Solar Panel StudyThere are many factors affecting the performance of photovoltaic (PV) panels converting solar energy to electricity. Very few of these are mentioned by the manufacturers of solar panels and those who install them. Some of them are simply beyond the control of the installers, who are generally following best industry practices and use popular software analysis tools to recommend the best system for a particular location.
Total Solar Irradiance (TSI)Solar irradiance is the amount of solar energy in watts per square meter. At the Earth's distance from the Sun, 1360 watts pass through a square meter perpendicular to the sun's rays. The color temperature of this light is the same as the sun, approximately 6,000K. (K designates degrees Kelvin, measured from absolute zero.) It is of deep significance, however, that the energy density of the radiation is much lower, only 300K. If we capture the visible light energy (absorb it) and see what it emits, it is converted into invisible infrared heat radiation. The Earth absorbs 6000K radiation during the day and emits it as 300K into the night sky. The day is a heat source, the night a heat sink. The Earth is a thermodynamic engine, extracting negative entropy (information) from the solar radiation, using it to power living things, as the great quantum physicist Erwin Schrödinger pointed out in his 1944 essay, "What Is Life?. The Solar Electricity Handbook is a great resource for solar irradiance. Their web page offers a calculator that provides monthly values of average solar irradiance for many cities. In our example for our Institute in Cambridge, we calculated irradiance for panels flat on the surface. It is clear that the production of power with panels flat in winter (1.8 kWh/m2) is greatly reduced from the rest of the year. In the summer it is 5.6 kWh/m2, over three times the power. The calculator lets you set the panels tilt angle, even adjusting panels throughout the year to follow the sun's elevation angle in different seasons We shall see below the reduction in winter is a combination of the spreading our of the sun's rays by the projection affect and the greater absorption of solar energy as the rays travel through the atmosphere at a low slanting angle when compared to the summer sun near overhead in the sky.
The Best Solar Panel AngleThe question perhaps most often asked is what orientation to mount a panel, including its elevation angle and azimuth (compass direction). The best (and most expensive) answer is to mount the panel on a tracking device to follow the solar path across the sky. Next best is to point the panel due south, angled up to the local latitude, which aims the panel directly at the sun when it is highest in the sky (solar noon) at the spring and fall equinoxes. But this is perfect for only two days at one moment of those days. At all other times the sun's direction varies widely. At sunrise and sunset, the sun is on the horizon (elevation angle 0°), and at solar noon it is high in the sky in summer, 23° above its equinox angle, and in winter low in the sky, 23° below the celestial equator. At the equinoxes, the sun's elevation angle is equal to the local latitude. Most all research recommending an angle says point it due south (in the northern hemisphere) with elevation equal to the latitude. Twice a year for a single moment the panel is exactly perpendicular to the sun's rays. Sadly, most residential installations have little choice of angle. Their angled roofs are in arbitrary directions and pitches. Flat roofs (typically commercial roofs are flat) can aim the panels in any direction, and usually choose an azimuth toward the earth's equator. But the solar panel elevation angle on commercial roofs varies widely, from flat (0°) to latitude. Why is this?
The Major Factors
Experimental MeasurementsWe can experimentally confirm the reduction in solar irradiance when the sun is at various angles with a white card and an inexpensive light meter. We can confirm the power output of a PV panel at various angles to the sun with an inexpensive voltmeter and ammeter. We can separate the production by direct sunlight from indirect scattered light with a board as large as the panel admitting only rays from the sun at a low elevation. We can analyze shading by panels using 3D capabilities of the solar installers' software. We purchased both Aurora and Helioscope for this study. We will ask solar panel manufacturers to loan us test panels, but will purchase leading solar panels if necessary.
QuestionsCan solar panel software analysis tools tell us the power generated by an array of panels at different times of day? If they cannot, how can we believe their monthly averages? Which of the major factors above reducing energy production are included in the algorithms of analysis software?
Sample ResultsWe began by modeling 47 panels (LG NeON 2 390W 72 Cell Mono 1500V SLV/WHT BiFacial Solar Panel, LG390N2T-A5) to the flat roof of our Information Philosophy Institute. We oriented the panels due south and tilted them to four different angles - 47° (our latitude), 18°, 10°, and 0° (flat on the roof). Helioscope software estimated the power output as 18.3 kW and generated the following monthly values for energy production. Right click to open in a new browser tab. We can see that panels flat on the roof have no shading losses, where those tilted at latitude lose 18.6% . We can use Aurora to visualize that shading at different times of day. The panels are separated enough to eliminate shading of a panel directly behind, but only at solar noon. At other times the shadow angles down to the sides, cutting off power from panels diagonally behind. We again arranged 47 LG bifacial panels on the roof by using 1" panel spacing and 24" spacing between rows. Aurora also estimated power at 18.3 kW. They are probably just multiplying 47 panels times 390W per panel! And the figure of 390W is when the LG bifacial is illuminated with 1000 W/m2, which is not achievable with panels in typical conditions. When we look down from our latitude angle, we see that there is no panel shading. Aurora's camera view point is not very far above the roof. To show panel shading from the sun's POV it should be infinitely far away. So panels at the rear appear to be shading because of their perspective. We can now rotate Aurora to see the panels from the east at the summer solstice, when the sun is 35° above the horizon and producing a bit under half the solar irradiance at its maximum for the day. From the east, the panels are not facing the sun, but are edge on. The near perspective again diverges from the sun's perspective. The point is that instead of nearly half power, there is no power. It's not clear whether the Aurora irradiance (or "solar access value) gives us this reduction.
Shading in AuroraOn the flat unshaded part of the roof solar access is 100% and the irradiance is 1410 kWh/m2/yr. When the cursor is on the unshaded portion of a panel tilted at 20° the solar access is 100% and the irradiance increases to 1610 kWh/m2/yr. A panel that was tilted to face the sun directly would have still higher irradiance. Aurora shows the monthly variation in irradiance. Aurora shows the shading on a panel as the color changing from bright yellow to a dark purple. Above the cursor is on the shaded portion of a panel. Solar access averages only 75% and is way down in the winter months. Shading reduces irradiance to 1214 kWh/m2/yr. Normal | Teacher | Scholar