When designing and constructing solar photovoltaic power stations, it is necessary to consider parameters such as the solar altitude angle, solar azimuth angle and sunshine hours in the project area, so as to ensure that the power station design can meet the needs of users’ power generation to the greatest extent. For example, the inclination angle of the modules and the distance between the module arrays during construction are directly related to the azimuth angle of the sun, and their value also directly affects the amount of power generated by the photovoltaic modules. Therefore, you must understand the corresponding astronomical knowledge in the photovoltaic industry. Supplements are made according to engineering requirements and involve certain complex calculations. Of course, corresponding software can be used to complete the corresponding calculation problems in the project.
⑴The law of sun and earth movement
①The relationship between the sun and the earth The relationship between the sun and the earth is shown in Figure 1.
As shown in Figure 1, the earth revolves from west to east around the “earth axis” passing through its south pole and north pole every day, which is called “rotation”, and one rotation is 24 hours. In addition to its rotation, the earth also revolves around the sun in an elliptical orbit called the “ecliptic”, called “revolution”, with a period of one year (actually 365 days, 6 minutes and 9 seconds). The inclination angle between the earth’s rotation axis and the normal of the ecliptic plane during the revolution is 23°26′. When the earth revolves, the direction of the rotation axis always points to the north pole of the earth. Therefore, the location of direct sunlight is sometimes southerly or sometimes northerly, which forms the four seasons of the earth. Figure 1 shows four typical seasonal changes that occur when the earth rotates and revolves around the sun.
In the Northern Hemisphere, the direct sun point on the vernal equinox (around March 21) reaches the equator from the south of the equator, and the direct sun point on the autumnal equinox (around September 23) reaches the equator from the north of the equator. The sun directly hits the earth’s equatorial plane, at this time the solar declination angle δ=0°, the sunrise is due east, and the sunset is due west. The altitude of the sun at noon in the northern hemisphere is equal to 90°﹣ φ (φ is the latitude of the geographic location of the observer).
On the summer solstice day (around June 22nd), the sun hits the Tropic of Cancer at 23°26′ north latitude, and the solar altitude angle reaches the maximum at noon in the northern hemisphere as=90°﹣φ﹣23°26′, the summer solstice has the longest day in the northern hemisphere, and the astronomical summer Start.
On the winter solstice day (around December 22), the sun hits the Tropic of Capricorn at 23°26′ south latitude, and the solar altitude angle reaches the minimum at noon in the northern hemisphere as=90°←φ﹣23°26′. The winter solstice day is the longest night in the northern hemisphere and is astronomical. Winter begins.
②Longitude and latitude are determined on the map and the globe. We can see thin lines, horizontal and vertical, much like a square on a chessboard. These are the lines of longitude and latitude, as shown in Figure 2. According to these latitude and longitude lines, the position and direction of any place on the ground can be accurately determined.
How are these lines of latitude and longitude determined? The earth is constantly rotating around its axis (the axis is an imaginary line that passes through the north and south poles of the earth and the center of the earth). Draw a large circle perpendicular to the axis of the earth in the middle of the earth to make the circle Every point on the map is at the same distance from the north and south poles. This circle is called the “equator”. On the north and south sides of the equator, draw many circles parallel to the equator, called “latitude circles”; the line segments that make up these circles are called latitude lines. We set the equator as 0° latitude and 90° from south to north. The south latitude is called south latitude and the north latitude is north of the equator. The north pole is 90° north latitude, and the south pole is 90° south latitude. The high and low latitude also marks the hot and cold climate, such as no winter at the equator and low latitudes, no summer at the poles and high latitudes, and four distinct seasons in the middle latitudes. The latitude of a point is the degree of the angle formed by the radius of the sphere passing through the point and the equatorial plane. Latitude is the angle formed by the line and plane.
Secondly, from the north pole to the south pole, you can draw many large circles perpendicular to the earth’s equator in the north-south direction. These are called “warp circles”. The line segments that make up these circles are called meridians. In 1884 AD, it was internationally stipulated that the longitude line passing through the Greenwich Observatory in the suburbs of London, England was used as the starting point for calculating the longitude, that is, the longitude is zero degrees, zero minutes and zero seconds. To the east of it is east longitude, totaling 180°; to the west of it is west longitude, totaling 180°. Because the earth is round, the longitude 180° east and 180° west longitude are the same longitude. The 180° meridian has been established by various countries as the “international date change line”. The longitude of a point is the degree of the dihedral angle between the half-plane determined by the meridian and the axis of the earth passing through this point and the half-plane determined by the meridian of 0° (primary meridian) and the axis of the earth, so the longitude is the angle formed by the plane.
⑵ Several definitions about the position of the sun
① The angle of declination of the sun δ The angle of intersection between the sun’s rays and the earth’s equatorial plane is defined as the angle of declination of the sun, which is usually expressed by δ. The sun’s direct rays move between the Tropic of Cancer throughout the year, so the sun’s declination angle δ varies between “+23°26′” and “-23°26′”. The declination of the sun is a continuous function of time, which is related to the day of the year and has nothing to do with the location on the earth, that is, the declination of the sun is the same at any position on the earth. To calculate the solar declination on any day of the year, it can be calculated according to the Cooper equation, namely
δ=23.45°sin (360°×(284+n/365)) (1)
In the formula, δ is the sun’s declination (°); n is the number of days in a year, n=1 from New Year’s Day, the vernal equinox is about n=81, and on December 31 n=365.
Example 1-1 calculate the solar declination on September 22.
Solution: On September 22, n=265, substituting equation (1), we get
δ=﹣0.6°
According to formula (1), the solar declination angle can be calculated on any day of the year.
②Solar hour angle ω The hour angle at the center of the solar surface, that is, the angular distance from the celestial meridian of the observation point along the celestial equator to the time circle where the sun is. Usually expressed by ω, its value is equal to the time from noon multiplied by 15°, that is, ω=0° at noon, negative in the morning and positive in the afternoon.
ω=15°x(ST﹣12) (2)
In the formula, ω is the solar time angle (°); ST is the solar time.
Example (2) Calculate the solar hour angles at 11 o’clock in the morning, 8 o’clock in the morning, 1 o’clock in the afternoon, and 3 o’clock in the afternoon.
Solution: At 11 o’clock in the morning, ST=11.
ω=15°x(11﹣12)
ω=﹣15°
The same is true: 8 o’clock in the morning,
ω=15°x(8﹣12)=﹣ 60°
At 1 pm, ω=15° x(13﹣12) = 15°
At 3 pm, ω=15°x(15﹣12) =45°
③The solar altitude angle as The solar altitude angle is the angle between the direct sun’s rays and the local horizontal plane, usually expressed as as. The solar altitude angle is expressed as
sinas = sinφsinδ + cosφcosφcosω (3)
In the formula, as is the solar altitude angle (°); φ is the current geographic latitude (°); δ is the solar declination angle (°); ω is the solar hour angle (°)
At noon, ω=0, the formula (1﹣3) can be simplified as
sinas =sin[90°±(φ﹣δ)] （4）
For the northern hemisphere,
as=90°﹣(φ﹣δ) (5)
For the southern hemisphere,
as=90°+(φ﹣δ) (6)
④The azimuth angle of the sun γ The azimuth of the sun, that is, the angle between the projection line of the sun’s rays on the ground plane and the south direction of the ground plane, usually expressed by γ. Its expression is
Sinγ=cosδsinω/cosαs (7)
or
COSγ = (sinαssinφ﹣sinδ)/cosαscosφ (8)
In the formula, γ is the solar azimuth (°); φ is the local geographic latitude (°); δ is the solar declination (°); αs is the solar altitude Angle (°).
⑤Sunshine time N Sunshine time refers to the period of time the sun enters the horizon from the east to the west to the horizon. The moment the sun hits the horizon, the sun’s altitude angle is 0°, and the earth rotates 15° per hour, so the sunshine time
The time N can be obtained by dividing the sum of the absolute values of the sunrise and sunset angles by 15°, namely
N=(ωfall＋|ωout|)/15=(2/15)arccos(﹣tanφtanδ) (9)
The calculated value of the above formula refers to the time when the sun passes through the horizon, but for solar photovoltaic power generation systems, according to the World Meteorological Organization (WMO)) in 1981, the definition of sunshine duration is to use the sunshine intensity of 120W/m2 as the threshold. The sunshine time is the sum of the time measured and calculated when the solar sunshine intensity is greater than 120W/m2 in a day, and the resolution is 10min.
