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Calculating your daily
solar energy harvest


By Rex A. Ewing
Colorado

Have you been thinking of going solar? If so, one of the most important tasks you'll undertake is determining just how much usable energy your expensive solar array will be able to produce, day in and day out, every month of the year. Lacking solid data, many solar neophytes simply take a good guess and cross their fingers.

Fortunately, most of the guesswork has been removed from solar equations by the Analytical Studies Division at the National Renewable Energy Laboratory (NREL) in Golden, Colorado. Compiled from data gathered over the 30-year period from 1961 to 1990, NREL's Solar Radiation Data Manual for Flat-Plate and Concentrating Collectors (commonly known as the Redbook), gives a wealth of information about the monthly solar radiation characteristics at hundreds of locations across the United States and its territories. Seasonal tilt of the solar array

The Redbook offers several blocks of data that you can use to determine how much solar energy you will be able to collect under various solar array configurations. In other words, you will know how much solar radiation (in kilowatt hours per square meter per day, or kWh/m2/day) will fall on your array, on average, during each day of any month of the year. To show a city's variability, the highest and lowest monthly averages taken over the 30-year period are also given.

In the first data block, you can see the difference in energy gathered by a solar array set at five different tilt angles, ranging from horizontal to vertical. When collecting solar energy, you will reap your biggest yield by positioning your array as close to perpendicular to the sun's rays as possible, and seeing the statistical difference in the amount of energy available with different array attitudes really drives this point home. For instance, by perusing the data for nearby Boulder, Colorado, I can see that during the month of December, an array tilted at latitude (40 degrees, in our location) plus 15 degrees (for a total of 55 degrees) will be bombarded by solar radiation equal to 4.5 kWh/m2/day. If I lower the array to latitude (40 degrees) the energy falls to 4.2 kWh/m2/day; and if I were to absent-mindedly keep it at the summer setting of latitude minus 15 degrees (25 degrees), the radiation hitting my array in December would drop to 3.5 kWh/m2/day.

The next two blocks of data give solar radiation statistics for one- and two-axis solar trackers, respectively. Solar trackers are pole-mounted, sunlight-activated mechanisms designed to keep your solar array pointed toward the sun. One-axis trackers simply follow the azimuth (the horizontal path traced by the sun as it travels from east to west across the sky), keeping the array at a fixed, though manually adjustable, elevation. Two-axis trackers go one step further by continually adjusting for both azimuth and elevation, thereby positioning the array directly perpendicular to the sun at all hours of the day.

The fourth block of data pertains to parabolic concentrating collectors and is of no practical use to the homeowner. The fifth (and final) data block, however, contains monthly climatic information and, of interest to those of you considering adding a wind turbine to your energy equation, the average wind speeds for each month of the year. You should bear in mind, however, that unlike solar radiation, wind speeds vary drastically from site to site so you should not use the Redbook's wind data as your only resource.

Though it is currently out of print, the Redbook is freely available in PDF format at: http://rredc.nrel.gov/solar/pubs/redbook/. You can download the whole thing, or each state individually. Most states have several cities to choose from, so you're likely to find a location within just a few miles of your home. (To see really good wind maps, on the other hand, visit Southwest Windpower's website at: www.windenergy.com.)

Making sense of the data

Once you've downloaded the data for your state, you need to know what to do with the numbers. Specifically, you'd very much like to know how many kilowatt hours of actual, usable electricity you can hope to generate, on average, during each day of any given month. Since the kWh/m2/day given in the Redbook is the actual amount of solar radiation available, without taking into account solar cell and other system inefficiencies, the numbers are really not all that telling by themselves.

Fortunately, kWh/m2/day is essentially equivalent to "hours of full noontime sun per day," so to estimate how much solar energy you can produce in a day, you simply calculate how many kilowatts your array is rated for, multiply it by the kWh/m2/day for your location, then times it by an efficiency factor to allow for unavoidable system inefficiencies. For standard charge controllers, use an efficiency factor of 0.70. For Maximum Power Point Tracking (MPPT) charge controllers or grid-tied inverters, an efficiency factor of 0.80 should be more accurate, since MPPT technology effectively turns extra array voltage-power that is normally wasted, especially in winter-into usable amperage.

For example, the rated output of our array is 1,620 watts (1.62 kilowatts), and the average solar radiation for Boulder in the month of January is 4.8 kWh/m2/day for a fixed array set at latitude plus 15 degrees. This gives me a theoretical power output of 7.77 kWh per day. Factoring in the system efficiency of 0.80 (since we use an MPPT charge controller), I arrive at a daily harvest of 6.21 kWh, which is extremely close to the average amount of power the system produces each day during January. (The full range for last January runs from a high of 9.8 kWh to a low of 0.2 kWh, collected during a blizzard.)

Armed with NREL's Redbook, LaVonne and I can easily calculate how much power we could produce in various locales in January, or any other month, with our 1,620 watt solar array, in the unlikely event we decided to pack up our PV system and head across country. For purposes of comparison-especially for those of you who may be thinking about investing in a solar tracker-I've included three sets of figures in the table above. The first column shows the expected power production with the array set at latitude. The second column shows latitude plus 15 degrees-an optimal setting for January-while the third column illustrates how much the numbers improve when the array is mounted on a two-axis solar tracker.

What do these numbers tell us? Well, aside from learning that Erie, Pennsylvania, is a thoroughly dismal place to spend the winter, we see that changing the tilt angle from latitude to an optimal winter setting of latitude +15 degrees generally adds another 5% to 8% usable power to your solar energy equation, while a two-axis tracker will improve your gain by 10% or 15%. Does that mean you should invest in a tracker? It's your call. My personal feeling is that the money used to buy a tracker would be better spent on additional solar panels for a fixed array, as solar panels have a much longer life expectancy than solar trackers, and they have no moving parts that will eventually require maintenance. At exactly the wrong time.

So there you have it. With just a few keystrokes you can access all the painstakingly gathered facts you'll need to help you accurately determine just how much solar energy you can expect to harness for your off-grid or grid-tied home, anytime, anywhere. Best of all, it's free. Just like all the other good things in life.

Except, of course, chocolate.





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