Solar Radiation On Tiled Surface By Hybrid Solar Power :
The efficiency of a PV Solar module depends on both the power contained in the sunlight and on the angel between the PV Solar Module and the Sun. When the PV Solar module is perpendicular to the sunlight then the power density will be maximum. The power density of a fixed pv solar module is always less than the sunlight as the sun is shifting consistently and the surface is fixed.
The figure below shows how to calculate the radiation incident on a tilted surface (Smodule) given either the solar radiation measured on horizontal surface (Shoriz) or the solar radiation measured perpendicular to the sun (Sincident).
The equations of Smodule, Shoriz and Sincident are:
The elevation angle is α
β is the tilt angle of the module measured from the horizontal.
The elevation angle has been previously given as:
where φ is the latitude; and
δ is the declination angle previously given as:
where d is the day of the year. Note that from simple math (284+d) is equivalent to (d-81) which was used before. Two equations are used interchangeably in literature.
From these equations a relationship between Smodule and Shoriz can be determined as:
The tilt angle got a major impact on solar radiation incident on a PV Module surface. For a fixed tilt angle, the maximum power over the course of a year is obtained when the tilt angle is equal to the latitude of the location. However, steeper tilt angles are optimized for large winter loads, while lower title angles use a greater fraction of light in the summer. The simulation below calculates the maximum number of solar isolation as a function of latitude and module angle.
As we see from the above figure, for a module tilt of 0°, the Module Power and Power on Horizontal are equal since the module is lying flat on the ground. At a module tilt of 80°, the module is almost vertical. The Module Power is less than the Incident Power except when the module is perpendicular to the sun’s rays and the values are equal. The module is orientated to the equator so it faces north in the Southern Hemisphere and south in the Northern Hemisphere. As module moves from the Northern to Southern Hemisphere (latitude = 0°), the module is turned to face in the opposite direction and so the Module Power curve flips. When the light is incident from the rear of the module the Module Power drops to zero . Try setting the latitude to your location and then varying the module tilt to see the effect on the amount of power received throughout the year.