Because solar energy is a clean energy source, its application is growing rapidly worldwide. Generating electricity using sunlight is one way to utilize solar energy; however, the cost of building a solar power system is still relatively high. In my country, the cost of solar cell modules currently accounts for approximately 30-40% of the total cost. Therefore, selecting the azimuth and tilt angles of the solar cell array is a crucial issue for more efficient and effective utilization of solar energy.
1. Azimuth
The azimuth angle of a solar array is the angle between the array's vertical plane and the south direction (eastward deviation is defined as a negative angle, and westward deviation as a positive angle). Generally, the solar array generates the most power when facing due south (i.e., the angle between the array's vertical plane and due south is 0°). At a deviation of 30° from due south (in the Northern Hemisphere), the array's power generation decreases by approximately 10%–15%; at a deviation of 60°, the power generation decreases by approximately 20%–30%. However, in clear summer weather, the peak of solar radiation occurs slightly after noon. Therefore, a slightly westward azimuth will yield maximum power generation in the afternoon. In different seasons, slightly eastward or westward azimuth of the solar array can also result in periods of maximum power generation. The placement of solar arrays is constrained by many factors, such as the azimuth of the land when installed on the ground, the azimuth of the roof when installed on a roof, the azimuth to avoid solar shadows, as well as layout planning, power generation efficiency, design planning, and construction objectives. To adjust the azimuth to match the peak load and peak power generation times of the day, please refer to the following formula. For grid-connected power generation, it is recommended to comprehensively consider all the above factors when selecting the azimuth. Azimuth = (Peak load time of the day (24-hour system) - 12) × 15 + (Longitude - 116). The curves showing the relationship between solar radiation and time for solar arrays in Beijing on October 9th at different azimuth angles are shown. The peak solar radiation times vary depending on the season and the azimuth.
2. Inclination angle
The tilt angle is the angle between the plane of the solar array and the horizontal ground, and it is desirable that this angle represents the optimal tilt angle for maximizing the array's power generation throughout the year. The optimal tilt angle for the year is related to the local latitude; higher latitudes require larger tilt angles. However, similar to the azimuth angle, the design must also consider limitations such as the roof tilt angle and the tilt angle for snow roll-off (slope greater than 50%-60%). For the snow roll-off tilt angle, even with lower power generation during snowy periods, the total annual power generation may still increase. Therefore, especially in grid-connected systems, snow roll-off is not necessarily the primary consideration; other factors must also be taken into account. For due south (azimuth 0°), as the tilt angle gradually transitions from horizontal (0°) to the optimal tilt angle, the solar radiation continuously increases until it reaches its maximum value, and then decreases with further increases in the tilt angle. Particularly after the tilt angle exceeds 50°–60°, the solar radiation drops sharply until the final vertical placement, at which point power generation reaches its minimum. There are practical examples of arrays placed from vertically to tilted at angles of 10° to 20°. When the azimuth angle is not 0°, the solar radiation on the inclined surface is generally lower, with the maximum solar radiation occurring near the tilt angle close to the horizontal plane. The above describes the relationship between azimuth angle, tilt angle, and power generation. For the specific design of an array, the azimuth angle and tilt angle should be further considered in conjunction with the actual situation.
3. The impact of shading on power generation
Generally, our calculations of power generation are based on the assumption that the solar array surface is completely free of shadows. Therefore, if the solar cells are not directly exposed to sunlight, only diffused light is used for power generation, resulting in a 10% to 20% reduction in power generation compared to a shadowless array. In this case, we need to correct the theoretical calculations. Typically, when there are buildings or mountains around the solar array, shadows will be cast after sunrise. Therefore, the location for installing the solar array should be chosen to avoid shadows as much as possible. If it is impossible to avoid shadows, the wiring method of the solar cells should be adjusted to minimize the impact of shadows on power generation. Additionally, if the solar arrays are placed one in front of the other, the shadow of the front array will affect the power generation of the rear array when the distance between them is close. Consider a bamboo pole of height L1 with a north-south shadow length of L2. The solar altitude (elevation angle) is A. At an azimuth angle of B, assuming the shadow multiplier is R, then:
R = L2/L1 = ctgA×cosB
This formula should be calculated based on the winter solstice.
Because the shadow is longest on that day. For example, if the height of the upper edge of the array is h1 and the height of the lower edge is h2, then the distance between the arrays is a = (h1-h2)×R. At higher latitudes, the distance between the arrays increases, and the area required for installation also increases accordingly. For arrays with snow protection measures, their tilt angle is large, thus increasing the height of the arrays. To avoid the influence of shadows, the distance between the arrays also increases. Generally, when arranging arrays, the structural dimensions of each array should be selected individually, and its height adjusted to a suitable value, thereby minimizing the distance between the arrays by utilizing their height differences. In the specific design of a solar cell array, in addition to reasonably determining the azimuth and tilt angles, a comprehensive consideration should be given to ensure the array reaches its optimal state.
