Understanding Solar Radiation for PV Installlation

Examining the Effects of the Sun’s Path on the Earth

To succeed as a PV system designer and installer, you need to have a firm grasp on the relationship of the sun and the earth, particularly in terms of how they’re positioned relative to each other throughout the calendar year.

For someone in northern Alaska, these changes are much more dramatic than for someone in Hawaii, but you need to understand the concepts regardless. In the following sections, I describe general seasonal effects based on the earth’s movement, the sun’s relationship to your client’s specific location, and solar time; I also explain how to analyze sun charts and introduce the solar window.

Getting a Grip on Seasonal Effects

The number of daylight hours each day has an obvious effect on a PV array’s production: More sun means more solar energy. As a PV installer, you need to be able to visualize how the position of the sun changes with each season and the effect that has on the arrays you’re designing and installing. In other words, you need to be able to take seasonal effects into account.

One important factor to consider is the motion of the earth around the sun. Earth takes an elliptical path around the sun, meaning that on the summer solstice (approximately June 21), the earth is actually at its farthest point from the sun. On this day, the Northern Hemisphere is tilted toward the sun, and that half of the world has its longest day (and shortest night) of the year. Time moves on, and the earth continues to orbit the sun.

On the winter solstice (approximately December 21), the planet is as close to the sun as it’ll ever get; on this day, the Northern Hemisphere is tilted away from the sun, creating the shortest day and longest night. The other factor to consider when it comes to seasonal effects is the tilt of the earth’s axis. When viewed from space, the earth’s axis has a tilt of 23.5 degrees.

Because of this tilt, during the times between the spring equinox (approximately March 21) and the fall equinox (approximately September 21), the Northern Hemisphere is actually pointing toward the sun, whereas the Southern Hemisphere is pointed away from it (see Figure 7).

Figure 7. The earth’s movement around the sun.

As the earth’s orbit continues toward winter, the hemispheres swap their positions, so the Northern Hemisphere points away from the sun, and the Southern Hemisphere points toward the sun. On the equinoxes, the earth isn’t pointing toward or away from the sun; instead, it’s directly perpendicular with it.

Take a look at Figure 8 and pretend that your perspective of earth is the same as the sun’s (doing so helps you visualize how the tilt of the earth affects the amount of sunlight striking any part of the earth).

Notice how the tilt during the winter and summer restricts the sun’s access to the hemispheres that are pointed away from the sun and how the sun has full access to the entire globe on the equinoxes.

On the summer solstice, the sun is directly over the Tropic of Cancer in the Northern Hemisphere, where the latitude equals 23.5 degrees. This is the date when the Northern Hemisphere receives the most sunlight. On each of the equinox dates, the sun is directly perpendicular to the equator.

Figure 8. How earth’s tilt affects the amount of daylight on the solstices and equinoxes.

On these dates, the earth receives equal hours of light and darkness because it’s pointed neither toward nor away from the sun. Finally, on the winter solstice, the Northern Hemisphere experiences its longest night of the year and shortest day because the North Pole is pointed 23.5 degrees away from the sun, and the Tropic of Capricorn in the Southern Hemisphere is perpendicular to the sun.

Understanding the sun’s relationship to your location: Altitude and azimuth

As I show you in the preceding section, the motion of the sun across the sky is due to the tilt of the earth in relationship to the sun and the path the earth takes around the sun. (Yes, I know the sun is the stationary object, and the earth is actually orbiting the sun. But for simplicity’s sake, I refer to the sun moving across the sky and how the sun’s position changes.)

In the next sections, I show you how these facts relate to where you sit on earth because as a PV system designer and installer, that’s what you really care about.

When talking about the sun’s position in the sky, I use a couple key terms: altitude and azimuth. The altitude refers to how high in the sky the sun actually is, and the azimuth describes where the position is in relation to north. (Check out Figure 9 to get an idea of what I’m talking about.)

Altitude: You’re probably well aware that the angle of the sun off the horizon varies throughout the year. The amount of variation is consistent across the globe, with the exact measurement dependent on the time of day and your specific latitude on the earth.

Latitude is defined as the number of degrees north or south of the equator. Your latitude affects where the sun is positioned in the sky throughout each day (relative to your position, that is). I explain how to visualize these solar positions with the help of sun charts later in this article.

To view the changes in the solar altitude, picture yourself standing on the equator for an entire year (I suggest picturing yourself with your favorite cold beverage in hand because a year can be a long time).

On the spring equinox, the sun is directly overhead, or 90 degrees from your perspective. As the earth continues to orbit the sun, it moves toward the summer solstice. When it gets to June 21, the sun is no longer directly over your head; it has actually moved 23.5 degrees to the north.

As the earth continues its path, it comes back around to the fall equinox, and the sun is directly overhead once again. And as you can probably figure out by now, when the earth moves to the winter solstice position, the sun is now 23.5 degrees to the south of your location on that day. By the time the earth gets back to March 21, your year is over, and the sun is again directly overhead.

You can now apply this motion and sun-to-earth relationship for any latitude on earth. The position directly over your head is known as the zenith angle, and it has a numerical value of 90 degrees. The sun’s highest altitude on each and every equinox is the zenith angle (90 degrees) minus the latitude you’re standing at.

Alternatively, the sun is at a posi- tion of 23.5 degrees greater than the equinox position on the summer solstice and 23.5 degrees less than the equinox position on the winter sol- stice (in the Northern Hemisphere, that is; in the Southern Hemisphere, the calculations are the same except that the summer solstice down there is December 21 and the winter solstice is June 21).

If you’re having trouble with this concept, head to the later “Interpreting sun charts” section; the charts really help drive this point home.

Azimuth: Just as the sun has a position in the sky based off of the horizon (altitude), it also has a position in the sky that moves from east to west. This position is known as the solar azimuth, and it has a steady movement on a daily basis.

The earth rotates around its own axis once every day, or once every 24-hour period. Because a full rotation of the earth measures 360 degrees, the motion of the sun is 360 degrees divided by 24 hours, which equals 15 degrees per hour. So over the course of an hour, the motion of the sun from east to west is 15 degrees.

Typically, north is considered the zero point, and the number of degrees the sun is from that point gives you the azimuth angle. The zero point is true north. Using this convention, when the sun is at a position directly to the east of your location, it can be described as having an azimuth of 90 degrees.

If it’s directly to the south of your position, it has an azimuth of 180 degrees. And when it moves due west of you, it has an azimuth of 270 degrees. With this convention, you don’t need to give a direction as well as the number of degrees because the numerical value tells the whole story.

Not all sources use this convention though. Some use south as the zero point and require you to designate the direction (east or west) along with a numerical value to describe the position of the sun along the horizon. I find it easiest, however, to keep the convention with zero being north, east at 90 degrees, south at 180 degrees, and west at 270 degrees.

Ticking Off Solar Time

One point worth noting is the difference between solar time and clock time because the two very rarely match. When looking at your client’s location, you care about locating the array based on solar time, not necessarily the time on your watch. The sun (and lucky ol’ Arizona and Hawaii) doesn’t have a clue about daylight saving time; it operates solely on solar time. Jumping from clock time to solar time when you’re in the field isn’t a crucial task.

You need to be aware of the distinction, though, especially when you’re discussing the solar window (which I fill you in on later in this article) and how that window relates to your client’s site.

Interpreting Sun Charts

Sun charts allow you to figure out how the sun’s path looks on paper. You can use them to pinpoint the sun’s location at any time of day and any time of year, which is helpful when you’re evaluating a particular site for potential shading issues.

The sun charts in this section are the basis for the shading-analysis tools, so don’t skip over this material. The solar resource available at a location is affected by that location’s position on the globe, the time of year, and the local climate. However, the path of the sun may look exactly the same in two very different locations.

For example, from where I sit in Oregon, the path of the sun on a daily basis will appear identical to someone in Milwaukee, Wisconsin, because we’re sitting at similar latitudes, but the exact number of peak sun hours (solar energy) we experience each day will be different because of the differences in our weather patterns.

So I may not notice any differences in the days when I go to watch the Milwaukee Brewers play some baseball, but if I bring my PV array with me, it’ll probably perform differ- ently than it does back home in Oregon.

Figure 10. A sun chart for 30 degrees north latitude.

Figure 10, the sun chart for 30 degrees north latitude shows a typical sun path. The curves represent the path of the sun across the sky for various times of the year. The tallest curve is the path of the sun on the summer solstice, the middle curve represents the equinox paths (March 21 and September 21), and the lowest curve is the path on the winter solstice.

You can use a sun chart like the one in Figure 10 to quickly and accurately determine the sun’s altitude and azimuth. The azimuth angle is given along the x-axis, and the altitude angle is given along the y-axis. The times of day, which are based off of solar time (see the preceding section), are indicated by the dashed lines that intersect the sun paths moving east to west.

Notice that at solar noon on the equinox dates, the altitude of the sun is equal to the zenith minus the latitude (90 degrees – 30 degrees = 60 degrees). You can further evaluate the sun chart to see that the altitude difference between summer solstice and the equinox at solar noon is 23.5 degrees. See how the sun rises north of east and sets north of west during the summer and just the opposite during the winter?

All of these parts of sun charts help you understand the path of the sun and describe the solar window, which is the basis of your solar site assessments; I introduce you to the solar window in the next section.

One thing I find extremely fascinating is the fact that no matter your latitude, the sun rises due east of south and sets due west of south on the equinox dates. When you stop and think about it in terms of the earth’s relationship with the sun, as I describe earlier in this article, it makes sense. Nonetheless, it always strikes me as an interesting fact of life.

Opening up to the Solar Window

If you think about the motion of the sun across the sky at your location, you can imagine it appearing at various positions over the course of a year. In fact, this movement is very predictable and relatively easy to represent with the sun charts described in the preceding section. All the points between the solstices can be defined as the solar window.

Figure 11 shows the portion of the sky considered in the solar window.

The path of the sun on each solstice date defines the extreme sun paths for a location. By defining these two paths, you know that the sun will always be within that “window” every day of the year. (The solar window is represented by the half gray, half clear arc in Figure 11.)

As you design a PV system, your goal is to keep as much of that window open for the PV array as possible. If a tree or building is inside that window, the PV array will be shaded for some amount of time, reducing the energy output.

The exact solar window varies based on the latitude of your client’s site, but it’s equally important regardless of location. Because the sun will always appear in the solar window over the course of a year, you need to keep this window clear from objects that will cast a shadow on the PV array.

You don’t have to go to the ends of the earth to make every minute of this window clear, but you should plan for the window to be open three hours before and three hours after solar noon every day of the year. I cover how to apply this window when selecting a site for your client’s PV system in next article.

Positioning PV Modules to Make the Most of the Solar Resource

After you know how the sun moves at your client’s location, you need to relate that movement to the placement of the PV modules. The angle off of the horizon on which the modules are mounted and the direction they’re pointed in reference to true north are the key factors for your installation.

I explain some basics to know in the sections that follow; flip to next article for full details on performing a site-survey analysis for a PV system.

Introducing tilt angle

Tilt angle is the number of degrees the PV modules are mounted off of the horizon. It’s a critical consideration in any PV system installation. Installations vary from nearly flat on some large commercial roofs (called low-slope roofs) to a very slight tilt (5 to 10 degrees) in some applications to vertical walls (which are at a 90-degree angle) and everything in between.

Tilt angle is one component in the goal of pointing the PV array toward the sun. The exact location and angle you place the modules will likely be based on a combination of design considerations, including

Aesthetics: Even though the PV nerd in me cringes to think of any sacri- fice in energy production, the realist in me knows that if PV installations look like absolute garbage on customers’ houses, the industry as a whole loses. So please keep in mind the aesthetics of the final product before you go trying to get every last kilowatt-hour out of an array.

Making aesthetics a priority means you may need to mount the PV array on a roof with a tilt angle other than the optimal tilt in order to keep the array from looking like an art project gone terribly wrong.

The end goal: Another consideration is what the end goal of the PV system is. If the system

Will be used as the primary power source in an off-grid home, then you want to do all you can to tilt that PV array at the optimum value for the client’s location
Is a grid-direct system in suburbia, you can take a hit on production by installing the array at a less-than-optimum tilt to maintain a reasonable installation because the utility will be present to help with power demands that are greater than what the PV array can produce
Resides on a commercial rooftop, you may consider keeping a very low tilt on the modules to help reduce structural loading on the facility

Knowing about the tilt of the earth’s axis (which is 23.5 degrees) relates to tilt angle. How? Refer to Figure 5 for a refresher on the solar radiation data sets. In particular, look at how the tilt angle of the modules is represented in terms of the number of degrees off the horizontal in relation to latitude. The tilt angles in relation to the site’s latitude are affected in the following ways:

If you adjust the tilt of the array by latitude minus 15 degrees, the PV array is perpendicular to the sun just before and just after the summer solstice. Because the sun is higher in the sky at these times of year, reducing the tilt angle of the array makes the array perpendicular to the sun and maximizes the array’s energy output during the summer months.
If the PV array is mounted with a tilt angle equal to the local latitude, it’s perpendicular to the sun twice a year (on each equinox date) and very close to perpendicular for the weeks before and after the equinox; this makes the array perpendicular to the sun’s position in the sky for the greatest number of hours throughout the year.
If the desire is to have the array perpendicular to the sun in the winter, then a tilt angle of latitude plus 15 degrees is optimum. This helps the array maximize energy production during the winter months.

The idea behind varying the tilt angle is to maximize the PV array’s energy production by pointing the array perpendicular to the sun as much as possible.

So if your client needs to maximize energy production in the summer months (perhaps because she’s running a water pump), you should mount the array so the tilt is equal to a value of latitude minus 15 degrees.

On the opposite end, if the client wants more energy production in the winter, the array should have a tilt angle of latitude plus 15 degrees.

The exact tilt angle that maximizes the annual energy production varies based on the local climate. For most locations, the optimum tilt angle (assuming you don’t change it) is somewhere between an angle that’s equal to latitude to an angle of latitude minus 15 degrees.

The NREL data for peak sun hours that I present earlier in this article can help you define the optimum tilt angle (see the “Referring to handy charts and maps” section). Simply compare the annual average peak sun hours for each tilt angle and see where your client’s site is maximized.

The reason for the magical 15-degree value is the fact that the sun moves 23.5 degrees between the equinox date and the solstice date and then back again. By adjusting the tilt angle by 15 degrees rather than the full 23.5, you allow the array to be perpendicular to the sun for the days and weeks surrounding the time of year you’re optimizing for.

Note: If you read almost any older textbook on the subject of PV module mounting and how best to determine tilt angle, you’ll see a nearly universal answer: Tilt the PV array at an angle equal to the latitude for maximum annual energy production.

Although this would be an absolutely correct statement if your client’s site were always free of cloud cover and other weather variations, such as a lot of fog in the fall and winter, it may not be an absolute truth for your client’s location.

In next article, I show you how to use some commonly available tools to help you determine the tilt angle that’ll serve your client best.

Orienting your array to the azimuth

Another major component to consider when planning the array location to maximize energy output is the orientation with respect to true north, or the azimuth.

The best way to refer to the azimuth of an array is to refer to the number of degrees the array is facing with reference to true north, exactly the same as you refer to the sun’s position. With this notation, the array has an azimuth of 90 degrees if it faces true east, 180 degrees if it faces true south, and 270 degrees if it faces true west.

Bear in mind that true east, true south, and true west don’t refer to compass directions; instead, they take magnetic declination into account. (Magnetic declination is the difference between true north and magnetic north.)

Figure 12. A PV module with an azimuth of about 165 degrees.

For an example of what I mean, look at Figure 12. It shows a PV module that has an azimuth that’s east of south. You could also say that this module has an azimuth of approx- imately 165 degrees based on how far it is from true north.

Because irradiance directly affects the amount of current that a PV array produces (as I explain in the earlier “Relating current and voltage to irradiance” section), it stands to reason that you want a PV array perpendicular to the sun (in other words, directly facing it) as much as possible.

So generally you must point the modules as close to true south as possible (for installations in the Northern Hemisphere) or to true north (for installations in the Southern Hemisphere), but local weather conditions may require you to adjust that reasoning.

In many scenarios, such as a PV array on an existing house, you as the in- staller don’t have the ability to change the azimuth of the PV array, at least not easily. If sufficient room is available, you may choose to place the array on a racking system that can track the sun.

But often racking the system in such a manner that the array’s azimuth is different than that of the house it’s attached to isn’t worth it.

To Track or not to Track?

One of the most requested items in all PV systems is a tracking system, a mechanical assembly that holds the PV array and follows the sun throughout the day. Somewhere along the line, a majority of people decided that a tracking system is an absolute requirement for any PV array.

They’re definitely cool and a great idea (plus they can increase the overall energy output), but an honest evaluation must take place before you make the call that a tracking system is a necessity for a particular PV array.

First, you need to consider the fact that tracking systems contain assemblies that move and will eventually fail. One of the inherent beauties of PV arrays is the fact that they don’t require moving parts — you can’t say that for many power-producing systems. The addition of a tracking system takes away from that beauty somewhat.

Not only have PV module prices been dropping, but placing additional PV modules on inexpensive racking allows you to gain more energy than by placing a smaller array on a tracking system.

Second, consider that tracking systems increase the total energy yield of the array (after all, they keep the modules pointing at the sun a greater number of hours per day) — but at a cost.

Typically, tracking systems tend to cost three to four times as much as a similarly sized stationary racking system. In many situations, the economics of tracking systems and the maintenance they require make them less viable options.

On the other hand, some installations, such as a PV array that’s driving a water pump all summer long, are a perfect fit for a tracking system.

In this type of scenario, the additional hours may be a necessity, and a tracking system is the only way to achieve them. But for most folks, a simple stationary mount does just fine without adding another piece of equipment that you have to service periodically.

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