Meteorological-Data-Based Modeling for PV Performance Optimization

: Developing a sustainable and reliable photovoltaic (PV) energy system requires a comprehensive analysis of solar proﬁles and an accurate prediction of solar energy performance at the study site. Installing the PV modules with optimal tilt and azimuth angles has a signiﬁcant impact on the total irradiance delivered to the PV modules. This paper proposes a comprehensive optimization model to integrate total irradiance models with the PV temperature model to ﬁnd the optimal year-round installation parameters of PV modules. A novel integration between installation parameters and the annual average solar energy is presented, to produce the maximum energy output. The results suggest an increase in energy yields of 4% compared to the conventional scheme, where tilt angle is equal to the latitude and the PV modules are facing south. This paper uses a real-time dataset for the NEOM region in Saudi Arabia to validate the superiority of the proposed model compared to the conventional scheme, but it can be implemented as a scheme wherever real-time data are available.


Introduction
In addition to energy challenges related to the depletion of fossil fuels and their implications for energy security and sustainability, new challenges have emerged.For example, the impact of greenhouse gas emissions from fossil fuels on the global climate system is a rising concern to the international community.In addition, the high air pollution caused by the intensive use of fossil fuels, and its implications for public health, is alarming to many countries.A major transition to low-carbon energy systems is essential to mitigate the greenhouse gases caused by fossil fuels [1].Therefore, there serious interest exists in regard to reducing the impact of fossil fuel emissions.In 2015, 190 countries signed the Paris Agreement, which is a commitment to reduce emissions of carbon dioxide (CO 2 ), the underlying cause of greenhouse gases (GHG) [2], from fossil fuels.The agreement set an ambitious target to reach net-zero carbon emissions by 2050.
The intensive use of fossil fuels for energy has been challenging to the energy sector [3].The growth in annual energy demand was estimated to increase by 1.3% each year until 2040 [4].However, the global energy demand recorded a 5.4% increase in 2021 alone, as the world economy recovered from COVID-19 at an unprecedented rate, while energy intensity improvements stalled during the pandemic.The surging demand for energy in 2021 was mostly met by fossil fuels, which resulted in a record high of annual-basis increase in global CO 2 emissions, adding more challenges to the progress toward the global objective of net-zero carbon emission by 2050 [5,6].
The energy and energy-related challenges have to be comprehensively addressed through studies that identify strategies and solutions that may help to achieve sustainable and efficient systems that have lower carbon emissions [7].In this context, increasing the share of renewable energies in the energy mix is crucial for a sustainable supply for the energy demand, while maintaining the mission of curbing greenhouse gases [8].Installation of renewable energy systems is continuously achieving annual record growth, despite unforeseen disruptions.In 2021, for instance, a record annual increase of 17% in the renewables capacity was achieved.The total installed capacity reached 3146 GW, which was mainly driven by solar photovoltaic (PV) and wind power, despite the increased delivery lead time, increased prices of solar and wind energy system components, and the unprecedented supply chain disruption caused by COVID-19.In 2021, 28.5% of the world's electricity demand was supplied by renewable energies, yet, with the surging energy demand, most of the demand was met by fossil fuels, accounting for around 80%.Only 20% of the demand was met by renewables, mainly solar and wind energy sources, which is far from the required progress to achieve the mission of net-zero carbon emission by 2050 [6].
Many studies suggest the domination of solar and wind energy in regard to total renewable energy potential [9], however, the evaluation of the available renewable energy sources that can be sustainably harvested is decisive [7].Different constraints exist that affect the extractable net renewable energy, including intermittency [9] and land occupation constraints [10].With regards to the economics, ref. [11] emphasize the importance of considering the renewable energy availability constraints prior to assessing the energy return on investment (EROI) in renewable energy.In their work, they used a global gridcell approach to assess the global net solar energy potential.Of the constrained available global solar energy, which is significantly lower than previous estimates, EROI ratios of only 5, 7.5, and 9 can be achieved if 98%, 75%, and 15% of the available solar energy is extracted, respectively.
The high constraints impacting renewable energy availability, the technical efficiency, and the economic barriers [12], create a need for an optimized utilization of renewable energy systems.In the case of solar energy, which is the focus of this paper, numerous technology and scenario configurations exist that impact the parameters leading to the achievement of different harvesting levels of solar energy potential.In this context, different cell technologies are estimated to deliver distinct cell efficiencies.In a survey of solar cell supply companies for 2020, p-type monocrystalline silicon (p-type mono-si) cells were estimated to deliver 22.8% efficiency, while multicrystalline silicon (mc-si) cells had a lower average efficiency, estimated at 20.8% [13].
In addition, installation of fixed-tilt solar PV systems versus those installed with tracking capability is estimated to deliver different solar module efficiencies [14].Solar systems with tracking capabilities outperform fixed-tilt systems due to their ability to follow the sun's movement and, thus, maximize the solar irradiation reaching the surface of the solar panels.However, the tracking systems are rarely cost effective due to their high cost and demand for energy for operation.Therefore, cyclic adjustments of the solar panels elevations to the optimal tilt angles related to the horizon is an applicable way to optimize the output of the solar systems [15].
The problem of finding the optimal tilt angle has been a research interest for decades.Over the years, the problem of specifying the optimal tilt angle has been investigated through different approaches for different locations.Some researchers have treated the optimal tilt as a function of latitude only [16][17][18], while [19] formulated the optimal tilt angle as a function of latitude, type of energy demand, and weather characteristics.Qualitative, analytical, and quantitative treatments for the problem are continually being explored in the literature [20][21][22][23][24][25].
When it comes to specifying the optimal tilt angle for the best solar irradiance collection, a wide range of optimal tilt angles have been recommended in the literature, mostly for specific locations, months, and seasons.Ref. [26] recommended, for Lhasa, China, an optimal tilt angle fixed at 50 • .Ref. [15] concluded that, for Madinah, Saudi Arabia, the optimal tilt angles for spring, summer, fall, and winter were 17 • , 12 • , 28 • , and 37 • , respectively.Similarly, ref. [27] recommended that the optimal tilt angles for winter and summer were 43.3 • and nearly flat, respectively, which is about the latitude ±15 • .
Likewise, the optimal fixed tilt angle for solar panels has been widely recommended in relation to the latitude of the location.Ref. [15] concluded that the optimal annual average tilt angle for Madinah, Saudi Arabia, is 23.5 • , which is relatively close to Madinah's latitude of 24.5 • .Ref. [28] suggested that the optimal fixed tilt angle in Jeddah, Saudi Arabia, should be 24.5 • , which corresponds to the latitude of Jeddah (21.5 • ).Similar results were found for different locations, such as Ontario, Canada [29], New Delhi, India [30], Kuala Lumpur, Malaysia [31], and different cities in Saudi Arabia [32].
Despite the wide consensus in the literature on the relativity between the annual optimal tilt angle and the conventional orientation (latitude), it has been suggested that fixing the solar collector at an angle equal to the location's latitude could considerably limit the full utilization of the solar collection system.A study conducted by [33], for 18 locations in Saudi Arabia, concluded that the optimal tilt angle was significantly different from the latitude.Ref. [34] concluded that for San Francisco and Paris, a potential increase of 2.04% and 7.38%, respectively, could be achieved in yielded energy by optimizing the tilt angle compared to a fixed tilt angle corresponding to the latitude.Ref. [30] estimated that using a yearly average fixed tilt angle (latitude) resulted in a 15% loss in achievable energy compared to a monthly adjustment of the tilt angle.
Similarly, different conclusions have been reached regarding the effectiveness of monthly adjustments of the optimal tilt angle on the gains in collected solar energy.The results derived by [35] demonstrate that different monthly adjustments of the optimal tilt angle delivered significant changes in solar energy gains.They concluded that, for Dhaka, Bangladesh, a 15% average annual increase existed in the output of the solar energy system through monthly adjustments of the optimal tilt angle.Similarly, ref. [33] conducted a study on 18 different locations in Saudi Arabia and concluded that, for Riyadh, a 4.01% energy yield could be achieved through monthly adjustments of the optimal tilt angles.
On the other hand, ref. [26] reported a diminished significance of monthly adjustments of the optimal tilt angle on solar energy gains in their study carried out during the heating season (i.e., November 15 to March 15) in Lhasa, China.While the monthly optimal tilt angles were 50 • , 60 • , 60 • , 50 • , and 30 • for November, December, January, February, and March, respectively, the change in solar energy gains was not significant.The five monthly tilt angle adjustments, at a fixed azimuth angle of 5 • , did not exceed a maximum increase of 1.1% in the collected hourly average solar irradiance.Likewise, ref. [36] conducted a study to analyze the optimal tilt angle for a fixed building integrated photovoltaic (BIPV) system, south oriented tilted roof, at 20 different locations in 14 countries, and found that more than 98.5% of the system's performance can be obtained using a tilt angle identical to the location's latitude.Mixed results are reported in the literature regarding the optimal tilt angle.In addition, the solar panel's surface orientation (azimuth angle) is commonly assumed to be facing towards the equator when finding the optimal tilt angle, or the optimal tilt and azimuth angles are separately determined.
By considering the effects of both ambient temperature and wind speed on the temperature of photovoltaic modules, this work introduces a novel multi-objective optimization methodology to explore the optimal tilt angle and optimum azimuth angles simultaneously.Then, the output of the solar irradiance model and the PV temperature model are used, in conjunction with an equivalent electric circuit model and maximum power point tracking (MPPT), to provide a comprehensive estimate of the induced power density and annual energy, based on real-time meteorological data.Any site where a PV system is planned to be installed is suitable for the proposed project.Here, a cluster of sites has been determined using the proposed methodology, and the results are compared to those obtained using the conventional approach.
The remainder of this paper is structured as follows.The state-of-the-art solar irradiance, PV temperature, and energy yield prediction models are reviewed in Section 2. In Section 3, the results of the models presented in Section 2 are discussed.Section 4 concludes this paper.

PV Performance Investigation Methodology
For optimizing the PV output power and energy, a modeled process is implemented using MATLAB.Figure 1 represents the flowchart for the optimization process.It starts with defining the input data for a certain location and the PV module specifications for the certain manufactured model intended to be applied.The input data consists of solar data (irradiance and angles) and meteorological data (ambient temperature and wind speed).The solar data, with the range set of optimization factors (tilt β and azimuth γ), are taken into the solar irradiance model (Section 2.1).Next, the output of the solar irradiance model with the absorbed total global horizontal irradiance GH I t , with both meteorological data and selected PV module specifications, are inserted into the PV temperature model (Section 2.2), resulting in the absorbed cell temperature T c .This, combined with previous results, becomes the input of the PV equivalent electric circuit model (Section 2.3), which results in different values of PV output, in which several iterations are run, based on the range values of both β and γ, to find their optimum values.

Solar Irradiance Model
The meteorological data collected by the King Abdullah City for Atomic and Renewable Energy (KACARE) consists of different types of solar intensity, which are global horizontal irradiance (GH I), direct normal irradiance (DN I), and diffuse horizontal irradiance (DH I).GH I is the sum of both DN I and DH I on a horizontal surface.However, in this model, having more estimation accuracy requires recalculating the global irradiance to be compatible with the tilted surface (i.e., the tilted PV panel).The solar irradiance model on the tilted surface can be represented by either an isotropic or an anisotropic sky model.In this research, an isotropic sky model was utilized, since the distribution of the diffuse irradiance from the sky is assumed to be received uniformly [37,38].The following equation defined the total global irradiance on a tilted surface (GH I t ) as the sum of direct irradiance (DN I t ), diffuse irradiance (DH I t ), and reflected irradiance (RI t ).
The direct irradiance on the tilted surface, DN I t , can be written as: where R b is the geometric factor that represents the beam radiation ratio of a tilted to a horizontal surface at any time [37].This factor can be expressed as: where θ is the incidence angle of the directed normal radiation to a surface and, as in [4], cos θ represents the relationship between the sun's position and a plane on the earth in terms of several angles, such as the zenith angle, θ z , illustrated in Figure 2 [37].
where all the angles are defined in Table 1 and Figure 2. The solar declination can be expressed as: where n is the day number during the year (i.e., 1 to 365).The second term in (1) is the diffuse irradiance on a tilted PV module, DH I t , which is expressed as: where R d f is a geometric factor that represents the diffuse radiation ratio of a tilted to a horizontal surface at any time [37].This factor can be expressed as: The last term in (1) represents the reflected irradiance, RI t , which depends on the nature of the Earth and surrounding circumstances.The measurement of these impacts are evaluated using the geometric factor, R r , and the irradiance reflection coefficient (i.e., albedo factor), ρ [37]. where

PV Temperature Model
The temperature of the PV cell has a key impact on the PV performance.Three variables play a role in changing the PV cell temperature (T c ): solar radiation (G T ), ambient temperature (T a ), and wind speed (v w ) [37,39].The following function defines the relationship between those factors and the cell temperature, which can be determined from: -T NOCT : the nominal operating cell temperature when the ambient temperature is 20

PV Equivalent Electric Circuit Model and MPP Tracker
After determining both the irradiance that was delivered to the PV module and the PV cell temperature, as discussed in Sections 2.1 and 2.2, the electric power generated by the PV module needs to be estimated in order to determine the PV performance.Thus, in this section, an equivalent electric circuit for the PV cell and a maximum power point tracking algorithm are discussed.
By modeling the PV equivalent electric circuit, the output voltage and current can be determined.There are different electrical PV circuits for predicting PV cell output power, such as the single-diode (SD) PV model, double-diode (DD) PV model, and tri-diode (TD) PV model, as discussed in [40].Here, we choose the single-diode equivalent circuit model, shown in Figure 3, as a commonly used example in the literature [41].However, the proposed method in this paper is general and can easily be applied to the other model types.As illustrated in Figure 3, the equivalent circuit includes the dependent current source due to the photon delivered to the cell from the sunlight (I ph ), the p-n junction diode resulting from the fabrication of the semiconductor, and internal series and parallel resistances (R S , R P ).
The output current (I) of each cell is described by: where I ph is related to both the total global irradiance on a tilted PV module (G T ) and the PV cell temperature (discussed in the previous two sections).I d is defined by the Shockley diode equation, as in (11), which describes its voltage-current characteristic.I 0 is the reverse bias saturation current.V T is the thermal voltage.Both I 0 and V T are also proportional to the cell temperature.n is the diode ideality constant, which is between 1 and 2 [42].
To clarify the relation between the PV equivalent electric circuit model and the previous models of solar irradiance and PV cell temperature, more detailed sub-equations from (11) need to be described.
where -G n : the irradiance under standard test conditions, STC; -I SC : the desired short-circuit current for the PV module; -k i : the temperature current constant in kelvin; -T n : the temperature under standard test conditions, STC, in kelvin; -V OC : the desired open-circuit voltage for the PV module; -q: the electron's charge in coulomb (1.602 × 10 −19 C); -E g : the band gap, 1.12 eV, for the silicon under standard test conditions, STC; -k: the Boltzmann constant (1.38065×10 −23 J/ • K); and -N s : the number of series-connected cells in the PV module.Now, the output electric power can be determined, as the MPP tracker is implemented to deliver the maximum possible power from the PV unit.The MPP curve is generated over the current-voltage characteristics of the PV cell, as shown in Figure 4.The power delivered by the module is the product of voltage (V) and current (I).The MPP is the rated power (P R ), which is caused by the product of the designated rated voltage (V R ) and rated current (I R ) under different circumstances.Several types of MPPT algorithms exist that can be applied, such as the perturbation and observation (P&O) technique, the incremental conductance technique, and fractional open-circuit voltage technique [43,44].
-V W is the band gap, 1.12 eV for the Silicon under standard test condition STC.
-+ * is number of series connected cells in the PV module.Now, the output electric power can be determined as the MPP tracker is implemented deliver the maximum possible power from the PV unit.The MPP curve is generated over current-voltage characteristics of the PV cell as shown in Figure 3.The power delivered the module is the product of voltage (L) and current (#).The MPP is the rated power ( which is resulted by the product of the designated rated voltage (L N ) and rated current ( under different circumstances.There several types of MPPT algorithm can be appl practically such as the perturbation and observation (P&O) technique, the incremen conductance technique, fractional open-circuit voltage technique, and others [38] [39].

PV Performance Investigation Analysis and Results
The analysis in this paper will be focused on the NEOM, the planned cross-border region in the Kingdom of Saudi Arabia, as a case study.The investigation of the optimal installation of solar modules in the NEOM is of great interest due to the announced ambitious plans for the energy system in the region.The goal is to build a 100% carbon-free powered region, with a great emphasis on leveraging both solar and wind energy sources.The region is planned to cover a total area of 26,500 km 2 and, thus, it is represented by three adjacent cities (i.e., Tabuk, Hagl, Duba) due to data availability constraints.

Solar Irradiance Absorbed by the Tilted PV Module
The PV irradiance model presented in Section II.A was implemented in MATLAB to simulate the impact of module tilt and azimuth angles on the amount of incident solar radiation on the PV module.Three-dimensional planes, shown in Figures 5-7, were plotted to demonstrate the sensitivity of the incident solar radiation to the variation in the tilt and azimuth angles for the locations studied: Tabuk, Hagl, and Duba.The incident solar radiation values were calculated for azimuth angles which ranged from −100 • in the east direction to +100 • in the west direction, relative to the direction due south, with 1-degree increments.Simultaneously, the analysis was carried out for the tilt angles, which ranged from 0 • to 90 • , with 1-degree increments.
Figure 5 shows the behavior of the incident solar radiation on the PV module with the variation in the tilt and azimuth angles at Tabuk.The PV module was exposed to a higher intensity of solar radiation when moving from the vertical to the inclined surface, where the solar intensity increased gradually as the tilt increased to approximately 30 • .Then, it started to decrease.On the other hand, directing the PV module far away from due south, toward either the west or east, revealed that similar exposure of solar intensity was obtained.However, superior results were shown when the PV module was slightly directed to face southwest.Figures 6 and 7 show similar behaviors in Hagl and Duba, respectively.Table 2 summarizes the results presented in Figures 5-7, which identified both the optimal tilt angle (β opt ) and optimal azimuth angle (γ opt ) in Tabuk, Hagl, and Duba, as well as their corresponding optimized achievable solar intensity.Indeed, with this, we have identified the optimal elevations and orientations that serve to maximize solar intensity on the PV module, which is crucial to maximizing the energy yield.In Tabuk, for instance, the annual optimal tilt angle, annual optimal azimuth angle, and solar intensity on the PV module were estimated to be 33 • , 30 • , and 3.6392 MWh/m 2 , respectively.The results in Hagl and Duba were relatively similar to those of Tabuk.The annual optimal tilt angle, annual optimal azimuth angle, and estimated solar intensity on the PV module in Hagl and Duba were determined to be 37 • , 40 • , and 3.4323 MWh/m 2 and 33 • , 36 • , and 3.4948 MWh/m 2 , respectively.
In addition, Table 2 shows that the simulated optimal tilt angle and azimuth were different from the location's latitude and were not in agreement with the rule-of-thumb direction for a PV module (i.e., facing due south).Furthermore, the significance between the amount of solar radiation falling on the PV panel at different setups (i.e., optimal tilt and azimuth angles setup and latitude tilt and south facing azimuth setup) was evaluated.It was found that the optimal tilt and azimuth angles contributed 0.91%, 4.01%, and 2.28% improvements in the amount of solar intensity on the PV panel in Tabuk, Hagl, and Duba, respectively.

Impacts of Ambient Temperature and Local Wind Speed on PV Cell Temperature
The energy produced by a PV module is influenced by the variation between the PV cell temperature and the nominal operating cell temperature given by the manufacturer at standard test conditions (STC, as illustrated in Section 2.3).Therefore, the impact of the PV cell temperature must be parameterized in attempts to estimate the PV performance.The PV cell temperature is modeled as a function of solar radiation (G T ), ambient temperature (T a ), and wind speed (v w ), as discussed in Section 2.2.
Figure 8 illustrates the relationship between the PV cell temperature (T c ), ambient temperature (T a ), and wind speed (v w ) under the conditions listed in Section 2.2.More specifically, an increase in ambient temperature leads to a proportional elevation of the PV cell temperature, which impacts the PV module's performance.On the other hand, an increase in wind speed has a significant impact on the PV cell temperature, as a steep decline in the PV cell temperature is observed in response to an increase in wind speed from 0 m/s to 10 m/s.
The significance of the PV cell temperature on the PV performance is given by Equation (10), which shows that it is crucial to take the PV cell temperature into consideration when attempting to estimate the PV module's performance.

C. PV electric DC power and energy
In this section, we carry out power and energy performance analysis for the proposed equivalent DC circuit model of the PV cell discussed in section II.C.More specifically, first, we obtain the monthly average energy density (Wh/m 2 ) for the PV output alongside with GHI and !"# ! .Second, we evaluate the hourly power density (W/m 2 ) for the same three schemes.
To achieve more precision results, specifications of real 200W manufactured PV module by SunPowerÒ (SPR-200-BLK-U) is applied through this model.Table 3 shows the values of the electrical parameters for this product.

PV Electric DC Power and Energy
In this section, we carry out power and energy performance analyses for the proposed equivalent DC circuit model of the PV cell, discussed in Section 2.3.More specifically, first, we obtained the monthly average energy density (Wh/m 2 ) for the PV output coupled with the GH I and GH I t .Second, we evaluated the hourly power density (W/m 2 ) for the same three schemes.
To achieve more precise results, the specifications of a real 200 W manufactured PV module by SunPower (SPR-200-BLK-U) were applied throughout this model.Table 3 shows the values of the electrical parameters for this product.

Parameter Value
G n 1000 W/m 2 Using the optimal tilt and azimuth angles, Figures 9-11 show the average monthly energy of the PV output, calculated directly from the maximum power point using the MPPT algorithm, which was then averaged over a month period to obtain the required energy density.For the input-output comparison, we also obtained the average monthly energy of the global irradiance for both the horizontal and tilted surfaces.As can be seen from the same figures (i.e., , the average PV output energy achieved was around 110 Wh/m 2 throughout the year, since the studied locations were more or less sunny all the year.However, we noticed that, in December, January, and February, the output energy was slightly higher than in the remaining months.Moreover, it is evident that the optimized tilt and azimuth angles yield higher GH I, which shows the importance of placing the panel at the proposed optimal angles.
Using the optimal tilt and azimuth angles, Figure 8, Figure 9, and Figure 10 show the average monthly energy of the PV output calculated directly from the maximum power point using the MPPT algorithm, which then was averaged over a month period to obtain the required energy density.For input-output comparison, we also obtained the average monthly energy of the global irradiance for both horizontal and tilted surfaces.As can be seen from the same figure, the average PV output energy is achieving around 110 Wh/m 2 throughout the year since the studied locations are more or less sunny all the year.However, we notice that in December, January, and February, the output energy is slightly higher than the remaining months.Moreover, it is evident that the optimized GHI is higher than the GHI, which shows the importance of placing the panel at the proposed optimal angles.Similarly, the hourly power density of the PV module is depicted for a sample day as shown in Figure 11, Figure 12, and Figure 13.It is shown that power values approximate the wellknown bell shape curve.In addition, the highest power that can be achieved with the chosen module is around 200 W/m 2 at around 2:30 PM.This observation is also applicable for both GHI and optimized GHI, where the sun is in the middle of the sky.Similarly, the hourly power density of the PV module is depicted for a sample day in Figures 12-14.These figures show that the power values approximate the well-known bell-shape curve.In addition, the highest power that could be achieved with the chosen module was around 200 W/m 2 , at around 2:30 p.m.This observation was also applicable for both GH I and the optimized GH I, where the sun was in the middle of the sky.From the discussions above, it is concluded that the proposed schemes discussed in Section II as well as the proposed optimal tilt and azimuth angles can improve the solar panels implementations in the chosen regions, namely, Tabuk, Hagl and Duba, respectively.

IV. Conclusion
In this paper, given real-time data, we studied the problem of improving the PV performance parameters in the NEOM region, namely: Tabuk, Hagl and Duba.First, we proposed accurate mathematical models that precisely describe the total global irradiance delivered to a tilted PV module.Second, we investigated the impact of the PV cells temperature on its performance and provided a model that depicts the relationship between the PV cell temperature, the ambient temperature, and the wind speed.After determining both the total irradiance delivered to the PV module and the PV cell temperature, we thirdly, developed an equivalent electric circuit for the PV cell and a maximum power point tracking algorithm.Finally, we used these models to obtain the optimal tilt and azimuth angles that maximize From the discussions above, it was concluded that the proposed schemes discussed in Section 2, as well as the proposed optimal tilt and azimuth angles, can improve solar panel implementations in the chosen regions (i.e., Tabuk, Hagl, Duba).

Conclusions
In this paper, using real-time data, we studied how to improve the PV performance parameters in the NEOM region, namely: Tabuk, Hagl, and Duba.An optimization model, developed in MATLAB, is proposed to investigate the optimum values of the tilt angles combined with the azimuth angles.First, we proposed accurate mathematical models that precisely described the total global irradiance delivered to a tilted PV module.Second, we investigated the impact of the temperature of the PV cells on their performance and provided a model that depicted the relationship between the PV cell temperature, ambient temperature, and wind speed.After determining the total irradiance delivered to the PV module and the PV cell temperature, we, third, developed an equivalent electric circuit for the PV cell and a maximum power point tracking algorithm.Fourth, we used these models to obtain the optimal tilt and azimuth angles that maximized the PV output of annual energy: 33 • for both Tabuk and Duba and 37 • for Hagl.Similarly, we found that the optimal azimuth angles were 30 • , 40 • , and 36 • for Tabuk, Hagl, and Duba, respectively.Compared to elevation equal to the latitude and facing due south, it was shown that using the proposed optimal angles led to a 0.91%, 4.01%, and 2.28% improvement in the amount of solar intensity on the PV panel in Tabuk, Hagl and Duba, respectively.This, in turn, showed that the proposed schemes could be used to help design and implement solar panels in the studied region or any other location.

Figure 3 .
Figure 3. Equivalent circuit model for a PV cell.

Figure 3 :
Figure 3: Current-voltage characteristic and power curves for a photovoltaic module.

Figure 4 .
Figure 4. Current-voltage characteristic and power curves for a PV module.

Figure 4 :
Figure 4: Global horizontal irradiance GHI in terms of tilt and azimuth angles in Tabuk.

Figure 5 .
Figure 5. GH I in terms of tilt and azimuth angles in Tabuk.

Figure 5 :
Figure 5: Global horizontal irradiance GHI in terms of tilt and azimuth angles in Hagl.

Figure 6 .
Figure 6.GH I in terms of tilt and azimuth angles in Hagl.

Figure 6 :
Figure 6: Global horizontal irradiance GHI in terms of tilt and azimuth angles in Duba.

Figure 7 .
Figure 7. GH I in terms of tilt and azimuth angles in Duba.

Figure 7 :
Figure 7: Ambient temperature and wind speed impacts on the PV cell temperature.

Figure 8 .
Figure 8.The impact of ambient temperature and wind speed on PV cell temperature.

Figure 8 :
Figure 8: Average monthly energy density of the PV output for Tabuk.Figure 9. Average monthly energy density of the PV output for Tabuk.

Figure 9 .
Figure 8: Average monthly energy density of the PV output for Tabuk.Figure 9. Average monthly energy density of the PV output for Tabuk.

Figure 9 :
Figure 9: Average monthly energy density of the PV output for Hagl.

Figure 10 .
Figure 10.Average monthly energy density of the PV output for Hagl.

Figure 10 :
Figure 10: Average monthly energy density of the PV output for Duba.

Figure 11 .
Figure 11.Average monthly energy density of the PV output for Duba.

Figure 11 :
Figure 11: Hourly power density for a sample day in Tabuk.

Figure 12 .
Figure 12.Hourly power density for a sample day in Tabuk.

Figure 12 :
Figure 12: Hourly power density for a sample day in Hagl.

Figure 13 .
Figure 13.Hourly power density for a sample day in Hagl.

Figure 13 :
Figure 13: Hourly power density for a sample day in Duba.

Figure 14 .
Figure 14.Hourly power density for a sample day in Duba.

Table 1 .
Definitions of angles related to the angular position of the sun and PV panel.

Table 2 .
Optimal module tilt and azimuth angles to achieve maximum solar intensity.

Table 2 :
Optimal module tilt and azimuth angles to achieve maximum solar intensity

Table 3 :
Electrical parameters values for the product of SPR-200-BLK-U manufactured by SunPower.