EELE408 Photovoltaics Apparent motion of the sun Lecture 04: Apparent Motion of the Sum Dr. Todd J. Kaiser EAST [email protected] Department of Electrical and Computer Engineering Montana State University - Bozeman SOUTH WEST NORTH What time of year is this image true? March 22: Spring Equinox 2 Sept 23: Fall Equinox Capturing the Light Angle Effects 0⁰ • The power capture by a surface is going to be a function of the angle between the normal to the surface and the light 0 cos 1 3 All the power is incident on the surface 4 Angle Effects 15⁰ Angle Effects 30⁰ 15 cos 0.9659 30 cos 0.8660 96.6% of the power is incident on the surface 5 86.6% of the power is incident on the surface 6 1 Angle Effects 45⁰ Angle Effects 60⁰ 45 cos 0.7071 60 cos 0.5000 70.7% of the power is incident on the surface 7 50.0% of the power is incident on the surface 8 Angle Effects 75⁰ Angle Effects 90⁰ 75 cos 0.2588 90 cos 0.0000 25.9% of the power is incident on the surface 9 None of the power is incident on the surface 10 Declination Angle of Sun Declination Angle Summer Solstice d = 23.45º North Mar 23 Pole Declination () = 0º d Fall Equinox d = 0º Jun 23 Dec 23 Declination () = -23.45º d Declination () = 23.45º 360 23.45 sin d 80 Winter Solstice 365 Sep 23 d = ‐23.45º Declination () = 0º 11 12 12 2 Elevation Angle () Solar Time • Local Time (LT): varies with time zones and day light savings • Solar noon Local Solar Time (LST): time when sun is highest in the sky = 0⁰ • Hour Angle (HRA)=15⁰(LST‐12) –Zero at solar noon –Negative in the morning – Positive in the afternoon The elevation angle is the angular height the sun makes with the horizontal 13 14 Azimuth Angle Elevation and Zenith Angles Azimuth angle is the angle direction of the sun. f = latitude (Bz@ 45.68⁰) North is at 0 degrees The sun is directly south (180⁰) at solar noon sin cos cos sin cosHRA Azimuth cos1 The elevation angle is zero at sunrise cos and sunset Zenith True for mornings Angle The elevation angle is a maximum at use 360⁰‐Azimuth for afternoons N=0⁰ solar noon Elevation or Altitude Angle W=270⁰ E=90⁰ Elevation sin 1sin sin cos cos cosHRA 15 16 S=180⁰ Polar Plot of Sun Position Peak Elevation Angle (Bozeman) for Bozeman Summer Latitude + Declination Summer Fall/Spring 45 23.45 Latitude 68.45 Winter 45 Spring/Fall Latitude - Declination Winter 45 23.45 17 21.55 18 3 Solar Radiation on a Tilted Surface Arbitrary Angles Smodule Sincident cos sin cos sin cos S incident a: sun elevation angle Shorizontal b: module tilt angle y: azimuth angle the panel faces Q: sun azimuth angle Smodule • Most fixed panels are facing toward the equator (south in northern Hemisphere) = 180⁰ •Tracking Modules elevation angle t = 90⁰‐ Shorizontal Sincident sin tilt angle of panel t Smodule Sincident sin declination angle Shorizontal sin latitude Smodule sin 19 20 90 at solar noon Arbitrary Angles Measuring Solar Radiation N S Pyranometers A Acos( Smodule Sincident cos Sincident S N S: Unit vector pointing towards sun N : Unit vector normal to surface 21 22 Solar Irradiance Data Peak Sun Hours Area under curves = Solar Insolation 1kW/m2 Sunny Daily Average Data Daily Solar Daily Data Insolation n Monthly Average Data Equal Areas Solar Radiatio Solar Cloudy Day of the Month Time of Day Peak Sun Hours 23 24 4 MSU Weather Station 1 MSU Weather Station 2 • Sunny • Afternoon Clouds • (7 peak sun hours) 25 26 MSU Weather Station 3 MSU Weather Station 4 • Mostly Cloudy • Overcast: note the scale change 27 28 Isoflux Contour Plots The number of hours the sun is shining • d = day of the year • = latitude • = declination angle 360 23.45 sin 284 d 365 1 1 sin sin sunrise 12 cos 15 cos cos 1 1 sin sin sunset 12 cos 15 cos cos (In solar time) 29 30 5 Hours of Sunlight(Latitude & Day) Daily Solar Irradiance • HRA = hour angle • = elevation angle • h = hour of the day HRA 15 h 12 sin 1sin sin cos cos cos HRA 0.678 H d, 1.3670.7 AM 31 32 Power Density (Latitude & Day) Solar Insolation (latitude & tilt) Smodule Sincident cos sin cos sin cos a: sun elevation angle b: module tilt angle y: azimuth angle the panel faces Q: sun azimuth angle sunset 0.678 H 1.3670.7 AM hsunrise 33 34 Solar Isolation (latitude & tilt) Renewable Energy Technology Resource Maps for the United States • Updated August 2009 35 NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy operated by the Alliance for Sustainable Energy, LLC 6 U.S. Renewable Resources Including Transmission Lines Resource Solar PV/CSP) Wind Geothermal Water Power Biopower Resource Solar PV/CSP) Wind Geothermal Water Power Biopower Theoretical 206,000 GW 8,000 GW 39 GW 140 GW 78 GW Theoretical 206,000 GW 8,000 GW 39 GW 140 GW 78 GW Potential (PV) (onshore) (conventional) Potential (PV) (onshore) (conventional) 11,100GW 2,200 GW 520 GW 11,100GW 2,200 GW 520 GW (CSP) (offshore to (EGS) (CSP) (offshore to (EGS) 50 nm ) 4GW4 GW 50 nm ) 4GW4 GW (co-produced) (co-produced) U.S. Photovoltaic Solar Resource U.S. Concentrating Solar Resource U.S. Wind Resource (50m) U.S. Biomass Resource 7.