Thermal Performance of Dwellings with Rooftop PV Panels and PV/Thermal Collectors

energies

Article Thermal Performance of Dwellings with Rooftop PV Panels and PV/Thermal Collectors

Saad Odeh

Senior Program Convenor, Sydney Institute of Business and Technology, Sydney City Campus, Western Sydney University, NSW 2000, Australia; [email protected] or [email protected]; Tel.: +61-2-8236-8075 Received: 22 June 2018; Accepted: 17 July 2018; Published: 19 July 2018

Abstract: To improve the energy efficiency of dwellings, rooftop photovoltaic (PV) technology is proposed in contemporary designs; however, adopting this technology will add a new component to the roof that may affect its thermal balance. This paper studies the effect of roof shading developed by solar PV panels on dwellings’ thermal performance. The analysis in this work is performed by using two types of software packages: “AccuRate Sustainability” for rating the energy efficiency of a residential building design, and “PVSYST” for the solar PV power system design. AccuRate Sustainability is used to calculate the annual heating and cooling load, and PVSYST is used to evaluate the power production from the rooftop PV system. The analysis correlates the electrical energy generated from the PV panels to the change in the heating and cooling load due to roof shading. Different roof orientations, roof inclinations, and roof insulation, as well as PV dwelling floor areas, are considered in this study. The analysis shows that the drop in energy efficiency due to the shaded area of the roof by PV panels is very small compared to the energy generated by these panels. The analysis also shows that, with an increasing number of floors in the dwelling, the effect of shading by PV panels on thermal performance becomes negligible. The results show that insensitivity of the annual heating and cooling load to the thermal resistance of rooftop solar systems is only because the total thermal resistance is dominated by roof insulation.

Keywords: energy efﬁciency; roof shading; thermal performance; PV panel; PV/thermal collector

1. Introduction In building sustainability designs, three major assessments are considered: thermal performance, energy efficiency, and water conservation. The major factors affecting the thermal performance of buildings are basically related to the building architecture design, such as: the roof type (e.g., gable or flat), the roof orientation, shading from adjacent objects, building materials (e.g., double brick or brick veneer walls), insulation, and glazing. In cold-weather zones, shading the building’s façade or roof may reduce the heat gain of the building and increase the heating load during the cold season. On the other hand, in hot- or warm-weather zones, shading a building’s façade and/or the roof will reduce the cooling load and increase the building’s thermal performance. The effect of PV panels’ shading on heat transfer through a flat roof building was simulated and tested by [1]. Part of the roof was covered with PV panels and a ceiling temperature measurement was conducted to verify and validate the mathematical heat transfer model. The study showed that the reduction in cooling load due to the shaded roof by a PV panel is more than the reduction in heating load which enhances the annual net energy balance of the building by 4%. Another work by Kotak et al. [2] studied the effect of rooftop PV panels on the cooling load of a flat roof house using a computer simulation. The results show that there is a significant decrease in the cooling load due to the roof area shaded by PV panels. However, the heat transfer model in this study did not consider insulation to the roof or ceiling below the PV panels.

Energies 2018, 11, 1879; doi:10.3390/en11071879 www.mdpi.com/journal/energies Energies 2018, 11, 1879 2 of 14

A simulation model has been developed to evaluate cooling load and heat gain components through an inclined PV roof structure [3]. It was found that installing a PV rooftop may reduce the cooling load by 35% for the roof design considered in that work (a gable roof without a significant insulation layer). The air gap between PV panels and roof surface as well as the roof inclination angle were found to be major factors affecting the thermal and energy performance of the building. A thermal model for an inclined PV panel mounted on a ventilated structure was developed by [4]. This model evaluated the total heat loss coefficient of the panel surface and predicted its temperature response time. The study, which was validated by an experimental test, showed that heat loss by radiation between the panel surface and the sky is very low compared to the convective heat loss and it can be neglected in the thermal model. Roof orientation and inclination has a significant effect on solar heat gain as well as the power generated by the rooftop PV system. A review of the optimum tilt and azimuth angles of a rooftop PV panel was conducted considering climate conditions and surrounding obstacles [5]. The study concluded that the optimum tilt angle is closer to the location latitude if the clearness index value is constant during the year. It was observed that the optimum tilt and azimuth angle of the PV panel was influenced significantly by the surrounding obstacles, such as adjacent buildings. Another analytical study was conducted on a larger scale system (50 kW output) and concluded that the maximum PV panel yield occurs when the PV panel tilt angle is about 1.5◦ less than the site latitude angle [6]. The impact of roof design on the output of an urban building solar energy system (hot water of electricity) was studied by [7]. Three types of roof designs were considered in this study: flat, gabled, and lean-to-roof. The results showed that the contribution of solar energy to covering the demand of hot water and electricity of a building is higher in case of the flat roof than the gabled roof design. This is because, in the case of the gabled roof, there will be less irradiation on the side of the roof opposing the sun. The optimal configuration in the roof of the housing unit was implemented to increase the solar potential of the building’s integrated PV/Thermal system [8]. The effect of the roof configuration shape on energy performance in terms of heating and cooling load was investigated by computer modelling. It was found that the effect of different roof designs on heating and cooling loads is less than 5%. However, it was concluded that the integration of a PV/thermal system in the roof design of different orientations enables the spread of peak electricity timing over longer operation hours. This work did not show how to overcome the complexity in the PV rooftop installation associated with a folded roof design. A breakdown of heat loss and heat gain rate by a house envelope was investigated by [9]. They found that the highest amount of heat loss rate takes place in the ceiling/roof and represents 62% of the total heat loss from the building envelope. The heat gain rate by the ceiling/roof was found to be significant and represents 33.5% of the total heat gain rate by the building envelope. The literature review of rooftop PV systems does not show significant analysis of designs that have a roof space with insulation. Since the majority of roof designs in Australia have roof space, research work in this respect was found to be necessary to find the effect of the roof shaded area by PV panels on the energy efficiency of the dwellings. This paper studies the effect of shading developed by rooftop PV panels on the cooling and heating load. The proposed analysis correlates the electric energy generated from the PV panels to the heating and cooling load of a dwelling with a roof space design at different roof orientation angles.

2. Thermal Modelling of the Roof The type of roof considered in this study is a gabled roof with a PV panel arrangement similar to the design shown in Figure1. Thermal modelling for this design can be developed by considering the thermal resistance of different components between the external air and the inner space of the dwelling. There are nine major thermal resistances identiﬁed in this roof design, these are:

R1 Thermal resistance of external air adjacent to the roof surface. R2 Thermal resistance of PV panel or PV/thermal collector material. Energies 2018, 11, 1879 3 of 14

R3 Thermal resistance of the air space between a panel and the roof surface. R4 Thermal resistance of roof material (tiles or metal sheet). R5 Thermal resistance of the air gap between the roof material and a sarking sheet. R6 Thermal resistance of a gabled roof space. R7 Thermal resistance of the insulation above the ceiling. R8 Thermal resistance of ceiling material. R9 Thermal resistance of the inner space air adjacent to the ceiling. Some of these thermal resistances are quite standard and can be selected from tables based on the roof type and roof design, such as R4, R5, R6, R7, R8, and R9 [10]. The thermal resistance R2 can be calculated by adopting the PV module thermal conductivity given by [3,4]. The remaining thermal resistances R1 and R3 are affected by surrounding conditions and can be calculated by using conventional heat transfer formulas [11]. To find R1, two components of heat transfer coefficients are considered: the heat transfer coefficient by convection of the ambient air, and the heat transfer coefficient by radiation with sky temperature,

1 2 ◦ R1 = (m · C/W) (1) hc1 + hr1 where hc1 and hr1 are the heat transfer coefﬁcients by convection and radiation, respectively, and can be found by [11], k h = ( a )Nu1 (W/m2·◦C) (2) c1 L where Nu1 is the Nusselt number,

Nu1 = (0.037 × Re0.8 − 871) × Pr1/3 (with wind). (3)

Or, u1 = 0.59 × Ra1/4 (with no wind) (4) where Pr is the Prandtl number, Re is the Reynolds number, Ka is the thermal conductivity of air (W/m2·◦C), L is the PV array length (m), and Ra is the Rayleigh number found by [10]

L3 Ra = 9.81 × βt × (T − Trs) × ( ) × Pr (5) pb υ2 where v = kinematic viscosity of the ﬂuid (m2/s)

Trs = temperature of the roof surface, −1 βt = Thermal expansion = 1/Ta [K ], Tpb = Temperature of the PV panel’s back surface found by [3], and, Irr 3 T = T − ( ) (K) (6) pb pv 1000 where Tpv is the PV surface temperature given by [12] and is found by,

Tpv = Ta + (0.022)Irr (K) (7)

2 where Irr is the solar irradiation (W/m ) and Ta is the ambient temperature (K).

2 2 2 ◦ hr1 = ε pvσ(Tpv + Tsky)(Tpv + Tsky)(W/m · C) (8) where Energies 2018, 11, 1879 4 of 14

εpv = EmissivityEnergies 2018 of, 11 the, x FOR PV PEER panel’s REVIEW upper surface, 4 of 14 σ = Stefan–Boltzmann constant (5.670367 × 10−8 W·m−2·K−4), σ = Stefan–Boltzmann constant (5.670367 × 10−8 W·m−2·K−4), Tsky = Sky temperature (K) found by [13], Tsky = Sky temperature (K) found by [13],

Tsky = Ta − 20. (9) 𝑇 = 𝑇 − 20. (9)

Figure 1. Gabled roof covered with a photovoltaic (PV) panel. Figure 1. Gabled roof covered with a photovoltaic (PV) panel.

R2 can be evaluated by knowing the PV or PV/thermal panel thickness (x) and thermal Rconductivity2 can be evaluated (k), where by knowing the PV or PV/thermal panel thickness (x) and thermal conductivity (k), where 𝑅 =x 2 ◦ (m2·°C/W). R = (m · C/W). (10) (10) 2 k To find R3, a similar approach to R1 is considered using the heat transfer coefficient by natural To find R3, a similar approach to R1 is considered using the heat transfer coefficient by natural convection in the air gap (ℎ) and the heat transfer coefficient by radiation between the roof surface convection in the air gap (hc3) and the heat transfer coefficient by radiation between the roof surface and the PV panel’s back surface (ℎ), where and the PV panel’s back surface (hr3), where

2 𝑅1= 2 ◦ (m ·°C/W) (11) R3 = (m · C/W) (11) hc3 + hr3

where hc3 is the heat transfer coefficient by convection for open-ended space given by [3] where hc3 is the heat transfer coefﬁcient by convection for open-ended space given by [3]

. ℎka =( ) × 0.644xa × 𝑅𝑎×sin0.25(𝛽) 2 (W/m◦ 2·°C) (12) h = ( ) × 0.644 × ( )Ra× sin (β) (W/m · C) (12) c3 La La wherewhereLa is the La lengthis the length of the of air the gap air (m) gap between (m) between the roof the surface roof surface and the and solar the panel, solar panel,xa is the xa airis the gap air gap heightheight (m), and (m),β isand the β roofis the surface roof surface angle. angle. hr3 is foundhr3 is found from thefrom heat the radiation heat radiation equation equation between between two parallel two parallel surfaces surfaces [11], where [11], where

( )×() 2 2 2 ℎ =𝜎×(T + Trs)× (Tpb + T rs) (W/m·°C) pb ( ) 2 ◦ (13) hr3 = σ × (W/m · C) (13) ( 1 + 1 − 1) ε pb εrs where, εpb and εrs are the emissivity of the PV panel’s back surface and the emissivity of the roof where,surface,εpb and respectively.εrs are the emissivity of the PV panel’s back surface and the emissivity of the roof surface, respectively.The thermal model of the rooftop PV design presented by the thermal resistances R1 to R9 shown Thein Figure thermal 2 modeland their of theassociated rooftop Equations PV design (1)–(13) presented were by used the thermal to find resistancesout the effectR1 toof Rambient9 showntemperature, in Figure2 and optimum their associated insulation Equations size, and (1)–(13)solar irradiation were used on to heat ﬁnd transfer out the effectthrough of ambienta gabled and a temperature,flat roof optimum dwelling. insulation This design size, was and compared solar irradiation with an onuncovered heat transfer roof throughdesign by a gabledeliminating and aR2 and ﬂat roofR3dwelling. from the heat This transfer design was model compared as wellwith as adjustin an uncoveredg Equation roof (7) design to address by eliminating the roof tileR2 and temperatureR3 from theTrs heatrather transfer than the model PV surface as well temperature as adjusting EquationTPV. (7) to address the roof tile temperature Trs rather than the PV surface temperature TPV.

Figure 2. Thermal resistances of the gable roof.

Energies 2018, 11, x FOR PEER REVIEW 4 of 14

σ = Stefan–Boltzmann constant (5.670367 × 10−8 W·m−2·K−4), Tsky = Sky temperature (K) found by [13],

𝑇 = 𝑇 − 20. (9)

Figure 1. Gabled roof covered with a photovoltaic (PV) panel.

R2 can be evaluated by knowing the PV or PV/thermal panel thickness (x) and thermal conductivity (k), where 𝑅 = (m2·°C/W). (10)

To find R3, a similar approach to R1 is considered using the heat transfer coefficient by natural

convection in the air gap (ℎ) and the heat transfer coefficient by radiation between the roof surface and the PV panel’s back surface (ℎ), where

2 𝑅 = (m ·°C/W) (11)

where hc3 is the heat transfer coefficient by convection for open-ended space given by [3]

ℎ =( ) × 0.644 × 𝑅𝑎×sin(𝛽). (W/m2·°C) (12)

where La is the length of the air gap (m) between the roof surface and the solar panel, xa is the air gap height (m), and β is the roof surface angle. hr3 is found from the heat radiation equation between two parallel surfaces [11], where

( )×() 2 ℎ =𝜎× (W/m·°C) ( ) (13)

where, εpb and εrs are the emissivity of the PV panel’s back surface and the emissivity of the roof surface, respectively. The thermal model of the rooftop PV design presented by the thermal resistances R1 to R9 shown in Figure 2 and their associated Equations (1)–(13) were used to find out the effect of ambient temperature, optimum insulation size, and solar irradiation on heat transfer through a gabled and a flat roof dwelling. This design was compared with an uncovered roof design by eliminating R2 and R3 from the heat transfer model as well as adjusting Equation (7) to address the roof tile temperature Energies 2018, 11, 1879 5 of 14 Trs rather than the PV surface temperature TPV.

FigureFigure 2. 2.Thermal Thermal resistances resistances of of the the gable gable roof. roof.

3. Thermal Analysis of the Roof System The engineering equation solver package (EES) [14] was used to investigate the most signiﬁcant thermal resistances that affect heat transfer through the proposed roof design. The value of these thermal resistances is given in Table1. It is clearly shown that the optimum roof insulation R7 (4 m2·◦C/W) is greater than the total of the other roof components’ thermal resistance, which was 2 ◦ found to be in the range of 1.05–2.01 m · C/W. Since R7 is the major thermal resistance in the roof design of this study, it was important to investigate its effect on the heating and cooling load of a dwelling. Figure3 shows the effect of increasing R7 on heat gain from a PV rooftop and a non-PV roof design. It is worthwhile to mention here that the commercial thermal resistance of insulation R7 is represented by a value next to the symbol R, i.e., R1 means that the thermal resistance of the insulation 2 ◦ 2 ◦ equals 1 m · C/W, R2 means that the thermal resistance of the insulation equals 2 m · C/W, . . . etc.

Table 1. Thermal resistance of roof system.

Thermal Resistance Winter Value (m2·◦C/W) Summer Value (m2·◦C/W)

R1 0.0614 0.06 R2 0.0075 0.0075 R3 0.221 0.184 R4 0.02 0.02 R5 0.18 0.16 R6 0.34 1.36 R7 4.0 4.0 R8 0.06 0.06 R9 0.16 0.16

The difference in heat loss from the roof between both designs decreases as the value of 2 ◦ insulation increases up to a value of R7 equal to 4 m · C/W where the difference in heat loss starts to be negligible. The other finding from Figure3 is that the size of insulation (4 m 2·◦C/W) represents the optimum limit as, after this size, the heat loss tends to be almost constant and adding extra insulation becomes unfeasible. This size of insulation is considered to be standard in modern building designs to achieve the maximum energy efficiency of dwellings. To investigate the effect of using different types of rooftop solar energy systems, such as a solar thermal collector, R2 of Equation (10) is replaced by the thermal resistance of the thermal collector. This resistance is related mainly to the insulation at the collector’s back side [15], which was found 2 ◦ to be equal to 1.1 (m · C/W) [15]. This value of R2 is used in the roof thermal model described in Equations (1)–(13) to find the heat loss from a roof covered by a PV/thermal collector and the results are presented in Figure3. The results show that the heat loss from the roof covered by the PV/thermal collector is less than that from the roof covered by a PV panel alone. However, the difference between both cases becomes negligible at a ceiling insulation greater than 4 m2·◦C/W. Further investigation of the effect of ambient temperature on heat transfer through the roof is 2 conducted at constant irradiation (500 W/m ), an average wind speed of 3 m/s, and an R7 value equal to 4 m2·◦C/W. The results are shown in Figures4 and5 for winter and summer ambient temperatures. These figures show that the difference in heat loss or heat gain between the PV roof and the non-PV roof is quite small and it is in the range of 3–4.5%. EnergiesEnergiesEnergies 20182018 2018,,11 ,11 11,, 1879x, x FOR FOR PEER PEER REVIEW REVIEW 666 of of 1414 14 Energies 2018, 11, x FOR PEER REVIEW 6 of 14

Figure 3. FigureFigure 3. 3. TheThe The effect effect of of ceiling ceiling insulation’s insulation’s thermal thermal resistanceresist resistanceance on on the the heat heat loss loss from from a a PV, PV, non-PV, non-PV, andand and Figure 3. The effect of ceiling insulation’s thermal resistance2 on the heat loss from a PV, non-PV, and PV/thermalPV/thermal collector gabled roof atat irradiationirradiation ofof 500500 W/mW/m2,,2 a wind speedspeed ofof 33 m/s,m/s, and anan ambientambient PV/thermal collector gabled roof at irradiation of 500 W/m2 , a wind speed of 3 m/s, and an ambient temperaturePV/thermal collector of 10 ◦C. gabled roof at irradiation of 500 W/m , a wind speed of 3 m/s, and an ambient temperaturetemperature of of 10 10 °C. °C. temperature of 10 °C.

FigureFigure 4. 4. The The effect effect of of low low ambient ambient temperatures temperatures on on the the heat heat loss loss from from the the roof roof at at irradiation irradiation of of 500 500 FigureFigure 4. TheThe effect effect of of low low ambient ambient temperatures temperatures on on the the heat heat loss loss from from the the roof roof at irradiation at irradiation of 500 of W/mW/m2,2 ,a a wind 2wind speed speed of of 3 3 m/s, m/s, and and a a ceiling ceiling in insulationsulation thermal thermal resistance resistance value value of of 4 4 m m2·2°C/W.·°C/W.2·◦ 500W/m W/m2, a wind, a wind speed speed of 3 m/s, of 3 m/s,and a and ceiling a ceiling insulation insulation thermal thermal resistance resistance value value of 4 m of2· 4°C/W. m C/W.

FigureFigure 5. 5. The The effect effect of of high high ambient ambient temperatures temperatures on on the the heat heat gain gain from from the the roof roof at at irradiation irradiation of of 500 500 FigureFigure 5. TheThe effect effect of of high high ambient ambient temperatures temperatures on on the the heat heat gain gain from from the the roof roof at irradiation at irradiation of 500 of W/mW/m2,2 ,a a wind wind speed speed of of 3 3 m/s, m/s, and and a a ceiling ceiling in insulationsulation thermal thermal resistance resistance value value of of 4 4 m m2·2°C/W.·°C/W. 500W/m W/m2, a wind2, a wind speed speed of 3 m/s, of 3 m/s,and a and ceiling a ceiling insulation insulation thermal thermal resistance resistance value value of 4 m of2· 4°C/W. m2·◦ C/W.

Energies 2018, 11, x FOR PEER REVIEW 7 of 14

4. Transient Analysis of Roof System Heating and Cooling Load An annual performance analysis was conducted to evaluate the effect of covering the gabled roof by PV panels on the total heating and cooling load (Qhc) of a dwelling. The benchmark software “AccuRate sustainability” [16] for house energy ratings in Australia was used to perform energy modelling of a single-story, double-brick dwelling. The total floor area of the dwelling adopted in this study is 84 m2 divided into a 74 m2 conditioned area and a 10 m2 unconditioned area. The glazing to wall ratio of each dwelling side is: 18.5% N, 15.8% E, 11.9% W, and 10% S. The roof inclination of this dwelling is 22° following the Australian standard [17] and consists of the same parts shown in FigureEnergies 1.2018 The, 11 northern, 1879 side of the roof (facing the sun) was assumed to be fully covered by PV panels.7 of 14 The energy rating analysis was conducted on different dwelling orientations and different roof azimuth4. Transient angles Analysis (Z): 0° ofN, Roof 45° NE, System 90° HeatingE, 270° W, and and Cooling 315° NW Load with a PV arrangement similar to Figure 6. The energy rating simulation was conducted twice for each dwelling orientation, once with the roofAn covered annual performanceby PV panels analysisand another was run conducted without toPV evaluate panels. To the simulate effect of the covering roof shaded the gabled by a PVroof panel, by PV another panels layer on the with total a similar heating thermal and cooling conductivity load (Q hcand) of air a dwelling.gap was added The benchmark to the construction software option“AccuRate of “AccuRate”. sustainability” The [effect16] for of house roof insulation energy ratings on the in annual Australia heating was and used cooling to perform load energyof the prescribedmodelling dwelling of a single-story, was conducted double-brick for two dwelling. types of The roof: total a gabled ﬂoor area roof of design the dwelling and a flat adopted roof design. in this 2 2 2 Thestudy aim is of 84 this m analysisdivided is into to investigate a 74 m conditioned the effect of area transient and a 10weather m unconditioned conditions on area. the heat The transfer glazing throughto wall ratioa roof of covered each dwelling by PV panels. side is: 18.5% N, 15.8% E, 11.9% W, and 10% S. The roof inclination of ◦ thisThe dwelling effect is of 22 rooffollowing insulation the on Australian the annual standard (Qhc) load [17 ]of and the consists dwelling of was the sameestimated parts in shown MJ per in squareFigure 1metre. The northernof roof floor side area of the and roof the (facing results the are sun) presented was assumed in Figure to be 7. fully The covered annual by heating PV panels. and coolingThe energy load rating is estimated analysis wasby AccuRate, conducted which on different considers dwelling the orientationsthermal loss and from different different roof parts azimuth of ◦ ◦ ◦ ◦ ◦ dwellings,angles (Z): including 0 N, 45 theNE, roof, 90 walls,E, 270 floors,W, and and 315 windows.NW with The a trend PV arrangement of the results similar is quite to similar Figure to6. whatThe energy was shown rating in simulation Figure 3 where was conducted the optimum twice insulation for each dwellingsize was orientation,found to be onceabout with 4 m2 the·°C/W. roof Atcovered this size by of PV insulation, panels and the another type of run roof without design PV(gabled panels. or flat) To simulate does not the change roof shaded the total by heating a PV panel, and coolinganother load layer significantly. with a similar This thermal finding conductivity leads to the and conclusion air gap was that added adding to the new construction modules optionto the externalof “AccuRate”. surface Theof the effect roof, of such roof as insulation PV panels, on will the annualnot have heating a significant and cooling effect on load the of total the prescribed(Qhc) load ifdwelling roof insulation was conducted is within for the two optimum types of range. roof: aIt gabled is clear roof from design Figure and 7 that a ﬂat the roof gabled design. roof The has aim less of (thisQhc) analysisload than is the to investigate flat roof for the insulation effect of transientthermal resistance weather conditions values less on than the 2.5. heat This transfer is because through the a thermalroof covered resistance by PV of panels. the gabled roof’s air space becomes dominant at low R values of insulation.

FigureFigure 6. 6. TheThe house house model model and and PV PV rooftop rooftop arrangements. arrangements.

The effect of roof insulation on the annual (Qhc) load of the dwelling was estimated in MJ per square metre of roof floor area and the results are presented in Figure7. The annual heating and cooling load is estimated by AccuRate, which considers the thermal loss from different parts of dwellings, including the roof, walls, floors, and windows. The trend of the results is quite similar to what was ◦ shown in Figure3 where the optimum insulation size was found to be about 4 m 2· C/W. At this size of insulation, the type of roof design (gabled or flat) does not change the total heating and cooling load significantly. This finding leads to the conclusion that adding new modules to the external surface of the roof, such as PV panels, will not have a significant effect on the total (Qhc) load if roof insulation is within the optimum range. It is clear from Figure7 that the gabled roof has less ( Qhc) load than the flat roof for insulation thermal resistance values less than 2.5. This is because the thermal resistance of the gabled roof’s air space becomes dominant at low R values of insulation. Energies 2018, 11, 1879 8 of 14 EnergiesEnergies 2018 2018, 11, ,11 x ,FOR x FOR PEER PEER REVIEW REVIEW 8 of8 of14 14

FigureFigureFigure 7. 7. 7.TheThe The effect effect effect of of ofthe the the ceiling ceiling ceiling insulation’s insulation’s insulation’s therma thermal thermal resistance resistancel resistance on on on the the the annu annual annual alheating heating heating and and and cooling cooling cooling loadloadload of of ofa a dwellinga dwelling dwelling with with with a a gableda gabled gabled roof roof roof desi design designgn and and and a a dwelling dwellinga dwelling with with with a flat ﬂata flat roof roof design. design.

hc ItIt Itis is isworthwhile worthwhile worthwhile to to to mention mention mention here here here that that that the the the percentage percentage percentage change change change in in in Q Qhc hcduedue due to to to rooftop rooftop rooftop PV PV PV panel panel panel shadingshadingshading may may may have havehave a apositivea positive or or ornegative negative negative impact impact impact on on the on the theenergy energy energy consumption consumption consumption by by air-conditioning. byair-conditioning. air-conditioning. The The hc annualTheannual annual percentage percentage percentage of of change ofchange change in in Q inQ Qhcdue hcduedue to to toPV PV PV panel panel panel shading shading was was estimated estimatedestimated at at atdifferent differentdifferent roof roof roof orientationsorientationsorientations and and and is is isshown shown shown in in in Figure Figure Figure 88.. 8.In In some some roof roof orientations, orientations, such such as as the the West West roof roof (where(where (where thethe the ◦ hc azimuthazimuthazimuth angle angle angle is is is270°), 270 270°),), the the the percentage percentage percentage of of of decrease decrease decrease in in in QQ Qhc ishcis is3%, 3%, 3%, i.e., i.e., i.e., adding adding adding a a PVa PV PV panel panel panel to to to the the the roof roof roof will will will improveimproveimprove the the the dwelling’s dwelling’s thermalthermal thermal efﬁciencyefficiency efficiency duedue due to to theto th the reduction reductione reduction in in heatingin heating heating and and and cooling cooling cooling loads. loads. loads. It canIt Itcan becan hc beconcludedbe concluded concluded from from from Figure Figure Figure8 that 8 that8 the that percentagethe the percentage percentage of increase of of increase increase in Q inhc in Qin Q general hcin in general general is very is isvery smallvery small small (between (between (between 0.15 0.15and0.15 and 0.7%) and 0.7%) 0.7%) at the at atroofthe the roof azimuth roof azimuth azimuth angles angles angles of 0, of 45, of 0, and 0,45, 45, and 315 and◦ 315°due 315° due to due the to to increasethe the increase increase in heating in in heating heating load load at load these at atthese roofthese hc rooforientations.roof orientations. orientations. In general, In In general, general, Figure Figure Figure8 shows 8 shows8 shows that thethat that percentage the the percentage percentage of change of of change change in Q hcin in isQ veryQ ishc isvery small very small andsmall and it and is init it isthe isin in rangethe the range range of − of3 toof −3 0.74%.− to3 to 0.74%. 0.74%.

Figure 8. The percentage of change in annual heating and cooling load due to shading developed by FigureFigure 8. 8.The The percentage percentage of of change change in in annual annual heating heating and and cooling cooling load load due due to to shading shading developed developed by by PVPVPV panels panels panels on on on a a gableda gabled gabled roof. roof. roof.

TheThe low low percentage percentage of of change change in in Q hcQ canhc can be be justified justified by by examining examining the the yearly yearly change change of of roof roof space space The low percentage of change in Qhc can be justiﬁed by examining the yearly change of roof space temperaturetemperature in in PV PV roof roof and and non-PV non-PV roof roof cases cases by by using using ACCURATE ACCURATE with with the the non-modelling non-modelling option. option. temperature in PV roof and non-PV roof cases by using ACCURATE with the non-modelling option. TheThe results results show show that that the the hourly hourly temperature temperature differe differencence between between both both cases cases increases increases in in the the afternoon afternoon The results show that the hourly temperature difference between both cases increases in the afternoon hourshours and and approaches approaches to to zero zero during during no no sunlight sunlight hours. hours. The The temperature temperature difference difference is isaffected affected also also byby the the seasons seasons due due to to the the change change in in ambient ambient temp temperature.erature. Two Two extreme extreme days days shown shown in in Figure Figure 9a,b 9a,b

Energies 2018, 11, 1879 9 of 14

Energies 2018, 11, x FOR PEER REVIEW 9 of 14 hours and approaches to zero during no sunlight hours. The temperature difference is affected also bywere the selected seasons to due display to the the change roof space in ambient temperature temperature. profile Twoin winter extreme and dayssummer. shown It is in clear Figure that9a,b the werevariance selected in the to roof display space the temperature roof space temperature between the proﬁle two types in winter of roof and increa summer.ses in It winter, is clear by that about the variance31%, and in by the 6% roof in space summer temperature in the afternoon between thehours two as types shown of roof in Figure increases 9a,b. in winter,However, by about since 31%, this andincrease by 6% occurs in summer only in in a thelimited afternoon number hours of hours as shown of the in year, Figure the9a,b. change However, of heat since transfer this increaserate and, occurstherefore, only the in change a limited in numberthe total ofthermal hours load of the is year,not significant the change as of presented heat transfer in Figure rate and, 8. therefore, the change in the total thermal load is not signiﬁcant as presented in Figure8.

(a)

(b)

FigureFigure 9.9. RoofRoof spacespace temperaturetemperature proﬁleprofile inin ((aa)) winterwinter andand ((bb)) summersummer daysdays ofof aa househouse withwith aa ceilingceiling 2 insulationinsulationR Rvalue value ofof 44 mm2··◦°C/W.C/W.

TheThe EffectEffect ofof DifferentDifferent RooftopRooftop SolarSolar SystemsSystems onon thethe AnnualAnnual HeatingHeating and and Cooling Cooling Load Load The effect of shading developed by three types of roof—a bare surface roof, a roof surface The effect of shading developed by three types of roof—a bare surface roof, a roof surface covered covered with PV panels, and a roof surface covered with a PV/thermal collector—on the annual with PV panels, and a roof surface covered with a PV/thermal collector—on the annual heating and heating and cooling load of the dwelling was examined. The PV/thermal collector is mainly used to cooling load of the dwelling was examined. The PV/thermal collector is mainly used to provide dual provide dual output (thermal and electrical) and to improve PV panel efficiency due to cooling by output (thermal and electrical) and to improve PV panel efﬁciency due to cooling by the collector’s the collector’s working fluid. Different designs of PV/thermal collectors were found in the literature, working ﬂuid. Different designs of PV/thermal collectors were found in the literature, such as: such as: - a PV/thermal water system, in which the PV panel is attached to a traditional hot water solar collector [18–20]; and

Energies 2018, 11, 1879 10 of 14

- a PV/thermal water system, in which the PV panel is attached to a traditional hot water solar Energiescollector 2018, 11 [,18 x FOR–20]; PEER and REVIEW 10 of 14 - a PV/thermal air system, in which the PV panel is attached to a hot air collector [20–22]. - a PV/thermal air system, in which the PV panel is attached to a hot air collector [20–22]. The values of the thermal resistance R2 of different types of rooftop systems were deduced from The values of the thermal resistance R2 of different types of rooftop systems were deduced from References [3,19,20,23] and are summarized in Table2. These values were used in “AccuRate” to References [3,19,20,23] and are summarized in Table 2. These values were used in “AccuRate” to find ﬁnd the sensitivity of the results to different designs of rooftop collectors. The result of this analysis the sensitivity of the results to different designs of rooftop collectors. The result of this analysis shows shows that the annual heating and cooling load of dwellings with different rooftop designs are that the annual heating and cooling load of dwellings with different rooftop designs are almost almost identical. To illustrate this sensitivity, the Qhc of the highest R2 of the PV/thermal collectors identical. To illustrate this sensitivity, the Qhc of the highest R2 of the PV/thermal collectors given in given in Table2 was compared with the Qhc of a PV panel only and is presented Figure 10. It is clear Table 2 was compared with the Qhc of a PV panel only and is presented Figure 10. It is clear that the that the difference between the Qhc of the three types of roof is not signiﬁcant and it approaches zero at difference between the Qhc of the three types of roof is not significant and it approaches zero at high high ceiling insulation thermal resistances. ceiling insulation thermal resistances. Table 2. Thermal resistance of different types of rooftop PV/thermal collectors. Table 2. Thermal resistance of different types of rooftop PV/thermal collectors. 2·◦ NumberNumber Reference Reference Type Type of of Collector Collector RR2 2ValueValue m 2·°C/WC/W 11 [19 [19]] Single glazed glazed PV/T PV/T collector collector 0.51 0.51 22 [20 [20]] Single glazed glazed PV/T PV/T collector collector 0.19 0.19 3 [20] Double glazed PV/T collector 0.16 3 [20] Double glazed PV/T collector 0.16 4 [20] PV/T collector with no cover 0.03 54 [23 [20]] Flat PV/T plate collector without with no PV cover panel 0.03 0.25 65 [3 [23]] Flat plate collector PV panel without only PV panel 0.0075 0.25 6 [3] PV panel only 0.0075

There are two major reasons for this insensitivity of the annual Qhc to the different rooftop designs: There are two major reasons for this insensitivity of the annual Qhc to the different rooftop designs: (1) The domination of the thermal resistance of the roof insulation, especially at the standard value (1) The domination of the thermal resistance of the roof insulation, especially at the standard value (4 m2·◦C/W). (4 m2·°C/W). (2) The small contribution of the roof structure to the dwelling’s annual Qhc. For the dwelling design (2) The small contribution of the roof structure to the dwelling’s annual Qhc. For the dwelling design adopted in this work, the roof structure makes only a 9.1% contribution to the annual Qhc. adopted in this work, the roof structure makes only a 9.1% contribution to the annual Qhc.

Figure 10. Annual heating and cooling load of different types of gabled roof dwellings: bare roof, roof Figure 10. Annual heating and cooling load of different types of gabled roof dwellings: bare roof, roof covered with a PV panel only, and roof covered with the ﬁrst PV/thermal collector of Table2. covered with a PV panel only, and roof covered with the first PV/thermal collector of Table 2.

5.5. PV PV Energy Energy Contribution Contribution to to the the Heating Heating and and Cooling Cooling Load Load TheThe annual annual electricity electricity produced produced by by the the PV PV panels panels covering covering the the northern northern side side of of the the proposed proposed dwellingdwelling was was estimated estimated using using the simulation the simulation package package “PVSYST” “PVSYST” [24] under [24] Sydney under weather Sydney conditions weather conditions and at a site latitude of 33.5° south. The main specification of the PV system used in this study was adopted from [25], which uses an array of identical mono-crystalline silicon PV panels mounted on a 22° slope gabled roof. The total roof area of the adopted dwelling is 90 m2 divided evenly between north and south sides. The PV panel’s area covering the northern roof is 42 m2 and its estimated capacity is 4.4 kW.

Energies 2018, 11, 1879 11 of 14 and at a site latitude of 33.5◦ south. The main speciﬁcation of the PV system used in this study was adopted from [25], which uses an array of identical mono-crystalline silicon PV panels mounted on a 22◦ slope gabled roof. The total roof area of the adopted dwelling is 90 m2 divided evenly between north and south sides. The PV panel’s area covering the northern roof is 42 m2 and its estimated capacity is 4.4 kW. In order to investigate the overall impact of the rooftop PV panel on the dwelling’s energy efﬁciency, both solar energy generated by the PV system and the change in Qhc due to roof shading by the PV panels must be considered. A formula that describes the ratio of net energy produced by the solar PV system to the heating and cooling load Qhc with no PV rooftop system was developed and is given by Q − ∆Q PVR = PV hc (14) (Qhc)NPV and

∆Qhc = (Qhc)PV − (Qhc)NPV (15) where

PVR = The ratio of net PV energy to the heating and cooling load with no PV rooftop,

∆Qhc = The change in the total heating and cooling load between a PV roof and a non-PV roof (MJ/m2 of roof area). 2 QPV = The energy produced by PV system (MJ/m of roof area), 2 (Qhc)PV = The heating and cooling load of the dwelling with a PV rooftop (MJ/m of roof area), 2 (Qhc)NPV = The heating and cooling load of the dwelling with a non-PV rooftop (MJ/m of roof area). The PVR value in Equation (14) depends on two major factors:

- The energy produced by the PV panels covering the roof, and

- The size of the dwelling that contributes signiﬁcantly to the amount of Qhc.

The maximum PVR value can be achieved when QPV is maximum (the northern roof is covered completely with PV panels), and when (Qhc)PV is less than (Qhc)NPV. The energy produced by the rooftop PV panels is affected by two parameters: roof orientation and roof area. The PVSYST and ACCURATE packages were used to estimate the PVR at different roof orientations and the results are shown in Figure 10. It is quite obvious that the northern orientation yields the highest value of PVR due to its highest value of energy production. For the dwelling design adopted in this work, Figure 10 shows that the smallest value of PVR occurred when the roof is facing east, i.e., the azimuth angle ◦ equals 90 . It can be concluded from Figure 11 that the effect of change in Qhc due to the PV rooftop installation is negligible compared to the solar electricity produced, which can cover, with surplus, the heating and cooling load of the dwelling. However, this trend of PVR will not stay steady if the number of floors in the dwelling are increased. This was investigated by duplicating the ground floor area in ACCURATE and modelling the heating and cooling load of multi-floor dwellings. The effect of change in the total heating and cooling load (∆Qhc) between the PV roof and the non-PV roof decreases with the number of floors of the dwelling. This can be verified by Figure 12, which shows that ∆Qhc almost vanishes when the number of floors the dwelling has exceeds 5. The results show that the PVR ratio drops exponentially with an increase in the number of floors in the dwelling. It is clear that the energy produced by the rooftop PV system will not cover the Qhc if the number of levels in the dwelling exceeds 4. This result can provide a guideline for the limit of the rooftop PV system’s size to meet the dwelling’s energy need or the limit of zero energy design in multi-floor dwellings with reference to a PV rooftop system as an energy source to the dwelling. Energies 2018, 11, x FOR PEER REVIEW 11 of 14

In order to investigate the overall impact of the rooftop PV panel on the dwelling’s energy efficiency, both solar energy generated by the PV system and the change in Qhc due to roof shading by the PV panels must be considered. A formula that describes the ratio of net energy produced by the solar PV system to the heating and cooling load Qhc with no PV rooftop system was developed and is given by

𝑄 −∆𝑄 𝑃𝑉𝑅 = (14) (𝑄)

and

∆𝑄 = (𝑄) −(𝑄) (15)

where PVR = The ratio of net PV energy to the heating and cooling load with no PV rooftop,

∆𝑄 = The change in the total heating and cooling load between a PV roof and a non-PV roof (MJ/m2 of roof area). 2 𝑄 = The energy produced by PV system (MJ/m of roof area), 2 (𝑄) = The heating and cooling load of the dwelling with a PV rooftop (MJ/m of roof area), 2 (𝑄) = The heating and cooling load of the dwelling with a non-PV rooftop (MJ/m of roof area). The PVR value in Equation (14) depends on two major factors: - The energy produced by the PV panels covering the roof, and - The size of the dwelling that contributes significantly to the amount of Qhc.

Energies 2018, 11, x FOR PEER REVIEW 12 of 14

However, this trend of PVR will not stay steady if the number of floors in the dwelling are increased. This was investigated by duplicating the ground floor area in ACCURATE and modelling the heating and cooling load of multi-floor dwellings. The effect of change in the total heating and

cooling load (∆𝑄) between the PV roof and the non-PV roof decreases with the number of floors of the dwelling. This can be verified by Figure 12, which shows that ∆𝑄 almost vanishes when the number of floors the dwelling has exceeds 5. The results show that the PVR ratio drops exponentially with an increase in the number of floors in the dwelling. It is clear that the energy produced by the

rooftop PV system will not cover the Qhc if the number of levels in the dwelling exceeds 4. This result Figure 11. The ratio of net energy produced by the rooftop PV system to the heating and cooling load can provideFigure 11. a Theguideline ratio of for net energythe limit produced of the byrooftop the rooftop PV system’s PV system size to theto meet heating the and dwelling’s cooling load energy (the roof is facing north and is fully covered by PV panels). PVR, the ratio of net PV energy to the need(the or the roof limit is facing of zero north energy and isdesign fully covered in multi-floor by PV panels).dwellings PVR, with the reference ratio of net to PVa PV energy rooftop to the system heating and cooling load with a non-PV rooftop. as anheating energy and source cooling to the load dwelling. with a non-PV rooftop.

FigureFigure 12.12. The ratio of net energy produced byby thethe rooftoprooftop PVPV systemsystem toto thethe heatingheating andand coolingcooling loadload forfor multi-levelmulti-level dwellingsdwellings (roof(roof facingfacing north).north).

6.6. Conclusions InIn thisthis paper, paper, the the effect effect of installingof installing rooftop rooftop PV panelsPV panels on the on heating the heating and cooling and cooling load of load a typical of a dwellingtypical dwelling was investigated. was investigated. Thermal modellingThermal modell of a gableding of roof a gabled was developed roof was consideringdeveloped considering the thermal resistancethe thermal of resistance different roof of different components. roof compon The thermalents. modelThe thermal showed model that roof/ceilingshowed that insulation roof/ceiling is theinsulation key form is the of thermalkey form resistance of thermal in resistance the model inand the model the heat and gain the and heat loss gain from and theloss rooffrom becomes the roof almostbecomes steady almost when steady insulation when insulation size approaches size approaches 4 m2·◦C/W. 4 m At2·°C/W. this insulation At this insulation size, the modelsize, the showed model thatshowed adding that extra adding components extra components to the external to the external surface ofsurface the roof of the has roof a minor has a effect minor on effect heat gainon heat or heatgain loss.or heat The loss. thermal The modelthermal showed model thatshowed the barethat roofthe bare surface, roof roof surface, with roof a PV with panel, a PV and panel, roof with and PV/thermalroof with PV/thermal collector roof collector conﬁgurations roof configurations make a minor make difference a minor in di thefference annual in thermal the annual performance thermal ofperformance the dwelling of when the dwelling the ceiling when insulation’s the ceiling thermal insulation’s resistance thermal exceeds resistance 4 m2·◦C/W. exceeds To investigate4 m2·°C/W.the To effectinvestigate of shading the effect developed of shading by rooftopdeveloped PV by panels rooftop on thePV dwelling’spanels on the energy dwelling’s efﬁciency, energy two efficiency, types of softwaretwo types were of software used, namely were “ACCURATEused, namely sustainability”“ACCURATE sustainability” for thermal assessment for thermal of dwellingsassessment and of “PVSYST”dwellings forand energy “PVSYST” production for energy by the production PV system. by The the results PV system. of the thermalThe results assessment of the showedthermal assessment showed that in some roof orientations, such as the east and west roofs, adding a rooftop system will cause a reduction in the total thermal load of the dwelling. However, the ratio of this reduction is minor and represents only 3% of the total heating and cooling load. Another factor that causes this small reduction in heating and cooling load is that these PV panels cover only one side of the roof, which leaves the opposite side exposed more to variations in ambient conditions. The other factor that improves the dwelling’s energy efficiency is the solar electricity produced by the PV system. Both factors were integrated into one equation that estimates the value (PVR), which is the ratio of net energy produced by PV system to the energy required to cover the heating and cooling load of the dwelling. The results show that the thermal impact of adding a PV rooftop

Energies 2018, 11, 1879 13 of 14 that in some roof orientations, such as the east and west roofs, adding a rooftop system will cause a reduction in the total thermal load of the dwelling. However, the ratio of this reduction is minor and represents only 3% of the total heating and cooling load. Another factor that causes this small reduction in heating and cooling load is that these PV panels cover only one side of the roof, which leaves the opposite side exposed more to variations in ambient conditions. The other factor that improves the dwelling’s energy efficiency is the solar electricity produced by the PV system. Both factors were integrated into one equation that estimates the value (PVR), which is the ratio of net energy produced by PV system to the energy required to cover the heating and cooling load of the dwelling. The results show that the thermal impact of adding a PV rooftop system to a dwelling is negligible compared to the amount of solar electricity produced by that system, which covers with surplus the heating and cooling load. However, increasing the number of floors of the dwelling will reduce the PVR ratio exponentially, and the PV system output of a dwelling with a number of levels greater than 4 will not be able to cover the increase in the heating and cooling loads. It was verified that the insensitivity of the annual heating and cooling load to the thermal resistance of rooftop solar systems is only because the total thermal resistance is dominated by roof insulation. In the case of tropical dwelling designs, the results will be more sensitive due to low or no ceiling insulation and the type of rooftop system will have a stronger effect on the heating and cooling load. Future work will consider the effect of different designs of PV roofs, including PV-integrated roof tiles and solar hot water collectors, on a dwelling’s thermal performance.

Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Dominguez, A.; Kleissl, J.; Luvall, J. Effects of Solar Photovoltaic Panels on Roof Heat Transfer. Sol. Energy 2011, 85, 2244–2255. [CrossRef] 2. Kotak, Y.; EJ Gago, E.; Mohanty, P.; Muneer, T. Installation of Roof-Top Solar PV Modules and their Impact on Building Cooling Load. Build. Serv. Eng. Res. Technol. 2014, 35, 613–633. [CrossRef] 3. Yang, H.; Zhu, Z.; Burnett, J.; Lu, L. Simulation Study on the Energy Performance of Photovoltaic Roofs. ASHRAE Trans. 2001, 107, 129–135. 4. Armstrong, S.; Hurley, W. A Thermal Model for Photovoltaic Panels under Varying Atmospheric Conditions. Appl. Therm. Eng. 2010, 30, 1488–1495. [CrossRef] 5. Siraki, A.; Pillay, P. Study of Optimum Tilt Angles for Solar Panels in Different Latitudes for Urban Applications. Sol. Energy 2012, 86, 1920–1928. [CrossRef] 6. Singh, H.; Sirisamphanwong, C.; Rekha, S. Effect of Tilt and Azimuth Angle on the Performance of PV Rooftop System. Appl. Mech. Mater. 2016, 839, 159–164. [CrossRef] 7. Kantersa, J.; Wallb, M. The Impact of Urban Design Decisions on Net Zero Energy Solar Buildings in Sweden. Plan. Transp. Res. 2014, 2, 312–332. [CrossRef] 8. Hachem, C.; Athienitis, A.; Fazio, P. Design of Roofs for Increased Solar Potential BIPV/T Systems and their Applications to Housing Units. ASHRAE Trans. 2012, 118, 660–676. 9. Kwan, Y.; Guana, L. Design a Zero Energy House in Brisbane, Australia. Procedia Eng. 2015, 121, 604–611. [CrossRef] 10. Insulation Handbook 2014, Part 1 Thermal Performance, Total R-Value Calculation for Typical Building Applications; Version 2 Insulation Council of Australia and New Zealand; ICANZ: Canberra, Australia, 2014. 11. Cengel, Y. Introduction to Thermodynamics and Heat Transfer, 2nd ed.; McGraw Hill: New York, NY, USA, 2008, ISBN 13: 978-0071287739. 12. Odeh, S.; Behnia, M. Development of PV Module Efﬁciency Using Water Cooling. Heat Transf. Eng. J. 2009, 30, 499–505. [CrossRef] 13. Algarni, S.; Algarni, S.; Nutter, D. Survey of Sky Effective Temperature Models Applicable to Building Envelope Radiant Heat Transfer. ASHRAE Trans. 2015, 121, 351–363. 14. Kelvin, S. Engineering Equation Solver (EES); V10.278—3D, F-Chart Software; F - Chart: Madison, WI, USA, 2017. Energies 2018, 11, 1879 14 of 14

15. Dufﬁe, J.; Beckman, W. Solar Engineering of Thermal Processes: Chapter 6; John Published Online Wiley & Sons: Hoboken, NJ, USA, 2013; 755p. 16. AccuRate Sustainability Software; Commonwealth Scientiﬁc and Industrial Research Organisation (CSIRO): Sydney, Australia, 2015. 17. Roof Cladding, the National Construction Code of Australia (NCC) 2016. Volume 2. Available online: http://www.abcb.gov.au/ncc-online/NCC (accessed on 18 July 2018). 18. Herrando, M.; Markides, C.; Hellgardt, K. A UK-based assessment of hybrid PV and solar-thermal systems for domestic heating and power: System performance. Appl. Energy 2014, 122, 288–309. [CrossRef] 19. He, W.; Chow, T.; Ji, J.; Lu, J.; Pei, G.; Chan, L. Hybrid photovoltaic and thermal solar-collector designed for natural circulation of water. Appl. Energy 2006, 83, 199–210. [CrossRef] 20. Guarracino, I.; Mellor, A.; Ekins-Daukes, N.; Markides, C. Dynamic coupled thermal-and-electrical modelling of sheet-and-tube hybrid photovoltaic/thermal (PVT) collectors. Appl. Therm. Eng. 2016, 101, 788–795. [CrossRef] 21. Chow, T. A review on photovoltaic/thermal hybrid solar technology. Appl. Energy 2010, 87, 365–379. [CrossRef] 22. Phiraphata, S.; Prommasa, R.; Puangsombutb, W. Experimental study of natural convection in PV roof solar collector. Int. Commun. Heat Mass Transf. 2017, 89, 31–38. [CrossRef] 23. Chow, T.; Dong, Z.; Chan, L.; Fai Fong, K.; Bai, Y. Performance evaluation of evacuated tube solar domestic hot water systems in Hong Kong. Energy Build. 2011, 43, 3467–3474. [CrossRef] 24. Mermoud, A. PVSYST Photovoltaic Software; The University of Geneva: Geneva, Switzerland, 2012. 25. Odeh, S. Long term assessment of a grid connected solar PV system in Sydney. J. Energy Power Eng. 2016, 10, 591–599.

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).