Calculating Incident Solar Radiation on Inclined Surface (Easy Method)

For every PV installer, hobbyist and Solar Energy consultant, calculating incident Solar radiation on inclined surface can be extremely beneficial for two reasons:

1. Feasibility study can be carried out for a PV panel or a solar water heater installation
2. Optimal tilt angle  that maximizes that radiation received can be found for a given location (by reversing the calculation)

Finding solar radiation falling over a slope surface accurately requires complex calculations. It depends upon the time of the day, day of the year, position on earth and also orientation of the receiver.

Most irradiation is received when the receiver is perpendicular to the sun. By employing a tracking system the receiver can be constantly orientated to be perpendicular to sun rays. In many cases the employment of a tracking system is not practical, such as for roof installations. In such cases the receiver has a fixed orientation. The calculation mentioned herein can accept any orientation for the receivers  but it has to be a constant value.

In this article, equations of medium complexity are explored. More complex calculation will be the subject of another article. These calculations do not take into account the effect of cloud cover. The use of Microsoft Excel (or any other spread sheet) is most helpful.

Ignoring the cloud cover and other atmospheric effects,  the insolation is mainly dependent on two main factors:
a) Position of the sun
b) Orientation of the receiver

a) Position of the Sun

The position of the sun is changing constantly in the sky and with that the amount of insolation on the receiver also changes. The position of the sun in the sky is described by  the azimuth angle and the elevation angle. The elevation of the sun or how high it is in the sky is dependent upon the latitude as well as declination of the sun. The declination changes from day to day.
The elevation angle can be given as:
α=90-Φ+δ
The latitude Φ captures the position on the earth.
The declination δ captures time of the year.

For this mid-level calculation, the time of the day which is represented by the hour angle ω is not taken into account.

b) Orientation of the Receiver

The orientation of the receiver has two main features:

• What direction it is facing? (North, South, South East etc.)
  What is the tilt angle of the receiver?

The direction of the receiver is also sometimes referred to as aspect of the receiver. As mentioned earlier, for simplicity, the orientation of the receiver is considered fixed. To maximize the solar insolation the receiver should be  kept facing due south in Northern Hemisphere and vice-versa in Southern Hemisphere.

The energy received on the inclined surface G(inclined) is given as:

G (inclined) = G(horizontal) * Sin (α+β) / Sinα

The latitude Φ that is required for the calculation of the elevation angle α can be  found out for any location from this link

The declination can be calculated for a location using the following formula:

δ= 23.45° * Sin[ 360/365 (284+d)]

Where d is the day of the year. d = 1 for 1st January, d = 365 for 31st December.

The average Horizontal radiation “G(horizontal)” for any location can be gathered from the datasets on this NREL (National Renewable Energy Laboratory) website

Or from this NASA re**@nr***.ca” target=”_blank” rel=”noopener”>website

In a further article, more complex calculation that incorporates the azimuth of the receiver and the hour angle of the sun will be posted soon.