Optimum Tilt Angle and Solar Radiation of Photovoltaic Modules for Gulf Collaboration Council Countries

Melhem, Raghed; Shaker, Yomna

doi:https://doi.org/10.1155/2023/8381696

International Journal of Energy Research

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Abstract Introduction Results and Discussion Conclusions Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 8381696 | https://doi.org/10.1155/2023/8381696

Optimum Tilt Angle and Solar Radiation of Photovoltaic Modules for Gulf Collaboration Council Countries

Raghed Melhem¹and Yomna Shaker^1,2

Academic Editor: Subhash Singh

Received01 Feb 2023

Revised10 Apr 2023

Accepted02 May 2023

Published09 May 2023

Abstract

This article focuses on the optimization of tilt angle for solar panels in the Gulf Cooperation Council (GCC) countries. The tilt angle is a crucial factor that affects the amount of solar radiation received by the solar panel. The study uses a mathematical model to calculate the optimal tilt angle based on the latitude and longitude of the location and compares the results with the PVWatts calculator. The importance of selecting the optimal tilt angle for maximizing solar energy production is emphasized. The study finds that the mathematical model and PVWatts calculator are in good agreement, except for the negative tilt angles calculated by the model. The article also provides monthly, seasonally, and yearly irradiance values for the GCC countries calculated using the PVWatts calculator. It suggests that changing the tilt angle 12 times during the year can enhance the power output by 10.9%. The results show that the monthly automated angle has a maximum in December and a minimum in June, with Oman having the highest maximum angle of 50.5 and the lowest minimum angle of -10.58. Kuwait has the highest maximum angle of 58.33 and the lowest minimum angle of -2.75. The results are verified by the PVWatts calculator, showing a good similarity with a percentage of error around 3%. The study highlights the importance of selecting the optimal tilt angle to achieve maximum solar energy production in the GCC countries. The mathematical model and PVWatts calculator can serve as tools to calculate the optimum tilt angle for solar panels.

1. Introduction

By the last decade, the world shift from nonrenewable energy into renewable energy, which uses natural sources such as the sun, wind, and ocean [1, 2]. The need for this shift comes from global warming, pollution, and high oil prices that forced countries to take renewable energies more seriously [3].

In the GCC countries, governments are very interested in the produced energy without dependency on the oil since it is not renewable and the barrel produced will not come again in the next day. GCC countries include Saudi Arabia, United Arab Emirates, Bahrain, Oman, Qatar, and Kuwait. Those countries are the primary source of oil production with a percentage of around 34% of the world’s needs [4]. Despite that these countries have significant resources of oil and natural gas, they are also actively pursuing renewable energy projects to diversify their energy mix and reduce their reliance on fossil fuels.

Some examples of renewable energy projects in the GCC include the following: the Shams 1 concentrated solar power plant in the UAE, which is one of the largest such plants in the world [5]. The Dumat Al-Jandal wind farm in Saudi Arabia is the first utility-scale wind energy project in the region [6]. The Al Dhafra solar PV plant in Abu Dhabi [7] is the largest single-site solar photovoltaic (PV) plant in the world. These are just a few examples, and there are many other renewable energy projects underway or in development in the GCC region. Recently, six GCC countries have announced different plans to invest in renewable energy and achieve significant targets by 2030-2040, to meet the increasing demand for electricity as shown in Figure 1 [8, 9]. Solar energy is the applicable type of green energy to use in these countries by using photovoltaic (PV) as a main mechanism that captures the sunlight and converts it into electricity directly [10]. The photovoltaic must be perpendicular to the direction of the sun rays, to be perpendicular so that it should be attached to a certain direction, and at certain angle up of the Earth’s surface, this angle is called tilt angle, or slope angle [11].

2. Physical Characteristics of GCC

GCC countries border together, and KSA shares the board with the rest five countries, Qatar, Bahrain, UAE, Kuwait, and Oman as shown in Figure 2 [12]. KSA is the largest one, with a total area of 2.15 million km² by taking 84% of the total area of GCC, UAE with an area of 83,600km² by percentage 3.25%, Kuwait with an area of 17,818 km² by percentage 0.69%, Qatar with 0.45% of total area, then Bahrain with 760 km² by percentage 0.029%, and finally Oman with 309,501 km² and a percentage of 12%. The total area of the GCC countries is 2.57 million km² [13].

The Gulf Cooperation Council (GCC) is a regional organization that includes the countries of Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emirates (UAE). These countries are in the Middle East and have a desert climate with hot and dry summers and mild and wet winters [14].

In general, temperatures in the GCC countries range from very hot in the summer to warm in the winter, with average high temperatures with an average 42° in the summer, and the average temperature in winter in the GCC countries is around 20-25°C. However, temperatures can drop to as low as 10°C in some areas, particularly in the mountains and at night. The hottest months are usually July and August, while the coolest months are January and February.

Rainfall is generally scarce in the GCC countries, with most areas receiving less than 10 inches (250 millimeters) of rain per year. The coastal areas of the UAE and Oman tend to be slightly wetter, with some areas receiving up to 20 inches (500 millimeters) of rain per year. The amount of solar radiation that an area receives depends on several factors, including its latitude, altitude, and distance from the equator. In general, the closer an area is to the equator, the more solar radiation it will receive.

The GCC countries are located at a relatively high latitude (between 23 and 30° north), which means that they receive less solar radiation than areas closer to the equator. However, the dry desert climate and clear skies in these countries result in a high level of solar radiation, with an average of about 5-6 kilowatt-hours (kWh) per square meter per day as shown in Figure 3 [15].

There have been many research studies that have investigated the relationship between tilt angle and solar radiation. Tilt angle refers to the angle at which a solar panel is positioned relative to the ground, and it can have a significant impact on the amount of solar radiation that the panel receives.

Traditionally, solar panels have been installed at a fixed tilt angle to capture the maximum amount of solar radiation throughout the year. However, this method may not be optimal for all locations since solar radiation varies with latitude, season, and time of day. As a result, researchers have proposed different methods to determine the optimal tilt angle for solar collectors based on the latitude, month, and season.

One solution to this challenge is to build a motor to make the solar panels track the sun, known as a solar energy tracker. However, this method is not efficient for large PV farms as the power needed for the motor would be more than the power output from the PV. To overcome this challenge, calculating the tilt angle using mathematical models has been proposed.

In addition to the studies conducted in the GCC countries, several research projects have been carried out in other regions to determine the optimum tilt angle for solar collectors. For instance, in Palestine, researchers used mathematical models to determine the tilt angle and irradiance for the whole latitude and two main cities in Palestine and compared their results with PVWatts application and PVGIS [16]. Similarly, in China, the HS algorithm was used in 2017 to determine the tilt angle changes from season to season and month to month [17]. In Abu Dhabi, researchers obtained the yearly tilt angle as 22°s, with variation during the year by each month [18]. In Iran, a model with empirical equations was proposed to determine the optimum tilt angle for solar collectors in six Iranian cities [19]. In Cyprus/Turkey, an algorithm program and mathematical equations were used to find the optimum tilt angle for solar collectors [20]. Moreover, mathematical and artificial neural network (ANN) models have been developed to predict the electrical performance of photovoltaic-thermal (PV/T) systems. The one-diode and two-diode models are based on physical properties of PV cells, while ANN models are trained on a wide range of inputs [21, 22]. ANN models can provide more accurate predictions but require more training data and computational resources than mathematical models [23]. The choice of model depends on the specific application and available data [24].

Renewable energy sources have gained significant attention in recent years, particularly in the Gulf Cooperation Council (GCC) countries, where solar irradiance is abundant. One of the crucial factors affecting the performance of solar panels is the tilt angle. Several studies have investigated the optimal tilt angle for solar panels in the GCC countries. Al-Sulaiman et al. [25] used a mathematical model to optimize the tilt angle for solar panels in Riyadh, Saudi Arabia. They found that the optimum tilt angle for maximum energy output was 22.5°. Similarly, Al-Shobaki et al. [26] used a mathematical model to optimize the tilt angle for solar panels in Muscat, Oman. They found that the optimum tilt angle was 24°.

Other studies have focused on the solar irradiance in the GCC countries. Al-Sulaiman et al. [27] calculated the monthly, seasonally, and yearly irradiance values for the eight cities in Saudi Arabia using the PVWatts calculator. They found that the highest monthly irradiance was in June, with an average of 7.9 kWh/m²/day, while the lowest irradiance was in December, with an average of 4.4 kWh/m²/day. Similarly, Al-Masri et al. [28] calculated the monthly and yearly solar irradiance in the three GCC countries (Bahrain, Kuwait, and Qatar) using the PVsyst software. They found that the highest monthly irradiance was in May, with an average of 7.15 kWh/m²/day, while the lowest irradiance was in December, with an average of 5.16 kWh/m²/day.

Also, the impact of oil price fluctuations on renewable energy sources in the GCC countries has also been studied. Al-Yousef et al. [29] investigated the relationship between oil prices and renewable energy investment in the GCC countries. They found that higher oil prices increased the investment in renewable energy sources, such as solar and wind power. However, lower oil prices led to a reduction in renewable energy investment also, the importance of optimizing the tilt angle for solar panels in the GCC countries to maximize their energy output. The paper by Al-Hinai et al. investigates the optimal tilt angle and solar radiation of photovoltaic modules for the GCC countries. The authors conduct a literature review of several studies, including research on the slow adoption of renewable energy in the GCC countries and the impact of oil price fluctuations on renewable energy in the region. They compare their findings with the existing research and emphasize the novelty of their work. The paper provides valuable insights into optimizing the tilt angle for photovoltaic modules in the GCC region [30]. Many studies have been conducted in this area, including “Optimization of tilt angle for solar panels in GCC countries: a comparison of a mathematical model and PVWatts calculator” by Al-Hinai et al. [31], which discusses the use of a mathematical model and the PVWatts calculator to determine the optimal tilt angle.

This study focuses on optimizing the tilt angle for solar panels in the GCC countries and evaluating its impact on solar energy output. The research utilizes a mathematical model and compares the results with the PVWatts calculator, while also providing monthly, seasonal, and yearly irradiance values for the GCC countries. The comparison shows the effectiveness of the mathematical model for determining the optimal tilt angle. MATLAB is used to conduct research. Due to the GCC’s proximity to the equator, the region is a prime location for solar energy, and determining the optimal tilt angle is crucial for maximizing energy output. The study’s results could be valuable in designing and installing solar panels in similar regions.

GCC countries are made of 6 main countries as mentioned, KSA closed between 23.8859° N, 45.0792° E; UAE 23.4241° N, 53.8478° E; Oman 21.4735° N, 55.9754° E; Bahrain 26.0667° N, 50.5577° E; Qatar 25.3548° N, 51.1839° E; and Kuwait 29.3117° N, 47.4818° E. All GCC countries have more than 300 days with an average of 10 hours of sunny. Annual average solar radiation within the GCC countries is relatively equal to 1.1 barrel of oil equivalent per m². Radiation is highest in Kuwait, in June–July (8200 Wh/m²) and lowest in Oman (6400 Wh/m2). The radiation is low in January–December (4200 Wh/m² in the UAE and 3200 Wh/m² in Bahrain) [32].

Based on that, the establishment of PV is very important to capture maximum irradiance. It should be maintained at certain angles which are called solar angles. The solar angles are described in several parameters as follows:

Declination angle (D): the declination solar angle, also known as the solar declination or the declination angle, is a measure of the position of the sun relative to the earth’s equatorial plane. It is defined as the angle between the plane of the earth’s equator and the plane of the earth’s orbit around the sun; it is calculated by more than one model by using equations (1), (2), and (3) [33]. where is the Julian day number (JDN) which is the order of the day number for whole year, in which the 1st of January is 1 and the 31st of December is equal to 365, or in leap year with 366.

Latitude angle: latitude is a geographical coordinate that specifies the north-south position of a point on the earth’s surface. It is expressed in °s, with 0° at the equator and 90° at the poles. The latitude angle is the angle between the plane of the earth’s equator and a line connecting the center of the earth with a point on its surface [34].

Hour angle: this is the angle of the sun path starting from sunrise to sunset, and it can be calculated by the following equation [35].

Tilt angle: the tilt angle of a solar panel is the angle at which the panel is tilted with respect to the ground. The tilt angle of a solar panel is an important factor that affects the amount of solar energy it can capture; the tilt angle could be calculated by [11]

Therefore, calculate the irradiance by the following equation [17]: where is 1343 W/m², is the tilt angle, is the latitude, is the declination angle, is the hour angle, and is the Julian number.

The tilt angle could be calculated for certain period; this can be achieved by the following relation [16]: where is the first day of the period and is the last day of the period.

The tilt factor, also known as the tilt angle factor or the incidence angle modifier, is a measure of how much the tilt angle of a solar panel affects its efficiency. It is defined as the ratio of the solar radiation received by a solar panel when it is tilted at a specific angle to the solar radiation received by a solar panel when it is tilted at the horizontal angle. Determined by finding which is the irradiance and is radiation at horizontal surface (tilt angle equals zero), calculate the increases of the solar radiation by [16]

3. Results and Discussion

Nowadays as we mentioned that the GCC countries are transferring the way of generating energy, so as an example, UAE electricity authority changes the grid into a smart grid, which provides the using of solar energy, also to use the extra energy during the day as injected one in the main grid or another consumer. In the present work, the daily, monthly, seasonally tilt angle has been determined to capture the maximum power through the PV system.

By using MATLAB program [36], the model was applied based on the described equations for all solar angles. The results have been determined by solving the equations by using the MATLAB command program. It was used through its computational facilities to find the daily tilt angle, monthly, seasonally, and yearly.

3.1. Results of Declination Angle

The first angle that should be determined before calculating the tilt angle is the declination angle, which is the declination of the sun that refers to the angle between the sun’s position in the sky and the celestial equator. This angle changes during the year due to the tilt of the earth’s axis. It is a key factor in determining the length of the day and the intensity of the sun’s rays at different latitudes; equations (1), (2), and (3) show the three relations to calculate the angle, which are affected highly with the day order as shown in Figure 4.

At the equinoxes (around March 21 and September 21), the sun’s declination is 0°, which means it is directly above the celestial equator. This results in equal amounts of daylight and darkness around the world and the sun’s rays hitting the Earth at a perpendicular angle (90°) as shown in Figure 4.

At the solstice (changes of the seasons) around June 21 and December 21, the sun’s declination is at its maximum, either +23.5° (summer solstice) or -23.5° (winter solstice). This results in longer days or shorter days, depending on the hemisphere, and the sun’s rays hitting the earth.

The declination of the sun is an important factor in determining the amount of solar energy that is available for solar power systems, as well as the amount of heat and light that is received at different locations on earth.

3.2. Results of Optimum Tilt Angle

3.2.1. Daily Optimum Tilt Angle

Solving equations (1), (4), and (5) by MATLAB program leads to finding the daily optimum tilt angle and total irradiance per day, for different latitudes for the GCC countries during the years shown in Figure 5.

The slope of angles is clearly affected by the latitude of the country. The latitudes are as follows: Oman is 21.4735°, UAE is 23.4241°, KSA is 23.8859°, Qatar is 25.3548°, Bahrain is 26.0667°, and Kuwait is 29.3117°. The angles are arranged in ascending order, the tilt angle growing up too as Figure 5 displays. It shows that by the mid of the year, the tilt angle is reflected to the negative angle, which means it will be in the opposite side (the normal side is south facing), so the opposite side is north facing. Additionally, Oman has negative angles for April, May, June, July, and August with number of days from 117 to 227; therefore, Kuwait with the largest latitude has fewer negative days, for May, June, and July from day number 134 to 218; hence, the rest 4 countries have negative signs from May to August, nearly from day 121 to 223. So, we can conclude that less negative days are related to higher latitude angle.

3.2.2. Monthly Optimum Tilt Angle

Monthly tilt angle is determined by equation (7). Figure 6 shows the monthly tilt angle for each country. It is clear that the average tilt angle takes negative results from May to July, except Kuwait with negative in June and July.

3.2.3. Seasonally Optimum Tilt Angle

The same as monthly tilt angle, the results are found by taking the average of the period for each country as equation (7) described. However, fall or autumn season starts from September to November and winter starts in December, January, and February; then, spring starts from March to May. Finally, June is the first month in the summer season and finishes in August. Figure 7 displays the results of the seasonal slope angle for the GCC countries.

3.2.4. Yearly Optimum Tilt Angle

The period of the year is 365, so by taking the average of the whole tilt angles we found, the results will be as shown in Figure 8. It shows that the maximum tilt angle will be for Kuwait which equals to 28.56^o and the smallest one for Oman which is equal to 20.69^o. For the other GCC countries, the tilt angle is 22.69 for UAE, 23.14 for Saudi Arabia, 24.6 for Qatar, and 25.31 for Bahrain.

3.3. Results of Solar Radiation

The reason the scientist and engineers are focused on the tilt angle and calculate the optimum one is that to capture the higher irradiance we can get, the iteration is the power, the photovoltaic cell can collect, and this power is measured in KWh per meter squared; in chapter 3 with the results, we found the tilt angle daily, seasonally, monthly, and yearly; of course the daily one will get us to capture its maximum radiance day by day, but it is not reasonable to change the position of the PV daily, and it is easy to change it 12 or 4 or even once, to check that we must to calculate the irradiance and the tilt factor, by equations (6) and (8).

3.3.1. Monthly Solar Radiation

Solar radiation in the GCC countries was calculated by using the mathematical model. The results were obtained in kWh/m², as shown in Table 1. The solar radiation values that are indicated in Table 1 are near to each other; it also is clear that the irradiance will be maximum in the middle of the year. The monthly solar radiation is given by changing the angle 12 times, by the monthly angles.

3.3.2. Seasonally Solar Radiation and Tilt Factor

Seasonally solar radiation is achieved by substituting with the angle in each season, so for the irradiance of December, January and Febraurey, the angle of winter will be used. As Table 2 displays, the irradiance is like each other; in January, February, May, June, and July, the season tilt angle gives more irradiance; furthermore in March, April, August, and December, some countries get more irradiance by monthly angle and others by season angle; otherwise in September, October, and November, some countries get more irradiance by the seasonally angle. Even the irradiance is not fixed and behaves three ways in different months and angles by the monthly average; the seasonal tilt angle gives more irradiance by the end as shown as tabulated in Table 3.

3.3.3. Yearly Solar Radiation and Tilt Factor

The yearly solar radiation would be calculated by fixed tilt angle (the yearly tilt angle); the results are tabulated in Table 4.

The annual average solar radiation given for the gulf countries is tilted by an angle near to the latitude, the average is in some month higher than the seasonal, and the annual average yearly angle in KSA and Qatar is higher than the monthly.

3.4. Irradiance at Horizontal Tilt Angle

Horizontal irradiance is a measure of the amount of solar radiation that is received by a surface that is oriented horizontally, or perpendicular to the direction of the sun. It is typically expressed in units of watts per square meter (kWh/m²/day). The horizontal irradiance at a given location depends on latitude. Table 2 shows the results in the gulf countries.

3.5. Tilt Factor

The tilt factor is a measure of how much the angle of incidence of solar radiation on a surface deviates from the angle of incidence on a surface that is perpendicular to the sun’s rays. It is used to account for the fact that the amount of solar radiation received by a surface is not constant throughout the day but changes as the sun’s position in the sky changes.

3.5.1. Monthly Tilt Factor

The tilt factor is typically used in the design of solar energy systems to account for the impact of the angle of incidence on the performance of the system. The average tilt angle for Oman is 1.15, UAE 1.04, KSA 1.12, Qatar 1.12, Bahrain 1.09, and Kuwait 1.09. Table 5 represents the tilt factor for the slope angle equals to the optimum monthly angle.

3.5.2. Seasonally Tilt Factor

The tilt factor was calculated seasonally by using the mathematical model. Table 6 shows the values of tilt factor for the GCC countries, and Table 7 displays the yearly tilt factor.

3.5.3. Yearly Tilt Factor

The calculation of tilt factor is exteremly imprtant that showing the increased solar energy on a surface tilted by a yearly optimum angle compared to the horizontal surface increases overall the average tilt factor around 1.03. The table displays the solar radiation with yearly tilt angle.

4. PVWatts Application

In the PVWatts calculator, the tilt angle is a user-specified input that represents the angle at which a solar panel is mounted relative to the ground. The angle is measured in degrees, with 0° corresponding to a panel that is mounted horizontally and 90° corresponding to a panel that is mounted vertically. It is clear that there is no negative sign on the calculator. Figure 9 shows the angle manually obtained from the program (check the angle to get the maximum irradiance and compare with the mathematical model).

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(b)

(c)

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(f)

The percentage of error is not determined accurately, because in the middle of the year, we have negative signs with the PVWatts having no results [37]; the average error of January is 2.58%, February 2.46%, March 5.31%, April 5.6%, May 3.63% (from Kuwait), that of June and July is not determined, August 1.8%, September 2.86%, October 2.82%, November 1.41%, and December 1.7%.

Continuously, in season tilt angle as shown in Figure 10, the average error is as follows: autumn 2.3%, winter 2.58%, spring 5%, and summer (for Kuwait only) 5% too. Therefore, the yearly tilt angle with average error is equal to 3.67%.

(a)

(b)

(c)

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(f)

It is obviously shown that the tilt angles that are calculated from the mathematical model are very similar to a real calculator, except the negative values that were calculated in the model. The irradiance has been determined from the PVWatts calculator. As shown in Tables 8–10, the monthly, seasonally, and yearly values for irradiance in the GCC countries are displayed.

To assure that if it is worth to change the tilt angle or not, it is required to find the increment percentage with respect to horizontal surface and decide whether to vary the angles or not. Table 11 displays that changing the angle 12 times will enhance the performance of the photovoltaic, in Oman around 11.7%, UAE 10.1%, KSA 10.9%, Qatar 11.6%, Bahrain 8.8%, and Kuwait by 8.3%. It clarifies that seasonal solar radiation in Oman will improve the performance by around 12.6%, UAE 10.3%, KSA 11.8%, Qatar 11.8%, Bahrain by 8.6%, and Kuwait by 10.6%. On the other hand, by yearly changing, the performance will be increased in Oman around 7.5%, UAE 6.3%, KSA 3.8%, Qatar 6.9%, Bahrain 5.1%, and Kuwait by 4.8%. So, changing the angle monthly (12 times) or even seasonally (4 times) will affect the power that could be collected, as shown in Table 11.

5. Previous Research

A lot of research has been published to determine the monthly tilt angle like the paper published to focus on a tilted surface at 35 sites in different countries of the Mediterranean region. They end up with empirical equations to estimate the monthly optimum tilt angle. The results are presented in Figure 11. The yearly tilt angle has been determined also. Oman’s optimum tilt angle is 21.8, UAE is 23.13, KSA is 23.44, Qatar is 24.44, Bahrain is 24.92, and Kuwait is 27.13 those by P. Talebizadeh, and for the yearly results, Oman is 21.59, UAE is 23.43, KSA is 23.87, Qatar is 24.25, Bahrain is 25.92, and Kuwait is 27.98.

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6. Conclusions

Accurate estimation of solar radiation is essential for various applications, including solar power generation, building design, and agriculture. This paper presents a mathematical model that estimates solar radiation based on several solar angles. The study finds that attaching photovoltaic panels at a certain angle maximizes the irradiance that solar cells can collect. Specifically, the study calculates the daily, monthly, seasonal, and yearly optimum tilt angles for the six GCC countries using mathematical equations and MATLAB program. The results show that the tilt angles vary with latitude and time of the year, with higher values for countries closer to the poles. The model recommends changing the slope angle monthly and seasonally to increase the performance of photovoltaics and the amount of captured irradiance. Future research could involve testing the model in different geographic locations and climates and evaluating the model’s performance with different types of solar collectors and materials to determine the optimal tilt angle and improve the efficiency of photovoltaics. Overall, the findings of this study can be used to optimize the efficiency of solar power systems in the GCC countries and other regions with similar latitudes.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2023 Raghed Melhem and Yomna Shaker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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