A tree to the southeast casts a shadow on the panels in the morning during the winter, when the sun rises in the southeast and casts longer shadows because it doesn't climb as high in the sky. With time, the shadow swings to the right as the sun moves southward and shortens as the sun climbs higher in the sky, until it comes off the panels and then off the roof. This picture was taken at about 9:30am near the Winter Solstice (Dec. 21), when the sun is lowest and shadows longest (the worst day of the year for solar panels). My PV system still exceeds the predicted total annual production despite the shadows, because neither shadow affects the most productive times, namely 9am to 3pm during the spring, summer, and fall. The wintertime contribution to the total annual production is relatively small, and in fact I don't produce as much electricity as I consume in the winter (but it's made up for by producing double what I consume in the summer). The Next slide will show the effect of the two tree shadows on my actual PV production.
Solar installers may use a hand-held domed gadget to assess the shadowing situation, but I don't think it's particularly accurate. However, I calculated the path of the shadows (figure at right), so I knew about my shadowing situation in advance.
My computer program calculates the position of the end of the shadow from a tree or other object at any time of day and day of the year, based on equations that describe the path of the sun through the sky at 40°N latitude. The plot is a map view of my roof in red, and curves that show the path of the shadow from the indicated 45' tree, on the 21st day of each month between 8am and 4pm (each dot is an hour). The shadow path closest to the tree is June 21 (Summer Solstice), when the sun is highest and the shadows shortest. The shadow path furthest from the tree is December 21 (Winter Solstice), when the sun is lowest and the shadows longest. The second shortest shadow path is for Nov. 21 and Jan. 21, and so on in pairs because the sun's path is symmetric around the solstices. The leftmost dot on each curve is the end of the shadow at 8am, and the rigthtmost dot is at 4pm, and the dot due North of the tree is at solar noon when the shadow is shortest. The photo at left was taken on Dec. 21 at about 9:30am (2.5 hours before noon), which is shown as the blue line. The tree shadow affects my panels until about 11:30am. My panels are not affected at all by this tree from March to September, and in February and October the shadow sweeps across the panels between about 9-10am. I chose the L-shape panel layout (rather than a double row) in order to minimize the time it takes the shadow to traverse the panels in Jan.-Feb. and Oct.-Nov.