Modelling Solar Devices

Most of the irradiance of a surface such as a PV comes from two sources:

Direct beam irradiance from the sun.  The sun is treated as an intense point source of energy.

Diffuse irradiance from the sky.  The sky can be thought of as a hemisphere.

The contributions from direct and diffuse radiation are shown in the diagram below :

The direct beam irradiance can be modelled using Lambert's cosine law, the irradiance of the panel being at a maximum when the beam angle is zero (the panel is pointing directly at the sun).

The Clear Sky

Under a clear sky, the Bird model provides good estimates of direct and diffuse irradiance.  A reasonable estimate can be made using the Meinel model and the assumption that diffuse irradiance is approximately 15% of the direct component.

The Cloud Sky

Clouds complicate the modelling of solar devices.  The effect of clouds is related to climate.  In a desert or semi-arid region such as Arizona in the US where the frequency of occurrence of clouds is relatively low and where a high proportion of the cloud cover is high level clouds such a cirrus, their impact on the performance of solar dievices is relatively small.  However, in Northwest Europe, where the winter sky is often full of thick layers of stratus and the summer ones full of scattered cumulus with completely clear skies being comparitevely rare, the impact of clouds is significant.

The Overcast Sky

Under an overcast sky, the direct beam irradiance is zero, and the diffuse irradiance is more or less evenly distributed around the hemisphere of the sky.  This can be seen in the graph below.  This shows the results of irradiance measurements taken at different slope angles under clear and overcast sky.

The results for the clear day, show that the irradiance is at a maximum, when panel is pointing directly at the sun.  However, under an overcast sky, the irradiance is a maximum when the panel is horizontal.  There appears to be a linear relationship between slope and the irradiance.  When the panel is horizontal it is exposed to the full hemisphere, then it is tilted to 90 degrees, it is irradiated by only half of the hemisphere.

Optimisations

Several optimisations are possible to solar devices, with or without an economic element.  At one extreme in a desert area is to mount the panels on a tracking device so that the panel is always pointing at the Sun.  The most common form of installation in the Northern Hemisphere is orient the panels to the south and incline them at an angle close to the latitude of the instatllation, if the nature of mountings allow it, the angle can be adjusted so that it is steeper in winter when the altitude of the sun is low and shallower in summer when the Sun is higher in the sky.

The seasonal variation in the output of solar devices increases with distance from the equator, for some applications it may be desirable to maximise the output during the winter months.  There is an inference from our observations, that under a cloud sky, winter output can be inceased by mounting the panels on a shallow slope.  Work continues.

Related Pages

Solar Radiation and Clouds - A Discussion
Clouds and Direction of Maximum Irradiance - An Experiment
Clear Sky Solar Radiation - A Simple Model
Lamberts Cosine Law