EE Properties of Sunlight. Y. Baghzouz Professor of Electrical Engineering

Transcription

1 EE Properties of Sunlight Y. Baghzouz Professor of Electrical Engineering

2 Azimuth angle The azimuth angle is the compass direction from which the sunlight is coming. At the equinoxes, the sun rises directly east and sets directly west regardless of the latitude, thus making the azimuth angles 90 at sunrise and 270 at sunset. At solar noon, the azimuth angle is 0 o. In general however, the azimuth angle varies with the latitude and time of year.

3 Azimuth angle The azimuth angle is calculated as follows: For the solar morning, (i.e., HRA < 0 or LST <12): For the solar afternoon, (i.e., HRA > 0 or LST > 12): 360 o -

4 Sun s s position (recap.) The azimuth angle and the elevation angle at solar noon are the two key angles which are used to orient photovoltaic modules. However, to calculate the sun's position throughout the day, both the elevation angle and the azimuth angle must be calculated throughout the day. These angles are calculated using "solar time". In conventional time keeping, regions of the Earth are divided into time zones which do not necessarily correspond to the time when the sun is highest in the sky. Such conventions are necessary otherwise a place few blocks away would actually be different in time by several milliseconds. Solar time, on the other hand is unique to each particular longitude. The sun's position is defined by its elevation and azimuth angles.

5 Sun s s position calculation (recap:) Given the observer s location (latitude & longitude), day of the year (d) and local time from GMT (ΔT GMT ): Local Solar Time Meridian: EoT: Time Correction: Local Standard time: Hour angle: Declination: Elevation: Azimuth:

6 Sun position on polar plot: (radial = azimuth, concentric: elevation) Las Vegas NV: longitude ( W), latitude (36 o 10 N), GMT 9 d = 21, LT: 15:05 Altitude: 23 o Azimuth: 220 o d = 81, LT: 11:13 Altitude: 50 o Azimuth: 150 o d = 173, LT: 17:13 Altitude: 27 o Azimuth: 280 o

7 Sun position on polar plot: (radial = azimuth, concentric: elevation) Fairbanks, AK: longitude ( W), latitude (64 o 50 N), GMT 9 d = 356, LT: 11:00 Altitude: 2.5 o Azimuth: o d = 173, LT: 17:13 Altitude: 21 o Azimuth: 280 o

8 Accuracy of sun s position The algorithm presented so far are accurate to within about 1 and is sufficient for most terrestrial photovoltaic applications. For flat plate modules the siting is only accurate to a few degrees and the errors introduced by the simple algorithm are negligible when compared to the unknown factors at the location such as atmosphere effects. For concentrator modules, where the modules track the sun and focus the light, the simple equations introduce and unacceptable degree of error. As the concentration increases so does the need for sun tracking accuracy. For systems with concentration ratios of 1000:1 the sun must be tracked to within 3.5 minutes (0.06 ) of arc. There are numerous algorithms developed for more accurate sun tracking with a trade off between accuracy and complexity. One simplified algorithm that is accurate to within 0.5 minutes of arc is the PSA algorithm has been specially optimised in C++ code for microcontrollers and is available at

9 Solar radiation on a tilted surface The power incident on a PV module depends not only on the power contained in the sunlight, but also on the angle between the module and the sun. When the absorbing surface and the sunlight are perpendicular to each other, the power density on the surface is equal to that of the sunlight, (i.e., the power density will always be at its maximum when the PV module is perpendicular to the sun). However, as the angle between the sun and a fixed surface is continually changing, the power density on a fixed PV module is less than that of the incident sunlight. The amount of solar radiation incident on a tilted module surface is the component of the incident solar radiation which is perpendicular to the module surface. The next figure shows how to calculate the radiation incident on a titled surface (Smodule) given either the solar radiation measured on horizontal surface (Shoriz) or the solar radiation measured perpendicular to the sun (Sincident).

10 Solar radiation on a tilted surface α: sun elevation angle β: module tilt angle (measured from horizontal)

11 Example1: α = 50 o, β = 40 o Smodule = Sincident Shorizontal = Sincident α = 40 o, β = 30 o Smodule = 0.94 Sincident Shorizontal = Sincident

12 Example 2: A PV module is titled 30o in Las Vegas, NV. At solar noon on Dec 25 (i.e., d=360), Shorizonal measure 300 W/m 2. Determine the sun power density received by the module. Answer: Latitude = 36 deg Declination = deg Elevation angle at solar noon = = deg Smodule = 513 W/m 2

13 Solar radiation on a tilted 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. Steeper tilt angles are used for large winter loads, while lower tilt angles are used for large summer loads. As the tilts and orientations become more complicated, it is often easier to convert the solar directions of azimuth and elevation to vectors. The simplicity of using vector comes from the fact that the reduction in intensity of light on a tilted surface is simply the dot product between the incident ray and the normal to the module.