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# Calculus Class

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Diablo Valley College Calculus Class Presented by Osama Idrees Calculus and Developing Solar PV Projects 10 27 2008 Chevron 2007 Agenda CES Introduction What is Photovoltaic Calculus and Solar Projects Solar Resources Solar Tracking System modeling Project Financial Development Chevron 2007 Chevron Energy Solutions Lighting HVAC Energy Controls Solar Fuel Cells FACT Energy efficiency and conservation are the most affordable and readily available sources of new energy Chevron 2007 Biomass Cogeneration Now What What is Photovoltaic Chevron 2007 First is First Solar Resources Where is the Sun Determining the solar available resource is the first task for all Solar Systems NREL National Renewable Energy Lab solar map shows the United States available solar resources Depends on geographical location date and time tilt and azimuth of the collector Chevron 2007 Chevron 2007 Sun Path Diagram Chevron 2007 Understanding all this Need to understand the concepts behind all this Develop an algorithm with better accuracy with more applicable and usable functions Further reading http www osti gov bridge product biblio jsp query id 0 page 0 osti id 15003974 Chevron 2007 We use Math Equation of Time The equation of time is the difference over the course of a year between time as read from a sundial and a clock Chevron 2007 Equations EOT M where is the Sun s right ascension M is the Mean Anamoly and is the angle from the periapsis to the vernal equinox Using spherical trigonometry the right ascension is given by cos cos v cos where v is the true anomaly and is the Sun s declination The declination in turn is given by sin sin v sin where is the obliquity Chevron 2007 Chevron 2007 Equations EOT 0 258 cos x 7 426 sin x 3 648 cos 2x 9 228 sin 2x where x is defined as a function of the day number N is the Sun s declination X 360 N 1 365 242 0 39795 0 98563 N 1 Chevron 2007 Graphical EOT Chevron 2007 Graphical Solar Declination Chevron 2007 Solar Tracking Chevron 2007 Solar Tracking Solar

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