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… consider solar panel orientation

February 8, 2012

The question

While standing on a friend’s roof recently, I noticed some houses had photovoltaic (solar) panels oriented differently to others. Another friend said his solar installation quote had an additional item to achieve a better angle than his existing roof provides. It got me wondering:

  • What is the best orientation for fixed solar panels?
  • How much does it matter?
  • Is there benefit in having different positions for Summer and Winter?

Working it out

We start by looking at the sun’s path. For our purposes the earth is a sensible frame of reference, and we’ll consider the sun’s apparent path through the sky.

The University of Oregon has an online tool for solar path charts, but we really need numbers for modelling.  I found Greg Peletier’s spreadsheet (1), which includes solar path and related solar radiation models.

Starting with solar azimuth and elevation, I added a calculation for the angle of incidence of solar radiation onto a panel, for specified panel orientation. I chose to focus on two dates: one midway between the Summer solstice and an equinox, the other midway between Winter solstice and an equinox. These give an approximation of typical Summer and Winter conditions.

All calculations unless otherwise noted are at 30° South, an altitude of 220m, assuming flat terrain.

Daily solar incidence, Summer and Winter, for various panel orientations

The major horizontal groupings are panel azimuth. Minor divisions are panel elevation.

The vertical axis is the day’s average of cos(θ), where θ is the deviation of the sun from directly facing the panel. It’s calculated as the angle between two vectors, but eliminating any time the sun is below the horizon or “behind” an elevated panel.

The lower graph shows the Summer + Winter values combined, though the units are now incorrectly scaled.

I found this graph curious, as it shows a well-positioned panel can see near as much direct sunlight in Winter as it might in Summer.  While the Winter days are shorter, the sun’s path is a tighter curve, not moving as far away from the panel axis.

However, angle of incidence isn’t the only issue at work here.

Atmospheric Influences

The aforementioned spreadsheet also contains a model (2) for solar radiation onto flat ground, compensating for atmospheric reflection and diffusion. Starting with the energy loss of a direct beam through the atmosphere, we see an expected reduction in Winter.

Vertical units are W/m².

Adding diffuse radiation (the light that shines in the shadows), the differences diminish.  I reduce the modelled diffuse light collection by (panel elevation / 180°), which seems reasonable but may be inaccurate.

Caveat

Bird and Hulstrom’s model is for total solar radiation. Photovoltaic (PV) cells work with only a portion of the radiated spectrum, so electric energy yield is much lower than the numbers stated. Atmospheric effects would vary with wavelength, so the actual characteristic may be somewhere between the graphs above, or may be even more attenuated and diffused than shown here. If anyone can identify a more appropriate model, I’ll consider reworking this analysis.

Observations

Let’s zoom in on 3 sets of orientation: Due North (ideal), 30° (my home), and 75° (friend’s home, an extreme example). I’ve also added calculations at each solstice and an equinox.

  • Regardless of azimuth, Summer favours a horizontal panel.
  • The closer to North, the more benefit could be gained in Winter by tilting the panel
  • Even 75° away from North, a panel on a common sloped roof should perform well in Summer, though not so well in Winter.
  • The stacked totals on the previous graph show surprisingly little variation through a wide range of positions.
  • With a panel elevation of 20°, there’s only about 10% annual difference between facing North, and facing due East or West.

For my home, 30° from North-facing, I assessed three elevations through a whole year. These are monthly totals, not single days.

Taking the best option each month, I get an average of 273 W/m². That’s only a 4% improvement over a fixed installation at 20°, which doesn’t really warrant the effort of making panels adjustable, and moving them every few months.

Other Factors

  • Shade!  Nearby trees may be a problem, especially in Winter.
  • Elevation difference to roof can be a help or a hindrance. Mounting a panel more horizontal than the roof it’s on could cause it to be shaded at times.  On the other hand, panels could be angled to take advantage of light reflecting off another part of the roof.
  • Heat can be a problem, depending on the type of panel. Monocrystalline and polycrystalline solar cells perform poorly when hot, so ensure panels are mounted such that airflow under and around them is unhindered.  Amorphous cells are not so affected by heat, but degrade over time. They are cheaper but correspondingly less efficient; for the same power, and the same money, they require twice the space.
  • I’ve ignored cloud and smog. If Winter is typically more cloudy than Summer, positioning should be tuned more toward Summer.
  • I’ve assumed that the aim is maximizing total energy collected per year. If running a home entirely on solar power, it’s probably more important to optimize for Winter.
  • I’ve assumed time of day is unimportant to the end user. If generated electricity is priced differently throughout the day, or there’s insufficient energy storage/sharing to distribute the generated power, that would matter.
  • This is all about a fixed installation. Where space is available and other power sources are expensive or unavailable, a tracking system would be much better.  House roofs are less suited to tracking systems, as one panel would likely shade the next, defeating any gains. A roof with a long North-South ridge could host a tracking array at the top quite effectively though it would have to withstand additional wind in that location.

Disclaimer

I am not a solar radiologist. I am not a solar panel installer (though I suspect few of them would have better than a pre-printed list of acceptable angles, if anything). My analysis has not been reviewed by any recognised scientist nor authority. I have not verified any of this empirically.  Do not base commercial decisions solely on the advice here.  My analysis was conducted for a specific latitude, making several assumptions; I have tried to identify the major ones.

Bibliography

1. Solrad.xls by Greg Pelletier of the Washngton Department of Ecology, available from http://www.ecy.wa.gov/programs/eap/models.html

2. Bird and Hulstrom’s model from the publication “A Simplified Clear Sky model for Direct and Diffuse Insolation on Horizontal Surfaces” by R.E. Bird and R.L Hulstrom, SERI Technical Report SERI/TR-642-761, Feb 1991. Solar Energy Research Institute, Golden, CO.

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