Optimization of tilt angle for solar panel: Case study for Madinah, Saudi Arabia

In the search for a feasible alternative to conventional energy production, solar power is a proposed solution with a lot of upside, as the sun delivers a massive amount of energy to the Earth daily.  Roadblocks to the implementation of solar and other renewable include cost, infrastructure, and efficiency.  Improving in any of these areas will serve to hasten the transition to solar power.  Efficiency can be further broken down into the categories of technology and logistics.  While extensive research is needed to develop new materials to improve on the modern components of solar panels, the logistics of giving the panels the best opportunity to harness the sun’s power are not as worrisome.  We currently have an extensive amount of data as to which locations receive the most light, and how to place panels to fully use it.  One method of improving solar efficiency is using tilted solar panels.  Conventional flat solar panels are less efficient, because the sun hits them at an angle, decreasing the potential surface area of the panels.  By tilting the panels to hit the sun’s rays head on, we are able to fully utilize a panel’s surface area.  The first tilted panels have been installed to get the most utility out of the sun based on annual averages, at an angle approximately equal to their latitude.  However, as Benghanem discovered, a month-to-month angular model can significantly increase the panels’ efficiency.—Donald Hamnett
Benghanem, M., 2010. Optimization of tilt angle for solar panel: case study for Madinah, Saudi Arabia. Elsevier, doi:10.1016/j.apenergy.2010.10.001.

The amount of solar energy incident on a panel is a complex calculation, and is variable based on the time scale used.  It is a function of local radiation climatology, the orientation and tilt of the collector surface, and ground reflection properties.  Orientation and tilt is the factor that we have control over.  Though modeling this situation is not new, the existing models make an assumption that yields incorrect values.  The current models assume that sky radiation is isotropically distributed at all times; in other words, it is uniformly distributed in all directions.  This is not the case on our planet, so Benghanem’s model arrives are a more sophisticated expression for solar energy potential.  He developed an estimate based on anisotropic modeling methods, using horizontal solar radiation data from meteorological databases.  The sky-diffuse radiation can be expressed as the ratio of the average daily diffuse radiation on a tilted surface, to that on a horizontal surface.  This relation is composed of values for the following variables: daily beam radiation incident on a horizontal surface, extra-terrestrial daily radiation incident on a horizontal surface, daily ground reflected radiation incident on an inclined surface, ratio of average daily beam radiation incident on an inclined surface to that on a horizontal surface, and the surface slope from the horizontal.  Other factors included in the overall analysis were tracking the sun’s movement throughout the day to keep the panels perpendicular to the sun’s radiation, the zenith angle, which requires use of solar time and hour angle as opposed to the human established time-zone times.  The cosine of the zenith angle can be calculated as a function of hour angle, latitude, and solar declination.
This analysis confirmed that the optimum tilt angle is indeed different for each month of the year, and that the yearly optimum tilt angle equals the latitude of the site.  At Madinah site, which was the example modeled, the winter months (December-February) required an angle of 37 degrees, the spring months (March-May) required an angle of 17 degrees, the summer months (June-August) required an angle of 12 degrees, and the autumn months (September-November) required an angle of 28 degrees.  Overall, using yearly averages as opposed to monthly averages lost about 8% of the energy that would have been produced using monthly averages for the site at Madinah.

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