.1 connected to the fan-coils and to the generator, which was an electric air-to-water inver heat pump. The air-to-water heat pump in all the dynamic simulations was sized to satisfy t thermal power requested by the building under the design winter conditions (reported Table 4); nine different heat pumps, in order to satisfy the load of the nine buildings in account, were considered. In Figure 4, the thermal power output and the coefficient performance (COP) of the heat pump are reported for building B1, placed in Milan, different inverter frequencies. The other heat pumps presented the same COP, but a d ferent thermal output, scaled by a factor; to better explain, the heat pump employed f building B1 in Milan guaranteed a maximum thermal power of 10 kW when it operat The air-to-water heat pump in all the dynamic simulations was sized to satisfy the thermal power requested by the building under the design winter conditions (reported in Table 4); nine different heat pumps, in order to satisfy the load of the nine buildings into account, were considered. In Figure 4, the thermal power output and the coefficient of performance (COP) of the heat pump are reported for building B1, placed in Milan, at different inverter frequencies. The other heat pumps presented the same COP, but a different thermal output, scaled by a factor; to better explain, the heat pump employed for Buildings 2022, 12,1936 6 of 14 building B1 in Milan guaranteed a maximum thermal power of 10 kW when it operated at an air outdoor temperature of −5 • C, while the heat pump for the building B1 placed in Naples guaranteed a maximum thermal power of 7.5 kW when the outdoor temperature was 2 • C. at an air outdoor temperature of −5°C, while the heat pump for the building B1 placed in Naples guaranteed a maximum thermal power of 7.5 kW when the outdoor temperature was 2 °C.

Dynamic Simulation Set-Up and Parameters
Dynamic simulations were carried out using Trnsys software, version 17, [22,23], in order to determine the thermal and electric energy demand of the heat pump during the heating season. The building was modeled by means of type 56 multizone building [22], while the heat pump was modeled by means of types that permit interpolation between given values; in fact, the COP and the output thermal power of the heat pump were known for different inverter frequencies, as reported in Section 2.2. The simulation timestep was set to 30 s, and a total of 27 dynamic simulations were performed, considering the three different buildings placed in the three different municipalities and considering a different set-point temperature tset of the building thermal zones as reported in Table 5; the values were 20 °C, 19 °C and 18 °C, except for zone BA (bathroom), in which the set-point was set to 22 °C in scenario S1. The decision to conduct analyses considering different indoor air set-point temperatures from the typical comfort temperature of 20 °C came from the recent disposition of Italian government that imposes the reduction in temperature in residential buildings, in response to the energy crisis [7]. Results from the dynamic

Dynamic Simulation Set-Up and Parameters
Dynamic simulations were carried out using Trnsys software, version 17, [22,23], in order to determine the thermal and electric energy demand of the heat pump during the heating season. The building was modeled by means of type 56 multizone building [22], while the heat pump was modeled by means of types that permit interpolation between given values; in fact, the COP and the output thermal power of the heat pump were known for different inverter frequencies, as reported in Section 2.2. The simulation timestep was set to 30 s, and a total of 27 dynamic simulations were performed, considering the three different buildings placed in the three different municipalities and considering a different set-point temperature t set of the building thermal zones as reported in Table 5; the values were 20 • C, 19 • C and 18 • C, except for zone BA (bathroom), in which the set-point was set to 22 • C in scenario S1. The decision to conduct analyses considering different indoor air set-point temperatures from the typical comfort temperature of 20 • C came from the recent disposition of Italian government that imposes the reduction in temperature in residential buildings, in response to the energy crisis [7]. Results from the dynamic simulations are Buildings 2022, 12, 1936 7 of 14 useful to establish the reduction in thermal energy demand for the three buildings in the municipalities into account and are presented in Section 4.1.

Economic Analysis
In this section, the set-up of the economic analysis performed is presented, aiming to determine the competitiveness of the heat pump with respect to a gas boiler for building heating.
We supposed to compare the annual cost of electricity demand of the heat pump (obtained with the 27 dynamic simulations performed) to the annual cost of the gas that a gas boiler requires. In particular, in all the 27 cases, a gas boiler that presented an efficiency (η) of 0.88 and a lower heating value of the gas (LHV) of 9.5 kWh/Sm 3 was considered.

Data for the Analysis
Data related to prices of electricity and gas were obtained by Italian Regulatory Authority for Energy, Networks and Environment (ARERA) [24,25]. In Italy, household customers can choose, for electricity and gas supply, between market offers and standardoffer market. In the first case, the gas/electricity price is regulated by the agreement signed between the customer and the energy provider, and the price per unit (EUR/kWh for electricity or EUR/Sm 3 for natural gas) can be fixed for a certain period or can be variable. In the case of the standard-offer market, the price of electricity and gas is variable and is established by ARERA every 3 months. According to the ARERA report [26], 41.5% of household customers in 2021 had a standard-offer market for electricity and 34.6% for natural gas. Due to the large variability of electricity and gas prices in the market offers, this analysis considered the price defined by Italian Regulatory Authority from the year 2019 to the year 2022; therefore, the analysis results refer to the "standard-offer market" prices; however, as reported above, this reflects the gas and electricity prices paid by an important part of the total Italian household customers.
In this analysis, the "fixed costs" (i.e., costs that cannot be related to the unit of energy, such as the annual cost of the gas flow/electricity meter) were not considered. More in detail, the unit electricity and natural gas prices analyzed consist of four components, as stated by ARERA: energy price, transportation and meter-management price, system charges and taxes (excise duties and VAT).
Focusing on the electricity price, Figure 5 shows that the cost of electricity hugely increased starting from the final quarter of the year 2021 to the final quarter of the year 2022 (from 0.190 EUR/kWh to 0.674 EUR/kWh). If we considered the entire analyzed period (2019-2022), it could be also observed that the price component shares strongly changed; during the year 2019, the energy price and system charges showed approximately the same share in the composition of final unitary electricity price (30-45% for both), while during the last year, the energy price component was the largest part, reaching up to 84% of the unitary electricity price. Furthermore, it could be observed that starting from final quarter of 2021, the share of system charges was 0%, because the Italian government eliminated them for customers, in order to limit the electricity price increase. Regarding natural gas unitary price over the last three years ( Figure 6), an important increase starting from the last quarter of the year 2021 until the entire 2022 (from 0.745 EUR/Sm 3 to 1.191 EUR/Sm 3 ) could be noticed, similarly to the electricity price. In the natural gas case, the energy price component and the taxes were the most important components in terms of shares, up to the third quarter of 2021; later on, the energy price component became predominant. To limit the gas price increase, two measures were adopted by Italian government, starting from the last quarter of 2021: the reduction in VAT on gas from 22% to 5% and the elimination of the system charges (in some cases, giving them negative values, as can be observed in Figure 6). Concerning the analysis of unitary gas prices, three relevant aspects were considered and should be briefly explained: Regarding natural gas unitary price over the last three years ( Figure 6), an important increase starting from the last quarter of the year 2021 until the entire 2022 (from 0.745 EUR/Sm 3 to 1.191 EUR/Sm 3 ) could be noticed, similarly to the electricity price. In the natural gas case, the energy price component and the taxes were the most important components in terms of shares, up to the third quarter of 2021; later on, the energy price component became predominant. To limit the gas price increase, two measures were adopted by Italian government, starting from the last quarter of 2021: the reduction in VAT on gas from 22% to 5% and the elimination of the system charges (in some cases, giving them negative values, as can be observed in Figure 6). Concerning the analysis of unitary gas prices, three relevant aspects were considered and should be briefly explained: Regarding natural gas unitary price over the last three years ( Figure 6), an important increase starting from the last quarter of the year 2021 until the entire 2022 (from 0.745 EUR/Sm 3 to 1.191 EUR/Sm 3 ) could be noticed, similarly to the electricity price. In the natural gas case, the energy price component and the taxes were the most important components in terms of shares, up to the third quarter of 2021; later on, the energy price component became predominant. To limit the gas price increase, two measures were adopted by Italian government, starting from the last quarter of 2021: the reduction in VAT on gas from 22% to 5% and the elimination of the system charges (in some cases, giving them negative values, as can be observed in Figure 6). Concerning the analysis of unitary gas prices, three relevant aspects were considered and should be briefly explained:  • Starting from October 2022, ARERA decided to update the gas price for the standardoffer market monthly, to better define its real price, in relation to the possible fluctuations that characterize the market after the beginning of the 2021 global energy crisis. At the time of writing this manuscript, only gas prices up to 30 October 2022 defined by ARERA were available; therefore, in the economic analysis of the last two months of 2022, the gas prices used referred to October 2022.

•
The unitary gas price in the standard-offer market varies in relation to the gas amount consumed during the year by household costumers; some progressive consumption bands were defined by Authority (the 1st band refers to yearly gas consumption up to 120 Sm 3 , the 2nd band between 121 and 480 Sm 3 and the 3rd band between 481 and 1560 Sm 3 [25]) and were thus considered in the economic analysis. • Unlike the electricity price, which is the same for the entire Italian territory, the gas unit price varies across the Italian territory because of different local taxation on natural gas. Generally, the gas price tends to be cheaper in the north of Italy and more expensive in the center and south of Italy. In this study, the different gas unit prices due to the different local taxation were considered, and Figure 7 reports the different unitary gas prices for Milan, Rome and Naples [27].
Buildings 2022, 12, x FOR PEER REVIEW 9 of 14 defined by ARERA were available; therefore, in the economic analysis of the last two months of 2022, the gas prices used referred to October 2022.

•
The unitary gas price in the standard-offer market varies in relation to the gas amount consumed during the year by household costumers; some progressive consumption bands were defined by Authority (the 1st band refers to yearly gas consumption up to 120 Sm 3 , the 2nd band between 121 and 480 Sm 3 and the 3rd band between 481 and 1560 Sm 3 [25]) and were thus considered in the economic analysis.

•
Unlike the electricity price, which is the same for the entire Italian territory, the gas unit price varies across the Italian territory because of different local taxation on natural gas. Generally, the gas price tends to be cheaper in the north of Italy and more expensive in the center and south of Italy. In this study, the different gas unit prices due to the different local taxation were considered, and Figure 7 reports the different unitary gas prices for Milan, Rome and Naples [27].

Results
In Section 4.1, the results obtained with the dynamic simulations are presented, focusing in particular on the thermal and electric energy differences arising from a different building's set-point temperature; in Section 4.2, attention is paid to the economic analysis, i.e., the determination of energy costs for the heating season in the cases of a heat pump and of a gas boiler.

Energy Analysis Results
In Table 6, the results of the dynamic simulations performed are reported. ET refers to the annual thermal energy demand of the building; EE refers to the annual electric energy demand of the heat pump; EP is the annual thermal energy demand of the corresponding building referred to the floor area; SCOP is the seasonal coefficient of performance of the heat pump considered, defined as the ratio between the heat pump thermal energy output and the total electric energy input during the heating season. In Table 6, the annual gas consumption, Vgas (Sm 3 ), is also reported, considering the case in which the building heating demand (ET) is supplied by a gas boiler, instead of a heat pump. The gas consumption is determined as

Results
In Section 4.1, the results obtained with the dynamic simulations are presented, focusing in particular on the thermal and electric energy differences arising from a different building's set-point temperature; in Section 4.2, attention is paid to the economic analysis, i.e., the determination of energy costs for the heating season in the cases of a heat pump and of a gas boiler.

Energy Analysis Results
In Table 6, the results of the dynamic simulations performed are reported. ET refers to the annual thermal energy demand of the building; EE refers to the annual electric energy demand of the heat pump; EP is the annual thermal energy demand of the corresponding building referred to the floor area; SCOP is the seasonal coefficient of performance of the heat pump considered, defined as the ratio between the heat pump thermal energy output and the total electric energy input during the heating season. In Table 6, the annual gas consumption, V gas (Sm 3 ), is also reported, considering the case in which the building heating demand (ET) is supplied by a gas boiler, instead of a heat pump. The gas consumption is determined as where LHV is the lower heating value of natural gas.

Economic Analysis Results
In Table 7, the economic analysis results are reported, considering electricity and gas prices provided by ARERA and discussed in the previous section and employing the electricity demand in the case of a heat pump generation system for heating or the gas demand in the case of a gas boiler as the heating generation system. For each case, in Table 7, the annual costs for the two alternative generation systems (C GAS (EUR/y) for the gas boiler and C EE (EUR/y) for the heat pump) is reported, obtained using the following equations:  In Equation (2), V gas,i (Sm 3 ) is the gas consumed by the gas boiler in the i-th quarter of the heating season, and uc GAS,i (EUR/Sm 3 ) is the unit gas cost of the i-th quarter; analogously, in Equation (3), EE i (kWh) is the electricity consumption of the heat pump in the i-th quarter, and uc EE,i (EUR/kWh) is the unit electricity cost of the i-th quarter considered.

Energy Analysis Discussion
Let us first focus on the energy analysis. Table 6 shows that the reduction of 1 K in the indoor temperature (cases in S2 with respect to cases in S1) led to a reduction in thermal energy demand of the building in all cases, but in particular, the percentage reduction was higher for buildings B2 and B3 (the percentage reduction for B1 in Milan was 11.8%, while for B2, it was 14.1%, and for B3, it was 19.5%). Therefore, it can be stated that the major reduction emerged for buildings that presented lower EP. It could also be observed that for the same building, the reduction was higher in mild climates (Rome and Naples) than in Milan; for instance, for building B1 in Milan, the thermal energy demand reduction was 11.8%, for Rome, it was 18.6%, and for Naples, it was 18.8%. Table 6 shows that the same conclusion could also be drawn considering buildings B2 and B3 in the three climates. Now, focusing on a reduction in the indoor set-point temperature of 2 K, another important reduction in thermal energy demand could be observed, especially for buildings B2 and B3, in mild climates (the percentage reduction for B1 in Milan was 19.9%, while the maximum percentage reduction was observed for building B3 in Rome and Naples, reaching 51%).
Moreover, considering the thermal energy difference, in absolute value, between scenarios S1 and S2, building B1 displayed a major reduction with respect to buildings B2 and B3; the thermal energy demand of building B1 in Milan and under condition S1 was 1304 kWh/year lower than the same building under condition S2; for Rome, the reduction for B1 was 1198 kWh/year, and for Naples, 1209 kWh/year. Therefore, we could assert that the energy demand reduction in absolute values was higher for building B1 in all the municipalities considered, compared with buildings B2 and B3.
Concerning Table 6, let us now focus on the SCOP of the heat pump for all 27 simulations. As predictable, SCOP was higher for heat pumps installed in mild climates (Rome and Naples) than in colder climates (Milan). SCOP values for Milan ranged from 3.13 to 3.31, while for Naples, the range was 3.40-3.59. Moreover, for the same municipality, the SCOP generally decreased for buildings with lower EP and minor thermal energy demand (B2 and B3); this may have been attributed to the efficiency decrease of the heat pump, which performs on-off cycles due to a building's low energy demand.

Economic Analysis Discussion
In Table 7, the yearly costs for the two different heat generation systems are reported for the years 2019-2022. From an economic point of view, the heat pump was almost, in all cases, the best generation system with respect to the gas boiler. The higher annual cost difference between the two systems was obtained from building B1 in Milan; for the year 2020, the difference was EUR 344. Smaller differences were obtained from building B3 in all the climates.
In Figure 8, the annual fuel cost differences between the gas boiler and the heat pump are reported for the years 2019-2022 in scenario S1. A general reduction in yearly fuel cost difference could be observed in the year 2022, corresponding to a minor economic benefit if adopting a heat pump with respect to a gas boiler. Moreover, the heat pump was more convenient than the gas boiler, except for buildings placed in Milan, i.e., the coldest climate investigated in the present analysis, for the year 2022.
Concerning Table 6, let us now focus on the SCOP of the heat pump for all 27 simulations. As predictable, SCOP was higher for heat pumps installed in mild climates (Rome and Naples) than in colder climates (Milan). SCOP values for Milan ranged from 3.13 to 3.31, while for Naples, the range was 3.40-3.59. Moreover, for the same municipality, the SCOP generally decreased for buildings with lower EP and minor thermal energy demand (B2 and B3); this may have been attributed to the efficiency decrease of the heat pump, which performs on-off cycles due to a building's low energy demand.

Economic Analysis Discussion
In Table 7, the yearly costs for the two different heat generation systems are reported for the years 2019-2022. From an economic point of view, the heat pump was almost, in all cases, the best generation system with respect to the gas boiler. The higher annual cost difference between the two systems was obtained from building B1 in Milan; for the year 2020, the difference was EUR 344. Smaller differences were obtained from building B3 in all the climates.
In Figure 8, the annual fuel cost differences between the gas boiler and the heat pump are reported for the years 2019-2022 in scenario S1. A general reduction in yearly fuel cost difference could be observed in the year 2022, corresponding to a minor economic benefit if adopting a heat pump with respect to a gas boiler. Moreover, the heat pump was more convenient than the gas boiler, except for buildings placed in Milan, i.e., the coldest climate investigated in the present analysis, for the year 2022.
Lastly, Table 7 shows that the reduction of 1 K in the indoor set-point temperature reflected economic savings with both heating generation systems.  Lastly, Table 7 shows that the reduction of 1 K in the indoor set-point temperature reflected economic savings with both heating generation systems.

Conclusions
In the present paper, an analysis of the variation in building thermal energy demand for different indoor air set-point temperatures was conducted, and attention was paid to a comparison of the fuel costs of a heating generation system based either on an air-to-water heat pump or on a gas boiler. Dynamic simulations were performed, considering three different residential building characteristics of the Italian building stock and placing them in different Italian municipalities (Milan, Rome and Naples). For the economic analysis, the detailed gas and electricity prices related to the years 2019-2022 provided by Italian Regulatory Authority for Energy, Networks and Environment (ARERA) were employed.
The analysis led to the following conclusions:

•
The energy prices and their variability strongly affect the use costs of a heating generation system, and the dependence is affected by the climate conditions. Moreover, energy prices are affected by government choices, such as taxation, that affect the economic opportunity of a generation system versus a different one.
• For heating, the management of a heat pump always resulted to be more economic than that of a gas boiler in Rome and Naples (mild climate); in the case of Milan, i.e., a colder climate, there was no economic advantage of a heat pump with respect to a gas boiler for the year 2022, due to an important increase in the electricity price since the last quarter of 2021.

•
The reduction of 1 K in the indoor set-point temperature led to important reductions in the building energy demand, especially for most isolated buildings in mild climates, in percentage; if the absolute value of energy saved was considered, the major advantage was obtained for buildings in a cold climate (Milan).
Further developments of this work may consider the analysis of other building typologies and other, different heating systems. Moreover, the analysis could be extended to the influence of cooling systems. From an economic point of view, we could consider the energy prices of other European countries that have been affected by the global energy crisis of 2021. More in detail, in fact, the role of taxation on the different fuel energy prices and the interconnection of prices of energy fuels are aspects that, among others, may affect the convenience of a heating generation system with respect to another one.