Solar Angles and Tracking Systems - Lesson

Diagram shows two crossed arrow lines with ends marked N, S, E and W. Rising from their intersection point are two more lines, one vertical, and the other angled 40° from the plumb line, denoting the angle of the sun.

Figure 2: The angle of the position of the sun in Boulder, CO, on the equinox. The latitude in Boulder is 40°.

On one day every year, called the equinox, the sun is positioned directly above our planet's equator. On this day, the angle between a line that points to the sun and a line that points straight up (vertical) exactly matches the latitude of the place you are standing. If you live on the equator, then in the very middle of the day (solar noon) the sun will be directly above you, or at 0º from the vertical. If you live in Boulder, CO, which is in the northern hemisphere at the latitude of 40º, then on the equinox the sun will be 40º to the south from the vertical (see Figure 2). The sun's position on the equinox is the average location of the sun throughout the year and is a great reference to use when designing a solar system for a specific location.

But keep in mind, the sun is always moving. In the summer, the sun appears higher in the sky, which increases the duration of sunlight seen in a day, and in the winter it appears lower, which decreases the length of sunlight in a day. The sun is highest in the sky on the summer solstice. To be more exact, it is 23.45º higher than on the equinox, or at 40 - 23.45 = 16.55º to the south of vertical.

The winter solstice is the day when the sun appears lowest in the sky. On this day, the sun is 23.45º lower than on the equinox, or at 40 + 23.45 = 63.45º to the south of vertical in Boulder. So, if you live in the northern hemisphere at latitude higher than 23.45º, then the sun will never shine from the north. This means the north side of your house would be a bad place for a solar panel (or a garden).

A diagram shows a solar panel, the four cardinal directions, zenith, and the sun's position, with many angle relationships denoted by Greek letters.

Figure 3: Solar angles used in power calculations for PV panels.

Below is an overview of the angles involved in calculating the amount of solar radiation that a PV panel receives at any given time (also see Figure 3). The angle at which the sun hits a PV panel is the basis for understanding how to design the most efficient PV array for a specific location. This is one of the first topics presented in solar engineering textbooks.

Zenith Angle, Θ_z: This is the angle between the line that points to the sun and the vertical — basically, this is just where the sun is in the sky. At sunrise and sunset this angle is 90º.

Solar Altitude Angle, α_s: This is the angle between the line that points to the sun and the horizontal. It is the complement of the zenith angle. At sunrise and sunset this angle is 0º.

Solar Azimuth Angle, γ_s: This is the angle between the line that points to the sun and south. Angles to the east are negative. Angles to the west are positive. This angle is 0º at solar noon. It is probably close to -90º at sunrise and 90º at sunset, depending on the season. This angle is only measured in the horizontal plane; in other words, it neglects the height of the sun.

Angle of Incidence, θ: This is the angle between the line that points to the sun and the angle that points straight out of a PV panel (this is also called the line that is normal to the surface of the panel). This is the most important angle. Solar panels are the most efficient when pointing at the sun, so engineers want to minimize this angle at all times. To know this angle, you must know all of the angles listed and described next.

Hour Angle, ω: This is based on the sun's angular displacement, east or west, of the local meridian (the line the local time zone is based on). The earth rotates 15º per hour so at 11am, the hour angle is -15º and at 1pm it is 15º.

Surface Azimuth Angle, γ: This is the angle between the line that points straight out of a PV panel and south. It is only measured in the horizontal plane. Again, east is negative and west is positive. If a panel pointed directly south, this angle would be 0º.

Collector Slope, β: This is the angle between the plane of the solar collector and the horizontal. If a panel is lying flat, then it is 0º. As you tip it up, this angle increases. It does not matter which direction the panel faces.

Declination, δ: This is the angle between the line that points to the sun from the equator and the line that points straight out from the equator (at solar noon). North is positive and south is negative. This angle varies from 23.45 to -23.45 throughout the year, which is related to why we have seasons.

Latitude, φ: This is the angle between a line that points from the center of the Earth to a location on the Earth's surface and a line that points from the center of the Earth to the equator. This can be easily found on a map.

Now let's talk about how to apply all of this information. Figure 1 shows a small portion of North America's largest solar PV power plant (as of 2010). The 14-megawatt power plant is located at Nellis Air Force Base in Nevada and is expected to provide more than 30 million kilowatt-hours of electricity each year. A typical compact fluorescent lamp (CFL) uses 15 watts, so when the sun is shining, this plant could power almost a million CFLs. At this site, 72,000 PV panels are placed across 140 acres of land. This power plant has more than just PV panels. Look at Figure 1 to see if you notice anything else that might affect the efficiency of the panels.

Photo shows 56 concave mirrors forming a panel mounted on a stand in the sunny desert.

Figure 4. One of the most efficient PV panels in the world — this dual-axis PV tracking system uses small mirrors to focus sunlight on high-efficient cells. It supplies electricity to the Arizona Public Service grid.

It might not be obvious at first, but look closely at the bases supporting the panels. They are designed to move! SunPower Corporation, a German company that specializes in PV power systems, designed this PV power plant with an east-west single-axis tracking system. That means that the panels rotate from east to west throughout the day to follow the sun and optimize panel efficiency. Because of this tracking system, these panels produce 30% more power than they would if they were fixed facing south.

Further panel efficiency can be obtained by tracking the sun not only along a single axis, but on two perpendicular axes. Figure 4 shows one of the most efficient PV panels in the world (more than 40% conversion efficiency) created by Spectrolab. These PV panels are extremely expensive so this module uses very small panels and less expensive mirrors to reflect sunlight from a larger area onto the small PV panel. The process of concentrating the sunlight for photovoltaic power production is explained in more detail in the Concentrated Solar Panel lesson. For this high-tech system, it is important to track the sun's location exactly throughout the day to provide the maximum amount of sunlight for the module at all times. To do that, this module has a double-axis tracking system that moves from east to west and an adjustable collector slope, β, to follow the height of the sun in the sky throughout the year.