DOC PREVIEW
Calculus Class

This preview shows page 1-2-3-19-20-38-39-40 out of 40 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 40 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Diablo Valley College Calculus Class Presented by Osama IdreesAgendaChevron Energy SolutionsNow What?First is First – Solar ResourcesSlide Number 6Sun Path DiagramUnderstanding all thisWe use MathEquations:Slide Number 11Equations:Graphical: EOTGraphical: Solar Declination (δ)Solar TrackingSolar TrackingTilt TrackingAzimuth TrackingSlide Number 19Project Idea?PV System ComponentsModeling PV Systems performanceModeling PV Systems performanceSlide Number 24Slide Number 25Slide Number 26Slide Number 27Power TrackingDVC System - DataDVC System – DataModeling PV Systems performancePower TrackingSlide Number 33Slide Number 34Project Idea?Project Financial Development:Slide Number 37Slide Number 38Presentation Sources and Further ReadingsSources and Further Reading© Chevron 2007Diablo Valley College Calculus ClassPresented byOsama IdreesCalculus and Developing Solar PV Projects10/27/2008© Chevron 2007AgendaCES IntroductionWhat is Photovoltaic? Calculus and Solar Projects:• Solar Resources• Solar Tracking• System modeling Project Financial Development© Chevron 2007Energy ControlsChevron Energy SolutionsLighting & HVACCogenerationFuel CellsSolarBiomassFACT: Energy efficiency and conservation are the most affordable and readily available sources of “new” energy© Chevron 2007Now What?What is Photovoltaic?© Chevron 2007First is First – Solar ResourcesWhere 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 resourcesDepends on geographical location, date and time, tilt and azimuth of the collector© Chevron 2007© Chevron 2007Sun Path Diagram© Chevron 2007Understanding all thisNeed to understand the concepts behind all thisDevelop 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 2007We use MathEquation 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 2007Equations:EOT = α-M+Ψwhere α is the Sun’s right ascension, M is the Mean Anamoly, and Ψis the angle from the periapsis to the vernal equinox. Using spherical trigonometry, the right ascension is given bycos α = cos (v- Ψ) / cos (δ)where v is the true anomaly and δ is the Sun's declination. The declination in turn is given bysin δ = sin (v- Ψ) / sin (ε)where ε is the obliquity.© Chevron 2007© Chevron 2007Equations:EOT = 0.258 cos x – 7.426 sin x - 3.648 cos 2x – 9.228 sin 2xwhere x is defined as a function of the day number N, δ is the Sun's declination :X= 360 (N-1) / 365.242δ = 0.39795 [0.98563(N-1)]© Chevron 2007Graphical: EOT© Chevron 2007Graphical: Solar Declination (δ)© Chevron 2007Solar Tracking© Chevron 2007Solar Tracking Solar Tracking works to maximize solar exposure to the collector, aligning the collector plane perpendicular to solar rays Solar Tracking improves performance by up to 30% A typical solar tracking PV system works on either or both of two axis:a) Azimuth Trackingb) Tilt Tracking© Chevron 2007Tilt Tracking© Chevron 2007Azimuth Tracking© Chevron 2007© Chevron 2007Tracking Algorithms:Azimuth tracking – follow the sun path from east to west at a certain tilt and dayTilt tracking – follow the sun path to optimize tilt for a given hour_ noon?_ at a fixed azimuthResources:http://cere.udc.edu/2006Full1992.pdfhttp://www.windsun.com/PDF/pvangles.pdfhttp://instruct1.cit.cornell.edu/courses/ee476/FinalProjects/s2005/tp62/website/solartracker.pdfProject Idea?© Chevron 2007PV System Components© Chevron 2007Understand PV Modules behavior:• Irradiance: solar energy per unit area (Watt/m²)• Electrical Modeling: current voltage characteristics of the panels• Thermal Modeling: impact of cell temperature on performanceModeling PV Systems performance© Chevron 2007 Module current (I) and Power increases with Solar Irradiance Voltage isn’t impacted by irradiance, however, it is inversely proportional to Temperature Silicon modules have 10-20% conversion efficiency, the remaining energy is transformed into heat, Cell temperatures reaches up to 20-25 ºC higher than ambient Efficiency decreases with increase in cell temperature, cool sunny days are the most efficient environment for silicon PV modulesModeling PV Systems performance© Chevron 2007Electrical and Thermal Modeling:Module production are different from one another: Different Si structures and material behavior Different enclosure materials Different Thermal characteristicsUsing field data and empirical constants, module power production can be calculated and modeledTheoretical conversion equation:Irradiance (W/m²) * Modules Area (m²) * Conversion Efficiency * Thermal Factor (appx - 0.5% for every degree) * Array Losses (wiring, soiling, mismatch, etc ~10-15%) * Inverter Efficiency© Chevron 2007Irradiance© Chevron 2007Basic Equations:1. Isc = Iscoڄf1(AMa)ڄ{(Ebڄf2 (AOI)+fdڄEdiff) / Eo}ڄ{1+αIscڄ(Tc-To)}2. Imp = Impo ڄ{C0ڄEe + C1ڄEe²}ڄ{1 + αImpڄ(Tc-To)}3. Voc = Voco + Nsڄδ(Tc)ڄln(Ee) + βVoc(Ee)ڄ(Tc-To)4. Vmp = Vmpo + C2ڄNsڄδ(Tc)ڄln(Ee) + C3ڄNsڄ{δ(Tc)ڄln(Ee)}² +βVmp(Ee)ڄ(Tc-To)5. Pmp = ImpڄVmp6. FF = Pmp / (IscڄVoc)7. Ee = Isc / [Iscoڄ{1+αIscڄ(Tc-To)}]8. δ(Tc) = nڄkڄ(Tc+273.15) / q9. Ix = Ixoڄ{ C4ڄEe + C5ڄ Ee²}ڄ{1 + (αIsc)ڄ(Tc-To)}10. Ixx = Ixxoڄ{ C6ڄEe + C7ڄEe²}ڄ{1 + (αImp)ڄ(Tc-To)}© Chevron 2007PV Performance Modeling© Chevron 2007Power Tracking© Chevron 2007DVC System - Data© Chevron 2007DVC System – Data© Chevron 2007Understand Inverter behavior:• Maximum Power Point Tracking: Inverter looks for the MPP to maximize energy production• Inverter Efficiency: DC to AC conversion efficiency plus any losses• Maximum Output: Inverter rating in AC WattsModeling PV Systems performance© Chevron 2007Power Tracking© Chevron 2007Inverter Modeling:© Chevron 2007System Modeling:© Chevron 2007Project Idea?Compare Theoretical and Actual Data: Conversion efficiency vs. actual output Inverter efficiency Empirical data estimationMaximum Power Tracking Techniques: Hill Climb, Perturb & Observe Incremental Conductance dP/dI or dP/dV feedback control Fuzzy Logic, Neural


Calculus Class

Download Calculus Class
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Calculus Class and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Calculus Class 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?