sustainability

Article Optimal Orientation and Tilt Angle for Maximizing in-Plane Solar Irradiation for PV Applications in Japan

Cao Yu 1,2,*, Yong Sheng Khoo 3, Jing Chai 3, Shuwei Han 3 and Jianxi Yao 1,4

1 School of Renewable Energy, North China Electric Power University, Changping District, Beijing 102206, China; [email protected] 2 China Three Gorges New Energy Co., Ltd., Xicheng District, Beijing 100053, China 3 Solar Energy Research Institute of Singapore, Singapore 117574, Singapore; [email protected] (Y.S.K.); [email protected] (J.C.); [email protected] (S.H.) 4 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Changping District, Beijing 102206, China * Correspondence: [email protected]; Tel.: +86-(010)-8342-8086



Received: 3 February 2019; Accepted: 31 March 2019; Published: 4 April 2019


Abstract: To maximize the direct insolation received by flat-plate photovoltaic (PV) modules, the tilt angle is usually the site’s latitude and the modules are oriented towards the equator. However, this may not be the optimal placement, as the local climatic conditions will influence the optimal orientation and tilt angle. Transposition models can be used to simulate the insolation on planes with various tilts and azimuths, using a single set of (horizontal) global and diffuse irradiance measurements. Following this method, five maps including optimal orientations, tilt angles, maximum annual tilted irradiations, percentage improvements of the optimally-tilted PV installation versus the conventional latitude-tilted PV installation, and annual diffuse fraction were plotted over the geographical area of Japan. Spatial patterns in these maps were observed and analyzed. The key contribution of this work is to establish a database of optimal PV installations in Japan. Compared to the conventional rule of thumb of tilting the module at latitude facing south, it is shown that the optimally tilted surface receives up to 2% additional annual solar irradiation.

Keywords: solar irradiance; PV modules; optimal tilt angle; orientation; maximizing irradiation; Japan

1. Introduction After the Fukushima nuclear disaster in 2011, the Japanese government announced plans to expand the solar photovoltaic (PV) installations to reduce reliance on nuclear power. Following the implementation of Japan’s renewable energy feed-in-tariff (FIT) scheme in July 2012, photovoltaic (PV) installation has grown rapidly [1]. In this paper, the optimal orientation and tilt angle for maximizing in-plane solar irradiation in Japan was studied to understand the potential of PV adoption in Japan. The orientation (azimuthal rotation) and tilt angle for fixed array installation are critical parameters that affect a photovoltaic (PV) system performance, directly determining the solar radiation received by the PV modules. Various studies have been carried out to determine the optimal orientation and tilt for different locations [2–8]. Khoo et al. studied the optimal orientation and tilt angle for maximizing in-plane solar irradiation for fixed-tilt PV modules in Singapore [8]. Using the methodology from previous work and the publicly available countrywide weather data in Japan, this paper presents a visual database of optimal orientation and tilt angles in Japan and correlates it to local climatic conditions such as irradiation intensity and diffuse fraction.

Sustainability 2019, 11, 2016; doi:10.3390/su11072016 www.mdpi.com/journal/sustainability Sustainability 2019, 11, x FOR PEER REVIEW 2 of 8

Sustainabilitypaper presents2019, 11 a, 2016visual database of optimal orientation and tilt angles in Japan and correlates2 it of to 8 local climatic conditions such as irradiation intensity and diffuse fraction.

2.2. MaterialsMaterials andand MethodsMethods ThisThis sectionsection brieflybriefly describes describes the the data data setset used,used, thethe modelmodel usedused forfor thethe transposition,transposition, andand methodmethod ofof determiningdetermining thethe optimaloptimal orientation orientation and and tilt tilt angle. angle. 2.1. Data Collection 2.1. Data Collection The global horizontal irradiance (GHI) and diffuse horizontal irradiance (DHI) are the required The global horizontal irradiance (GHI) and diffuse horizontal irradiance (DHI) are the required inputs for determining the optimal orientation and tilt angle. GHI and DHI for locations across inputs for determining the optimal orientation and tilt angle. GHI and DHI for locations across Japan Japan were obtained from Japan’s New Energy and Industrial Technology Development Organization were obtained from Japan’s New Energy and Industrial Technology Development Organization (NEDO), using meteorological test data for photovoltaic systems (METPV-11) [9]. The dataset consists (NEDO), using meteorological test data for photovoltaic systems (METPV-11) [9]. The dataset consists of post-processed hourly meteorological data for a 1-year period (similar to a typical meteorological of post-processed hourly meteorological data for a 1-year period (similar to a typical meteorological year dataset) at 837 locations extracted from ground measurements spanning 20 years (1990–2009). year dataset) at 837 locations extracted from ground measurements spanning 20 years (1990–2009). Similar to typical meteorological year (TMY3) data from the National Solar Radiation Data Base Similar to typical meteorological year (TMY3) data from the National Solar Radiation Data Base (NSRDB), METPV11 data accurately represent the long-term solar resource distribution across Japan. (NSRDB), METPV11 data accurately represent the long-term solar resource distribution across Japan. To promote ease of use of the data for different sites in Japan, NEDO provides a user-friendly web To promote ease of use of the data for different sites in Japan, NEDO provides a user-friendly web interface app [10]. The locations covered in this study are shown in Figure1, whereby each colored interface app [10]. The locations covered in this study are shown in Figure 1, whereby each colored pixel pixel denotes a station, with the color indicating the annual solar irradiation. denotes a station, with the color indicating the annual solar irradiation.

FigureFigure 1.1. Geographic locations locations of of the the 837 837 weather weather stations stations in inJapan Japan used used for forthis thisstudy. study. Each Each colored colored pixel pixeldenotes denotes a station, a station, while the while color theindicates color the indicates annual global the annual horizontal global irradiation horizontal value irradiation in kWh/m value2. in kWh/m2. 2.2. Transposition Model to Convert Horizontal Irradiance to Tilted Irradiance 2.2. Transposition Model to Convert Horizontal Irradiance to Tilted Irradiance To determine the optimal orientation and tilt angle of a flat-plate PV module, first we converted the GHITo determine and DHI theinto optimal tilted irradiance orientation using and a tilt transposition angle of a flat-plate model. PVThe module, direct beam first weradiation converted on a thetilted GHI surface and DHI can intobe calculated tilted irradiance using geometric using a transposition relations, whereas model. the The conversion direct beam for radiation the diffuse on aradiation tilted surface is more can complex be calculated and has using been geometric approach relations,ed using whereasdifferent the models, conversion for example for the Liu diffuse and radiationJordan [11], is moreKlucher complex [12], Hay and and has Davies been approached [13], and Perez using et differental. [14], etc. models, For this for study, example the LiuPerez and et Jordanal. transposition [11], Klucher model [12], is Hay used and due Davies to its proven [13], and accuracy Perez et [8,15–21]. al. [14], etc. For this study, the Perez et al. transposition model is used due to its proven accuracy [8,15–21]. Sustainability 2019, 11, 2016 3 of 8

The Perez et al. model [14] is an empirical model based on a detailed statistical analysis of the sky’sSustainability diffuse components. 2019, 11, x FOR PEER The REVIEW model breaks the diffuse irradiance into the three components3 of 8 of isotropic background, circumsolar and horizon zone: The Perez et al. model [14] is an empirical model based on a detailed statistical analysis of the sky’s diffuse components. The model 1 + cosbreaksβ  the diffuse irradiancecos θ into the three components of Id,tilt = Id (1 − F1) + F1 + F2 sin β (1) isotropic background, circumsolar and 2horizon zone: cos θz 1 + cos𝛽 cos𝜃 where Id,tilt is the total tilted𝐼, diffuse=𝐼 irradiance, 1−𝐹β the +𝐹 tilt angle,+𝐹θissin𝛽 the angle of incidence, and(1) θz the 2 cos𝜃 zenith angle; F1 and F2 are complex empirically fitted functions to describe circumsolar and horizon brightnesswhere I [d,tilt14]. is the total tilted diffuse irradiance, β the tilt angle, θ is the angle of incidence, and θz the zenith angle; F1 and F2 are complex empirically fitted functions to describe circumsolar and horizon 2.3. Determiningbrightness [14]. the Optimal Orientation and Tilt Angle

2.3.For Determining each location, the Optimal the hourly Orientation GHI and and DHI Tilt Angle data over the 1-year period were used as an input to the Perez et al. transposition model to calculate the hourly tilted irradiance for all possible orientations For each location, the hourly GHI and DHI data over the 1-year period were used as an input to ◦ ◦ ◦ ◦ (0 tothe 360 Perez) and et tiltal. anglestransposition (0 to 90model). The to hourlycalculate tilted the hourly irradiance tilted was irradiance summed for to all get possible the annual tiltedorientations irradiation (0° for to the360°) different and tilt angles orientations (0° to 90°). and The tilt hourly angles. tilted The irradiance results arewas thensummed represented to get the as a ◦ polarannual contour tilted plot, irradiation as can befor seenthe di infferent Figure orientations2, using Tokyo and tilt city angles as. an The example. results are For then Tokyo represented (35.69 N, 139.76as◦ aE), polar a maximumcontour plot, annual as can be tilted seen irradiation in Figure 2, ofusing 1847 Tokyo kWh/m city as2 isan achievableexample. For through Tokyo (35.69° a surface orientedN, 139.76° around E), 179 a maximum◦ SE with annual a tilt angle tilted of irradiation 35◦. Extending of 1,847 the kWh/m same2 methodologyis achievable through across 837a surface locations in Japan,oriented the around optimal 179° orientation SE with a tilt and angle tilt of angle 35°. Extending that yield the the same highest methodology annual tiltedacross irradiation837 locations were thenin determined, Japan, the optimal see Figures orientation3–5. and tilt angle that yield the highest annual tilted irradiation were then determined, see Figures 3–5.

FigureFigure 2. Polar 2. Polar contour contour plot plot of of annual annual tilted tilted irradiationirradiation for for different different tilts tilts and and orientations orientations in Tokyo, in Tokyo, Japan.Japan. A surface A surface facing facing 179 179°◦ SE SE with with a a tilt tilt angle angle ofof around 35° 35 ◦receivesreceives the the highest highest annual annual irradiation irradiation of 1,847 kWh/m2, shown as the ‘x’ in the polar contour plot. of 1847 kWh/m2, shown as the ‘x’ in the polar contour plot.

3. Results3. Results ConventionalConventional rule rule of thumbof thumb suggests suggests that that the the PV PV array array should should be be installed installedfacing facing thethe equatorequator and and tilted toward the sun’s average elevation, i.e., having a tilt angle equal to the latitude of the tilted toward the sun’s average elevation, i.e., having a tilt angle equal to the latitude of the array’s array’s location. For Japan, as seen in Figure 3, different locations’ optimal orientations are indeed location. For Japan, as seen in Figure3, different locations’ optimal orientations are indeed mostly mostly facing south, within◦ ±10° of true south. However, from Figure 4 we see that the optimal tilt facingangles south, for within different± 10locationsof true do south. not necessarily However, follow from the Figure conventional4 we see wisdom that the of optimal using latitude tilt angles as for differentthe tilt locations angle; the do deviation not necessarily can be up follow to 15° the from conventional the latitude-tilt wisdom values. of Comparing using latitude Figures as the 1 and tilt 4, angle; ◦ the deviationan interesting can bephenomenon up to 15 from is observed: the latitude-tilt the we values.stern side Comparing of Japan Figures(which 1has and lower4, an interestingannual phenomenonirradiation) is observed:tends to have the lower western optimal side tilt of Japanangles (whichcompared has to lower the eastern annual side irradiation) of Japan. To tends further to have lowerinvestigate optimal tilt this angles observation, compared the annual to the diffuse eastern fraction side of for Japan. all locations To further were investigate investigated this and observation, plotted Sustainability 2019, 11, 2016 4 of 8

Sustainability 2019, 11, x FOR PEER REVIEW 4 of 8 the annualSustainability diffuse 2019, 11 fraction, x FOR PEER for REVIEW all locations were investigated and plotted in Figure6. The4 diffuseof 8 fraction is the ratio of diffuse horizontal irradiance (DHI) and global horizontal irradiance (GHI). inin FigureFigure 6.6. TheThe diffusediffuse fractionfraction isis thethe ratioratio ofof diffusediffuse horizontalhorizontal irradianceirradiance (DHI)(DHI) andand globalglobal Figurehorizontal6 shows thatirradiance at a similar (GHI). latitude, Figure 6 shows the western that at sidea similar of Japan latitude, has the a higher western annual side of diffuse Japan has fraction a comparedhorizontal to the irradiance eastern (GHI). side of Figure Japan. 6 shows It can that be at seen a similar that latitude, the optimal the western tilt angle side is of correlated Japan has a with higherhigher annualannual diffusediffuse fractionfraction compcomparedared toto thethe easterneastern sideside ofof Japan.Japan. ItIt cancan bebe seenseen thatthat thethe optimaloptimal annual irradiation and diffuse fraction. Locations with lower annual irradiation are associated with tilttilt angleangle isis correlatedcorrelated withwith annualannual irradiationirradiation andand diffusediffuse fraction.fraction. LocationsLocations withwith lowerlower annualannual higherirradiationirradiation precipitation areare associatedassociated and hence withwith higher higherhigher annual precipitationprecipitation diffuse fractions andand hencehence (see higherhigher Figure annualannual6). When diffusediffuse the fractionsfractions diffuse fraction(see(see of theFigureFigure irradiance 6).6). WhenWhen is high, thethe diffusediffuse it is more fractionfraction optimal ofof thethe for irradianceirradiance the PV moduleisis high,high, ititto isis havemoremore optimal aoptimal larger forfor viewing thethe PVPV area modulemodule ofthe toto sky (i.e., behavehave inclined aa largerlarger at aviewingviewing lower tilt areaarea angle) ofof thethe to skysky capture (i.e.,(i.e., abebe larger inclinclinedined proportion atat aa lowerlower of thetilttilt angl diffuseangle)e) toto irradiance. capturecapture aa Thislargerlarger effect is alsoproportionproportion shown in ofof recent thethe diffusediffuse studies irradianceirradiance [22,23]... ComparisonThisThis effecteffect isis alsoalso of Figures shownshown 5 inin and recentrecent6 shows studiesstudies that [22,23].[22,23]. the locations ComparisonComparison with a of Figures 5 and 6 shows that the locations with a higher annual diffuse fraction tend to have lower higherof annualFigures diffuse5 and 6 fractionshows that tend the tolocations have lower with a annual higher tiltedannual irradiation, diffuse fraction and tend vice to versa. have lower annualannual tiltedtilted irradiation,irradiation, andand vicevice versa.versa.

Figure 3. Optimal orientations for fixed-tilt PV modules in Japan (interpolated using 837 data points). FigureFigure 3. Optimal 3. Optimal orientations orientations for for fixed-tilt fixed-tilt PV PV modulesmodules in in Japan Japan (interpolated (interpolated using using 837 837datadata points). points). The results are represented as the deviations from the south orientation. A negative (positive) angle The resultsThe results are representedare represented as theas the deviations deviations from from thethe southsouth orientation. orientation. A Anega negativetive (positive) (positive) angle angle means that the module faces slightly eastwards (westwards). meansmeans that thethat modulethe module faces faces slightly slightly eastwards eastwards (westwards). (westwards).

Figure 4. Optimal tilt angles for fixed-tilt PV installations in Japan (interpolated using 837 data points). Sustainability 2019, 11, x FOR PEER REVIEW 5 of 8 Sustainability 2019, 11, x FOR PEER REVIEW 5 of 8 Figure 4. Optimal tilt angles for fixed-tilt PV installations in Japan (interpolated using 837 data Figure 4. Optimal tilt angles for fixed-tilt PV installations in Japan (interpolated using 837 data points). points). Next, the percentage increase in annual irradiation on a fixed-tilt PV module surface mounted Next, the percentage increase in annual irradiation on a fixed-tilt PV module surface mounted at the optimal orientation and tilt angle compared to a south-facing latitude-tilted PV module was at the optimal orientation and tilt angle compared to a south-facing latitude-tilted PV module was determineddetermined (see (see Figure Figure 7). 7). As As can can bebe seen,seen, the increase inin annualannual tilted tilted irradiation irradiation for for an an optimally optimally orientedoriented and and tilted tilted PV PV module module is is upup toto 2%.2%. The gain isis highesthighest in in the the northwestern northwestern region region of ofJapan. Japan. SustainabilityThisThis is isbecause because2019, 11the the, 2016 optimal optimal tilt tilt angles angles in in thisthis region deviatedeviate more more from from latitude, latitude, due due to to the the high high annual annual5 of 8 diffusediffuse content. content.

FigureFigure 5. 5. OptimalOptimal annualannual tiltedtilted irradiation for for fixed-tilt fixed-tilt photovoltaic photovoltaic (PV) (PV) modules modules in inJapan Japan (interpolatedFigure(interpolated 5. Optimal using using 837 annual837 data data points). tiltedpoints). irradiation for fixed-tilt photovoltaic (PV) modules in Japan (interpolated using 837 data points).

Figure 6. Annual diffuse fraction map of Japan (interpolated using 837 data points). The diffuse fraction is the ratio of diffuse horizontal irradiance (DHI) and global horizontal irradiance (GHI).

Next, the percentage increase in annual irradiation on a fixed-tilt PV module surface mounted at the optimal orientation and tilt angle compared to a south-facing latitude-tilted PV module was determined (see Figure7). As can be seen, the increase in annual tilted irradiation for an optimally oriented and tilted PV module is up to 2%. The gain is highest in the northwestern region of Japan. This is because the optimal tilt angles in this region deviate more from latitude, due to the high annual diffuse content. Sustainability 2019, 11, x FOR PEER REVIEW 6 of 8

Figure 6. Annual diffuse fraction map of Japan (interpolated using 837 data points). The diffuse fraction is the ratio of diffuse horizontal irradiance (DHI) and global horizontal irradiance (GHI).

In the real world, the ultimate parameter of interest is the energy output of the PV systems. To accurately calculate the energy output, many loss mechanisms have to be included, as shown in a detailed model by King et al. [24]. To simplify the modeling, the optimal orientation and tilt angle was Sustainabilitydetermined2019 solely, 11, 2016 from the annual tilted irradiation received by the PV modules. This approach6 of is 8 reasonable because a PV system’s electrical output is proportional to the annual irradiation it receives.

FigureFigure 7.7. PercentagePercentage increaseincrease in in annual annual tilted tilted irradiation irradiation on on a fixed-tilta fixed-tilt PV PV module module surface surface mounted mounted at optimalat optimal orientation orientation and tiltand angle tilt comparedangle compared to a south-facing to a south-facing latitude-tilted latitude-tilted PV module (interpolatedPV module using(interpolated 837 data using points). 837 data points). In the real world, the ultimate parameter of interest is the energy output of the PV systems. 4. Conclusions To accurately calculate the energy output, many loss mechanisms have to be included, as shown in a detailedMETPV-11 model by provides King et al.very [24 ].comprehensive To simplify the represen modeling,tative the optimalweather orientation conditions and across tilt angle different was determinedlocations in solelyJapan. from Modeling the annual was performed tilted irradiation using receivedhourly measured by the PV global modules. horizontal This approach irradiance is reasonable(GHI) and because diffuse a horizontal PV system’s irradiance electrical output(DHI) isfr proportionalom METPV-11 to the to annualcalculate irradiation the hourly it receives. tilted irradiance for different orientations and tilt angles for 837 locations in Japan. The flat-plate PV 4.modules’ Conclusions optimal orientation and tilt angles were then determined by finding the value for which the totalMETPV-11 radiation provides on a particular very comprehensive orientation and representative tilt was the weatherhighest. While conditions the optimal across differenttilt angle locationswas found in Japan.to deviate Modeling by up was to 15° performed from the using conventional hourly measured latitude global tilt, the horizontal increase irradiancein annual (GHI)tilted andirradiation diffuse for horizontal an optimally irradiance oriented (DHI) and from tilted METPV-11 PV module to is calculate up to 2%. the It hourlywas also tilted found irradiance that annual for differentdiffuse fraction orientations plays and a major tilt angles role forin determining 837 locations the in Japan.optimal The tilt flat-plate angle. For PV the modules’ same optimallatitude, orientationcompared andto locations tilt angles with were a lower then determined annual diffuse by finding fraction, the locations value for whichwith a thehigher total annual radiation diffuse on a particularfraction were orientation found to and have tilt a waslower the optimal highest. tilt While angle. the It optimalwas hypothesized tilt angle was that found for locations to deviate with by a uphigh to diffuse 15◦ from fraction, the conventional it is more advantageous latitude tilt, the for increase PV modules in annual to be tilted tilted irradiation at a lower forangle, an optimallyto “see” a orientedlarger sky and area tilted for capturin PV moduleg the is diffuse up to 2%.irradiance. It was also found that annual diffuse fraction plays a majorAs role there in determining are uncertainties the optimal in the data tilt angle. and transposition For the same model, latitude, which compared were tonot locations investigated with in a lowerthis study, annual the diffuse percentage fraction, gain locations value presented with a higherin this annualstudy should diffuse only fraction be used were as foundan indication to have on a lowerhow to optimal optimally tilt angle. orient It and was tilt hypothesized the PV system that at for the locations location with of interest. a high diffuse For accurate fraction, PV it issystem more advantageousperformance modeling, for PV modules onsite tomeasurements be tilted at a lowershould angle, be carried to “see” out. a larger sky area for capturing the diffuse irradiance. As there are uncertainties in the data and transposition model, which were not investigated in this study, the percentage gain value presented in this study should only be used as an indication on how to optimally orient and tilt the PV system at the location of interest. For accurate PV system performance modeling, onsite measurements should be carried out. Sustainability 2019, 11, 2016 7 of 8

Author Contributions: All the authors collectively carry out the research and analysis. C.Y. conceived the main idea and led the paper writing with contribution and guidance from Y.S.K. and S.H. C.Y., Y.S.K. and J.C. contributed to the computer simulation, and J.Y. critically revised the manuscript. Funding: This research was supported by the North China Electric Power University, Solar Energy Research Institute of Singapore (SERIS), and China Three Gorges New Energy Co., Ltd. under China Pingshan 10MW PV system project research grant. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Inoue, M.; Genchi, Y.; Kudoh, Y. Evaluating the Potential of Variable Renewable Energy for a Balanced Isolated Grid: A Japanese Case Study. Sustainability 2017, 9, 119. [CrossRef] 2. Pourgharibshahi, H.; Abdolzadeh, M.; Fadaeinedjad, R. Verification of Computational Optimum Tilt Angles of a Photovoltaic Module Using an Experimental Photovoltaic System. Environ. Prog. Sustain. Energy 2015, 34, 1156–1165. [CrossRef] 3. Zang, H.; Guo, M.; Wei, Z.; Sun, G. Determination of the Optimal Tilt Angle of Solar Collectors for Different Climates of China. Sustainability 2016, 8, 654. [CrossRef] 4. Guo, M.; Zang, H.; Gao, S.; Chen, T.; Xiao, J.; Cheng, L.; Wei, Z.; Sun, G. Optimal Tilt Angle and Orientation of Photovoltaic Modules Using HS Algorithm in Different Climates of China. Appl. Sci. 2017, 7, 1028. [CrossRef] 5. Nfaoui, M.; El-Hami, K. Optimal tilt angle and orientation for solar photovoltaic arrays: Case of Settat city in Morocco. Int. J. Ambient. 2018, 1–18. [CrossRef] 6. Rezaei, A.; Hosseini, S.M.; Sharifi, S.; Hekmat, M.; Yektay, N.; Hossein, M.; Bayaz, J.D. Analytical Approaches for Determining Optimal Tilt Angle and Orientation of PV Modules Considering Regional Climate Conditions. In Proceedings of the Iranian Conference on Electrical Engineering (ICEE) 2018, Mashhad, Iran, 8–10 May 2018; pp. 1119–1124. 7. Al Garni, H.Z.; Awasthi, A.; Wright, D. Optimal orientation angles for maximizing energy yield for solar PV in Saudi Arabia. Renew. Energy 2019, 133, 538–550. [CrossRef] 8. Khoo, Y.S.; Nobre, A.; Malhotra, R.; Yang, D.; Rüther, R.; Reindl, T.; Aberle, A.G. Optimal Orientation and Tilt Angle for Maximizing in-Plane Solar Irradiation for PV Applications in Singapore. IEEE J. Photovolt. 2014, 4, 647–653. [CrossRef] 9. New Energy and Industrial Technology Development Organization (NEDO) Meteorological Test Data for Photovoltaic System. Available online: http://www.nedo.go.jp/library/nissharyou.html (accessed on 13 November 2018). 10. NEDO Solar Radiation Browsing System. Available online: http://app0.infoc.nedo.go.jp/metpv/metpv. html (accessed on 13 November 2018). 11. Liu, B.; Jordan, R. Daily insolation on surfaces tilted towards equator. ASHRAE J. 1961, 10, 53–59. 12. Klucher, T. Evaluation of models to predict insolation on tilted surfaces. Sol. Energy 1979, 23, 111–114. [CrossRef] 13. Hay, J.E.; Davies, J.A. Calculation of the solar radiation incident on an inclined surface. In Proceedings of the First Canadian Solar Radiation Data Workshop, Toronto, ON, Canada, 17–19 April 1978; pp. 59–72. 14. Perez, R.; Seals, R.; Ineichen, P.; Stewart, R.; Menicucci, D. A new simplified version of the perez diffuse irradiance model for tilted surfaces. Sol. Energy 1987, 39, 221–231. [CrossRef] 15. Polo, J.; Garcia-Bouhaben, S.; Alonso-García, M.C. A comparative study of the impact of horizontal-to-tilted solar irradiance conversion in modelling small PV array performance. J. Renew. Sustain. 2016, 8, 53501. [CrossRef] 16. Yang, D.; Dong, Z.; Nobre, A.; Khoo, Y.S.; Jirutitijaroen, P.; Walsh, W.M. Evaluation of transposition and decomposition models for converting global solar irradiance from tilted surface to horizontal in tropical regions. Sol. Energy 2013, 97, 369–387. [CrossRef] 17. Noorian, A.M.; Moradi, I.; Kamali, G.A. Evaluation of 12 models to estimate hourly diffuse irradiation on inclined surfaces. Renew. Energy 2018, 33, 1406–1412. [CrossRef] 18. Utrillas, M.P.; Martinez-Lozano, J. Performance evaluation of several versions of the Perez tilted diffuse irradiance model. Sol. Energy 1994, 53, 155–162. [CrossRef] Sustainability 2019, 11, 2016 8 of 8

19. Reindl, D.; Beckman, W.; Duffie, J. Evaluation of hourly tilted surface radiation models. Sol. Energy 1990, 45, 9–17. [CrossRef] 20. Muneer, T. Solar Radiation and Daylight Models; Routledge: London, UK, 2012. 21. Duffie, J.A.; Beckman, W.A.; McGowan, J. Solar Engineering of Thermal Processes; Wiley: New York, NY, USA, 1991. 22. Appelbaum, J.; Aronescu, A. The effect of sky diffuse radiation on photovoltaic fields. J. Renew. Sustain. 2018, 10, 033505. [CrossRef] 23. De Morais, M.V.B.; De Freitas, E.D.; Marciotto, E.R.; Guerrero, V.V.U.; Martins, L.D.; Martins, J.A. Implementation of Observed Sky-View Factor in a Mesoscale Model for Sensitivity Studies of the Urban Meteorology. Sustainability 2018, 10, 2183. [CrossRef] 24. Kratochvil, J.A.; Boyson, W.E.; King, D.L. Photovoltaic Array Performance Model; United States Department of Energy: Washington, DC, USA, 2004; pp. 2004–3535.

© 2019 by the authors. 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/).