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Solar Radiation on a Tilted Surface


Solar Radiation on a Tilted Surface: Incident power on a PV module depends on both the contained power in the sunlight, as well as the angle formed between the sun and the solar module. When the sunlight is perpendicular to the module absorbing surface, the power density on the module surface is equal to the power density of the sunlight (i.e. the power density is always at its maximum when the direction of the PV module is perpendicular to the sun). But since the angle between any fixed surface and the sun is frequently changing, the power density on the fixed PV module is less than the power density of the incident sunlight.


Incident radiation calculation

The following equations relate to the radiation incident on the module tilted surface (Smodule), the measured solar radiation on horizontal surface (Shoriz) and measure the solar radiation perpendicular to the sun (Sincident).


Shoriz = Sincident sin α

Smodule = Sincident sin (α+β)


α : elevation angle; and
β : module tilt angle measured from the horizontal.

The elevation angle equation:

α = 90 – φ +δ



φ: latitude;
δ: declination angle , which is equal to

δ= 23.45o sin [ (360/365) * (284 + d ) ]


d:day of the year.

From these equations a relationship between Smodule and Shoriz can be determined as:

Smodule =Shoriz  (sin (α+β) / sin α )


Power optimization

Tilt angle has a big effect on the solar radiation incident on the surface. The maximum power for a fixed tilt angle, over a year interval is achieved when the tilt angle is equal to the location’s latitude. Tilt angles can be optimized to be steeper for expected large winter loads, while smaller title angles use a greater portion of light in the summer.

Latitude and module tilt have a huge effect of on the amount of solar radiation received throughout the year and determine the maximum possible output from any Solar module set up.


The relation between Radiation on a tilted surface and a horizontal surface

The above formulas can be used to confirm that tilting a module surface up can increase the incident irradiance. Numerous factors affect the actual amount, such as the latitude, the day of the year, the tilting angle and the surface azimuth, clearness index, and albedo.

Optimum Surface Orientation

In order to maximize the direct irradiance on a surface, rotating the surface around two axes is required; the tilt and the azimuth angle.

Fixed Tilt

When there is no option of moving the surface, the optimum tilt angle for the maximum direct beam irradiance is equivalent to the location’s latitude.

Seasonal Tilt

One should adjust the tilt angle for winter and summer seasons in areas where majority of the irradiance occurs in summer.


New technologies provide advanced options for optimizing the module tilt by tracking techniques


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