1 Solar Radiation – The Estimation of the Optimum Tilt Angles 2 for South-Facing Surfaces in Pristina 3

Solar energy is derived from photons of light coming from the sun in a form called 12 radiation. Solar energy finds extensive application in air and water heating, solar cooking, as well 13 as electrical power generation, depending on the way of capturing, converting and distribution. To 14 enable such application, it is necessary to analyze the horizontal tilt angle of horizontal surfaces – in 15 order that when the solar energy reaches the earth surface to be completely absorbed. This paper 16 tends to describe the availability of solar radiation for south-facing flat surfaces. The optimal 17 monthly, seasonal, and annual tilt angles have been estimated for Pristina. The solar radiation 18 received by the incident plane is estimated based on isotropic sky analysis models, namely Liu and 19 Jordan model. The annual optimum tilt angle for Pristina was found to be 34.7°. The determination 20 of annual solar energy gains is done by applying the optimal monthly, seasonal and annual tilt 21 angles for an inclined surface compared to a horizontal surface. Monthly, seasonal and annual 22 percentages of solar energy gains have been estimated to be 21.35%, 19.98%, and 14.43%. Losses of 23 solar energy were estimated by 1.13 % when a surface was fixed at a seasonal optimum tilt angle, 24 and when it was fixed at an annual optimum tilt angle, those losses were 5.7%. 25


Introduction
Because of a significant increase in energy demands, conventional energy sources are being violently consumed, leading to an increase of pollutants, which are released from the burning of fossil fuels.Knowing that solar equipment's do not have moving parts, they are considered to have agreater lifetime and do not cause pollution compared to other energy sources.
Therefore, solar energy is considered as one of the best solutions.
In most cities of Kosovo, the maximum global solar radiation is reached during July, whereas the minimum during December.
The performance of solar equipment's (i.e.solar collectors for water and air heating, power generation, photovoltaic systems, etc.), is closely related to the inclined angle from the surface that absorbs the light of the sunshine (i.e. with their placement plane).
Sun tracking systems are used to increase the acceptance of solar radiation.The usage of these systems has a significant cost to the normal operation of an entire system, due to the consumption of a considerable energy generated.
Hence, the estimation of the optimal tilt angle has a crucial effect on the solar technology.Additionally, trackers need periodic maintenance and calibration and require input energy for their operation which is in the range of 5-10% of the energy produced (Eldin et al).( 2016) [1].Further, trackers are made up of sophisticated mechanical parts which add to capital cost and an increase in cost of absolute power produced from solar PV panels (Sinha and Chandel, 2016) [2].Other method readily suggested by researchers is to optimize the orientation of flat surfaces at optimum tilt inclination (βopt) (Yakup et al., 2001) [3].Vieira et al. (2016) [4] performed an experimental study which suggested that the sun tracking panel exhibited a low average gain in power generated, relative to the fixed panel.In another study conducted by Sinha and Chandel [2], it was reported that the horizontal axis weekly adjustment tracking systems and vertical axis continuous adjustment tracking systems, produced less energy annually than the existing PV systems at fixed tilt.Optimum tilt inclination can be adjusted daily, monthly, seasonally, bi-annually or annually for maximizing the performance of the device in use (Ahmad and Tiwari, 2009) [5].
In the city of Shterpca, the annual solar radiation is estimated to be 1333.7 kWh/m 2 /year, while in the city of Gjakova 1495.1 kWh/m 2 /year.Furthermore, knowing the geographical position of the aforementioned cities, we can accept an average value of solar radiation of1400 kWh/m 2 /year for the climate conditions of Kosovo (Ministry of Energy and Mining of Kosovo, 2010) [6].
This solar radiation potential can be utilized in desalination, solar-thermal collectors, building heating,day-lighting, and Photovoltaic (PV) Cells etc..Researchers are therefore concerned to maximize the amount of useful energy that can be extracted through the incoming solar radiations.It is believed that proper installation of these devices can make a remarkable change in the observed performance.Hence, climatology, latitude, orientation, tilt angle, azimuth angles and the usage over a period in a specific geographical region affect the performance of the abovementioned devices (Yakup and Malik, 2001) [3].
The tilt of a surface (β) is one of the significant factors that considerably affect the availability of solar radiation on a flat surface.Optimization of the performance of solar-based devices requires option-like solar tracking equipment, which follow trajectories of Sun's motion to enhance incident radiation (Ahmad et al.,2016) [7] and (Okoye et al.,2016) [8].However, these options are not always economical.

Location under study
Pristina -the capital city -(42.65˚N, 21.15˚ E and 573 m a.s.l.) is situated in the north-east of Kosovo.Pristina has a humid continental climate with maritime influences.
The city features warm summers and relatively cold snowy winters.According to a study conducted by the Ministry of Energy and Mining of Kosovo of Kosovo MEM (2010) [6] for zones with solar radiation potential, Kosovo has been divided into four zones of rough solar radiation.
Population density in Kosovo is greater in the central and western parts compared to the eastern parts.Hence, the division into three zones in an acceptable approximation since the solar radiation in Zone 3, and Zone 4 do not change much, as well as the opportunities to widely use solar energy in Zone 4 (which is smaller regarding surface area) are practically not that greater.The highest value of solar radiation are shown in Zone 1 while the lowest appear in Zone 4. The division of municipalities by area of solar radiation intensity is presented in Table 1.MEM (2010) [6].

Solar radiation data
In this paper, we used meteorological data for daily mean global and diffuse radiation on a horizontal plane, which are taken from the Meteorological Institute of Kosovo and are presented in Figure 1.The surface reflection factor is assuMEM to be 0.20.
The maximum values of monthly mean solar radiation are reached in July and the minimum values in December.In Figure 2 is presented the annual average global radiation on a horizontal plane for Kosovo.As can be seen from Figure 1, the highest value of average global solar radiation from all cities of Kosovo is Gjakova.In Figure 3 is presented the annual average direct normal radiation on a horizontal plane for Kosovo cities.

Estimation of Solar Radiation on the Inclined Surface
Data on monthly mean global solar radiation for an inclined surface are necessary for the designing of solar energy systems.
These data are often not available.Therefore, we need tend to estimate the data by considering the monthly average global solar radiation on a horizontal plane, (presented in Figure 3) which is the most important parameter for estimating the optimum tilt angle.
In this study, we present a simple and universal method for determining the mean monthly global radiation based on the methodology released by Surface Meteorology and Solar Energy (SSE) (2016) [34].The total solar energy received on an inclined surface is the sum of the beam, diffuse, and reflected radiation.
Thus, the monthly average total solar radiation (in kWh/m 2 -day) for an inclined surface is given by this equation: Where mathematically, the optimal value of the tilt angle (βopt) is determined by differencing Eq. 1 depending on the angle of inclination (β).
R is the ratio between the mean monthly global radiation on an inclined surface than for the horizontal one.R ratio, defined by Bakirci (2012) [9], Liu and Jordan (1962) [35]: H and D H are the monthly average daily global and diffuse radiations on a horizontal surface; b R is the ratio of the mean daily direct radiation on an inclined surface to that on a horizontal surface, and the parameters correlated by ground reflection coefficient (albedo ρ=0.2); β is the tilt angle.The beam radiation falling on an inclined surface is given by Liu and Jordan (1962) [35]: Reflected radiation is the part of total solar radiation that is reflected by the surface of the earth, and by any other surface intercepting object such as trees, terrain or buildings on to a surface exposed to the sky is termed as ground reflected radiation [36].Reflected radiation on an inclined surface is given by: is the reflected conversion factor: where ρ is the constant which depends on the type of ground surrounding tilted surfaces and is called the ground reflectance or albedo.The value of albedo most commonly used is ρ= 0.2 for hot and humid tropical locations, ρ= 0.5 for dry tropical locations, and ρ= 0.9 for snow covered ground [37].The ground reflection coefficient is assumed 0.2 for the climate conditions in Pristina.
Diffused radiation ( ) D H is that fraction of total solar radiation which is received from the sun when its direction has been changed by atmospheric scattering [38].The direction of diffused radiation is highly variable and difficult to determine.It is a function of the condition of cloudiness and atmospheric clearness which is extremely unpredictable.The diffused radiation fraction is the sum of three components namely isotropic, circumsolar, and horizon brightening.The isotropic diffuse radiation component is received evenly from the entire sky dome.The circumsolar diffuse part is received from the onward dispersion of solar radiation and concentrated in the section of the sky around the sun [39].The horizon brightening component is concentrated near the horizon and it is most obvious in the clear skies [40].In general, the diffuse fraction of radiation on inclined surface is composed of isotropic, circumsolar, and horizon brightening factors.In Liu and Jordan (1960) [41] model, it was assumed that the diffuse radiation is isotropic only; whereas, circumsolar and horizon brightening were taken as zero.
Diffuse radiation falling on an inclined surface is given by: where d R is the diffuse conversion factor presenting the ratio of diffuse solar radiation on an inclined surface to diffuse solar radiation on a horizontal surface, given as: Data on monthly average daily global radiation which were taken from Figure 3., are used in the following expressions for determination of other parameters.The following expression determines the monthly average daily diffuse radiation [34]: where SSHA is the sunset hour angle in degrees on the "monthly average day (n)", which can be calculated from the following equation: NHSA is the noon solar angle from the horizon in degrees on the "monthly average day (n)" and can be calculated from the following relation: The monthly average clearness index T K is the ratio of monthly average daily radiation on a horizontal surface to the monthly average daily extraterrestrial radiation and can be obtained from: where, 0 H is the monthly mean daily extraterrestrial radiation on a horizontal surface (Alboteanu et al., 2015) [42], which are calculated using: sunset) angle on a horizontal surface; δ is the declination of the sun.The "monthly average day" is the day of the month, whose solar declination is closest to the average declination for that month [43].Declination angle (δ) ranges from a maximum value of +23.45˚ on June 21 st -22 nd ,to a minimum value -23.45˚ on December 20 th -21 st .The declination value is zero on March 22 nd and September 22 nd of the year, see Table 2.According to Cooper (1969) [44], declination angle is calculated using the following relation: where n is the day of the year.
The angle of incidence for a surface oriented in any direction can be mathematically expressed by following relation (Duffie and Beckman, 2006) [53]: For a surface in northern hemisphere facing south (i.e.γ = 0o) Eq. ( 16) can be simplified as: For a horizontal surface (β=0 o ), the angle of incidence (θ) becomes equal to zenith angle (θz).Substituting this value in Eq. ( 17), zenith angle can be written as: The total solar energy received on an inclined surface is the sum of beam and diffuse radiations directly incident on a surface and reflected radiations (reflected by the surroundings).
According to Liu and Jordan (1960) [41], the beam conversion factor b R is given as: where ω is the sunrise (or sunset) hour angle for the inclined surface.The hour angles at sunrise and sunset ωs are very useful parameters.Considering that numerically these two angles have the same value the sunrise angle is negative, and the sunset angle is positive.Both can be calculated from the following expression: If a surface is inclined from the horizontal, the Sun may rise over its edge after it has risen over the horizon.Therefore, the surface may shade itself for some days.The sunrise and sunset angles for an inclined surface ( ) facing the equator (i.e.facing south for the northern hemisphere) is given by:

Results and Discussions
In this paper, Equations  are applied to determine the monthly mean daily global solar radiation on the south-facing inclined surface for the current location.By changing the tilt angle from 0° to 90° in steps of 0.1°, the optimal tilt angle is defined by the corresponding value of maximum solar radiation for a given period.
Using the procedure described in the previous Section 3, and based on the Liu and Jordan (1960) [41] model, estimations have been made to obtain the optimum monthly, seasonal, and annual tilt angles by corresponding to global solar radiation on an inclined surface.Table 3 presents the results for determining the optimum monthly, seasonal and annual tilt angles at certain periods.For the location under study, the monthly optimal tilt angle has been estimated with the method described in Section 3. The results are shown in Table 4.The daily extraterrestrial radiation on a horizontal surface, clearness index, diffuse solar radiation on a horizontal plane, optimal tilt angle βopt, monthly average daily global radiation in optimal tilt angle, and the comparison with (in percentage), has also been estimated.Table 4 shows the minimum and maximum value of, which correspond with December and July respectively.
For the location under study, the monthly optimal tilt angle has been estimated with the method described in Section 3. The results are shown in Table 4.The daily extraterrestrial radiation on a horizontal surface 0 H , clearness index T K , diffuse solar radiation on a horizontal plane d H , optimal tilt angle βopt, monthly average daily global radiation in optimal tilt angle T H , and the comparison H with T H in percentage, has also been estimated.Table 4 shows the minimum and maximum value of T H , which correspond to the months of December and July respectively.For all the months and different tilt angles, monthly average total solar radiation was calculated using Eq. ( 1).The results have been plotted and are shown in Figure 4 for Pristina, where the tilt angle has been varied in the range of 0-90˚ (in steps of 10˚). Figure 4 (a) shows the total solar radiation versus tilt angle for the months from January to June while Figure 4 (b) shows the same for the remaining months of July to December.It is apparent from the Figure 4 that the solar radiation is an intensive function of tilt angle.The calculated solar energy radiation incident on the flat surface is increased, with the increasing of horizontal position from 0˚ to an angle of inclination, but a further increase of the tilt angle of the flat surface will result in the decreasing of solar radiation received.
The result also indicated that the optimum angle varies with the months of the year.The maximum solar radiation is achieved for every month with unique optimum tilt angle.The optimum tilt angle increases in winter months and decreases to the minimum value in summer & autumn months, (see Figure 5).Figure 6 compares the average annual solar radiation on a tilted surface fixed at monthly, seasonal and annual optimum tilt angles for Pristina.As observed from the Figure 6, the annual average total solar radiation estimated at monthly optimum tilt angle is found to be the highest, followed by average annual solar radiation estimated at seasonal and annual optimum tilt angles value.The monthly, seasonal and annual optimal tilt angles are also plotted in Figure 5.
where i= monthly, seasonal and annual Therefore, four seasonal optimum tilt angles were obtained (corresponding to each season) -62.1˚ in winter, 25.7˚ in spring, 8.9˚ in summer, and 50.9˚ in autumn.Thus, winters have a higher value of optimum tilt angle, while summers observe a lower tilt angle value.Annual optimum tilt angle was calculated by using expressions from Section 3 and has resulted to be 34.7˚ for Pristina.
Annual average total gains of solar radiation on an optimally tilted angle of a surface in comparison to a horizontal surface are 21.35% (monthly optimum tilt angle), 19.98% (seasonal optimum tilt angle) and 14.43% (annual optimum tilt angle).
The difference between the total solar radiation at monthly, seasonal, and annual optimum tilt angles is very small.However, there is a loss in solar radiation available, when a surface is fixed on seasonal or annual optimum tilt angle in comparison to a fixed monthly optimum tilt angle.
Losses of solar radiation available on an inclined surface are defined by: , ( ) (%) 1 100 ( (mothly) where j= seasonal, annual.Losses of solar energy were estimated by 1.13 %, when a surface was fixed at the seasonal optimum tilt angle, and when it was fixed at the annual optimum tilt angle, those losses were 5.7 %.
For the location under study, the data have been estimated for the seasonal and annual optimal tilt angles with the method described in Section 3. Table 5 shows the results for the diffuse radiation on a horizontal plane; the annual and seasonal optimal tilt angles for each season; the monthly average daily global radiation for optimal tilt angle; and the comparison of H with HT in percentage.

Figure 1 .Figure 2 . 3 .
Figure 1.Monthly means daily global radiation Gm and diffuse radiation Dm on horizontal plane of Pristina

Figure 4 .
Figure 4. Monthly mean solar radiation data for Pristina when the tilt angle changes from 0 o to 90 o : (a) January-June and (b) July-December

Figure 5 . 6 .
Figure 5. Average maximum total solar annual Figure 6.Variations of monthly, seasonal and

Figure 8 .
Figure 8.(a) Beam conversion factor at different tilt angles for Pristina, (b) Diffuse and reflected conversion factors.

Figure 8 .
Figure 8.a describes the variation of beam conversion factor with days of the year at various tilt angles for the city of Pristina.Also, Figure 8.b shows the variation of diffuse and reflected conversion factors at different tilt angles.

3 August 2017 doi:10.20944/preprints201708.0010.v1
where I0 is the solar constant (1367 W/m 2 ); n is the number of daily readings of the month and is counted from 1 January (1-365);  is the geographic latitude of the location; ωs is the sunrise (or Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted:

Table 2 .
Monthly representative day and its corresponding declination (δ in degrees) 

Table 3 .
Monthly, seasonal, and yearly optimum tilt angles (βopt in degrees) for Pristina city

Table 5 .
, βopt, T H and the comparison with H of Pristina for seasonal and annual tilt angles d H