① Irradiance
The sun is a nuclear fusion reactor and may continue to shine for millions of years. When the sun burns, the peak of the energy from the sun reaching the top of the earth’s atmosphere is 1367kW/m², which is called the solar constant. Its peak energy attenuation through the atmosphere and reaching sea level is about 1kW/m². The solar radiant flux obtained per unit area is called radiant intensity.
| parameter | symbol | Quantity and unit |
| radiation | G | kW/㎡ W/㎡ |
| Solar constant | Gsc | 1.367 kW/㎡ 1367W/㎡ |
| Peak sea level | Go | 2.0kW/㎡ 1000W/㎡ |
| Rated value | — | 0.8kW/㎡ 1000W/㎡ |
②Geometric effect
Latitude, time of day, and season all affect the amount of solar energy that hits the earth’s surface horizontally. Assume that the area of the flat current collector is A, the angle of inclination is β, and it faces the sun perpendicularly. Assume that at 9:00 am, 12 rays of the sun hit the current collector from the y direction of the altitude angle. However, if the current collector is laid horizontally on the surface of the earth, that is, β=0°, the current collector only captures 9 rays, as shown in Figure 1.
Obviously, when the sunlight is directly above and the current collector is placed horizontally, it will capture all the sun’s rays, as shown in Figure 2.
To make the solar cell module always face the sun to obtain the maximum energy, it can be achieved by using a “tracking” device to make the current collector follow the sun. Solar trackers are not suitable for home solar systems with only 1 or 2 photovoltaic modules, but they can be used in larger systems.
In a home solar system, the solar cell modules should be inclined at a certain angle (y), as shown in Figure 3, facing true north or true south (depending on whether they are located in the southern or northern hemisphere), so that there is a gap between sunlight and photovoltaic modules The included angle is 90°.
The photovoltaic modules in the northern hemisphere should face true south, and the photovoltaic modules in the southern hemisphere should face true north. The best tilt angle is usually local latitude plus 5°~15°, but it should also depend on the exact location and specific application.
In the tropics (between the Tropic of Cancer and the Tropic of Capricorn), the sun can be found in the north or south of the photovoltaic module. Generally, photovoltaic modules located in the southern hemisphere face north, and photovoltaic modules located in the northern hemisphere face south. In the place where the latitude is 0°~15°, the photovoltaic module should usually have a horizontal tilt of 10°C (it is conducive to maintaining self-cleaning). For latitudes between 15° and 23.5°, photovoltaic modules should generally be tilted between 15° and 20°.
The position of the sun is determined by two angles:
(1) The solar altitude angle y is the angle between the sun’s rays and the horizontal plane.
(2) The solar azimuth a is the angle between the projection of the sun’s rays on the horizontal plane and the true north direction. The azimuth is rotated 359° clockwise from 0° (true north), 90° to the east, 180° to the south, and 270° to the west.
The schematic diagram of the sun’s altitude and azimuth is shown in Figure 4.
The unit of the azimuth angle is (°), and the height is calculated by rotating clockwise from the north. The solar altitude angle is the angle between the ground plane and the sun when facing the sun. Figure 5 shows the changes in the solar altitude and azimuth of Sydney in June and December over time. From Figure 5, it can be seen that the solar altitude is the largest in a day at noon. The photovoltaic modules installed on the surface of the southern hemisphere are compared with the June phase. In comparison, it receives direct radiation at a larger elevation angle in December, so the power generation unit will also receive higher radiation in December. When designing an independent power generation system, it is necessary to consider the total radiation received by photovoltaic modules in different months.
③Sun path diagram
The path of the sun to any specific location in the sky can be described by a two-dimensional diagram of the path of the sun. This map can be used to determine the position of the sun in the sky at any time. The solar path diagram has two different projection methods: cylindrical projection and polar projection. The most commonly used form in the photovoltaic industry is polar stereographic projection.
The composition of the solar path diagram is as follows:
(1) The azimuth angle is represented by a circle in the figure, in some figures it is marked from 0° to 360° relative true north (Figure 6 and Figure 7), and in some figures it is represented in 4 directions, namely, north and south ,thing.
(2) The height angle is expressed by concentric circles.
(3) The path of the sun changes from east to west on different dates.
(4) The time when the daily line crosses the solar path line.
(5) Local latitude location information.
Figure 6 is a diagram of the solar path at 32° south latitude, and Figure 7 is a diagram of the solar path at the equator. Figure 6 is horizontally symmetrical, indicating that the sun has the same time in the northern and southern directions of the local sky.
④ Magnetic North and True North
The magnetic north pole is the direction in which the compass is pointing at any given point. The solar cell module must be aligned with true north (or geographic north pole), that is, aligned with the direction pointing to the north pole along the surface of the earth. The magnetic north pole and the geographic north pole should be the same in theory, but due to the deviation of the magnetic flux lines in different places on the earth, the two are actually different, as shown in Figure 8. For example, in Sydney, the magnetic deviation is about 13° eastward, that is, true north is about 13 west of magnetic north.
⑤Atmospheric effect
Since solar radiation reaches the top of the earth’s atmosphere, a large part of it is reflected. The concept of reflectivity is involved here. The presence of the earth’s atmosphere changes the amount of radiation reaching the surface of the earth. Clouds and other particles can reflect or scatter solar energy in the atmosphere, as shown in Figure 9.
The radiation reaching the surface of the earth is composed of direct radiation and scattered radiation. Scattered radiation is usually not as dense as direct radiation, but it can still generate heat for solar collectors and energy for solar cells.
Because of the atmospheric effect, if the radiation has to pass through a thicker atmosphere to reach the surface, the surface will get a lower level of solar radiation. The radiation reaching the surface of the earth also has a different spectrum than the radiation outside the atmosphere. In particular, the water and CO2 in the atmosphere absorb some wavelength bands.
Atmospheric quality is a measure of the relative distance that solar radiation travels through the atmosphere to a given location. Air quality (AM) is defined as
AM=1/cosθ
Where θ——the angle between the sun and the straight line connecting directly above, as shown in Figure 10.
The air quality of the outer atmosphere is zero (AM0), and AM1 corresponds to the air quality when the sun shines from directly above (the standard conditions for evaluating solar photovoltaic modules are AM1.5, radiation measurement 1kW/m², and battery temperature 25°C).
During the day when the sun is shining, the temperature of the module is usually higher than the ambient temperature.
⑥Radiation amount and peak sunshine hours
The amount of radiation refers to the total amount of solar radiation received per unit area in a given period of time, such as daily, monthly or yearly.
The International Unit (SI) of energy is Joule (J). J is a relatively small quantity. When the energy order is large, such as solar radiation, it is usually expressed in megajoules (MJ).
Daily radiation usually refers to the peak sunshine hours (PSH) per day.
PSH is the number of hours required to obtain the equivalent energy of the day at an intensity of 1kW/㎡.
Figure 11 represents the solar radiation curve. The area under the curve is the total energy received in a day (MJ or kW·h).
The area of the rectangle is equal to the area of the entire area under the curve. If radiation is performed at a rate of 1kW/m², the equivalent total energy can be provided within 4h (10:00 am to 2:00 pm), and the PSH is 4h.
⑦Solar radiation data
Solar radiation data is very important in system design. This data can usually be obtained from the national meteorological bureau, or it may be provided by the supplier of the solar cell module. In Australia, you can refer to the “Solar Radiation Data Handbook” from the Australian Bureau of Meteorology, which can be obtained from the Australian New Zealand Solar Energy Society (ANZSES). NASA also provides data on most countries in the world on the Internet.Figure 12 lists the PSH in some cities in Australia.
The solar pyrometer is usually based on the measurement of direct radiation and scattered radiation, recorded as radiation per hour (W/m²), and provides the total daily radiation (MJ/m²). The sum of direct radiation and scattered radiation is called total radiation, which can be used to calculate the aforementioned peak sunshine hours.
⑧Sun altitude angle
Due to the revolution of the earth, the sun moves between the Tropic of Cancer (23.45°N) and the Tropic of Capricorn (23.45°S). When the sun is at a certain tropic, it is the winter solstice or summer solstice, and when the sun is at the equator, it is the vernal or autumnal equinox.
In the northern hemisphere, the sun reaches the Tropic of Cancer at the summer solstice (June 22) and at the winter solstice (December 22), passing the equator at the spring equinox on March 21 and the autumnal equinox on September 23. This means that in a calendar year, the noon altitude angle of the sun has changed a total of 46.9°.
The formula for calculating the altitude angle γe of the sun over the equator is
γe=90°﹣latitude
The formula for the altitude angle γt of the sun in space on the Tropic of Cancer is
γt=90°﹣Latitude ±23.45°
For a specific latitude position, when the sun is on the Tropic of Capricorn or the Tropic of Cancer, the solar altitude angle can be determined by the above formula. The use of “+” or “one” depends on the location (Southern Hemisphere or Northern Hemisphere) and the Tropic of Capricorn or Tropic of Cancer on which the sun is located. When applying this formula, the angle is calculated assuming you face the equator, that is, the angle between facing north in the southern hemisphere and the horizontal line of the north. The rule of thumb is to add 23.45° when the latitude of the location is in the same hemisphere as the tropic line of the sun, and subtract 23.45° when the latitude and the tropic line of the sun are in the opposite hemisphere.
The schematic diagram of the solar altitude angle in Darwin is shown in Figure 13.
In the tropics, it must be remembered that the sun can appear in both the northern sky and the southern sky, as shown in Figure 13. In the equatorial region, the sun shines at the same time in the northern and southern hemispheres. In tropical regions, it is necessary to determine the time and duration of the sun in the northern sky and southern sky throughout the year to ensure that trees and buildings will not block solar photovoltaic modules.
A schematic diagram of Sydney’s annual solar elevation angle is shown in Figure 14.
The previous article took Sydney as an example for analysis. Table 2 provides the solar altitude angles at different latitudes in tropical regions of the southern hemisphere (such as Australia). The table provides the sun’s altitude angle of the vernal and autumnal equinoxes, and also indicates that the sun is in the northern sky. This can help locate possible obstacles that block photovoltaic modules at different times of the year.
| latitude | The height of the sun at the autumnal equinox | The height of the sun at the autumnal equinox | Date of the sun in the south of the sky |
| June 21 | December 22 | ||
| 5°S | 61.55°N | 71.55°S | October 3-March 9 |
| 10 °S | 56.55°N | 76.55°S | October 17-December 24 |
| 15 °S | 51.55°N | 81.55°S | October 31-February 9 |
| 20 °S | 46.55°N | 86.55°S | November 19-February 21 |