Photovoltaic Systems Engineering The Solar Resource, cont. SEC598 Photovoltaic Systems Engineering (SEC501 Solar Engineering and Commercialization, I) Session 03 The Solar Resource, cont. August 27, 2018

Session 03 Components The Solar Resource Definitions Solar radiation Orientation Effects Shading Effects

The Solar Resource – the sun’s output Messenger & Ventre, Fig 2.2

The Solar Resource – atmospheric effects The Solar Constant = 1367 W/m2

The Solar Resource – Irradiance Häberlin, Photovoltaics, Fig 2.6

The Solar Resource – air mass Markvart, Solar Electricity, Fig 2.2

The Solar Resource – air mass

The Solar Resource – Definitions Sex Solar Irradiance, the power density at the outer edge of the atmosphere at a plane perpendicular to the direction of the sun Gex Extraterrestrial Irradiance, the power density at the outer edge of the atmosphere at a horizontal plane parallel to earth’s surface Hex Extraterrestrial Irradiation, the energy density at the outer edge of the atmosphere at a horizontal plane parallel to earth’s surface G Irradiance, the power density at the earth’s surface at a horizontal plane parallel to earth’s surface H Irradiation, the energy density at the earth’s surface at a horizontal plane parallel to earth’s surface

The Solar Resource – altitude and azimuth Markvart, Solar Electricity, Fig 2.7b

The Solar Resource – altitude, azimuth, hour angle Messenger & Abtahi, Fig 2.6

Motion of Sun Diagram – Example #1 Arbitrary Latitude zenith latitude Summer Solstice North Pole Equinox 23.5o Winter Solstice 23.5o N S

Motion of Sun Diagram – Example #2 zenith Tropic of Cancer Latitude = 23.5o Summer Solstice Equinox Winter Solstice 23.5o 23.5o North Pole N S

The Solar Resource – Definitions fL Latitude, the angular location north or south of the equator, north positive, -90o < fL < +90o d Declination, the angular position of the sun at solar noon with respect to the plane of the equator, -23.45o < d < +23.45o. The inclination of the earth to its orbital plane is 23.45o a Altitude, the angle between the horizontal plane and the direct line to the sun, 0 < a < 90o qz Zenith angle, the angle between the normal to the horizontal plane and the direct line to the sun, 0 < qz < 90o. It is the compliment to the altitude y Azimuth, the angular deviation of the projection of the sun onto the horizontal plane with zero due south, east negative, west positive, -180o < y < +180o

The Solar Resource - Special Case South facing module, Solar noon w = hour angle = 0 qinc = incident angle = 0 b = tilt angle = f – d = qz = latitude = declination qz = zenith angle S Messenger & Abtahi, Fig 2.15

The Solar Resource – Formulas Declination The solar hour angle

The Solar Resource – Formulas Altitude and Azimuth (parametric equations) The sunrise angle

The Solar Resource – Connection to Altitude and Azimuth

The Solar Resource – Module with southern orientation Markvart, Solar Electricity, Fig 20.7

The Solar Resource – altitude vs azimuth Häberlin, Photovoltaics, Fig 2.5

The Solar Resource - SunChart http://solardat.uoregon.edu/SunChartProgram.html

The Solar Resource – arbitrary module orientation

The Solar Resource – Formulas Relation between incidence angle and other solar angles

The Solar Resource – Definitions fL Latitude, the angular location north or south of the equator, north positive, -90o < fL < +90o b Module tilt, the angle between the horizontal plane and the normal to the module plane, 0 < b < 90o qi Incident angle, the angle between the normal to the module plane and the direct line to the sun, 0 < qi < 90o. yW Wall angle, the rotation (orientation) of the module plane, -180o < yW < +180o

The Solar Resource As we have seen, the solar resource changes continuously, month to month, day to day, hour to hour, because of the movement of the earth This has an impact on the deployment of the photovoltaic modules. The solar resource is optimally used when the modules have perpendicular orientation to the sun rays One can construct a mounting system for the modules that continuously changes its orientation to match the sun’s position (a tracking system) OR One can mount the modules at a constant orientation that represents an engineering compromise (a fixed system)

The Solar Resource – radiation paths to a horizontal surface Häberlin, Photovoltaics, Fig 2.29

The Solar Resource – radiation paths Markvart, Solar Electricity, Fig 2.7b

The Solar Resource – radiation paths to a tilted surface Häberlin, Photovoltaics, Fig 2.31

GG Global Irradiance HG Global Irradiation The Solar Resource – radiation paths to a tilted surface (the solar generator plane) GG Global Irradiance HG Global Irradiation Note: These variables are defined for a tilted surface

The Solar Resource – the sun’s output GAM1.5 = 1000 W/m2 Peak Solar Hours (PSH) Messenger & Ventre, Fig 2.3

References H.Häberlin, Photovoltaics, System Design and Practice, 2012, John Wiley and Sons, 978-1-119-99285-1 R.Messenger and A.Abtahi, Photovoltaics Systems Engineering, 4th Ed., 2017, CRC Press, 978-1-4987-7277-8 T.Markvart, Solar Electricity, 2nd Ed., 2000, John Wiley and Sons, 0-471-98852-9