EELE408 Photovoltaics Lecture 04: Apparent Motion of the um Dr. Todd J. Kaiser tjkaiser@ece.montana.edu Apparent motion of the sun EAT Department of Electrical and Computer Engineering Montana tate University - Bozeman OUTH NORTH WET What time of year is this image true? March 22: pring Equinox ept 23: Fall Equinox 2 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 on the surface 4 Angle Effects 15⁰ Angle Effects 30⁰ 15 cos 0.9659 30 cos 0.8660 96.6% of the power is on the surface 5 86.6% of the power is 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 on the surface 7 50.0% of the power is on the surface 8 Angle Effects 75⁰ Angle Effects 90⁰ 75 cos 0.2588 90 cos 0.0000 25.9% of the power is on the surface 9 None of the power is on the surface 10 Declination Angle of un Declination Angle ummer olstice North Pole d = 23.45º Mar 23 Declination () = 0º d Fall Equinox d d = 0º Jun 23 Declination () = 23.45º Dec 23 Declination () = -23.45º Winter olstice d = 23.45º 360 23.45 d 80 365 ep 23 Declination () = 0º 11 12 12 2
Elevation Angle () olar Time Local Time (LT): varies with time zones and day light savings olar noon Local olar Time (LT): time when sun is highest in the sky = 0⁰ Hour Angle (HRA)=15⁰(LT 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. North is at 0 degrees The sun is directly south (180⁰) at solar noon f = latitude (Bz@ 45.68⁰) cos cos cos HRA Azimuth cos 1 cos True for mornings use 360⁰ Azimuth for afternoons N=0⁰ Zenith Angle The elevation angle is zero at sunrise and sunset The elevation angle is a maximum at solar noon Elevation or Altitude Angle W=270⁰ E=90⁰ Elevation 1 cos cos cos HRA =180⁰ 15 16 Polar Plot of un Position for Bozeman Peak Elevation Angle (Bozeman) ummer Latitude + Declination ummer pring/fall 45 23.45 68.45 Latitude 45 Fall/pring Winter Winter 17 Latitude - Declination 45 23.45 21.55 18 3
olar Radiation on a Tilted urface Arbitrary Angles cos cos cos elevation angle tilt angle of panel declination angle latitude 90 horizontal at solar noon horizontal horizontal 19 a: sun elevation angle b: tilt angle y: azimuth angle the panel faces Q: sun azimuth angle Most fixed panels are facing toward the equator (south in northern Hemisphere) = 180⁰ Tracking Modules t = 90⁰ t 20 Arbitrary Angles N Measuring olar Radiation A Acos( Pyranometers cos N : Unit vector pointing towards sun N : Unit vector normal to surface 21 22 olar Irradiance Data Peak un Hours unny Daily Average Data Area under curves = olar Insolation 1kW/m 2 Daily olar Insolation Daily Data Monthly Average Data n olar Radiation Equal Areas Cloudy Day of the Month Time of Day Peak un Hours 23 24 4
MU Weather tation 1 MU Weather tation 2 unny (7 peak sun hours) Afternoon Clouds 25 26 MU Weather tation 3 MU Weather tation 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 23.45 284 d 365 1 sunrise 12 15 1 sunset 12 15 1 cos cos 1 cos cos cos cos (In solar time) 29 30 5
Hours of unlight(latitude & Day) Daily olar Irradiance HRA = hour angle = elevation angle h = hour of the day HRA 15 H 1 h 12 cos cos coshra AM d, 1.3670.7 0. 678 31 32 Power Density (Latitude & Day) olar Insolation (latitude & tilt) a: sun elevation angle b: tilt angle y: azimuth angle the panel faces Q: sun azimuth angle H cos cos cos sunset hsunrise 1.367 0.7 AM 0.678 33 34 olar Isolation (latitude & tilt) Renewable Energy Technology Resource Maps for the United tates Updated August 2009 35 NREL is a national laboratory of the U.. Department of Energy Office of Energy Efficiency and Renewable Energy operated by the Alliance for ustainable Energy, LLC 6
U.. Renewable Resources Including Transmission Lines Resource olar PV/CP) Wind Geothermal Water Power Biopower Theoretical 206,000 GW 8,000 GW 39 GW 140 GW 78 GW Potential (PV) (onshore) (conventional) 11,100GW 2,200 GW 520 GW (CP) (offshore to (EG) 50 nm) 4GW (co-produced) Resource olar PV/CP) Wind Geothermal Water Power Biopower Theoretical 206,000 GW 8,000 GW 39 GW 140 GW 78 GW Potential (PV) (onshore) (conventional) 11,100GW 2,200 GW 520 GW (CP) (offshore to (EG) 50 nm) 4GW (co-produced) U.. Photovoltaic olar Resource U.. Concentrating olar Resource U.. Wind Resource (50m) U.. Biomass Resource 7