Solar Energy PDF - ESET 222 - Winter 2020

Wind & Solar Energy ESET 222 Wind & Solar Energy Winter, 2022 Professor: Arun Hor. Solar Energy ESET 222: Wind & Solar Energy ( Winter 2020 ) Solar Energy SOLAR POSITION AT ANY TIME OF DAY Notice that time in these equations is expressed by a quantity called the hour angle, H. The hour angle is the...

Wind & Solar Energy ESET 222 Wind & Solar Energy Winter, 2022 Professor: Arun Hor. Solar Energy ESET 222: Wind & Solar Energy ( Winter 2020 ) Solar Energy SOLAR POSITION AT ANY TIME OF DAY Notice that time in these equations is expressed by a quantity called the hour angle, H. The hour angle is the number of degrees that the earth must rotate before the sun will be directly over your local meridian (line of longitude). As shown in figure below, at any instant, the sun is directly over a particular line of longitude, called the sun’s meridian. The difference between the local meridian and the sun’s meridian is the hour angle, with positive values occurring in the morning before the sun crosses the local meridian. Thus, the hour angle H at 11:00 A.M. solar time would be +15◦ (the earth needs to rotate another 15◦, or 1 hour, before it is solar noon). In the afternoon, the hour angle is negative, so, for example, at 2:00 P.M. solar time H would be −30◦ ESET 222: Wind & Solar Energy ( Winter 2020 ) Solar Energy SOLAR POSITION AT ANY TIME OF DAY The location of the sun at any time of day can be described in terms of its altitude angle β and its azimuth angle φs as shown in figure below: The subscript s in the azimuth angle helps us remember that this is the azimuth angle of the sun. By convention, the azimuth angle is positive in the morning with the sun in the east and negative in the afternoon with the sun in the west. Notice that the azimuth angle shown in figure uses true south as its reference. The azimuth and altitude angles of the sun depend on the latitude, day number, and the time of day. The following two equations allow us to compute the altitude and azimuth angles of the sun. ESET 222: Wind & Solar Energy ( Winter 2020 ) Solar Energy SOLAR POSITION AT ANY TIME OF DAY Example: Find the altitude angle and azimuth angle for the sun at 3:00 P.M. solar time in Montreal, Quebec (latitude 45◦) on the summer solstice. Solution: Since it is the solstice we know, without computing, that the solar declination δ is 23.45◦. Since 3:00 P.M. is three hours after solar noon, we can say, the altitude angle is sin β = cosL cosδ cosH + sinL sin δ = cos 45◦ cos 23.45◦ cos(−45◦) + sin 45◦ sin 23.45◦ = 0.74β = sin−1(0.74) = 47.730 The azimuth angle is So, φS = sin−1(−0.9644) = −75◦ (75◦west of south)