Solar Energy Production

Solar Panels in Action!

After passing all inspections and approvals my ten solar panels are finally producing usable energy. 😎

I can monitor solar energy production throughout the day on my laptop and phone. For example, the next image shows energy produced on June 26th, the best day I've had so far.

June 26th began with completely clear skies which lasted until about 2:00 pm. After 2:00 pm hazy clouds slowly thickened until sunset. Although thin clouds covered most of the sky, energy production continued as significant sunlight continued to reach the panels.

Notice how the production curve above is almost perfectly symmetric. I believe this results from the smoothly changing angle of sunlight on the panels throughout the day.

Imagine two arrows. One arrow points down perpendicularly into the solar panels. Call this the panel arrow. The panel arrow direction is fixed because the panels are rigidly attached to my immovable house. The second arrow points from the Sun to the panels. Call this the solar radiation arrow. The solar radiation arrow changes direction from sunrise to sunset as the Sun changes elevation and moves across the sky. When the solar radiation arrow is parallel to the panel arrow (that is, when there is zero angle between the two arrows) sunlight falls perpendicularly on the panels for maximum absorption. When the solar radiation arrow is perpendicular to the panel arrow, no solar radiation falls into the panel because radiation then skims along parallel to the panel surface without entering. During the day the angle between the two arrows varies smoothly, from some large value as the Sun rises, up to some minimum amount near midday, and then back to some large value as the Sun sinks. Radiation absorption varies with the changing angle between the two arrows. Energy production varies with the cosine of the angle between the arrows, or vectors. It varies with the "dot product" of the two vectors.

Also notice the flat peak energy production around noon when the Sun was highest in the sky. It looks like the panels produce the same maximum amount of energy for a few hours while the angle between the two vectors is near minimum. I investigated radiation absorption issues in detail for my particular system. For the day of June 20th I explicitly calculated the angle between the panel vector and the solar radiation vector between the hours of 9:00 am and 2:00 pm (DST). The minimum angle value of 0.61 degrees occurred near 11:30 am when radiation absorption was 99.99 percent of the maximum possible. The absorption rate was greater than 98 percent for one hour and 40 minutes from about 10:40 am to 12:20 pm. During this time the angle between the two vectors was 11 degrees or less. This calculation is only valid for one day, June 20th. Obviously, the Sun will take different paths across the sky at different times of the year. 

Another interesting phenomenon is illustrated in the June 26th graph above. Notice the asymmetrical tail after about 6:00 pm. After about 6:00 pm on June 26th my roughly southeastward-facing panels were in the shade! The Sun was still above the horizon, but below my roof peak line. Yet some energy was still being produced! I think reflected sunlight from the sky, clouds, and surrounding buildings was still falling on the panels, so they were still producing some energy.

My system was activated on June 18th, two days before the summer solstice! This is the best time of year for solar energy production when the Sun is highest in the sky and above the horizon for the longest time. I hoped to see what would happen on a cloud free day day with transparent blue skies from sunrise to sunset. Unfortunately, in my area of Virginia at this time of year, clouds show up in some form almost every day. For example, on June 22nd the morning was clear, but afternoon thunderstorms developed and cut off energy production after about 2:30 pm as you can see in the next graph.

On June 23rd the morning was cloudy, but the afternoon was mostly clear. So not much energy was produced during the morning in the next graph.

June 25th was cloudy and rainy almost all day. Nevertheless, enough infrared light fell on the panels to produce some energy, as you can see in the next graph below. It's amazing how the panels still produce energy even on cloudy days in the absence of bright yellow sunlight. Obviously, some visible and infrared light is getting through the clouds. Otherwise we would be stumbling around in complete darkness on a cloudy day.

A new electric meter was installed to accommodate solar energy production. The new meter continuously cycles between four different digital displays. Two displays are irrelevant. The other two displays alternate between the amount of energy I have received from Dominion Power and the amount of energy the panels have put back into the Dominion power grid.

Meter readings on the morning of June 19th showed 10 kwhrs received from Dominion and 5 kwhrs sent back to Dominion. We were gone for the next week. When we returned on June 26th meter readings showed we had received 35 kwhrs from Dominion and sent back 95 kwhrs to Dominion! We were a net energy producer during that week! Of course, we were away, so only the refrigerator and occasional air conditioning needed power.

How much energy is used by various electrical devices in my house and how much energy can the panels deliver? The kilowatt-hour (kwhr) is the relevant energy unit here. Over the past 19 days the panels have produced a daily average of 16.3 kwhrs. Here are some examples of energy use.

The energy needed to fully recharge a completely discharged car battery in my Chevy Volt hybrid is about 17.5 kwhrs. This would require a full day of solar energy collection on most days. But I almost never completely discharge the battery in typical trips around town. Instead, it usually takes only 2 to 8 kwhrs to bring the battery to full charge after local drives. This amount could be completely supplied by the panels. It's interesting to think I can be driving my car around town completely powered by solar energy!

Air conditioning is our major household electrical energy requirement. We usually only run air conditioning overnight. Our small house is so well insulated that overnight cooling is sufficient to keep the house comfortable during most of the daylight hours. A typical hot, humid, overnight air conditioning run might use about 16 kwhrs. So the panels could supply this energy amount during a day of operation. Of course, the panels don't produce energy overnight, but any extra they produce during the day is sent back to Dominion Power and deducted from our bill.

Laundry also requires substantial energy, especially the electric dryer. Laundry day consumes about 11 kwhrs.

Let's consider a day when the temperature is in the 60's all day and night. Then air conditioning isn't needed. If the washer and dryer aren't used, and the electric car doesn't require recharging, only the refrigerator, a few lights, laptops, stove, and the TV need power. In this case our house typically only consumes about 4 kwhrs during the day! The panels easily deliver this amount and send extra energy back to Dominion under these circumstances. Energy consumed by lights in our house is negligible.

Of course, the financial bottom line comes with an actual electric bill. So far I haven't received a bill with kwhrs displayed. Dominion Power said it would take "two billing cycles" before my new situation was entered in their system. In the meantime, naturally, they are still deducting payment. Somehow they can manage to calculate and obtain their payment, but they can't manage to produce a bill. Such is the wonder of modern technology. Last year my bill for June was $65.12. This year, with the panels operating from June 18th onward, the June bill was $41.44. Last year during July we used 945 kwhrs. This July, with the panels, we are on track to use less than about 400 kwhrs from Dominion. So my July bill should be cut approximately in half. It will be very interesting to see how much money we actually save during the course of a year.