applied sciences

Article Solar and Systems for Domestic Hot Water Production on a Small Island: The Case Study of Lampedusa

Marco Beccali 1 , Marina Bonomolo 2,*, Biagio Di Pietra 3, Giuliana Leone 2 and Francesca Martorana 2 1 D’ARCH—Department of Architecture, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy; [email protected] 2 DII—Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy; [email protected] (G.L.); [email protected] (F.M.) 3 ENEA—Dipartimento Unità per l’Efficienza Energetica (DUEE)-Via Anguillarese, km 1.150, 00123 Roma, Italy; [email protected] * Correspondence: [email protected]

 Received: 27 July 2020; Accepted: 25 August 2020; Published: 28 August 2020 

Abstract: The achievement of United Nations Sustainable Development Goals, related to energy and resource use, is a critical issue for small and insulated communities. In many minor islands, solar energy is not correctly exploited, and electrical heaters are connected to weak grids with very a high share of generation by fossil . As a consequence, there is the necessity to assess the potential and the suitability of diffusion of alternative systems to avoid dependency on the and reduce carbon emissions. This paper aims to evaluate the technical and economic performances of some alternative systems exploiting renewable energy for domestic hot water production. Four different systems were simulated and studied: a heat pump connected to the grid, a heat pump coupled with a photovoltaic plant, a heat pump combined with a , and a solar thermal plant. Moreover, heat and storages were studied for reducing impacts on the distribution network. The work presents data gathered for a study on energy-retrofit strategies on Lampedusa Island (Italy, 35◦3005600 north (N), 568 degree-days). Finally, to select the most cost-effective plant, an economic analysis of the chosen systems was carried out. This analysis shows that the best net present values are associated with the heat pump (HP) coupled with a stand-alone PV system and a small battery and solar thermal-assisted HP. The shortest payback time was calculated for the solar thermal system.

Keywords: small islands; renewable sources; energy consumption; heat pump water heater; domestic hot water

1. Introduction Most minor islands are not interconnected to the main national electrical grids, and energy is provided by power generation systems consisting of thermal power plants [1]. This causes a financial dependency on the price of fossil fuels [2] and high electricity generation costs [3]. For this reason, island communities are facing numerous energy challenges regarding import dependency and the transport of fuel supply [4]. Furthermore, small islands represent a typical example of such communities, for which the final users’ energy consumption often depends on an electricity source provided by diesel and heavy-fuel oil power plants [5]. Neves et al. [6] proposed a characterization of island energy load based on economic, demographic, and cultural criteria. They underlined how islands with the highest demand per capita are generally located in developed countries, while

Appl. Sci. 2020, 10, 5968; doi:10.3390/app10175968 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 5968 2 of 24 they have a considerable tourist vocation that strongly influences both the energy consumption and the load profile of the island itself. It would be consequently advantageous to increase the energy efficiency of the whole system via the use of local renewable energy sources (RES) at large scale or by implementing retrofit strategies at the end-user level (including building automation control, small RES plants, etc.) [7,8]. As Papadopoulos [9] affirmed, RES installation is a suitable action to decrease the dependency on fossil fuels and resulting environmental problems, because, in general, they are free from large emissions and locally available. Many studies are available on the use of renewable energy sources on islands. For example, Chen et al. [10] studied a pathway for small islands to replace fossil fuels by renewable sources, applied to a case study in Jamaica. They found that renewable energy can be achieved in such a manner as to satisfy and be in line with the Intergovernmental Panel on Climate Change guidelines for limiting temperature rise to 1.5 ◦C. The aim of the study of Alves et al. [11] was to analyze the impact of the interconnection of two Azores small islands in the path to 100% RES for the whole energy system. Bertheau [12] focused his attention on Cobrador Island in the Philippines to study the impact of providing more affordable, reliable, and sustainable access to energy on consumption patterns, appliance uptake, and overall socio-economic development. To do this, similarly to this study, a survey was conducted to assess the impact of providing a continuous renewable-based power supply on local development and the sustainable development goals. Meschede et al. [13] proposed a general method to classify global islands with regard to RES installation potentiality, employing cluster analysis based on climatic, physical, and socio-economic parameters. The possibility to convert the existing thermal-power plant into combined heat and power (CHP), i.e., a cogeneration system, including the construction of district heating/cooling networks, was investigated by Beccali et al. [14]. Nevertheless, this study conducted on six Italian small islands demonstrated that CHP technology is only moderately economically attractive when public support mechanisms are included in the analysis. Better results are achieved if hybrid renewable poly-generation systems are considered; however, once again, huge investments are needed. Indeed, the economic attractiveness of such systems is related to the linear density of the energy demand and to the fact that the majority of the energy available for heating and cooling purposes is currently used. Calise et al. [15] studied an innovative poly-generation system powered by solar and geothermal sources on Pantelleria Island. The described plant is able to cover the electricity and the heat demands of a small community, as well as to simultaneously cover the freshwater demand of the island. In another work, Calise et al. [16] investigated the possibility of integrating energy and water supply systems so that excess wind power production could be used in desalination units to supply the freshwater demand on Cape Verde Island. The main idea was to use desalinated water in a pumped hydro system in order to store the extra produced power from wind and to fulfill the gap between intermittent RES production and the island energy demand. Despite the recognized RES potentiality within small islands, the current share of installed RES plants with respect to the total electricity production is generally very low, even if a high potential of exploitation is available within the territory [17,18]. In this regard, Ciriminna et al. [19] identified some critical barriers against a significant penetration of renewable energy on Sicilian islands, which are mainly related to local regulations and landscape management that usually forbid RES large-scale plant installations. It was also observed that an interactive strengths, weaknesses, opportunities, and threats (SWOT) analysis on the energy system could contribute to a collective and social learning process facing institutional, organizational, or common problems that usually inhibit the application of sustainable strategies on small islands [20]. Even though RES large-scale plants could undergo economic and administrative barriers, retrofit actions at the building level could, in turn, be diffusively proposed. Indeed, it was largely proven that they could lead to a substantial reduction in the energy demand toward a Net Zero Energy Building target [21]. Moreover, the extensive use of renewable energy sources could strongly influence the load curve of the community, as demonstrated by Ilkan et al. [22] for the island of Northern Cyprus where the use of solar thermal water heater was intensely encouraged by the local government, leading to a maximum yearly saving about 72 GWh [23]. Indeed, solar thermal technologies can be a very good solution to decrease the electricity demand Appl. Sci. 2020, 10, 5968 3 of 24 by domestic hot water [24], because a great amount of energy consumption also takes place during the operational period, in order to satisfy the demand of domestic hot water (DHW) [25]. Moreover, the use of active and smart systems at the building level, enabling the possibility of implementing demand-side management (DSM) policies, could be easily applied in a typical building on Lampedusa Island (Italy), controlling the effect of flexible electrical loads on the load curve of the island. Among flexible loads, the one most influencing the peak and the energy consumption of a typical house in Lampedusa is the electrical storage water heater (ESWH). For example, Aguilar et al. [26] studied how photovoltaic systems interact with the heat pump water heater (HPWH) for domestic hot water (DHW) production without relying on batteries but only on a thermal storage tank. It is then reasonable to suppose that better results could be achieved if both strategies (use of RES source with high efficiency of water heater and demand response strategies) were applied. The present work relies on energy-retrofit strategies on Lampedusa Island (Italy, 35◦3005600 north (N) 12◦3402300 east (E), 568 degree-days). Lampedusa is one of the Italian small islands not connected to the mainland electric grid, for which the Italian Government established financial support to avoid a local inhabitant fee for extra costs in electricity production, according to a social equity principle. Since 2014, the government proposed to gradually abolish the support mechanism while promoting the use of RES. Specifically, in 2017, it introduced a legislative decree aimed at financing different energy-retrofit strategies, including the installation of solar thermal plants or heat pumps for domestic hot water (DHW) production. The general goal for Lampedusa Island by 2030 is to reduce the yearly electricity consumption by up to 37,660.0 MWh via installing photovoltaic plants with an overall 2140.0-kW peak power and via installing 2370 m2 of solar thermal collectors. It is necessary to carefully investigate the best integration patterns for having an optimal system implementation together with suitable operation strategies [27] and to compare alternative systems for the optimization of plants [28] both in economic and in environmental terms [29]. Razavi [30] compared combinations of a solar-assisted ground-source heat pump to meet heating and DHW loads in Zahedan city, Iran. They studied the potential exploitation of a geothermal source and of solar energy. Furthermore, Guarracino et al. [31] developed a dynamic model of a hybrid photovoltaic/thermal (PVT) collector with a sheet-and-tube thermal absorber. The aim was to evaluate the annual generation of electrical energy, along with the provision of DHW, from the thermal energy output. They highlighted the importance of using real input data at high resolution for a correct estimation of the yearly and monthly performance of the system, as opposed to averaged data. This could be very important, especially if a novel control strategy that can adjust the system’s outputs in response to varying demands has to be designed. According to this legislative panorama and to the state of art, the present work analyzes the impact of the substitution of existing electric storage water heaters (ESWH) with dedicated HPWH, eventually coupled to a photovoltaic (PV) plant, a solar thermal plant (ST), or a solely ST system. The goal is to evaluate how thermal and electrical storage could interact with each other while exploiting renewable energy sources and guaranteeing DHW supply at a proper water temperature and to evaluate the technical and economic performances of these alternative systems exploiting renewable energy for domestic hot water production. The paper is organized as follows: Section2 shows the method applied to conduct the work, describes the simulated systems and the models, and defines the domestic hot water tapping profiles; Section3 presents the results and, in particular, the performances of the heat pump. the conventional electric heater, and the photovoltaic-assisted systems, along with a description of the solar thermal-assisted water heaters and an economic analysis; finally, the last section reports the conclusions.

2. Methods The present work is based on model simulations by the TRSNSYS 17 platform. It is based on an hourly weather database from Meteonorm software and on the DHW demand input inferred by a monitoring campaign on some residential consumer units (users) in Lampedusa. Two users in Lampedusa were chosen as representative with respect to statistical data. They are both families made Appl. Sci. 2020, 10, 5968 4 of 24 up by two components living in a typical residential home on the island (120 m2). The experimental campaign, as well as data processing, was carried out by researchers from the University of Palermo and National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA) involved in the project. Data were acquired with a 10-min time-step. In order to obtain reliable data via simulation, a 10-min time-step was chosen, and results were then processed on hourly, daily, and monthly bases.

2.1. Workflow In this study, the operation and the efficiency of a set of systems for DHW production were determined through dynamic simulation models using the TRNSYS 17 platform [32]. In order to appreciate the interactions with electrical grids and to test time-shifting actions that can be implemented, an analysis on a short time scale (minutes) was conducted. A preliminary task was to correctly identify the typical DHW consumption hourly profile (tapping) and the volume of the daily-consumed DHW via a representative final user on Lampedusa Island. These values (hourly tapping profile and DHW demand per day) depend on the number of persons in the consumer unit and on their habits. Moreover, the use of hot water is influenced by seasonal fluctuations due to climatic conditions. The method is based on data extracted from the observations of a representative consumer unit during an experimental campaign. In addition, statistical data on population and housing in Lampedusa and the results of previous studies [33,34] were considered. According to the last population census, most families in Lampedusa are formed of two or three people (about 42%). Through a survey, presented in previous studies [5], it was verified that the most widespread DHW production plant is an 80-L ESWH equipped with a 1200-W electric resistance. Moreover, due to the touristic vocation of the island, the number of people living in apartment units varies from two in the winter to three in the summer. In order to identify the average daily DHW consumption, the monitored data of energy consumption in the most critical seasons (EDHW) were compared with those calculated using a Trnsys model of the heater. Indeed, simulations were conducted by varying the hot water volume demand per day until energy consumption matched the averaged recorded data in the critical months. Maximum (VDHW,max) and minimum DHW demand values (VDHW,min) were respectively calculated in the winter and summer as follows:

VDHW,i = fm,iVDHW,max (L), (1)

ni nmax fm,i = − (VDHW,max VDHW, min) + VDHW,max (L), (2) − nmax n − − min where i is the generic number of the month in the year, nmax and nmin are respectively the months in which VDHW,max and VDHW,min values were recorded from the experimental campaign, and fm,i is a monthly correction factor. A linear trend was then used to extrapolate the daily DHW volume for the other months. In order to generalize results, hot water consumption per person per day was calculated. Similarly, the hourly frequency of on/off ESWH cycles was calculated from monitored data to build the hourly tapping profile as follows: fh xh = (%), (3) fMAX where xh is an hourly factor for the VDHW,i, fh is the operation time of the ESWH, and fMAX is the maximum frequency value in the day. Yearly energy consumption and temperature trends in the water storage were used to run the simulation models of possible retrofit options. Based on the actual DHW demand, remarks on plant sizing and service modes were made using simulations in real operating conditions. In order to evaluate the role of the thermal storage for the best exploitation of solar energy while ensuring comfort conditions, we introduced three indices. Appl. Sci. 2020, 10, 5968 5 of 24

They were utilized for a first sizing of the proposed plants and can be calculated as follows:

Xh n.hourT_DHW40 DI = 1 (%), (4) − i=1 n.hourtot_1

h X n.hourT_DHW40 PDI = (%), (5) n.hourtot_2 i=1

Xh n.hour : (T < Tset) SPI = DHW (%), (6) i=1 n.hour where TDHW is the outlet tank temperature, n.hourT_DHW40 is the number of hours when the outlet tank temperature is 40 ◦C, n.hourtot_1. is the number of hours for which mDHW > 0, and Tset is the setpoint temperature. Additionally, the discomfort index (DI) and the potential discomfort index (PDI) [35] were introduced in order to check how many hours in a given period (month, year) the outlet tank temperature (TDHW) dropped to a minimum comfort temperature (TDHW.-comfort = 40 ◦C) during tapping events (number of hours, n.hourtot_1, for which mDHW > 0) and no-tapping events (number of hours, n.hourtot_2, for which mDHW = 0). The setpoint index (SPI) allows quantifying how many times in a detected period (n.hour) the tank temperature goes below a desired setpoint value (Tset). Furthermore, three additional indices [36,37] were calculated to measure the electric storage and evaluate its behavior. In particular, the average fractional state of charge (FSOCav) is equal to the ratio between the mean values of charge in a defined period (Ebattery.av) and its nominal capacity (Ebattery.max). The electric storage index (ESI) quantifies how many times in a detected period that the charge in the battery (SOC) drops to a minimum value (SOCmin) or overcomes a maximum threshold. The first was set equal to the HPWH daily consumption (BImin), while the second was assumed to be equal to its nominal capacity. They can be calculated using the following formulas:

Ebattery.av FSOCav = (%), (7) Ebattery,max

Xh n.hour : (SOCh < SOCmin) ESImin = (%), (8) i=1 n.hour

Xh n.hour : (SOCh < SOCMAX) ESIMAX = (%), (9) i=1 n.hour where Ebattery.av is the mean value of charge in a defined period, Ebattery.max is the nominal capacity, SOC is the state of charge in the battery, SOCmin is the minimum allowed value of the state of charge in the battery, SOCMAX is the maximum value of the state of charge in the battery, and SOCh is the calculated state of charge in the battery in a specified time-step. Finally, two financial indices were further introduced and calculated for the studied systems. They are the net present value (NPV) and the simple payback time (SPT)

XTeq Rz Mz NPV = CO + − (€), (10) − z=1 (1 + i)z

C SPT = O (year), (11) R where Co is the initial cost, including purchase and installation costs, Teq is the equivalent time, Rz is the economic saving with respect to the current DHW production system, and Mz is the maintenance cost of the retrofit plant. The above-described methodology is represented in Figure1. Appl. Sci. 2020, 10, 5968 6 of 24 Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 24

FigureFigure 1. 1. WorkflowWorkflow of of the the presented presented work. work. 2.2. Simulated Systems 2.2. Simulated Systems Four different combinations of plants for DHW production were considered as alternatives to Four different combinations of plants for DHW production were considered as alternatives to the standard ESWH (Figure2). The following categories of technologies, currently available on the the standard ESWH (Figure 2). The following categories of technologies, currently available on the marketplace, were selected: marketplace, were selected: • System 1, heat pump water heater connected to the grid; • System 1, heat pump water heater connected to the grid; • System 2, heat pump water heater coupled with PV plant; • System 2, heat pump water heater coupled with PV plant; • System 3, heat pump water heater coupled with ST collector; • System 3, heat pump water heater coupled with ST collector; • SystemSystem 4, 4, solar solar thermal thermal plant. plant. • Moreover,Moreover, in in order order to to further further investigate investigate the the pe performancerformance of of PV-assisted PV-assisted HPWHs, HPWHs, two two different different sizessizes of of System System 2, 2, operating operating in in stand-alone stand-alone mode, mode, were were simulated. simulated. In In particular, particular, the the so-called so-called system system 2.12.1 was was characterized characterized by by a a peak peak power power of of 720 720 Wp, Wp, while while system system 2.2 2.2 was was characterized characterized by by a a power power of of 12001200 Wp. Wp. Solutions Solutions 2.1a 2.1a and and 2.2a, 2.2a, as as well well as as 2.1b 2.1b and and 2.2b, 2.2b, share share the the same same battery battery set-up, set-up, i.e., i.e., 2400 2400 and and 48004800 Wh, Wh, respectively. respectively. TheThe stand-alone stand-alone plants plants were were analyzed analyzed in in order order to to verify verify how how the the electrical electrical storage storage size size influences influences thethe overall overall system system performance performance while while ensuring ensuring comfort comfort conditions conditions and andthe energy-saving the energy-saving goal. goal.The electricalThe electrical storage storage was wassized sized based based on the on theworst worst work workinging conditions conditions for for the the overall overall plant, plant, i.e., i.e., the the day day withwith thethe highest highest daily daily consumption consumption and lowestand lowest solar irradiation. solar irradiation. In addition, In anaddition, electrical an consumption electrical consumptionof 1200 Wh for of the 1200 HPWH Wh for was the assumed. HPWH was Electrical assumed. storage Electrical was supposed storage towas be supposed able to ensure to be two able and to ensurefour days two of and autonomy four days (N ofaut autonomy). The two (N selectedaut). The solutions two selected (2400 solutions and 4800 (2400 Wh) were and 4800 applied Wh) to were both appliedstand-alone to both configurations. stand-alone configurations. They were named They system were 2.1a, named system system 2.1b, 2.1a, system system 2.2a, 2.1b, and system system 2.2a, 2.2b. andAdditionally, system 2.2b. a grid-connected Additionally, a plant grid-connected (system 2.5) plant was (system investigated. 2.5) was System investigated. 2.5 was sizedSystem in order2.5 was to sizedmeet in the order yearly to consumptionmeet the yearly of consumption the HPWH without of the HPWH accounting without for contemporaneityaccounting for contemporaneity issues between issuesload and between production. load Inand that production. way, the overall In that yearly way, energy the balanceoverall betweenyearly energy produced balance and consumedbetween producedenergy was and set consumed to zero. Furthermore, energy was theset HPWHto zero. couldFurthermore, be considered the HPWH to virtually could consumebe considered only theto virtuallyrenewable consume energy only generated the renewabl by the PV,e energy using generated the electrical by gridthe PV, as virtualusing the electric electrical storage. grid as virtual electric storage.

Appl. Sci. 2020, 10, 5968 7 of 24 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 24

FigureFigure 2. 2. SchemeScheme of of the the simulated simulated plants. plants.

2.3.2.3. Simulation Simulation Models Models TheThe HPWH HPWH considered considered for for systems systems 1, 2, and 33 waswas anan all-in-oneall-in-one air-to-waterair-to-water device. device. This This kind kind of ofsystem system uses uses its its DHW DHW tank tank as as a hota hot sink sink and and includes includes two two wrap-around wrap-around heat-exchangers. heat-exchangers. The The first first one oneis usedis used as as a condensera condenser in in the the heat heat pump pump cycle, cycle, while while thethe otherother is suitable for for connecting connecting additional additional heatheat sources. sources. The The main main features features of of the the HPWH HPWH are are listed listed in in Table Table 1.1. These These data data refer refer to to the the standard standard UNIUNI EN EN 16147:2011 16147:2011 [38] [38] that that introduced introduced two testing cycles.cycles. Both teststests relyrely onon aa heatingheating cycle cycle aimed aimed at atwarming warming water water from from 10 10◦ C°C to to 55 55◦ C.°C. In In the the first first test, test, inlet inlet air air temperature temperature and and humidity humidity were were fixed fixed at at7 7◦ C°C and and 89%, 89%, respectivelyrespectively (cycle(cycle A7A7/W10-55),/W10-55), whilewhile the second test test relied relied on on inlet inlet air air temperature temperature atat 15 15 °C◦C and and relative relative humidity humidity at at 74% 74% (cycle (cycle A15/W10-55). A15/W10-55). The The HPWH HPWH model model was was run run in in stationary stationary conditionsconditions with with an an input input according according to to EN EN 16147:2011. 16147:2011. Since no Trnsys type is available for simulating the described HPWH, a specific model was set Table 1. Heat pump water heater (HPWH) features from technical datasheet. DHW—domestic up for the heat pump operation (Figure 3). It was based on the combined use of two available types. hot water. In particular, type 938 [39] was used for performing the air-to-water heat pump cycle obtaining the heat delivered to the water sink (Q-to-water)Features at a given time step (15 min). Q-to-water was used as input in type 1237 [40] to evaluate the water tank temperature at the specific tapping condition. The Heating with heat pump, maximum temperature 65 ◦C water temperature wasWarm-up used timeas input at chosen in type cycle 938 A15 /wiW10-55(*)th the tank as 5:17 the heat h:min sink of the HP. The refrigerant flow rate Warm-upwas evaluated time at as chosen a function cycle A7 of/W10-55(*) Q-to-water, forcing 6:10 a h:mintemperature difference between the inlet/outletEnergy of consumption the fluid equal by chosen to 5 °C cycle in each A15/ W10-55time-step. 3.95The proposed kWh model was run at Energy consumption by chosen cycle A7/W10-55 4.05 kWh the nominal condition describedCOPDHW in EN-16147:2011 A15/W10-55 (A15/W10-55 3.07and A7/W10-55 - cycles). It was validated through the comparisonCOPDHW of figures A7/W10-55 of energy consumption, 3.00 coefficient - of performance (COP), and warm-upMaximum time reported power consumptionin the technical with data heat sheet, pump obtaining 490 relative W errors below 10%. Figure 3 shows the simulationBack-up model electric scheme. resistance heater power 2000 W Nominal air-flow rate 480 m3 h 1 · − Volume 200 litres Table 1. Heat pump water heater (HPWH) features from technical datasheet. DHW—domestic hot Maximum tank temperature with electric resistance 90 ◦C water. U-Value of the DHW tank shell 0.9 W(m2 K) 1 · − Features Since no TrnsysHeating type with is availableheat pump, for maximum simulating temperature the described HPWH, 65 a specific °C model was set up for the heat pumpWarm-up operation time at (Figure chosen3). cycle It was A15/W10-55(*) based on the combined 5:17 use h:min of two available types. In particular, typeWarm-up 938 [39] was time used at chosen for performing cycle A7/W10-55(*) the air-to-water heat 6:10 pump h:min cycle obtaining the heat delivered to theEnergy water consumption sink (Q-to-water) by chosen at a given cycle time A15/W10-55 step (15 min). 3.95 Q-to-water kWh was used as input in type 1237 [40]Energy to evaluate consumption the water by tank chosen temperature cycle A7/W10-55 at the specific 4.05 tapping kWh condition. The water temperature was used as inputCOPDHW in type A15/W10-55 938 with the tank as the heat 3.07 sink of the - HP. The refrigerant flow rate was evaluated asCOPDHW a function ofA7/W10-55 Q-to-water, forcing a temperature 3.00 di -ff erence between the Maximum power consumption with heat pump 490 W

Appl. Sci. 2020, 10, 5968 8 of 24 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 24 inlet/outlet of the fluidBack-up equal to electric 5 ◦C in resistance each time-step. heater Thepower proposed model 2000 was Wrun at the nominal condition described in EN-16147:2011Nominal (A15 air-flow/W10-55 rate and A7/W10-55 cycles). 480 It was m3 validated·h−1 through the comparison of figures of energy consumption,Volume coefficient of performance 200 (COP), litres and warm-up time reported inMaximum the technical tank data temperature sheet, obtaining with electric relative resistance errors below 90 10%. Figure °C 3 shows the simulation model scheme. U-Value of the DHW tank shell 0.9 W(m2·K)−1

Figure 3. HPWH simulation model. Figure 3. HPWH simulation model. As previously mentioned, System 2 was modeled to test how thermal and electrical storage could interactAs previously each other mentioned, for achieving System the 2 maximumwas model energyed to test (electricity) how thermal saving and target electrical by ensuring storage comfortcould interact conditions each and other by exploitingfor achieving the the solar maximum radiation energy source as(electricity) much as possible.saving target For this by ensuring reason, threecomfort different conditions PV plants and were by exploiting supposed basedthe solar on the radiat resultsion ofsource HPWH as simulation:much as possible. two stand-alone For this reason, (SA) systems,three different characterized PV plants by two were diff supposederent rated based peak on powers, the results and a of grid-connected HPWH simulation: system. two The stand-alone PV panel component(SA) systems, system characterized characteristics by aretwo presented different inrated more peak detail powers, in the nextand paragraph,a grid-connected while componentsystem. The featuresPV panel are component listed in Tables system2 and characteristics3. are presented in more detail in the next paragraph, while component features are listed in Tables 2 and 3. Table2. Photovoltaic (PV) panel features by technical datasheet. GC—grid-connected; SA—stand-alone. Table 2. Photovoltaic (PV) panel features by technical datasheet. GC—grid-connected; SA—stand- PV Plant PV η Pmp (W) Vmp (V) Imp (A) A (m2) alone. GC Mono-crystalline 15.4% 300 37.6 8 1.9 PV SAPlant Mono-crystalline PV 15.4%η Pmp 240 (W) 30.8 Vmp (V) 8Imp (A) 1.6 A (m2) GC Mono-crystalline 15.4% 300 37.6 8 1.9 For the systemsSA basedMono-crystalline on combination 15.4% with solar240 thermal 30.8 collectors 8 (3 and 1.6 4), different configurations were supposed. First of all, the main solar thermal component consisted of a flat-plateFor collector the systems with highlybased selective on combination surface properties with solar (effi thermalciency parameters collectors are(3 listedand 4), in Tabledifferent3). Furthermore,configurations we were considered supposed. a forced First circulation of all, the main water solar loop thermal scheme, component driven by a consisted 50-W pump. of a Systemflat-plate 4 iscollector a solar thermalwith highly plant selective with a conventional surface properties electric (efficiency heater as back-up. parameters System are 3listed includes in Table a solar 3). thermalFurthermore, system coupledwe considered with an a HPWH.forced circulation In the latter water case, loop the STscheme, system driven was connected by a 50-W with pump. a second System wrap-around4 is a solar thermal plant with present a conventional in the HPWH electric tank. heater as back-up. System 3 includes a solar thermal system coupled with an HPWH. In the latter case, the ST system was connected with a second wrap-aroundTable heat 3. PV exchanger panel and solarpresent thermal in the plant HPWH (ST) collectortank. features by technical datasheet.

2 TablePV-Technology 3. PV panel and solarη thermalPmp plant (W) (ST) collector Vmp features (V) by Imp technical (A) Adatasheet (m ) . Mono-crystalline 15.4% 300 37.6 8 1.9 2 Mono-crystallinePV-Technology 15.4%η Pmp 240 (W) Vmp30.8 (V) Imp 8 (A) 1.6 A (m ) Mono-crystallineST technology η15.4% a1 (W(m 3002 K) 1) a2 (W(m 37.6K) 2) A (m2) 8 1.9 0 · − · − FlatMono-crystalline plate collector 0.7615.4% 3.48 240 0.016 30.8 2.2 8 1.6 ST technology η0 a1 (W(m2·K)−1) a2 (W(m·K)−2) A (m2) In orderFlat to plate compare collector the analyzed 0.76 systems, 3.48 the same tapping 0.016 profile 2.2 and thermal storage characteristics (200-L DHW tanks equipped with a 2000-W back-up electric heater) were adopted for In order to compare the analyzed systems, the same tapping profile and thermal storage characteristics (200-L DHW tanks equipped with a 2000-W back-up electric heater) were adopted for

Appl. Sci. 2020, 10, 5968 9 of 24 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 24 allall case studies. The DHW tank was simulated using thethe Trnsys typetype 12371237 [[32].32]. Such storage is suitable toto bebe connected with didifferentfferent energy sources and includes a wrap-around HX calculation algorithm, appropriateappropriate forfor di ffdifferenterent alternative alternative generation generation sources sources (Figure 3(Figure). Furthermore, 3). Furthermore, the same components the same andcomponents types were and used types for were all theused simulated for all the models. simulated Daily models. and monthly Daily and schedules monthly were schedules applied were for determiningapplied for determining the hourly the tapping hourly input tapping as inferred input as from inferred the monitoredfrom the monitored data. As data. mentioned As mentioned before, inbefore, order in to order assess to the assess seasonal the fluctuationseasonal fluctu of DHWation thermalof DHW energy thermal demand energy due demand to climate due conditions,to climate theconditions, calculated the water calculated temperature water temperature in the tank wasin the set tank as input was set for as the input for the cut-othermostatff. Inlet cut-off. water temperatureInlet water temperature from the public from waterthe public network water was network set equal was to set ground equal to temperature ground temperature at 2 m depth at 2 bym meansdepth by of typemeans 77 of [32 type]. In 77 systems [32]. In 1,systems 2, and 3,1, 2, boiler and setpoint3, boiler temperaturesetpoint temperature was based was only based on HPWHonly on constraintsHPWH constraints (Table1) (Table and was 1) fixedand was at 63 fixed2 atC. 63 ± 2 °C. ± ◦ OnOn thethe otherother hand,hand, inin systemsystem 4,4, wheneverwhenever aa usefuluseful solarsolar contributioncontribution waswas availableavailable fromfrom thethe collectorcollector loop, temperature temperature in in the the boiler boiler was was allow alloweded to torise rise to tothe the maximum maximum value value (see (see Table Table 1) (881) (±88 2 °C);2 otherwise,C); otherwise, it was it was set according set according to the to theHPWH HPWH limits. limits. The The aim aim was was to exploit to exploit the the water water tank tank as ± ◦ asmuch much as aspossible possible for for the the storage storage of ofthe the available available solar solar thermal thermal source. source. TheThe overalloverall logicallogical schemescheme ofof simulationssimulations isis depicteddepicted inin FigureFigure4 4..

Figure 4.4. Trnsys modelmodel scheme.scheme.

AnalysesAnalyses were performed on yearly and monthly bases and for a typical day per each month, whichwhich waswas selectedselected according according to to the the median median daily daily irradiation irradiation values values on on a horizontala horizontal surface surface (Figure (Figure5). In5).Appl. fact,In Sci.fact, all 2020 the all, 10 solar the, x FOR collectorssolar PEER collectors REVIEW were considered were considered with a horizontal with a horizontal tilt angle totilt fulfill angle building to fulfill integration building10 of 24 andintegration landscape and protection landscape constraints. protection constraints.

Figure 5. Cont.

Figure 5. Analysis of specific horizontal irradiation values on Lampedusa Island, Italy (35°30′56″ north (N)).

2.4. Empirical Definition of Domestic Hot Water Tapping Profiles Figure 6 shows the average daily energy consumption per month calculated from monitored data for two users equipped with a conventional ESWH system. It is worth noting that, even if different magnitudes of values were observed, monthly data regarding the two detected users had similar decreasing trends from February until July/August. Furthermore, data for the month of September ere probably affected by the presence of a larger number of persons in the residential units.

Figure 6. Monitored data.

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Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 24

Appl. Sci. 2020, 10, 5968 10 of 24

Figure 5. Analysis of specific horizontal irradiation values on Lampedusa Island, Italy (35°30′56″ north (N)). FigureFigure 5. 5.Analysis Analysis ofof specific specific horizontal horizontal irradiation irradiation values values on on Lampedusa Lampedusa Island, Island, Italy Italy (35 (35°30◦30056′5600″ north (N)). 2.4. Empiricalnorth Definition (N)). of Domestic Hot Water Tapping Profiles 2.4. Empirical Definition of Domestic Hot Water Tapping Profiles Figure2.4. Empirical 6 shows Definition the average of Domestic daily Hot energy Water Tappingconsum Profilesption per month calculated from monitored Figure6 shows the average daily energy consumption per month calculated from monitored data data for twoFigure users 6 shows equipped the average with a daily conventional energy consum ESWHption system. per month It is calculatedworth noting from that,monitored even if for two users equipped with a conventional ESWH system. It is worth noting that, even if different differentdata magnitudes for two users of equippedvalues were with observed, a conventional monthly ESWH data system. regarding It is theworth two noting detected that, userseven ifhad magnitudes of values were observed, monthly data regarding the two detected users had similar similardifferent decreasing magnitudes trends offrom values February were observed, until Ju monthlyly/August. data Furthermore,regarding the two data detected for the users month had of decreasing trends from February until July/August. Furthermore, data for the month of September ere Septembersimilar ere decreasing probably trends affected from by February the presence until Juofly/August. a larger numberFurthermore, of persons data for in thethe month residential of probably affected by the presence of a larger number of persons in the residential units. units. September ere probably affected by the presence of a larger number of persons in the residential units.

Figure 6. Monitored data. FigureFigure 6. 6. MonitoredMonitored data. data.

Data were processed for determining the frequency of operation of the ESWH system during a typical tapping. Moreover, to obtain the most consistent tapping profile, hourly frequencies when the power values were below the daily median were excluded. Figure7 shows results in terms of percentage by hour the ESWH was “switched on” with respect to monitored data and to the introduced constraints (Figure7). Appl.Appl. Sci. 2020 Sci. 2020, 10,, x10 FOR, x FOR PEER PEER REVIEW REVIEW 11 of11 24 of 24

DataData were were processed processed for for determining determining thethe frequencyy of of operation operation of ofthe the ESWH ESWH system system during during a a typicaltypical tapping. tapping. Moreover, Moreover, to to obtain obtain the the most most consistentconsistent tapping tapping profile, profile, hourly hourly frequencies frequencies when when the the powerpower values values were were below below the the daily daily medianmedian were excluded.excluded. Figure Figure 7 7shows shows results results in termsin terms of of percentage by hour the ESWH was “switched on” with respect to monitored data and to the percentageAppl. by Sci. 2020hour, 10, 5968the ESWH was “switched on” with respect to monitored data11 ofand 24 to the introduced constraints (Figure 7). introduced constraints (Figure 7).

Figure 7. Tapping profile. Figure 7. Tapping profile. A Trnsys calibration routine wasFigure carried 7. out Tapping to fit theprofile. experimental data with calculations. The model wasA Trnsysrun, introducing calibration the routine tapping was carriedprofile outas hourly to fit the input. experimental Daily water data consumption with calculations. at 40 °C The model was run, introducing the tapping profile as hourly input. Daily water consumption at 40 C (input)A Trnsys was calibrationvaried until routinethe simulated was carried monthly out en toergy fit consumption the experimental (output) data matched with calculations. the recorded◦ The (input) was varied until the simulated monthly energy consumption (output) matched the recorded modelfigures was with run, a introducingrelative error thebelow tapping 5%. The profile hot water as hourly consumption input. forDaily the monitoredwater consumption consumer units at 40 °C figures with a relative error below 5%. The hot water consumption for the monitored consumer units (input) was varied until the simulated monthly energy consumption (output) matched the recorded variedvaried from from 90 90L Lper per day day in FebruaryFebruary to to 45 L45 per L dayper inday July in (user July 1) (user and from 1) and 180 Lfrom per day 180 in L February per day in figuresFebruary withto 120 ato Lrelative per120 dayL per inerror Septemberday below in September (user5%. The 2). Average(user hot water 2) values. Average consumption between values users between for were the successively monitoredusers were applied successivelyconsumer for units variedapplied fromdetermining for 90 determining L per a common day ain linearcommon February monthly linear to trend. 45monthly L This per was tren day calculatedd. inThis July was according (user calculated 1) to and Equation according from (2) 180 in to order LEquation per to day in February(2) inobtain orderto 120 the to L monthlyobtain per day the correction monthlyin September factor correction (fm,i (user) (Figure factor 2)8. ). Average(fm,i) (Figure values 8). between users were successively applied for determining a common linear monthly trend. This was calculated according to Equation (2) in order to obtain the monthly correction factor (fm,i) (Figure 8).

FigureFigure 8. DHW 8. DHW consumption consumption per per day day at at 40 40 °C◦C for analyzedanalyzed consumer consumer residential residential unit. unit. 3. Results 3. Results 3.1. Analysis of Heat Pump Water Heater Performance 3.1. AnalysisFigure of Heat 8. DHW Pump consumption Water Heater per Performance day at 40 °C for analyzed consumer residential unit. Comparing the simulation results and reference values of the technical data sheet, relative errorsComparing below 5%the weresimulation obtained. results COP and was reference calculated valu accordinges of the to international technical data standard sheet, procedures. relative errors 3. Results belowAs 5% suggested were obtained. by EN 16147:2017 COP was [38], ancalculated error below accord 10% foring the to energy international consumption standard in both warming-upprocedures. As suggestedcycles wasby EN obtained. 16147:2017 These [38], results an demonstratederror below 10% a good for accuracy the energy of the consumption model. in both warming- 3.1. Analysis of Heat Pump Water Heater Performance up cyclesAs was described obtained. in SectionThese 2results, before demo analyzingnstrated the proposeda good accuracy systems, of an the ordinary model. ESWH was also simulated in order to obtain electricity consumption reference values of 1137 kWh per year with As described in Section 2, before analyzing the proposed systems, an ordinary ESWH was also Comparingmonthly values the simulation varying from results 125 kWh and in January reference to 67 valu kWhes in of August the technical for the tapping data profile sheet, adopted. relative errors belowsimulated 5%The were simulated in obtained.order results to obtain forCOP system electricitywas 1 calculated were consumption compared accord with referenceing those to of international the values ESWH of (Figure 1137 standard 9kWh). per procedures. year with As suggested by EN 16147:2017 [38], an error below 10% for the energy consumption in both warming- up cycles was obtained. These results demonstrated a good accuracy of the model.

As described in Section 2, before analyzing the proposed systems, an ordinary ESWH was also simulated in order to obtain electricity consumption reference values of 1137 kWh per year with

Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 24 monthlyAppl. Sci. 2020 values, 10, x FORvarying PEER REVIEWfrom 125 kWh in January to 67 kWh in August for the tapping 12profile of 24 adopted. The simulated results for system 1 were compared with those of the ESWH (Figure 9). monthlyAppl. Sci.values2020, 10 varying, 5968 from 125 kWh in January to 67 kWh in August for the tapping12 of profile 24 adopted. The simulated results for system 1 were compared with those of the ESWH (Figure 9).

Figure 9. Comparison between electrical storage water heater (ESWH) and HPWH energy consumption. FigureFigure 9. 9.ComparisonComparison betweenbetween electrical electrical storage storage water heaterwater (ESWH) heater and (ESWH) HPWH energy and consumption.HPWH energy Itconsumption. is worth noting that, through the replacement of the conventional system with a heat pump, an averageIt iselectrical worth noting energy that, saving through equal the replacement to 65% could of the be conventionalachieved. This system is consistent with a heat with pump, the an rated COPaverage Itand is worththe electrical higher noting available energy that, saving through storage equal thecapacity to replacement 65% could due to be the achieved.of thehigher conventional This DHW is consistent tank system volume with with theof the rateda heat heat COP pump, pump and the higher available storage capacity due to the higher DHW tank volume of the heat pump system. system.an average In particular,electrical energy yearly savingenergy equal consumption to 65% co wasuld reducedbe achieved. from This 1137 is to consistent 375 kWh, with avoiding the rated 761 In particular, yearly energy consumption was reduced from 1137 to 375 kWh, avoiding 761 kWh kWhCOP andelectricity the higher withdrawals available fromstorage the capacity local grid. due It to is the worth higher noting DHW that, tank according volume of to the the heat technical pump electricity withdrawals from the local grid. It is worth noting that, according to the technical datasheet, datasheet, the considered HPWH was able to match the thermal demand of the so-called “L” tapping system.the consideredIn particular, HPWH yearly was energy able to matchconsumption the thermal was demand reduced of the from so-called 1137 to “L” 375 tapping kWh, profile avoiding [41]. 761 profile [41]. Therefore, it could deliver up to 11.66 kWh of thermal energy per day [42]. Results from kWhTherefore, electricity it withdrawals could deliver upfrom to 11.66 the local kWh ofgrid. thermal It is energyworth pernoting day [that,42]. Results according from to simulations the technical simulationsdatasheet,presented the presented inconsidered a previous in a HPWH previous work [ 5was,33 work,34 able] show [5,33,34] to match that, sh in theow the thermal that, worst in case thedemand (January),worst of case the the (January), so-called average “L” thermalthe averagetapping thermalprofiledemand [41]. demand Therefore, can be can about be it about 4.1could kWh 4.1 deliver of kWh thermal upof thermalto energy 11.66 per energykWh day. of per ther day.mal energy per day [42]. Results from simulations presented in a previous work [5,33,34] show that, in the worst case (January), the average 3.2.thermal Analysis3.2. demand Analysis of Stand-Al of can Stand-Alone beone about Photovoltaic Photovoltaic 4.1 kWh Systemsof Systems thermal energy per day. AccordingAccording to the to the present present work work purposes, purposes, four four stand-alonestand-alone configurations configurations (HPWH (HPWH (2.1), (2.1), (2.2), (2.2), (2.3),3.2. Analysis(2.3), and and(2.4)) of (2.4)) Stand-Al were were consideredone considered Photovoltaic to to outline outline Systems electrical electrical storagestorage behavior. behavior. Preliminary Preliminary simulations simulations were were useful for determining PV plant features to be tested. Looking at the results of simulations, January useful for determining PV plant features to be tested. Looking at the results of simulations, January andAccording December to appearthe present as the mostwork critical purposes, months four with stand-alone average daily configurations electrical consumption (HPWH equal (2.1), to (2.2), and December appear as the most critical months with average daily electrical consumption equal to (2.3),1.4 and kWh (2.4)) per were day (Figure considered 10). to outline electrical storage behavior. Preliminary simulations were 1.4useful kWh for per determining day (Figure PV 10). plant features to be tested. Looking at the results of simulations, January and December appear as the most critical months with average daily electrical consumption equal to 1.4 kWh per day (Figure 10).

Figure 10. Daily energy consumption for the system. Figure 10. Daily energy consumption for the system.

Figure 10. Daily energy consumption for the system.

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Moreover, the HPWHHPWH was switched on mainly in conjunction with tapping events in the early morning and in the evening. As mentioned above, the median value of irradiation was calculated. Based on these data, a day for each month characterizedcharacterized by irradiation figuresfigures closest to the median was selected. For these 12 days (one per month), th thee daily frequency of on and off off operation of the heat pump in the selected time range was evaluated. Figure 11 shows the percentage of time that the HPWH was “on” in an hour during thethe yearyear withwith respectrespect toto thethe adoptedadopted tappingtapping profile.profile.

Figure 11. Percentage of time that the HPWH was “on” in an hour during the year with respect to the adopted tapping profile.profile. To check the thermal storage behavior in operating conditions, further simulations were run. To check the thermal storage behavior in operating conditions, further simulations were run. In In this case, the energy produced by the PV plant was exclusively considered to drive the HP, this case, the energy produced by the PV plant was exclusively considered to drive the HP, without without any electrical storage support. Whenever the temperature tank dropped to the setpoint any electrical storage support. Whenever the temperature tank dropped to the setpoint value and, value and, simultaneously, whenever the power from the PV string was suitable to drive the cycle simultaneously, whenever the power from the PV string was suitable to drive the cycle without without relating to the electrical grid or battery, the model allowed the switching on of the HPWH. relating to the electrical grid or battery, the model allowed the switching on of the HPWH. As As described above, four different PV plant sizes were considered: 720 Wp, 1200 Wp, 1440 Wp, described above, four different PV plant sizes were considered: 720 Wp, 1200 Wp, 1440 Wp, and 1680 and 1680 Wp. They correspond to three, five, six, and seven PV panels, respectively. Table4 shows Wp. They correspond to three, five, six, and seven PV panels, respectively. Table 4 shows the plant the plant configuration with respect to the following features: number of days of autonomy (Naut) for configuration with respect to the following features: number of days of autonomy (Naut) for stand- stand-alone (SA) plants, inverter (PInv) and plant power (PPV), battery capacity (CSt), and number alone (SA) plants, inverter (PInv) and plant power (PPV), battery capacity (CSt), and number of PV of PV panels, for which characteristics could be inferred from Tables2 and3. It can be noted that panels, for which characteristics could be inferred from Tables 2 and 3. It can be noted that systems systems 2.3 and 2.4 were definitively oversized in order to use them as comparison terms with respect 2.3 and 2.4 were definitively oversized in order to use them as comparison terms with respect to to system 2.1 and system 2.2 considering that no battery storage is available. system 2.1 and system 2.2 considering that no battery storage is available. In Table4, the characteristics of the four selected PV plants (systems 2.1, 2.2, 2.3. and 2.4) are In Table 4, the characteristics of the four selected PV plants (systems 2.1, 2.2, 2.3. and 2.4) are listed. The last two plants were definitely oversized in order to use them as comparison terms. listed. The last two plants were definitely oversized in order to use them as comparison terms.

Table 4. PV plant features. Table 4. PV plant features. PV-plant Type; Naut PInv (W) PPV (Wp) CSt (Wh) No. of PV panels Ppanel (Wp) PV-plant Type; Naut PInv (W) PPV (Wp) CSt (Wh) No. of PV panels Ppanel (Wp) SystemSystem 2.1 SA; 2-4 1500 720 2400(a)/4800(b)2400(a)/4800(b) 3 3 240 240 SystemSystem 2.2 SA; 2-4 750 1200 2400(a)/4800(b)2400(a)/4800(b) 5 5 240 240 System 2.3 SA; 0 1500 1440 0 6 240 SystemSystem 2.3 2.4 SA; 0 20001500 16801440 0 7 6 240 240 SystemSystem 2.4 2.5 SA; GC 0 2000 750 1680 300 0 1 7 300 240 System 2.5 GC 750 300 0 1 300

It is possiblepossible to see inin FigureFigure 1212 thatthat allall plantplant configurationsconfigurations couldcould match the summer DHW demand (from May until October) withoutwithout discomfort events (month (monthlyly DI DI and PDI equal to 0%); moreover, asas seenseen byby lookinglooking atat thethe irradianceirradiance valuevalue (Figure5 5 in in Section Section2 )2) and and the the adopted adopted tapping tapping profileprofile (Figures(Figures7 7 and and9 9in in Section Section2), 2), winter winter months months appeared appeared the the most most critical. critical. The The next next step step was was to to calculate the discomfort indices DIDI andand PDIPDI (Figure(Figure 1212).).

Appl. Sci. 2020, 10, 5968 14 of 24 Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 24 Appl.Appl. Sci. Sci. 2020 2020, ,10 10, ,x x FOR FOR PEER PEER REVIEW REVIEW 1414 ofof 2424

Figure 12. Temperature trend with referencereference toto comfortcomfort limit.limit. FigureFigure 12.12. TemperatureTemperature trendtrend withwith referencereference toto comfortcomfort limit.limit. As in this case, the most critical results were recorded in December for the 720-Wp plant (system AsAs inin thisthis case,case, thethe mostmost criticalcritical resultsresults werewere recordedrecorded inin DecemberDecember forfor thethe 720-Wp720-Wp plantplant (system(system 2.1) because of the small size of PVPV generatorgenerator compared to the HP nominal power and to the low 2.1)2.1) becausebecause ofof thethe smallsmall sizesize ofof PVPV generatorgenerator comparedcompared toto thethe HPHP nominalnominal powerpower andand toto thethe lowlow valuesvalues ofof irradiation.irradiation. A higher PV plant power obviouslyobviously leadsleads toto betterbetter resultsresults (Figure(Figure 1313).). valuesvalues ofof irradiation.irradiation. AA higherhigher PVPV plantplant powerpower obviouslyobviously leadsleads toto betterbetter resultsresults (Figure(Figure 13).13).

Figure 13. Yearly comfort indices for the tested PV plants. FigureFigure 13. 13. YearlyYearly comfort comfort indicesindices forfor thethe testedtested PVPV plants.plants. Nevertheless, an auxiliary electrical load would be necessary to avoid oversizing of the PV Nevertheless,Nevertheless, ananan auxiliary auxiliaryauxiliary electrical electricalelectrical load loadload would wouldwould be necessarybebe necessarynecessary to avoid toto avoidavoid oversizing oversizingoversizing of the PVofof the respectthe PVPV respect to the HPWH nominal power. In any case, using the plant characterized by a power of 1200 respecttorespect the HPWH toto thethe HPWHHPWH nominal nominalnominal power. power.power. In any InIn case, anyany using case,case, usingusing the plant thethe plantplant characterized characterizedcharacterized by a by powerby aa powerpower of 1200 ofof 12001200 Wp Wp (system 2.2), the contemporaneity between the energy needed for DHW production and PV Wp(systemWp (system(system 2.2), 2.2), the2.2), contemporaneity thethe contemporaneitycontemporaneity between betweenbetween the energy thethe energyenergy needed neededneeded for DHW forfor DHW productionDHW productionproduction and PV andand useful PVPV useful production reached values higher than 90% (Figure 14). usefulproductionuseful productionproduction reached reachedreached values values highervalues higher thanhigher 90% thanthan (Figure 90%90% (Figure (Figure14). 14).14).

Figure 14. Contemporaneity between DHW production load and PV useful production. FigureFigureFigure 14. 14. ContemporaneityContemporaneity between between DHW DHW production production load load andand PVPV usefuluseful production.production.

Appl. Sci. 2020, 10, 5968 15 of 24

Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 24 Figure 15 shows the results obtained for discomfort and storage indices in the most critical month (December)Figure for15 theshows SA systems.the results obtained for discomfort and storage indices in the most critical month (December) for the SA systems.

Figure 15. Temperature and battery indices.indices.

ItIt is worth noting noting that, that, except except for for the the HPWH HPWH + +STST (2.1a) (2.1a) systems, systems, all allother other SA SAsystems systems with with PV PVplants plants allowed allowed satisfying satisfying comfort comfort conditions, conditions, with with PDI PDIand andDI indices DI indices equal equal to 0%. to 0%.This Thismeans means that thattank tanktemperature temperature never never dropped dropped below below the 40 the °C 40 co◦mfortC comfort limits. limits. On the On other the otherhand, hand,only the only 1200- the 1200-WpWp plants plants were werealmost almost suitable suitable to preserve to preserve the temperature the temperature as close as closeas possible as possible to the to setpoint the setpoint one. one.Finally, Finally, focusing focusing on the on thestorage storage indices, indices, some some differences differences among among analyzed analyzed systems systems could could bebe underlined (Figure 1616).). Remembering that the BImin index was introduced to evaluate critical situations in which the state of charge drops to the minimum value (HPWH daily consumption), it can be noted that it varied from 68% for the HPWH + ST (2.2a) plant to 0% for the HPWH + ST (2.1b) one. Intermediate values, almost acceptable, were calculated for the HPWH + ST (2.1b) and HPWH + ST (2.2a) systems, with 26% and 44%, respectively. On the other hand, the BIMAX and FSOCav indicate how electric storage was exploited in the critical month. In this way, some oversizing conditions were highlighted for the HPWH + ST (2.2b) configuration (73%). Actually, a higher BIMAX denotes a higher time when the state of charge is close to the battery nominal capacity, indicating that it was not properly used in the system. Summarizing from the present analysis, the HPWH + ST (2.2a) system had the worst performance because it weakly matched comfort requirements. On the other hand, the HPWH + ST (2.1b) system resulted to be oversized with respect to DHW load demand fulfilled by the HPWH. Finally, the GC (2.5) system accounted for a 300-Wp panel. The simulation results show that system 2.5 can annul the yearly consumption of non-renewable primary energy since the PV plant entirely produces the electricity required by the HPWH. Nonetheless, despite the peak power of the system being less than the power required by HPWH, all the produced energy is sold back to the utility. Economic consequences are investigated in Section 3.4.

Appl. Sci. 2020, 10, 5968 16 of 24 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 24

Figure 16. Temperature indices and storage temperatures for solar thermal systems without electric Figure 16. Temperature indices and storage temperatures for solar thermal systems without electric back up. back up. 3.3. Analysis of Solar Thermal System Assisted Water Heaters Remembering that the BImin index was introduced to evaluate critical situations in which the stateSimilarly of charge to drops the PV to the plant minimum investigation, value (HPWH a preliminary daily consumption), check concerning it can the be temperature noted that it indices varied relatedfrom 68% to the forsolar the HPWH thermal + systemsST (2.2a) was plant carried to 0% out for withoutthe HPWH considering + ST (2.1b) any one. back-up. Intermediate values, almostIt is acceptable, worth noting were that, calculated also in for this the case, HPWH during + ST tapping (2.1b) events,and HPWH the comfort+ ST (2.2a) conditions systems, were with generally26% and ensured44%, respectively. all year long On (Figure the other 15), hand, while the potential BIMAX discomfortand FSOCav conditions indicate how were electric recorded storage only inwas winter exploited months. in the On critical the other month. hand, In considering this way, some a setpoint oversizing temperature conditions of 65were◦C, highlighted it has to be for noted the thatHPWH the SPI+ ST index (2.2b) had configuration average yearly (73%). values Actually, of 53% a whilehigher it BI reachedMAX denotes 0% in a winter higher months. time when This the means state thatof charge the solar is thermalclose to systemthe battery was notnominal able to capacity, continuously indicating ensure that the it setpoint was not temperature properly used in the in tank the (Figuresystem. 15 Summarizing). Two alternative from back-up the present electrical-based analysis, systemsthe HPWH were + consequently ST (2.2a) system introduced. had the Firstly, worst a typicalperformance 2-kW electricalbecause it resistance weakly matched was provided comfort in therequirements. tank (ST (4) On system). the other Moreover, hand, the the HPWH previously + ST studied(2.1b) system heat pump resulted water to heaterbe oversized was coupled with respect with a solarto DHW thermal load loopdemand (HPWH fulfilled+ ST by (3)). the Figure HPWH. 17 showsFinally, the the comparison GC (2.5) system between accounted the electrical for a consumption 300-Wp panel. results The ofsimulation the simple results HPWH show and that the resultssystem for2.5 thecan ST annul (4) and the HPWH yearly +consumptST (3) systems.ion of non-renewable Taking as a reference primary the energy HPWH since results, the thePV STplant (4) entirely system ledproduces to an extra the electricity 4% energy required consumption by the from HPWH. the grid, Nonetheless, while the despite HPWH the+ ST peak (3) systempower of allowed the system 58% electricalbeing less saving. than the Regardless power required of the choice by HPWH, of electrical all th back-up,e produced the adoption energy is of sold solar back thermal to the collectors utility. ledEconomic to achieving consequences tank temperatures are investigated generally in Section included 3.4. between 65 and 80 ◦C (SPI index in Figure 17 with yearly average figures of 70% and 11%). 3.3. Analysis of Solar Thermal System Assisted Water Heaters Similarly to the PV plant investigation, a preliminary check concerning the temperature indices related to the solar thermal systems was carried out without considering any back-up. It is worth noting that, also in this case, during tapping events, the comfort conditions were generally ensured all year long (Figure 15), while potential discomfort conditions were recorded only in winter months. On the other hand, considering a setpoint temperature of 65 °C, it has to be noted that the SPI index had average yearly values of 53% while it reached 0% in winter months. This means that the solar thermal system was not able to continuously ensure the setpoint temperature in the

Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 24

tank (Figure 15). Two alternative back-up electrical-based systems were consequently introduced. Firstly, a typical 2-kW electrical resistance was provided in the tank (ST (4) system). Moreover, the previously studied heat pump water heater was coupled with a solar thermal loop (HPWH + ST (3)). Figure 17 shows the comparison between the electrical consumption results of the simple HPWH and the results for the ST (4) and HPWH + ST (3) systems. Taking as a reference the HPWH results, the ST (4) system led to an extra 4% energy consumption from the grid, while the HPWH + ST (3) system allowed 58% electrical saving. Regardless of the choice of electrical back-up, the adoption of solar Appl.thermal Sci. 2020 collectors, 10, 5968 led to achieving tank temperatures generally included between 65 and 8017 °C of 24(SPI index in Figure 17 with yearly average figures of 70% and 11%).

Figure 17. Top: electrical consumption of the systems; bottom: monthly setpoint index (SPI). Figure 17. Top: electrical consumption of the systems; bottom: monthly setpoint index (SPI). 3.4. Economic Analysis and Comparison between Systems 3.4. Economic Analysis and Comparison between Systems The previous results demonstrated in which ways the selected plants could ensure comfort conditionsThe while previous exploiting results the demonstrated thermal and/ orin electricalwhich wa storageys the capacityselected ofplants the systems. could ensure For the comfort sake of clarity,conditions the followingwhile exploiting systems the were ther analyzed:mal and/or electrical storage capacity of the systems. For the sake of clarity, the following systems were analyzed: System (1), HPWH + grid: heat pump water heater without any RES plant assistance; • • System (1), HPWH + grid: heat pump water heater without any RES plant assistance; System (2.1a), HPWH + PV, heat pump water heater with a PV plant having 2400 Wh storage • • System (2.1a), HPWH + PV, heat pump water heater with a PV plant having 2400 Wh storage capacity and 720 Wp capacity and 720 Wp System (2.2b), HPWH + PV, heat pump water heater with a PV plant having 2400 Wh storage • • System (2.2b), HPWH + PV, heat pump water heater with a PV plant having 2400 Wh storage capacity and 1200 Wp capacity and 1200 Wp System (2.5), HPWH + GC PV, heat pump water heater with a 300-Wp PV plant directly connected • • System (2.5), HPWH + GC PV, heat pump water heater with a 300-Wp PV plant directly to the grid; connected to the grid; System (3), HPWH + ST: heat pump water heater coupled with a solar thermal plant • • System (3), HPWH + ST: heat pump water heater coupled with a solar thermal plant • System (4), ST plant: commercial solar thermal plant relying on a solar thermal collector with an • System (4), ST plant: commercial solar thermal plant relying on a solar thermal collector with an electricalelectrical resistance resistance back-up back-up and and DHW DHW tank tank SystemsSystems HPWH HPWH (2.1b) (2.1b) and and HPWH HPWH (2.2a) (2.2a) were were “discarded” “discarded” because because the the sizing sizing was was not not proper. proper. FromFrom the the energy energy saving saving point point of view, of view, taking taking as a reference as a reference an ordinary an ordinary ESWH ESWH system system (with 1137 (with kWh 1137 electrical consumption per year), all plants achieved energy savings in a range from 100% for the PV plants to 86% for the HPWH + ST (3) system, with an average of 66.5% for the HPWH and ST (4) system (Figure 18). Appl. Sci. 2020,, 10,, xx FORFOR PEERPEER REVIEWREVIEW 18 of 24 kWh electrical consumption per year), all plants achieved energy savings in a range from 100% for Appl. Sci. 2020, 10, 5968 18 of 24 the PV plants to 86% for the HPWH + ST (3) system,, withwith anan averageaverage ofof 66.5%66.5% forfor thethe HPWHHPWH andand STST (4) system (Figure 18).

Figure 18. Comparison of the DHW energy saving.

DiDifferencesfferences could be be noted noted when when looking looking at at econom economicic indices. indices. In InFigure Figure 19 and19 and in Table in Table 5, the5, thecalculated calculated net netpresent present value value and and the the payback payback time time (PBT)(PBT) (PBT) forfor for thethe the proposedproposed proposed systemssystems systems areare are reported.reported. System initial costs were estimatedestimated viavia anan analysis ofof the Italian Italian market market [[43,44[43,4443,44].]. The The average average electricity electricity cost from aa user’suser’s bill was considered in the calculationcalculation (0.23 €€/kWh),/kWh), while the sellingselling price for thethe producedproduced electricityelectricity forfor thethe grid-connectedgrid-connected PVPV plantplant waswas consideredconsidered equalequal toto 0.100.10 €€/kWh./kWh.

Figure 19. Cash flow flow and net present value of selected solutions (without national incentive).incentive).

A 20-year useful lifetimelifetime waswas assumedassumed forfor allall thethe plants.plants. First of all, it can can be be noted noted that, that, if if no no public public subsidy subsidy is is considered, considered, stan stand-aloned-alone PV PV plants plants show show a anegative negative cash-flow cash-flow rate, rate, with with a aconsequently consequently negative negative NPV NPV (Figure (Figure 19).19). At At the the same time, thesethese systems present thethe worstworst paybackpayback time,time, higherhigher thanthan 2121 years.years. On On the otherotheother hand, allall otherother systemssystems presentpresent positivepositive NPVNPV varying from 760 €€ forfor thethe HPWHHPWH systemsystem to 1902 € forfor thethe solarsolar thermalthermal plant withwith electricelectric back-up.back-up. ST ST (4) and HPWH + gridgrid (1) (1) systems, despite simi similarlar energy saving values, strongly didifferffer in NPVNPV and in PBT, withwith the latter having the lowest value, i.e., half of of the the first. first. Finally, Finally, lowlow didifferencesfferences couldcould bebe notednoted inin allall figuresfigures betweenbetween thethe GCGC (2.5)(2.5) andand STST (4)(4) plants.plants.

Table 5.5. Payback time and net present valuevalue (without(without nationalnational incentive).incentive).

HPWH HPWHHPWH ++ +GridGridGrid (1)(1) (1) HPWH HPWH HPWH (2.1a)(2.1a) HPWH HPWH (2.1.b) (2.1.b)(2.1.b) GC GC GC (2.5) (2.5)(2.5) HPWH HPWH HPWH (3) (3)(3)ST ST ST (4) (4)(4) PBTPBT (years) (years) 15.2 15.2 24.1 24.1 21.6 21.6 13.1 13.1 14.7 14.7 7.6 7.6 NPV (€) 769 974 384 1.405 1065 1902 NPV (€) 769 −−974 −−384 1.405 1065 1902

Appl. Sci. 2020, 10, 5968 19 of 24

Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 24 The Italian incentive mechanism for such a system allows for some reduction in the purchase price forThe plant Italian components incentive tomechanism be distributed for such in 10 a yearlysystem payments.allows for Incentivesome reduction values in vary the frompurchase 50% to 65%price for for PV plant components components and forto be ST distributed and HPWH in components,10 yearly payments. respectively. Incentiv Undere values such vary circumstances, from 50% allto systems 65% for have PV a positivecomponents net presentand for value ST estimatedand HPWH at 20components, years (Figure respectively. 20). Under such circumstances, all systems have a positive net present value estimated at 20 years (Figure 20).

Figure 20. Cash flow and net present value of selected solutions (with national incentive). Figure 20. Cash flow and net present value of selected solutions (with national incentive). The best NPV is associated with the HP coupled with a stand-alone PV system and a small battery The best NPV is associated with the HP coupled with a stand-alone PV system and a small (system HPWH (2.1b)) and the solar thermal-assisted HP (system HPWH + ST (3)). The shortest battery (system HPWH (2.1b)) and the solar thermal-assisted HP (system HPWH + ST (3)). The payback time was calculated for the solar thermal system (Table6). shortest payback time was calculated for the solar thermal system (Table 6).

Table 6. Payback time and net present value (national incentive). Table 6. Payback time and net present value (national incentive).

HPWHHPWH ++ GridGrid (1) (1) HPWH HPWH (2.2a) (2.2a) HPWH HPWH (2.1b) GC (2.5)(2.5) HPWH (3)(3) ST ST (4)(4) PBTPBT (years) (years) 6.9 6.9 11.9 11.9 9.5 12.1 6.76.7 3.63.6 NPVNPV (€) (€) 2357.02 2357.02 2280.30 2280.30 3015.43 1620.35 3061.53 2719.032719.03

4.4. Conclusions Conclusions InIn this this paper, paper, the the use use of heatof heat and and electricity electricity storage, storage, as well as well as solar as solar thermal thermal and photovoltaicand photovoltaic panels topanels be coupled to be to coupled a heat pump,to a heat was pump, investigated. was investigated. To do this, To four do technologiesthis, four technologies from the marketplace from the weremarketplace chosen, simulated, were chosen, and simulated, analyzed: and a heat analyzed: pump a water heat pump heater water connected heater toconnected the grid, to a heatthe grid, pump watera heat heater pump coupled water heater with a coupled photovoltaic with a plant, photovoltaic a heat pump plant, water a heatheater pump coupledwater heater with coupled a solar thermalwith a solar thermal collector, and a typical solar thermal plant. First of all, the electricity consumption of collector, and a typical solar thermal plant. First of all, the electricity consumption of an ordinary an ordinary ESWH for a family on Lampedusa Island was calculated through simulation (yearly 1137 ESWH for a family on Lampedusa Island was calculated through simulation (yearly 1137 kWh, varying kWh, varying from 125 kWh in January to 67 kWh in August). This value was used as a reference to from 125 kWh in January to 67 kWh in August). This value was used as a reference to calculate the calculate the energy savings achievable with the other systems. It was found that the replacement of energy savings achievable with the other systems. It was found that the replacement of the reference the reference system with an electric heat pump could provide an average energy saving equal to system65%. withIndeed, an in electric this case, heat the pump yearly could energy provide consum an averageption can energy be reduced saving from equal 1137 to 65%. to 375 Indeed, kWh, in thisavoiding case, the 761 yearly kWh energy of electricity consumption withdrawal can befrom reduced the local from grid. 1137 Regarding to 375 kWh, the avoiding heat pump 761 water kWh of electricityheater coupled withdrawal with a from PV plant, the local four grid.further Regarding stand-alone the and heat one pump grid-connected water heater photovoltaic coupled with plants a PV plant,were four considered. further stand-alone Moreover, andtwo one solar grid-connected thermal-based photovoltaic systems introduced: plants were one considered. coupled with Moreover, an twoelectrical solar thermal-based back-up resistance systems (called introduced: ST (4)) and one th couplede other with with the an heat electrical pump back-up itself (called resistance HPWH (called + STST (4)) (3)). and Firstly, the other all proposed with the solar heat assisted pump itselfplants (called were run HPWH without+ ST accounting (3)). Firstly, for electrical all proposed storage solar assisted(photovoltaic plants wereplants) run or a without back-up accounting system (solar for thermal electrical plant) storage in order (photovoltaic to check for plants)their performance or a back-up systemby means (solar of thermal a set of plant) comfort in orderindices. to checkBased foron theirthe comfort performance conditions, by means the most of a set suitable of comfort size for indices. a Basedstand-alone on the comfort PV-plant conditions, was detected. the mostSome suitablecomfort sizeissues for were a stand-alone detected for PV-plant the systems was with detected. 720 Wp. Some comfortwhile a issues peak power were detected of 1200 Wp for could the systems dramatically with 720mitigate Wp. such while a aproblem. peak power Then,of two 1200 alternative Wp could dramaticallyelectric storages mitigate were such evaluated a problem. through Then, a two calcul alternativeation of electricvalues storagesfor the “battery were evaluated indices”. through The a calculationfollowing PV-based of values plants for the were “battery then selected: indices”. a Thesystem following characterized PV-based by a plants power were of 1200 then Wp selected: and a a systemstorage characterized capacity of 2400 by a Wh power (called of 1200 HPWH Wp (2.1a)) and a storageand system capacity characterized of 2400 Wh by a (called power HPWH of 720 Wp (2.1a)) andand system a storage characterized capacity of 4800 by a Wh power (called of 720HPWH Wp (2.2b)). and a storageSimilarly, capacity the ST plant of 4800 was Wh firstly (called evaluated HPWH

Appl. Sci. 2020, 10, 5968 20 of 24

(2.2b)). Similarly, the ST plant was firstly evaluated by means of comfort indices. The results showed that, if back-up systems are not included in the systems, setpoint temperature could only not be maintained in the tank during winter months and some potential discomfort events could be detected. By using the system characterized by 1200 Wp, the contemporaneity between the energy needed for domestic hot water production and PV useful yield achieved values higher than 90%. Looking at the comparison between the electrical consumption of the electricity-driven pump water heater and those driven by the solar thermal (called ST (4)) and the pump water heater coupled with solar thermal systems (called HPWH + ST (3)), the solar thermal (called ST (4)) one achieved an extra 4% of energy taken from the grid. By comparing the pump water heater consumption with that of the pump water heater coupled with solar thermal systems (called HPWH + ST (3)), a 58% reduction was evaluated. In general, from an energy-saving point of view, all plants achieved energy savings concerning the traditional electric storage water heater in use, varying from 100% for the selected photovoltaic plants to 86% for the pump water heater coupled with solar thermal systems (called HPWH + ST (3)), with an average 66.5% for the solely pump water heater and solar thermal systems (ST (4)). For all of them, an economic analysis was performed in order to select the most affordable in economic terms. Net present value and payback time for the proposed systems were evaluated. When not considering the national economic incentives, the stand-alone photovoltaic plants showed a negative cash-flow rate with a consequently negative net present value. Contrariwise, the other analyzed domestic hot water plant plants led to positive net present values varying from 760 € for the solely pump water heater (payback time = 15.1) to 1902 € for the solar thermal plant with an electrical heater back-up (payback time = 7.6). If Italian incentives are considered, the net present value is strongly reduced and the values are positive for all analyzed plants. From an energy-saving point of view, the most promising plants include the use of the pump water heater coupled with a proper photovoltaic (100% energy saving) or solar thermal plant (86% energy saving). This fact is verified even if the photovoltaic plant needs an incentive support to be economically attractive. Similarly, the PBT calculated for the pump water heater-based plant shows a value close to the estimated useful life for the plant (14.7 vs. 20 years), if national incentives are not considered. On the other hand, the electric storage water heater with a solar plant, ensuring 66% of energy saving, should have the highest economic advantages in terms of net present value and payback time, even if no incentives are taken into account. Based on the presented results, it would be of interest to test hybrid solar–thermal technologies in order to optimize RES plant support for DHW production by means of an HPWH system. At the same time, new kinds of heat pumps are currently being commercialized. These are split technology pumps with instantaneous production of DHW by means of a wrap-around heat exchanger. Furthermore, they are tested to nominally ensure a larger DHW thermal energy demand (between 19.07 and 24.53 kWh per daily tapping with greatest tapping events equal to 4.42 and 6.24 kWh, respectively) with respect to the here-studied HPWH (11.665 kWh per daily tapping with greatest tapping event in a day equal to 3.605 kWh). Considering that the current research focused on a small island’s residential DHW provision, it would also be of interest to test a split HPWH coupled with a hybrid plant producing DHW for micro-communities in islands made up of few families living in small blocks.

Author Contributions: Data curation, M.B. (Marina Bonomolo) and G.L.; formal analysis, F.M.; project administration, M.B. (Marco Beccali) and B.D.P. All authors have read and agreed to the published version of the manuscript. Funding: The study presented was funded by ENEA (Italian National Agency for New Technologies, Energy, and Sustainable Economic Development) in the framework of the projects “Technologies for building buildings of the future”. Acknowledgments: The study presented is partially based on the result of a collaboration between ENEA (Italian National Agency for New Technologies, Energy, and Sustainable Economic Development) and the DII (Department of Engineering) of the University of Palermo in the framework of the projects “Technologies for building buildings of the future”, Annual Implementation Plan 2016, Simulation and comparison of technologies for air conditioning and domestic hot water installed at the end-users of smaller islands not connected to the national grid in order Appl. Sci. 2020, 10, 5968 21 of 24 to reduce energy costs and make the island’s electrical system more efficient, and Annual Implementation Plan 2017, Experimental and numerical analysis of solar driven technologies for air conditioning and the production of DHW and ICT systems for control and reduction of electrical loads in the smaller islands not connected to the national grid. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

BAC building automation control BIMAX Maximum allowed energy charged for the chosen value of battery index BImin Minimum allowed energy charge value for the chosen value of battery index CHP Combined heat and power COP Coefficient of performance CSt Storage capacity DHW Domestic hot water DI Discomfort index DSM Demand-side management Ebattery State of charge ESI Electric storage index ESWH Electrical storage water heater fm,i Monthly correction factor FSOCav Average fractional state of charge GC Grid-connected HPWH Heat pump water heater HPWH + grid Heat pump water heater combined with grid supply HPWH + ST Heat pump water heater combined with solar thermal plant Imp Current at maximum power mDHW Domestic hot water mass flowrate @ 40 ◦C NPV Net present value NZEB Net zero energy building PBT Payback time PDI Potential discomfort index Pinv Inverter deliverable power Pmp Power at maximum power Ppanel PV panel declared peak power PPV PV plant power PV Photovoltaic RES Renewable energy sources SA Stand-alone SOCMAX Maximum value of the state of charge in the battery SOCmin Minimum value of the state of charge in the battery SPI Setpoint index SPT Simple payback time ST Solar thermal SWOT Strengths, weaknesses, opportunities, and threats TDHW Outlet tank temperature of domestic hot water system VDHW,max Maximum valued of volume demand of domestic hot water VDHW,min Minimum valued of volume demand of domestic hot water Vmp Voltage at maximum power Appl. Sci. 2020, 10, 5968 22 of 24

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