There 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.

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.

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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?

• Absorption by the Atmosphere

  The solar energy at the top of the atmosphere is 1360 W/m², but if the sun is in the zenith, directly overhead, only about 1050 W/m² of direct solar rays reaches the earth surface. Another 70 W/m² is scattered solar light from the blue sky and its ultraviolet light that causes sunburn even on cloudy days.

  At most times the solar radiation is slanting though the atmosphere at an angle. At an angle of 30°, the light passes through twice as much atmosphere. 1050/1360 = .77 passing through two atmospheres is .77 x .77 ≈ .6. At a 20° angle the sun passes through three times as much air so ≈ .45 or 45% gets through. At 15° only 35% reaches the earth surface.

• The Projection Effect
  
  But this increasing loss of light energy is further exaggerated because light shining at an angle is spread out over a large area!

  At 30°, light energy in W/m² is cut in half since the light falls on twice the area. At 20° it is one-third. At 15° one quarter.

  So the combination of absorption losses and projection losses is a reduction to 38% at 30°, 23% at 20°, and only 18% at 15°.

• Temperature Effect

  PV panels produce more electricity at low temperatures, less at high temperatures. So when are panels are getting maximum solar irradiance in summer, we must degrade their performance from the nominal output at 25°C/77°F.

  Temperature	5°C/41°F	15°C/59°F	25°C/77°F	35°C/95°F
  Gain/Loss	+10%	+5%	0%	-5%

So things are a bit worse in summer and better in winter

• Direct Sun vs. Indirect Scattered Light

  We noted above that about 7% of the energy reaching the surface (70 W/m²) is scattered light. When the sun's elevation angle is below 10°, almost half the energy is coming from this scattered light.

• First Surface Reflection

  But even these numbers are overoptimistic for low slant angles if the solar panel itself is flat on the surface. If it is tracking the sun at the 10°, angle, the panel would get 18% of the energy, plus some scattered light.

  If the panel lies flat, however, light can not enter the transparent glass surface as easily as it does when the light is perpendicular. The glass surface reflects more and more of the solar light at steep angles.

  We can probably ignore direct solar irradiance producing energy when the sun is less than 10 degrees above the horizon.

• Bottom Surface Reflection

  Some manufacturers have noticed that radiation is not completely absorbed in the panel. They (e.g., Sunpower) have added a mirror at the back surface, so the photons get a second chance at absorption as they travel back to the front of the panel.

• Environment Reflection

  Other manufacturers (e.g., LG) make the back surface transparent so radiation reflected from the environment, for example a white roof, can be absorbed. They argue that gains of as much as 30% can be achieved. LG and Sunpower have the two most efficient (and highest power) solar panels.

• Shading

  Shading by trees, by nearby buildings, and by structures on the roof can be evaluated by the most popular analysis software (e.g., Aurora Solar and Helioscope). But when tilting panels up to be more perpendicular to the sun's rays, while optimal for a single panel or one row of panels, may produce the most shading - of panels that are behind other panels, especially when the sun is at low elevation angles and at azimuths away from due south.

  Shading just part of a panel may reduce the production of power much greater than the percentage shadowed. In his classic book Renewable and Efficient Electric Power Systems, Gilbert Masters showed PV module power losses from shading just a few cells.

  

  

  Since most PV panels are divided into three strings, each with a protective bypass diode to remove a string from power production if some of its cells are shaded, it is important to orient panels in landscape mode, so that any number of cells at the bottom are in the same string.

  

  Compare shading of the bottom cells in portrait mode which compromises all three of the panel strings.

• Dirt or Snow on the Panel

  The higher the PV panel angle, the less likely that air pollution will collect and stay of the panel surface. A strong rain should clean it off. Panels lying flat on the roof are most likely to stay dirty and least likely to have snow slide off in winter.

  As we can see above, the 10% losses from dirt, in which all cells probably reduce power at the same rate, are less severe than even partial shading of a single cell.

We 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.

Can 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?

We 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.

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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.

On 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.