buildings

Article Optimal Sizing of Solar-Assisted Systems for Residential Buildings

Alessandro Franco * and Fabio Fantozzi Department of Energy, Systems, Territory and Constructions Engineering (DESTEC), University of Pisa, Largo Lucio Lazzarino, 56122 Pisa, Italy; [email protected] * Correspondence: [email protected]

 Received: 1 September 2020; Accepted: 27 September 2020; Published: 4 October 2020 

Abstract: This paper analyzes the optimal sizing of a particular solution for renewable energy residential building integration. The solution combines a photovoltaic (PV) plant with a heat pump (HP). The idea is to develop a system that permits the maximum level of self-consumption of renewable energy generated by using a small-scale solar array installed on the same building. The problem is analyzed using data obtained from an experimental system installed in a building in Pisa, Italy. The residential house was equipped with a PV plant (about 3.7 kW of peak power), assisting a HP of similar electrical power (3.8 kW). The system was monitored for eight years of continuous operation. With reference to the data acquired from the long-term experimental analysis and considering a more general perspective, we discuss criteria and guidelines for the design of such a system. We focus on the possibility of exporting energy to the electrical grid, from the perspective of obtaining self-consumption schemes. Considering that one of the problems with small-scale PV plants is represented by the bidirectional energy flows from and to the grid, possible alternative solutions for the design are outlined, with both a size reduction in the plant and utilization of a storage system considered. Different design objectives are considered in the analysis.

Keywords: renewable energy systems; smart grid; photovoltaic plants; ground heat pumps; experimental analysis; optimization

1. Introduction During the last decade, the development of intermittent renewable energy systems (RES)—mainly photovoltaic (PV) systems—and increasingly decentralized production have been observed in many countries. Accordingly, the number of small to medium scale plants has increased, and they are often installed in residential buildings [1]. In principle, this is considered to be a good result. However, in complex energy systems, maintaining the balance between energy production and energy demand when large fluctuations in renewable energy occur is a difficult task. Therefore, increasing the penetration of RES needs to be combined with the development of strategies aimed at increasing direct utilization of the energy produced, in order to achieve effective energy savings for the whole system. Without this, the significant effort expended to promote these energy systems will not lead to real reductions in the dependence on fossil fuel and carbon dioxide emissions. Several studies have shown that the penetration of RES, in particular PV plants, seemed to be limited to an upper level of technical considerations. A further increase in the level could be possible by integrating various energy uses (thermal, mobility, and electrical), which could be obtained mainly at the local level, for example, in civil and residential sectors. This requires an important shift from thermal energy production to the field of electricity. From this perspective, for example, a heat pump (HP) for hot and cold production and electric

Buildings 2020, 10, 175; doi:10.3390/buildings10100175 www.mdpi.com/journal/buildings Buildings 2020, 10, 175 2 of 18 mobility can directly and indirectly play a relevant role in the shift from fossil fuel use to renewable source supply, as the necessary electricity for a HP in an electric vehicle can be produced with RES [2–4]. Franco et al. [5] analyzed the problem in connection with the Italian energy system, which was characterized by an important modification to the structure from 2005 to 2020 as a consequence of an increase in the number of PV plants, other renewable energies, and the number of energy producers. In a complex energy system, one method to increase the system’s capability of introducing an increased share of intermittent RES, such as PV plants, depends on the possibility of increased electricity demand and the promotion of self-consumption schemes. For some years, at small power-generating facilities, with all the electricity produced from RES, a form of priority dispatch has been granted via a specific priority order. However, in the near future, this may not be maintained, and in any case, it must be compatible with participation in the electricity market. The simultaneous utilization of HP and PV modules yields a positive synergy, with respect to a shift from using fuel-based systems (such as natural in Italy) to electricity produced by means of renewable energies, as well as a consistent reduction in local pollution and carbon dioxide (CO2) emissions. This would guarantee the economical sustainability of investments in renewable energy sources without the need for subsidiary mechanisms [6]. The system involves the favorable integration of PV modules with a HP, and thereby generates heat and electricity in self-consumption schemes, with a reasonably high overall efficiency [7]. Regarding the typology of heat pumps, both air source and ground source heat pumps should be considered. One of the main limitations of air source heat pumps (ASHP) is the fact that the thermal power delivery curve is opposite to the environmental conditions, and the maximum PV electricity production occurs during daytime hours with higher ambient , while there is no production during evening hours when the maximum thermal power demand occurs. The use of more stable seasonal temperature ground source heat pumps (GHP) offers, in principle, considerable opportunities for reducing global energy consumption, due to their potentially higher efficiency. The efficiency of a HP is represented by the coefficient of performance (COP), which can move from values of 3–4 to even higher values, even though the installation is more complicated and significantly increases the investment cost [8,9]. However, the shift from PV production to a GHP energy use profile still remains, occurring mainly during the cold season. In all cases, the promotion of integrated solutions of solar-assisted heat pumps (both the air type and the geothermal type) and a PV plant to support a system producing electricity to supply the HP can, in principle, add “flexibility” to the system. In this case, a relevant problem is represented by the bidirectional energy flows of the external power grid, due to the electricity exported to the grid from a renewable-based system and the electricity imported from the grid depending on the electricity demand of a building. For public buildings, this is a minor problem because the peak energy consumption occurs during the daytime when peak energy is typically generated by the PV plant. It is a more important issue in the case of residential buildings, as discussed in [10]. If a building is equipped with photovoltaic (PV) modules, the use of electric storage could be particularly important to mitigate the effects of the time mismatch between the electrical production peak, which occurs between 11:00 and 15:00, and the thermal power demand peak, which occurs in the early morning or the late evening. In principle, a further increase in the number of PV plant installations is expected in the near future. Notably, during summertime, heat pumps typically contribute to an increase in the flexibility of the system, as they can consume electricity during hours of excess production, while they can also be effective during the winter. For this reason, it is important to consider the possible connection between the production of electricity and use of thermal energy, as obtained in the case of integrated PV and HP systems for building services [11,12]. Over recent years, several studies have proposed designs for solar-assisted HPs that have been tested using modelling. This has especially been the case for smart energy systems, which are considered an important element of the development of net zero-energy building (nZEB) systems— systems able to produce all of the energy required by a building using renewable energies. Buildings 2020, 10, 175 3 of 18

A recently published review article, [13], has been published in recent years on the topic, considering the different system boundaries and the main performance indicators used for assessing energetic and economic optimization, including economic assessment of solar photovoltaic and heat pump systems. The possibility of experimentally monitoring the behavior of different types of building–plant systems that cover the most widespread typologies, such as residential buildings, or that are considered “strategic” by the various energy efficiency programs, such as office buildings, supermarkets and educational buildings, is of fundamental importance to evaluate heat pump (HP) system performance in real conditions. Depending on the building typology and envelope characteristics, lay-out and use, it is important to properly select the size of each single component. The development of design methods for these systems could be particularly relevant for engineers and designers. The sizing of PV systems was considered in some recent papers [14,15], and it is usually based on various technical and economic criteria. The problem of energy flows from and to the grid was only considered occasionally and no boundary conditions were considered for energy flows to the grid. In this paper, we analyze data obtained from a real case in which a PV plant was used in a residential building to produce electricity for the operation of an HP, which provides heating and cooling, and for the miscellaneous energy loads of the house. Moving from the analysis of the data acquired during the long-term experimental analysis of the system, we then focus our analysis on the specific problem of energy flows to and from the power grid. In the second part of the paper, considering that in the near future plants will be sized to maximize the self-consumption capacity of a system, we propose guidelines for an optimum design strategy of the system under analysis to increase the share of energy produced by the PV plant and directly used in the building. The objective is to define the size of a PV plant necessary to maximize the direct use of the energy produced and minimize energy flows. The possibility of using a “small size” storage system is also considered. Starting from the analysis of the particular system considered here, some general guidelines for the design of such systems are discussed. The data analyzed in this paper can also provide insights both on the operation of the PV system and the operation of the GHP. General criteria and guidelines for the optimum design of PV plants for buildings, providing the use of HP for heating and cooling service are considered in the final part. While in general the possibility of using the electrical grid as a “buffer” for the energy produced is deemed optimal, we attempt to reconsider the perspective of obtaining effective self-consumption configurations. In this case, the electrical grid can be used for energy import and not for exporting the excess energy. This will support further increases in RES while avoiding state interventions, which are often designed in an uncoordinated manner and have led to increasing distortions of the wholesale electricity market, with negative consequences for investors.

2. Integrated PV-HP System for Residential Building: A General Description One of the methods used to transform a complex energy system and increase the amount of energy produced with intermittent RES, such as PV plants, is to increase the electricity demand and promote the in situ strategies for the direct utilization of the energy produced, minimizing the amount of energy flowing from and to the grid. An interesting solution is the use of solar-assisted heat pumps for heating and cooling purposes in residential buildings. The Energy Performance of Buildings Directive (EPBD) is the main legislative instrument at the European Union level for improving the energy efficiency of buildings. A fundamental element of this directive is represented by the requirements relating to zero-energy buildings (ZEB) or net zero-energy buildings (nZEB) and the related integration of renewable sources in the implementation of the relevant provisions. Buildings 2020, 10, 175 4 of 18

At the level of definition of nZEB buildings, the European Directive does not contain specific prescriptions in terms of the minimum absorbed energy, but provides a generic definition, that is, an nZEB is considered a building with very high energy performance, characterized by very low or almost zero energy needs, which should be covered to a very significant extent by energy from renewable sources present on site. The concept of a nearly zero-energy building therefore contains the notion of a synergy of interventions in terms of energy production from renewable sources and energy efficiency. Energy efficiency refers to the amount of energy, calculated or measured, necessary to meet the energy needs associated with normal use of the building, including, in particular, the reduction in energy used for heating, cooling, ventilation, the production of domestic hot water and lighting. In this definition, important factors come into play: the type of heating and conditioning system, the use of energy from renewable sources, the passive elements of heating and cooling, the shading systems, the quality of indoor air, adequate natural lighting, and the architectural features of the building. Considering the concept of nearly zero-energy buildings, interesting theoretical studies have been proposed based on experimental data [16,17]. Some articles deal with the topic of nearly zero-energy buildings from the perspective of regulatory interpretation [18], while others provide a descriptive collection of exemplary cases [19–21]. One solution considered in various cases as fundamental to the concept of nZEBs is the solar-assisted heat pump, consisting of a HP system assisted by a PV plant installed on the building. This solution enables the direct use of excess energy produced to operate the HP. During the last decade, a number of studies have investigated the design, modelling and testing of solar-assisted HP systems [22,23]. A recent review on the topic presents problems and perspectives of this solution [24]. The design criteria differ among papers and are often based on economic criteria. In general, the technical solutions proposed are not optimized from the point of view of the “energy system”. In particular, the size of the PV plant is not always correctly defined in this perspective. This problem is a consequence of the fact that, until some years ago, in many countries the electricity produced by renewable systems from small power-generating facilities had priority dispatch. In the near future, it is expected that priority dispatch should be deemed to be compatible with the participation in the electricity market of power-generating facilities using renewable energy sources. Plants can be optimized with the utilization of a consistent storage energy system. Moreover, the joint operation of a PV plant and HP does not permit a profitable use of energy during the winter period, therefore in a lot of cases an oversizing of the PV plant is observed, thus it is necessary for energy to be exported to the electrical grid. It is expected that in the near future, the utilization of such solutions could be connected with self-consumption schemes, in which only the import of energy will be possible, as shown in Figure1. Consequently, energy produced and not directly used or stored inside can be considered wasted energy, and it is not possible (or convenient) to export excess energy to the grid. The ideal condition is clearly the one in which all of the energy required by the building can be produced within, so that the level of energy imported approaches zero, as required in the ZEB configuration. Taking into account two of the most diffused technologies (i.e., ground source heat pumps (GHP) and the small size PV system) and the recent developments in terms of economic support policies, there has been strong growth in the use of both PV plants (determined by the effect of the feed-in tariff) and HP systems (aided by the effect of fiscal incentives) [25,26]. The typical integration proposed by [27] may contribute in the medium to long term to a relevant reduction in the use of conventional fossil fuels (e.g., natural gas) for heating purposes and to an increase in the production of solar energy. Buildings 2020, 10, x FOR PEER REVIEW 5 of 19 Buildings 2020, 10, 175 5 of 18

National Electrical grid

It is possible to It is not possible import energy to export energy from the grid in excess to the grid

nZEB-Building (RES based plants + Heat Pump + Storage systems + Miscellaneous Energy Devices)

Figure 1. Logic of a net zero-energy building (nZEB). RES: renewable energy system. Figure 1. Logic of a net zero-energy building (nZEB). RES: renewable energy system. 3. Integrated PV-GHP System for Residential Buildings: Experimental Analysis of a Specific Case Taking into account two of the most diffused technologies (i.e., ground source heat pumps (GHP)The and possibility the small ofsize monitoring PV system) the and behavior the rece of dintff developmentserent types of building–plantin terms of economic systems support to cover policies,the most there widespread has been typologies, strong growth such in as the residential use of both buildings, PV plants is of(determined fundamental by importancethe effect of tothe be feed-inable to tariff) analyze and the HP performance systems (aided of thoseby the systems effect of under fiscal realincentives) operating [25,26]. conditions. For this reason, we beganThe typical with theintegration analysis proposed of data obtained by [27] may from contribute an experimental in the medium system. to long term to a relevant reductionThe experimentalin the use of systemconventional under fossil analysis fuels (described (e.g., natural in [4]) gas) is located for heating in Pisa, purposes Italy, a town and to with an a 2 increasetypical Mediterraneanin the production climate. of solar The energy. building has a floor surface area of about 150 m and a volume of 450 m3. The heat pump installed is a typical “three circuit” type ground heat pump (GHP) system, 3.in Integrated which the PV-GHP fluid (water System and salt) for Residential that circulates Buildi in thengs: borehole Experimental Analysis is diofff aerent Specific to the Case fluid circulating in the HP (R407) and the water that circulates inside the house. TheThe possibility nominal electric of monitoring power ofthe the behavior HP is 3.8 of kW different and it types provides of building–plant up to 15.2 kWh systems of space to heating cover thefor most the entire widespread building, typologies, while reverse such cycle as residentia technologyl buildings, will also provideis of fundamental cooling during importance summer to with be ablea maximum to analyze load the ofperformance 11.4 kWh. of The those plant systems is composed under real of the operating HP and conditions. ground probes For this as wellreason, as awe PV begansystem with directly the analysis connected of data to the obta powerined from grid byan experimental means of an inverter. system. The plant was realized in the frameworkThe experimental of the “Conto-Energia” system under support analysis policy, (described active in Italy[4]) is from located 2006 in to Pisa, 2015. Italy, No storagea town systemswith a 2 typicalhad been Mediterranean installed at theclimate. time becauseThe building the priority has a floor dispatch surface policy area active of about in Italy 150 m permitted and a volume the export of 3 450of excessm . The electricity heat pump produced installed by is the a typical PV plant “three to the circuit” electric type grid. ground The PV heat plant pump was (GHP) sized according system, in to whichthe maximum the fluid output(water powerand salt) required that circulates by the heat in th pump;e borehole thus, heat the peak exchanger power is of different the PV plant to the (3.7 fluid kW) circulatingand peak electricin the HP power (R407) required and the by water the heat that pump circulates (3.8 kW) inside are the similar. house. The main characteristics and nominalThe nominal data of theelectric modules power used of the for HP the is PV 3.8 plant kW an ared providedit provides in up Table to 15.21. As kWh additional of space data, heating it is for the entire building, while reverse cycle technology will also provide cooling during summer with possible to include the temperature coefficient of the plant, that is, the value of 0.38%/◦C is declared a maximum load of 11.4 kWh. The plant is composed of the HP and ground probes as well as a PV for the modules if the operating temperature of the module is above 25 ◦C. Specifically, the nominal system directly connected to the power grid by means of an inverter. The plant was realized in the operating temperature of the module is 46 ◦C. framework of the “Conto-Energia” support policy, active in Italy from 2006 to 2015. No storage systems had been installed Tableat the 1. timeNominal because data the of the priority photovoltaic dispatch (PV) policy plant. active in Italy permitted the export of excess electricity produced by the PV plant to the electric grid. The PV plant was sized Nominal Power Number of Area of a Total Plant Nominal Power Nominal V I accordingof the PVto the Plant maximumModules outputModule power requiredSurface by theof heat a PV pump; Module thus,mpp the peakmpp powerEffi ofciency the PV plant (3.7 kW) and peak electric power required by the heat pump (3.8 kW) are similar. The main 3.74 17 1.24 m2 21.13 m2 220 41.0 V 5.37 A 17% characteristics and nominal data of the modules used for the PV plant are provided in Table 1. As additional data, it is possible to include the temperature coefficient of the plant, that is, the value of 0.38%/°CThe is typical declared climatic for the conditions modules of if Pisa the areoperat showning intemperature Figures2 and of 3the for module the heating is above and cooling 25 °C. Specifically,period, respectively. the nominal Figure operating2 provides temperature the distribution of the module of the is external46 °C. temperature, showing the number of hours the selected temperature can be observed. The value of the temperature is provided considering a range of variationTable 1. of Nominal 1 ◦C, while data on of thethe ordinatephotovoltaic axis, (PV) the plant. number of hours is characterized Buildings 2020, 10, x FOR PEER REVIEW 6 of 19 Buildings 2020, 10, x FOR PEER REVIEW 6 of 19 Nominal Power of Number of Area of a Total Plant Nominal Power of Nominal Vmpp Impp Nominalthe PV Power Plant of NumberModules of AreaModule of a TotalSurface Plant Nominala PV Module Power of NominalEfficiency Vmpp Impp the PV Plant Modules Module Surface a PV Module 41.0 5.37 Efficiency 3.74 17 1.24 m2 21.13 m2 220 17% 41.0V 5.37A 3.74 17 1.24 m2 21.13 m2 220 17% V A The typical climatic conditions of Pisa are shown in Figures 2 and 3 for the heating and cooling period,The respectively.typical climatic Figure conditions 2 provides of Pisa the are distribution shown in Figures of the 2external and 3 for temperature, the heating showingand cooling the period,numberBuildings respectively. 2020of hours, 10, 175 the selectedFigure 2 temperature provides the can distribution be observed. of Thethe valueexternal of thetemperature, temperature showing is provided6 the of 18 numberconsidering of hours a range the selected of variation temperature of 1 °C, can while be ob served.on the Theordinate value ofaxis, the thetemperature number isof provided hours is consideringcharacterized a byrange a well-defined of variation average of 1 °C,temperature while on value.the ordinate The period axis, from the 15number October of to hours 15 April is by a well-defined average temperature value. The period from 15 October to 15 April is considered. characterizedis considered. by Figure a well-defined 3 provides averagethe same temperature distribution value.for the The hot periodseason (consideringfrom 15 October the periodto 15 April from Figure3 provides the same distribution for the hot season (considering the period from 15 May to is15 considered. May to 30 September).Figure 3 provides the same distribution for the hot season (considering the period from 1530 May September). to 30 September). 450 450 400 400 350 350 300 300 n 250 250 n 200 200 150 150 100 100 50 50 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 T (°C) . T (°C) . Figure 2. Typical distribution of median outdoor temperature during the cold season (15 October–15 Figure 2. Typical distribution of median outdoor temperature during the cold season (15 October– FigureApril). 2. Typical distribution of median outdoor temperature during the cold season (15 October–15 April).15 April).

300 300 250 250 200 200 n 150 n 150 100 100 50 50 0 0 8 9 1011121314151617181920212223242526272829303132333435363738394041 8 9 1011121314151617181920212223242526272829303132333435363738394041 Text (°C) T (°C) ext FigureFigure 3. 3. TypicalTypical distribution distribution of ofaverage average outdoor outdoor temp temperatureerature during during the the hot hot season season (15 (15May–30 May– FigureSeptember).30 September). 3. Typical distribution of average outdoor temperature during the hot season (15 May–30 September). Pisa is characterized by a total annual irradiance of 1500 kWh/m2, for a surface with a south-facing Pisa is characterized by a total annual irradiance of 1500 kWh/m2, for a surface with a south- aspect. Using modules of high quality that are well exposed, the expected2 PV value could correspond facingPisa aspect. is characterized Using modules by a totalof high annual quality irradiance that are of well 1500 exposed, kWh/m the, for expected a surface PV with value a south- could to 1100–1150 kWh for each kW of peak power installed for each year of operation for a poly-crystalline facingcorrespond aspect. to Using1100–1150 modules kWh of for high each quality kW of thatpeak are po werwell installed exposed, for the each expected year of PV operation value could for a high-quality PV plant. Considering the HP used, this is a commercial heat pump that uses R-407 as the correspondpoly-crystalline to 1100–1150 high-quality kWh PV for plant. each ConsideringkW of peak pothewer HP installedused, this for is aeach commercial year of operationheat pump for that a ; the heating COP in nominal conditions is four, while the cooling COP is approximately poly-crystallineuses R-407 as the high-quality refrigerant; PV the plant. heating Considering COP in nominal the HP used,conditions this is is a four,commercial while the heat cooling pump COPthat three. In terms of the HP, the condenser temperature was 35/30 C while the temperature usesis approximately R-407 as the refrigerant; three. In terms the heating of the COPHP, inth enominal condenser conditions temperature◦ is four, was while 35/30 the cooling°C while COP the was considered 0 C. The geothermal heat exchanger is of the borehole type with a total depth of 50 m. isevaporator approximately temperature three.◦ Inwas terms considered of the 0HP, °C. Thethe geotcondenserhermal temperature heat exchanger was is 35/30of the °Cborehole while typethe The total length of the borehole heat exchanger is 200 m, this value was obtained using a reference value evaporatorwith a total temperature depth of 50 wasm. The considered total length 0 °C. of The the geot boreholehermal heat heat exchanger exchanger is is 200 of them, thisborehole value type was withof 50 a Wtotal/m fordepth the of heat 50 m. transfer The total value. length The of criterion the borehole used for heat the exchanger design was is 200 that m, the this energy value output was from the PV plant should be able to completely assist the operation of the GHP (for cooling purposes) and the consumption of all remaining electrical devices during the hot period. In the remaining part of the year, a relevant exchange of energy (from and to the power grid) could be possible. A schematic diagram of the system and its operational logic are provided in Figure4. According to the description, the energy produced by the PV plant, as measured by a counter, can be directly used by the various electrical devices or exported to the electrical grid. Energy used by the HP is measured with an Buildings 2020, 10, 175 7 of 18

additionalBuildings 2020 counter., 10, x FOR Other PEER relevant REVIEW additional data can be measured including the internal and external8 of 19 temperature (using thermocouples) and relative inside the house.

Figure 4. A schematic description of the plant composed by a (GHP) for houseFigure heating 4. A schematic and cooling, description assisted of by the a PV plant system composed and connected by a ground to the source electrical heat grid. pump (GHP) for house heating and cooling, assisted by a PV system and connected to the electrical grid. Some relevant data concerning the operation of the system can be directly measured or derived. The energy consumption, energy required by the HP, EGHP, and energy required by the rest of The total energy imported from the power grid, ETOT, corresponds to the whole energy used in the household devices, EDEV, as well as the size of the operation, are reported in Table 2. the house. The energy imported from the grid, EIMP, corresponds to the periods during which no productionIn a reference of the PV plantperiod was of available,operation orof there the plan wast, less it energyis possible than to the understand total required. how The the energy total production of the PV plant, EPV, is approximately the same as that required both for the operation of exported to the power grid, EEXP, reflects periods of excess energy production. A specific counter GHP and of the other devices (1399 kWh and 1448 kWh, respectively). While during the period from enabled us to directly measure the energy used by the GHP (EGHP) and another counter measured the April to June the PV production was higher than the total energy consumption, during the other energy produced by the PV plant, EPV, and directly exported to the power grid. periodsThe energy(autumn: produced from October–December, can be easily compared and wi withnter: the January–March) value that was estimatedthe PV production as the product was insufficient to power the GHP and all the other devices. of the annual solar irradiation typical for the specific place at a given exposure, HSN, of a balance of In order to obtain a kind of parity, considering the energy totally produced along the whole year, system efficiency, ηBOS, taking into account the various electrical losses in the system, and the peak an oversizing of the PV plant of a factor 1.5 (with a peak power of 5.5 kW corresponding to a 25 power of the PV plant, PPV. modules), while in the perspective of covering the electricity required in the period from October to EPV = (HSN ηBOS) PPV (1) March, could be necessary to increase the size of the· PV plant.· In this last case, it would be necessary to installThe maximum a power plant production with a power of a PV over system 10 kW expressed (for example, in kWh 13.4/ kWkW—equivalent in the specific to place61 modules). and the annualIn this solar case, irradiation the energy is aexported consequence to the of grid the factwould that drastically the nominal increase, power ofca theusing PV an plant impact is calculated on the consideringpower grid. a specific solar power of 1000 W/m2, a value referred to in the standard test conditions. ConsideringThe operation the of two the valuesHP during of the the energy year, includ used ining the both house, the heatingETOT, and mode energy and usedcooling by mode, the GHP, is EGHPdescribed, it is easy in Figure to evaluate 4. The theelectricity energy consumption used by the other values electrical range from devices. a lower value of 2–3 kWh/day, typical of the mid-season period, when the heat pump is used only for the production of sanitary hot water, up to values just below 35 kWh/day,EDEV typica= E l of theE winter season, when there may be 10 hours(2) TOT − GHP of operation per day. A good operation of the heat pump was evaluated in the winter phase, while duringFor the each summer day and cooling each period period, of the the COP year, value using wa thes slightly results lower of the than measurement, the nominal it wasone. possibleDuring tothe evaluate heating the phase, energy a monthly exchanged average with power the power value grid was to found understand to be very how close close to thethe systemnominal is value, to the which does not exist in the cooling phase when the heat pump works frequently in ON–OFF mode and the transient phase is therefore not negligible. Buildings 2020, 10, 175 8 of 18

model of a zero-energy building (ZEB) and the amount of energy exported, EEXP, or imported from the power grid, EIMP, according to the following definitions:

EEXP = EPV E 0 (3) − TOT ≥

EIMP = E EPV 0 (4) TOT − ≥ The value of the energy produced with the PV plant and directly used, ED, can be calculated by

ED = E EIMP 0 (5) TOT − ≥ The share of the energy produced by the PV plant and directly used in the building, measured with the dimensionless coefficient, IU, can be defined as

ED = IU (6) EPV where values range from zero to one. The ideal system would be the one in which the energy produced is directly used in the building, so that IU approaches unity. The energy consumption, energy required by the HP, EGHP, and energy required by the rest of the household devices, EDEV, as well as the size of the operation, are reported in Table2.

Table 2. Energy balance of the system (values of year 2009, first one of operation).

E E E E Period of the Year GHP DEV TOT PV (kWh) (kWh) (kWh) (kWh) January–March 1658 671 2329 850 April–June 377 550 927 1436 July–September 796 652 1448 1399 October–December 1005 622 1627 580 Total year 3836 2495 6331 4265

In a reference period of operation of the plant, it is possible to understand how the total production of the PV plant, EPV, is approximately the same as that required both for the operation of GHP and of the other devices (1399 kWh and 1448 kWh, respectively). While during the period from April to June the PV production was higher than the total energy consumption, during the other periods (autumn: from October–December, and winter: January–March) the PV production was insufficient to power the GHP and all the other devices. In order to obtain a kind of parity, considering the energy totally produced along the whole year, an oversizing of the PV plant of a factor 1.5 (with a peak power of 5.5 kW corresponding to a 25 modules), while in the perspective of covering the electricity required in the period from October to March, could be necessary to increase the size of the PV plant. In this last case, it would be necessary to install a power plant with a power over 10 kW (for example, 13.4 kW—equivalent to 61 modules). In this case, the energy exported to the grid would drastically increase, causing an impact on the power grid. The operation of the HP during the year, including both the heating mode and cooling mode, is described in Figure4. The electricity consumption values range from a lower value of 2–3 kWh /day, typical of the mid-season period, when the heat pump is used only for the production of sanitary hot water, up to values just below 35 kWh/day, typical of the winter season, when there may be 10 h of operation per day. A good operation of the heat pump was evaluated in the winter phase, while during the summer cooling period, the COP value was slightly lower than the nominal one. During the heating phase, a monthly average power value was found to be very close to the nominal value, which does not exist in the cooling phase when the heat pump works frequently in ON–OFF mode and the transient phase is therefore not negligible. Buildings 2020, 10, x FOR PEER REVIEW 9 of 19

Table 2. Energy balance of the system (values of year 2009, first one of operation).

EGHP EDEV ETOT EPV Period of the Year (kWh) (kWh) (kWh) (kWh) January–March 1658 671 2329 850 April–June 377 550 927 1436 July–September 796 652 1448 1399 October–December 1005 622 1627 580 Total year 3836 2495 6331 4265

Figure 5 provides the daily consumption and corresponding operating hours of the GHP throughout the year. The energy required for summer is approximately a third of the energy required for the winter period, and the maximum energy required for the operation of the HP occurs during the winter period, when the production of the PV plant is at its lowest levels. A further element of discussion concerns the results of the data obtained during long-term monitoring of a building–plant system. Table 3 shows the distribution of the various energy flows in the different years of operation of the experimental plant to verify the weak points and possible improvements that could be obtained for the integrated system under analysis. It can be observed that, while during winter (mainly in December and January) PV production was insufficient for supporting the operation of GHP, in summer (from June to September) the production of PV is sometimes excessive. It is interesting to analyze the behavior of the system during the period between the hot and cold seasons, that is, from February to May and from October to November. The data reported in Table 3 provide a summary of the various electricity consumptions within the system. We evaluated the electricity consumption of the house and the production of the PV system, during the years from 2013 to 2017, to compare them with 2009, the first year of operation. Considering the energy produced by the PV plant, the values are similar to those calculated using Equation (1), considering a value of ηBOS approximately equal to 0.75–0.8. As is evident from the analysis of the data, the PV plant has operated in quite a satisfactory way, even though some differences among the various years can be observed. Differences can be measured by the value of the difference between the maximum and the minimum value of the production, divided by the average production rate, defined as EE− = PV,, MAX PV MIN I PV (7) EPV, avg Buildings 2020, 10, 175 9 of 18 Based on the data in Table 4, this value was about 8.5%, which could be connected to the different weather conditions and the degradation of the modules over time. Figure5 provides the daily consumption and corresponding operating hours of the GHP With regard to the HP, it appears to be oversized for the particular operating conditions. As throughout the year. The energy required for summer air conditioning is approximately a third of the discussed before, the longest daily running time is 12 h during the coldest day of the year, but on energy required for the winter period, and the maximum energy required for the operation of the HP most days the heat pump operates for a reduced number of hours (usually less than two). occurs during the winter period, when the production of the PV plant is at its lowest levels.

Buildings 2020, 10, x FOR PEER REVIEW 10 of 19 (a) 1400

1200

1000

800

600

GHP operatingGHP hours 400

200

0 0 30 60 90 120 150 180 210 240 270 300 330 360 day of the year

(b)

FigureFigure 5. Daily 5. Daily energy energy consumption consumption of the of GHPthe GHP in a in typical a typical year year (a) and (a) and hours hours of operation of operation (b). (b)

A further elementTable of discussion 3. Annual energy concerns flows the of the results plant of under the various data obtained conditions. during long-term monitoring of a building–plant system. Table3 shows the distribution of the various energy flows ED EDEV EPV (kWh) EIMP (kWh) EEXP (kWh) ETOT (kWh) EGHP (kWh) in the different years of operation of the experimental(kWh) plant to verify the weak points(kWh) and possible improvements that2009 could4265 be obtained4923 for the integrated 2857 system1408 under6331 analysis. 3836 It can be observed2495 that, while during winter2013 (mainly3825 in December4518 and January) 2622 PV1203 production 5721 was insu 3370fficient for2351 supporting the operation of2014 GHP, in summer4059 (from4133 June to September) 2982 1077 the production5210 of PV 2924 is sometimes 2286 excessive. 2015 3947 4971 2784 1110 6081 3685 2396 It is interesting2016 to analyze 3957 the behavior4938 of the 2804 system during1153 the6091 period between 3210 the2881 hot and cold seasons, that is,2017 from February4084 to May4510 and from 2833 October 1251 to November.5761 The data 3382 reported2379 in Table3 provide a summary of the various electricity consumptions within the system. We evaluated the electricityTable consumption 4. PV module of the production house and in the productionmonths between of the the PV hot system, and cold during season the in yearsdifferent from years 2013 to 2017,(data to compare in kWh). them with 2009, the first year of operation. Considering the energy produced by the PV plant, the values arePV Prod similar to those calculated using Equation (1), considering a value of ηBOS February March April May October November approximately equal to 0.75–0.8.[kWh] As is evident from the analysis of the data, the PV plant has operated in quite a satisfactory way,2009 even though220 some diff350erences 413 among 575 the various316 years 161 can be observed. Differences can be measured2013 by the value221 of the di335fference 403 between 487 the240 maximum 160 and the minimum 2014 186 388 427 470 310 101 value of the production, divided by the average production rate, defined as 2015 210 312 445 582 256 111 2016 147 311 441 498 256 156 E E 2017 184 PV,MAX413 PV469,MIN 458 313 163 IPV = − (7) Average (2013–17) 190 352EPV ,avg437 614 275 139

The data, acquired over more than eight years of operation, demonstrate that the energy consumed by the GHP and the energy produced by the PV array are similar if the total amount is considered, and that the energy exchange with the electricity grid is relevant. Considering an average year of the five from 2013 to 2017, the average values of the energy exported to and imported from the grid in the various months of the year are provided in Figure 6. Table 5 provides the average values of the energy flows from January to December. Considering the data of Table 5, the index of direct utilization of the energy produced by the PV plant, IU, can be approximately estimated with a maximum level (0.55–0.56) in the winter and the minimum value occurring in May (average, 0.21). Buildings 2020, 10, 175 10 of 18

Table 3. Annual energy flows of the plant under various conditions.

EPV EIMP EEXP ED ETOT EGHP EDEV (kWh) (kWh) (kWh) (kWh) (kWh) (kWh) (kWh) 2009 4265 4923 2857 1408 6331 3836 2495 2013 3825 4518 2622 1203 5721 3370 2351 2014 4059 4133 2982 1077 5210 2924 2286 2015 3947 4971 2784 1110 6081 3685 2396 2016 3957 4938 2804 1153 6091 3210 2881 2017 4084 4510 2833 1251 5761 3382 2379

Based on the data in Table4, this value was about 8.5%, which could be connected to the di fferent weather conditions and the degradation of the modules over time.

Table 4. PV module production in the months between the hot and cold season in different years (data in kWh).

PV Prod [kWh] February March April May October November 2009 220 350 413 575 316 161 2013 221 335 403 487 240 160 2014 186 388 427 470 310 101 2015 210 312 445 582 256 111 2016 147 311 441 498 256 156 2017 184 413 469 458 313 163 Average (2013–2017) 190 352 437 614 275 139

With regard to the HP, it appears to be oversized for the particular operating conditions. As discussed before, the longest daily running time is 12 h during the coldest day of the year, but on most days the heat pump operates for a reduced number of hours (usually less than two). The data, acquired over more than eight years of operation, demonstrate that the energy consumed by the GHP and the energy produced by the PV array are similar if the total amount is considered, and that the energy exchange with the electricity grid is relevant. Considering an average year of the five from 2013 to 2017, the average values of the energy exported to and imported from the grid in the various months of the year are provided in Figure6. Table5 provides the average values of the energy flows from January to December. Considering the data of Table5, the index of direct utilization of the energy produced by the PV plant, IU, can be approximately estimated with a maximum level Buildings 2020, 10, x FOR PEER REVIEW 11 of 19 (0.55–0.56) in the winter and the minimum value occurring in May (average, 0.21).

Figure 6. Monthly energy flow from and to the grid, with a 3.74 kW PV plant. Figure 6. Monthly energy flow from and to the grid, with a 3.74 kW PV plant.

Table 5. Average monthly values of the energy flows in the period 2009–2017.

EPV EEXP EIMP EGHP EDEV ETOT ED Month IU (kWh) (kWh) (kWh) (kWh) (kWh) (kWh) (kWh) January 105 46 761 622 198 820 59 0.561 February 195 108 644 519 211 731 87 0.446 March 335 229 498 394 210 604 106 0.316 April 432 322 258 166 203 369 111 0.256 May 504 398 187 103 190 293 106 0.210 June 491 375 196 122 190 312 116 0.236 July 552 372 358 316 221 538 180 0.326 August 519 319 395 327 268 595 200 0.385 September 370 282 199 114 173 287 88 0.238 October 262 191 271 140 201 341 70 0.267 November 133 80 492 304 241 545 53 0.398 December 109 48 763 511 313 824 61 0.559 Total 4007 2771 5021 3639 2618 6257 1236 0.308

4. The Problem of Defining a Correct Size for PV-GHP and n-ZEB The particular solution proposed here is often considered one of the possible solutions for ZEBs, and the analysis conducted under real operating conditions have shown some interesting aspects and some critical elements concerning the modifications required. The solution experimentally analyzed was designed with the same values of power for the HP and the PV plants. The electrical grid is used as an “energy buffer” to decouple energy generation and energy use, mainly during the spring and autumn. The possibility of exporting energy to the electrical grid (often the national electrical grid) was a good method in principle to promote the installation of PV plants directly connected to residential building. This option is not available today because of the problems induced by the relevant penetration of such plants, already discussed in [5], with reference to an Italian case, where in 2020 more than 800,000 PV plants were present in the territory [28]. It is important to test different cases, and to ensure that excess energy can be stored using an electrochemical system, so that unused energy is not wasted. For this reason, in the present section, the system under analysis is modified. In particular, the objective was to maximize the energy production of the PV plant from the perspective that surplus energy cannot be exported to the power grid, although energy can be imported from the grid. Considering the schematic in Figure 4, this would result in a size reduction in PV power plants, or, if the introduction of a storage system was considered, the size of the PV system could be similar to those experimentally analyzed. The possibility of introducing an appropriately sized electrical storage unit could help reduce the amount of energy exchanged with the electrical grid.

4.1. A Reduction in the Size of PV Plants Buildings 2020, 10, 175 11 of 18

Table 5. Average monthly values of the energy flows in the period 2009–2017.

E E E E E E E Month PV EXP IMP GHP DEV TOT D I (kWh) (kWh) (kWh) (kWh) (kWh) (kWh) (kWh) U January 105 46 761 622 198 820 59 0.561 February 195 108 644 519 211 731 87 0.446 March 335 229 498 394 210 604 106 0.316 April 432 322 258 166 203 369 111 0.256 May 504 398 187 103 190 293 106 0.210 June 491 375 196 122 190 312 116 0.236 July 552 372 358 316 221 538 180 0.326 August 519 319 395 327 268 595 200 0.385 September 370 282 199 114 173 287 88 0.238 October 262 191 271 140 201 341 70 0.267 November 133 80 492 304 241 545 53 0.398 December 109 48 763 511 313 824 61 0.559 Total 4007 2771 5021 3639 2618 6257 1236 0.308

4. The Problem of Defining a Correct Size for PV-GHP and n-ZEB The particular solution proposed here is often considered one of the possible solutions for ZEBs, and the analysis conducted under real operating conditions have shown some interesting aspects and some critical elements concerning the modifications required. The solution experimentally analyzed was designed with the same values of power for the HP and the PV plants. The electrical grid is used as an “energy buffer” to decouple energy generation and energy use, mainly during the spring and autumn. The possibility of exporting energy to the electrical grid (often the national electrical grid) was a good method in principle to promote the installation of PV plants directly connected to residential building. This option is not available today because of the problems induced by the relevant penetration of such plants, already discussed in [5], with reference to an Italian case, where in 2020 more than 800,000 PV plants were present in the territory [28]. It is important to test different cases, and to ensure that excess energy can be stored using an electrochemical system, so that unused energy is not wasted. For this reason, in the present section, the system under analysis is modified. In particular, the objective was to maximize the energy production of the PV plant from the perspective that surplus energy cannot be exported to the power grid, although energy can be imported from the grid. Considering the schematic in Figure4, this would result in a size reduction in PV power plants, or, if the introduction of a storage system was considered, the size of the PV system could be similar to those experimentally analyzed. The possibility of introducing an appropriately sized electrical storage unit could help reduce the amount of energy exchanged with the electrical grid.

4.1. A Reduction in the Size of PV Plants Starting from the results obtained from the real plant and analyzed, in this section we propose alternative configurations for the system. The introduction of a storage system is considered together with the definition of an optimal size of both PV system and HP system. Table6 provides the results obtained in five different cases, considering as a first case the actual configuration of the plant, with a PV plant of 3.74 kW power. In this case, the amount of energy wasted was about 70% of the energy produced. By reducing the size of the plant, the amount of energy wasted is reduced, but the size of the plant is then too small. In the last case, the peak power of the PV plant is reduced to a level of 1.1 kW, the energy produced with the PV plant is approximately 1200 kWh, less than 20% of the energy required by the house, although the amount of energy wasted is reduced to less than 10%. In this case, it can be observed that the energy imported from the grid is similar to that of the reference case (5193 kWh and 5021 kWh, respectively). A reasonable compromise could be achieved by installing 10 modules of the same type, instead of 17, that is, with a total power rate of 2.2 kW (case four in Table6). Buildings 2020, 10, x FOR PEER REVIEW 12 of 19

Starting from the results obtained from the real plant and analyzed, in this section we propose alternative configurations for the system. The introduction of a storage system is considered together with the definition of an optimal size of both PV system and HP system. Table 6 provides the results obtained in five different cases, considering as a first case the actual configuration of the plant, with a PV plant of 3.74 kW power. In this case, the amount of energy wasted was about 70% of the energy produced. By reducing the size of the plant, the amount of energy wasted is reduced, but the size of the plant is then too small. In the last case, the peak power of the PV plant is reduced to a level of 1.1 kW, the energy produced with the PV plant is approximately 1200 kWh, less than 20% of the energy required by the house, although the amount of energy wasted is reduced to less than 10%. In this case, it can be observed that the energy imported from the grid is similar to that of the reference case Buildings 2020 10 (5193 kWh, , 175 and 5021 kWh, respectively). A reasonable compromise could be achieved by12 installing of 18 10 modules of the same type, instead of 17, that is, with a total power rate of 2.2 kW (case four in UsingTable this 6). configuration, Using this configuration, the amount of the energy amount imported of energy from imported the grid from is approximately the grid is approximately the same as the thatsame observed as that for observed the original for the solution, original while solution, the energy while the wasted energy is 1121wasted kWh is 1121 instead kWh of instead 2771 kWh. of 2771 FigurekWh.7 provides Figure 7 the provides energy flowsthe energy from theflows grid from and th thee grid energy and to the the energy grid (or to wasted). the grid A(or relevant wasted). A increaserelevant in self-consumption increase in self-consumption of the PV plant of the was PV obtained plant was even obtained if the totaleven amountif the total of amount energy isof less energy thanis 50% less of than the 50% total of energy the total amount energy necessary amount innecessary the house. in the house.

TableTable 6. Level 6. Level of energy of energy wasted wasted with with a reduced a reduced size ofsize the of PV the pant. PV pant.

PPV EIMP EW PPV (kW) No. of ModulesNo. of Modules E IMP (kWh) EW (kWh) (kW) (kWh) (kWh) BASIC 3.74BASIC 3.74 17 17 5021 5021 2771 2771 Case 1 2.2Case 1 2.2 10 10 5021 5021 1121 1121 Case 2 1.54Case 2 1.54 7 7 5042 5042 435 435 Case 3 1.32Case 3 1.32 6 6 5107 5107 263 263 Case 4 1.1Case 4 1.1 5 5 5193 5193 114 114

900 800 700 energy to the grid energy from the grid 600 500

[kWh] 400 300 200 100 0 jan feb mar apr may jun jul aug sep oct nov dec

Figure 7. Monthly energy (kWh) from and to the grid, with a PV plant of 2.2 kW power. Figure 7. Monthly energy (kWh) from and to the grid, with a PV plant of 2.2 kW power. 4.2. A Reduction in the Size of the PV Plant with the Introduction of a Storage System 4.2.The A configuration Reduction in the of theSize plantof the analyzedPV Plant with in the the previous Introduction section, of a Storage characterized System by a reduction in the size ofThe the configuration PV plant, clearly of the shows plant theanalyzed real problem in the pr connectedevious section, with thecharacterized development by a of reduction such a in solution.the size In of general, the PV the plant, amount clearly of shows energy the exchanged real problem with theconnected power with grid isthe important development and ifofthe such a producersolution. cannot In general, export energy the amount to the grid,of energy the amount exchanged of energy with wasted the power is also grid important. is important We tried and toif the establishproducer the optimization cannot export criteria energy to to solve the thisgrid, issue, the amou consideringnt of energy the installation wasted is ofalso an important. electrochemical We tried storageto establish and based the on theoptimization definition ofcriteria the optimal to solve size ofthis HP issue, and PV. considering the installation of an electrochemicalAs the building storage is equipped and based with a on PV the plant, defi thenition installation of the optimal of electric size storage of HP and mitigates PV. the effect of the timeAs mismatch the building between is equipped electricity with production a PV plant, and peakthe installation thermal load. of electric The scheme storage of the mitigates system the is providedeffect of in the Figure time8 mismatch, where it isbetween shown thatelectricity only a pr unidirectionaloduction and flow peak is thermal possible. load. A critical The scheme analysis of the of thesystem experimental is provided data in collectedFigure 8, where from the it is existing shown th systems,at only a combined unidirectional with flow the optimum is possible. design A critical strategy,analysis permitted of the usexperimental to develop guidelinesdata collected for thefrom optimal the existing combination systems, between combined the power with the rating optimum of PV generators and the energy capacity of thermal and electrochemical storage systems, and to define an appropriate sizing of the HP and the other components of the system. Buildings 2020, 10, x FOR PEER REVIEW 13 of 19 design strategy, permitted us to develop guidelines for the optimal combination between the power rating of PV generators and the energy capacity of thermal and electrochemical storage systems, and Buildings 2020, 10, 175 13 of 18 to define an appropriate sizing of the HP and the other components of the system.

Figure 8. A schematic description of the plant consisting of a GHP for house heating and cooling and Figure 8. A schematic description of the plant consisting of a GHP for house heating and cooling and assisted by a PV system with a storage system (it is not possible to export energy to the grid). assisted by a PV system with a storage system (it is not possible to export energy to the grid). A possible modification of the system from the perspective of increasing the utilization of the A energypossible produced modification consists of the of system the introduction from the perspective of a storage of system.increasing A the series utilization of attempts of the have energy been producedmade to defineconsists the of correctthe introducti size of theon storageof a storage system. system. We analyzed A series theseof attempts different have options been and made Table to 7 defineprovides the correct the results. size of We the found storage that system. installing We a an storagealyzed system these different of 6 kWh /optionsday capacity and Table would 7 provides reduce the theenergy results. wasted We found to approximately that installing zero, a storage if exporting system energyof 6 kWh/day to the powercapacity grid would is not reduce possible. the energy With the wastedinstallation to approximately of this storage zero, system, if exporting energy losses energy are reducedto the power to a low grid level. is Thenot particularpossible. With capacity the of installationthe storage of system this storage corresponds system, to energy about 35%–40%losses are ofreduced the total to energya low level. amount The produced particular for capacity each kW of of thePV storage power system installed. corresponds For example, to about just with 35%–40% the introduction of the total of energy a storage amount system produced of 6 kWh for/day each capacity kW ofthe PV electricity power installed. transfer For from example, and to the just grid with decreased the introduction drastically. of Ina particular,storage system in the of months 6 kWh/day of May capacityand June, the aelectricity general self-production transfer from and profile to the can grid be decreased obtained, whiledrastically. from JulyIn particular, to September, in the the months energy ofimported May and fromJune, thea general grid is self-production small, as shown profile in Figure can9 be. obtained, while from July to September, the energy imported from the grid is small, as shown in Figure 9. Table 7. Energy imported from the grid and wasted in five different configurations with storage system.

EIMP EW Storage Capacity PPV PV Plant (kWh) (kWh) (kWh) (kW) No. of Modules CASE 1 2800 551 13 3.74 17 CASE 2 3189 232 10 3.08 14 CASE 3 3348 156 9 2.86 13 CASE 4 3703 39 7 2.42 11 CASE 5 3903 0 6 2.2 10 Buildings 2020, 10, x FOR PEER REVIEW 14 of 19

Table 7. Energy imported from the grid and wasted in five different configurations with storage system.

EIMP EW PPV PV Plant Storage Capacity (kWh) (kWh) (kWh) (kW) no. of Modules CASE 1 2800 551 13 3.74 17 CASE 2 3189 232 10 3.08 14 CASE 3 3348 156 9 2.86 13 CASE 4 3703 39 7 2.42 11 CASE 5 3903 0 6 2.2 10 Buildings 2020, 10, 175 14 of 18

900 800 700 energy from the grid energy to the grid 600 500

[kWh] 400 300 200 100 0 jan feb mar apr may jun jul aug sep oct nov dec

Figure 9. Monthly energy from the grid (PV plant of 2.2 kW, and PV plant of 2.2 kW with 6 kWh Figure 9. Monthly energy from the grid (PV plant of 2.2 kW, and PV plant of 2.2 kW with 6 kWh storage). storage). 4.3. System with Higher Level of Self-Consumption 4.3. System with Higher Level of Self-Consumption One of the problems associated with the results provided in Sections 4.1 and 4.2 is that in all of the cases analyzed,One of a reductionthe problems in the associated size of the with PV plantthe results was necessary. provided Inin thisSections case, 4.1 it is and possible 4.2 is to that reach in all of the objectivethe cases of analyzed, reducing thea reduction production in the of surplus size of energy,the PV plant but the was total necessary. amount ofIn energythis case, produced it is possible by to the PVreach plant the is oftenobjective quite of low reducing (considering, the production for example, of surplus the results energy, of Table but5 ,the the total minimum amount energy of energy wastedproduced can be obtained by the PV with plant a plant is often of 1.1 quite kW peak low power).(considering, It could for be example, argued thatthe thereresults is aof reduced Table 5, the overallminimum utility associated energy wasted with this can solution.be obtained with a plant of 1.1 kW peak power). It could be argued that Inthere this is final a reduced section, overall we analyze utility theassociated various with possible this solution. optimal solutions, obtained according to different objectiveIn this final functions. section, The we availability analyze the of avarious storage po systemssible is optimal always considered.solutions, obtained Table8 provides according to the resultsdifferent of the objective most important functions. cases, The and availability it can be seenof a that storage some system of the self-consumption is always considered. situations Table 8 requireprovides unrealistically the results large of the PV most plants important (e.g., a PVcases, plant and of it aboutcan be36 seen kW that of some peak powerof the self-consumption is required to achievesituations the minimum require unrealistically energy import). large However, PV plants there (e.g., are a PV some plant interesting of about cases36 kW for of which peak power the is conditionrequired of relevant to achieve energy the production minimum and energy reduced import). values However, of energy wastethere areare available.some interesting In particular, cases for the casewhich in which the condition the minimum of relevant of the sumenergy of energyproduction flows and from reduced and to thevalues grid of (correspondent energy waste are to a available. size of 4.6In kW particular, of the PV the plant), case and in thewhich case the in whichminimum theplant of the provides sum of the energy maximum flows self-consumptionfrom and to the grid level (about(correspondent 99%), corresponding to a size of to4.6 a kW PV plantof the size PV of pl 2.6ant), kW and and the a 9case kWh in of which storage the system plant capacity,provides the can bemaximum considered self-consumption two interesting solutions.level (about 99%), corresponding to a PV plant size of 2.6 kW and a 9 kWh of storage system capacity, can be considered two interesting solutions. Table 8. Optimized size of the PV plant for different design objectives.

Storage System Energy Produced with Energy Produced with P Objective of the Design PV Capacity PV Plant and Directly Respect to the Total (kW) (kWh) Used (%) Required (%) Experimental System 3.7 - 30 19 PV plant minimizing energy 36 26 20 100 imported from the grid (ZEB case) PV plant minimizing the sum of 4.6 17 87 55 energy imported and wasted PV plant producing the same 5.9 11 65 52 amount of energy as that required PV plant with maximum 2.6 9 99 37 self-consumption level

5. Discussion and Guidelines for the Sustainable Sizing of a PV-HP System As a result of the analysis we carried out, here we pick out the general elements of discussion and criteria that may help set guidelines for the design of similar systems, that is, an integrated system including a heat pump (HP) and photovoltaic (PV) system, with the possible addition of storage (either electrical or thermal). Buildings 2020, 10, 175 15 of 18

An important preliminary step is the definition of the thermal load of the building and its fluctuations over the annual cycle. This can be achieved by means of a dynamic simulation or considering a typical value of the heat transmission, which defines the type of building and the test reference year (TRY), which defines the climate in the area, given by an average value of the heat trasmittance of the building (UA expressed in W/K). This information facilitates the determination of the average power of the heat pump and it is possible to calculate the electricity that is needed to supply the building to meet its thermal demand. Once the size of the HP has been determined, it is possible to define various options to satisfy the project’s specific objectives:

(1) The nominal power of the PV plant is similar to the nominal power of the HP: in this case, a relevant amount of the energy produced needs to be exported to the grid or will be wasted. (2) The nominal power of the PV plant can be considered as about 70% of the peak power of the GHP to reduce the amount of energy exported to the grid (or wasted), without increasing the energy imported from the grid. (3) The nominal power of the PV plant must be about 70% of the peak power of the GHP and an electricity storage system of 3 kWh for each kW of PV plant installed would be required to reduce energy waste to a level below 10%. (4) The energy produced with the PV plant is approximately the same as that required by the GHP and the other devices: in this case, the peak power of the PV plant is approximately 50% over the electric power of the GHP and a storage system of 2 kWh for each kW of PV plant installed would be necessary. (5) The PV plant energy production needs to cover the total energy use of the house: in this case, an oversizing of the PV plant is necessary (9–10 times the peak power of the HP), and a storage system (about 0.7 kWh for each kW installed) must be introduced.

Obviously, the previous statements are fairly specific to the case under analysis. To discuss more general elements, it could be necessary to take into account the variation of solar radiation, the type of PV module selected (and its relative performances), and all the other constraints. In general, two different optimization criteria can be considered. The first leads us to minimize energy losses by introducing an additional penalty to the surplus energy produced by the modules, which cannot be directly used in the building. In this case, a reduction in the PV plant size is desirable. An alternative criterion considers not the relevant the energy losses and the overproduction of the PV plant, but is particularly dependent on the cost of the electricity imported from the grid. In both cases, the definition of the size of the storage system is particularly important. It should be noted that these considerations are primarily connected with the specific climatic condition under analysis. While one might discuss the potential change to our findings in the case of different climatic conditions, it seems clear that the considerations outlined here will be quite similar regardless of climatic conditions.

6. Conclusions We first analyzed data obtained from the real operation of a building–plant system consisting of a domestic PV plant of reduced size that was supporting a GHP for heating and cooling. We attempted to develop criteria and guidelines for the correct sizing of such systems from the perspective of obtaining effective self-production of energy. The experimental analysis in Pisa, Italy, with typical Mediterranean-climate conditions, covers a period of about ten years of operation (2009–2018), with particular attention to the last five years. From the analysis, it is possible to conclude that it is difficult to obtain self-consumption schemes and real net zero-energy building configurations due to the time between energy production and energy use. Considering the experimental data acquired during the 10 years of operation, it was observed that 30% of the energy produced by the PV plant was directly used by the GHP and the other miscellaneous devices during the year (a minimum of 26.5% was recorded in 2014 and a maximum of Buildings 2020, 10, 175 16 of 18

33% was recorded in 2009). A large amount of the energy required by the GHP was imported from the electrical grid, mainly during winter, while an important amount of energy produced by the PV plant (67%–73.5%) was exported or lost, depending on whether or not electricity could be exported to the national electric grid. In the second part of the paper, we concentrated on finding a solution to mitigate the effects of the time between the electrical production peak and the thermal power demand peak through the reduction in the size of the PV plant, and by the introduction of a storage system. A reduction of about 30%–35% in the peak power of the PV plant (in this case using a plant with a peak power of between 2.2 and 2.6 kW ), combined with using a storage system of 6 kWh capacity, could reduce the need for exporting energy to the grid to almost zero. In this case, the majority of energy produced by the PV plant was directly used by the house appliances and energy was only imported from the grid. Solutions that considered using larger PV plants were also discussed. Excluding the case of a completely self-sufficient system (with a PV power of about 36 kW and a storage system of 26 kWh), an interesting compromise can be obtained with a PV plant of a larger size, in particular from 4.5 to 6 kW peak power. In all those cases, a combined use of a storage system of appropriate dimensions would be necessary. For a final comparison among the various optimized solutions, an economic analysis is required. Considering the pre-covid-19 pandemic scenario, the plant with a reduced size may be preferred for general development and promotion. Nevertheless, the new financial support for renewables applied to buildings (for example, Italy’s recent 110% “Ecobonus” financial support mechanism) leads us to consider the benefits of larger sized PV plants. From a critical analysis of the experimental data collected from an existing system and based on our further analytical consideration, we provided some guidelines for the optimal combination of power rating of PV generators and energy capacities of thermal and electrochemical storage systems, and we outlined how to determine the size of the system in order to pursue specific design objectives. In any case, it will be important to make use of the energy produced, reducing the energy wasted.

Author Contributions: A.F. defines the methodology, A.F. and F.F., conceived and designed the experiments and acquire the data; A.F. developed software and analyze the data, A.F., wrote the paper, A.F. reviewed and edited tbe paper; A.F. supervised the paper and acquire funds for publication. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the University of Pisa (PRA 2018–19, project no. 2018_38). Acknowledgments: Enrico Ciulli of the University of Pisa is acknowledged by the authors for the support given during experimental analysis. Conflicts of Interest: The authors declare no conflict of interest with respect to the research, authorship, and/or publication of this article.

Nomenclature

A Surface of the (m2) ASHP COPc Coefficient of performance in cooling mode COPh Coefficient of performance in heating mode E Electrical energy (kWh) ED Electricity produced by the PV plant and directly used in the house (kWh) EDEV Electricity used for the various house devices (kWh) EEXP Electrical energy exported to the grid (kWh) EGHP Electricity used by the ground source heat pump (kWh) EIMP Electrical energy imported from the grid (kWh) EPV Electricity produced by the PV plant (kWh) EPV,min Minimum value of the energy monthly produced by the PV plant (kWh) EPV,max Maximum value of the energy month produced by the PV plant (kWh) EPV,avg Average value of the energy monthly produced by PV plant in the years (kWh) ETOT Electricity used in the house considering GHP and other devices (kWh) Buildings 2020, 10, 175 17 of 18

Ew Electricity produced by PV plant, not used and wasted (kWh) GHE Ground neat exchanger GHP Ground (source) heat pump 2 HSN Annual solar irradiance (kWh/m ) HP Heat pump ISC Short circuit current (A) Impp Current of maximum power (A) IU Index of utilization of energy produced with the PV plant n Number of hours in which a well-defined outside temperature is observed nZEB net zero energy building PPV Power of PV system PV PhotoVoltaic Qin,solar Solar gain (kWh) RES Renewable energy system STC Standard test conditions t time (h) Tin internal temperature (◦C) Text average external temperature (◦C) UA average value of the transmittance of the building (W/K) Vmpp Voltage of maximum power for the PV module (V) Vop Voltage of open circuit for the PV module (V) ηBOS Balance of system efficiency for the PV plant ηPV efficiency of the PV module ZEB Zero energy building

References

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