Sustainable Energy Science and Engineering CenterSolar radiation: Refer to Lectures 5 & 6 of EML 4450 Fall 2006. Photovoltaic Systems EngineeringSustainable Energy Science and Engineering CenterIrradiance & IrradiationIrradiance is given in W/m2 and is represented by the symbol G. The rate at which radiant energy is incident on a surface per unit area of surface.Irradiation is given in J/m2and is the incident energy per unit area on a surface - determined by integration of irradiance over a specified time, usually an hour or a day.Insolation is a term used to solar energy irradiationRadiosity is the rate at which radiant energy leaves a surface, per unit area, by combined emission, reflection and transmission.Sustainable Energy Science and Engineering CenterTypical Solar IrradianceSustainable Energy Science and Engineering CenterPV Panel OrientationSustainable Energy Science and Engineering Centerhttp://rredc.nrel.gov/solar/pubs/redbook/PDFs/FL.PDFTallahassee Solar Radiation DataSustainable Energy Science and Engineering Center01234567Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonthly radiation (kWh/m2/day)Latitude - 15LatitudeLatitude + 150123456789Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonthly radiation (kWh/m2/day)No tracking1-Axis tracking2-Axis trackingTallahassee Monthly Solar InsolationSustainable Energy Science and Engineering CenterEglobal= 650 sin43α− 30⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + 325⎡ ⎣ ⎢ ⎤ ⎦ ⎥ × 8 ×10−5× h +1() W/m2For clear sky conditionAnnual Global IrradianceWhere α is the solar altitude in degrees and h is the geographic altitude in meters (Tallahassee: 21 m). Masato Oki & Hiroyuki Shiina, “Preliminary study on an estimation method for annual solar irradiance atvarious geological altitudes”, Eighth International IBPSA Conference, Eindhoven, Netherlands, August2003.Source: To find the solar altitude go to the following site:http://aa.usno.navy.mil/data/docs/AltAz.htmlSustainable Energy Science and Engineering CenterIbrahim Reda & Afshin Andreas, “Solar Position Algorithm for Solar Radiation Applications”, NREL/TP-560-34302, November 2005. http://www.nrel.gov/docs/fy06osti/34302.pdf AlgorithmSustainable Energy Science and Engineering CenterThe global spectrum comprises the direct plus the diffused light. Global RadiationSustainable Energy Science and Engineering CenterAM 1.5d Spectrum Energy DistributionSilicon solar cells with a bandgap of 1.13ev can maximally absorb 77% of the terrestrial solar energy.Sustainable Energy Science and Engineering CenterPV Electricity Applications (market share in 2002)• Grid connected systems (71%)• Off-grid industrial applications (15%)• Rural electrification in developing countries (7%)• Consumer applications (7%)Net producer of energy: generating between 5 and 12 times more energy over their lifetime than is required for their manufacture. Ideally suited for distributed generation of electricity and easily scalable.Sustainable Energy Science and Engineering CenterGrid connected PV competes with retail electricity. Unlike grid power, customers incur a high upfront cost and, depending on the level of customer incentives offered by state or utility programs, a high LCOE over the project life to invest in PV.This economic disadvantage of PV is reduced significantly through government incentives and a growing market for PV environmental attributes such as green tag trading.In terms of a purchase decision, different economic metrics are used, such as:- upfront cost - payback period - internal rate of return-net present value - levelized cost of electricity - years till cumulative positive cash flowPV EconomicsSustainable Energy Science and Engineering CenterEconomic Metricshttp://www.ef.org/documents/EF-Final-Final2.pdfSustainable Energy Science and Engineering CenterSystem Price Drivershttp://www.ef.org/documents/EF-Final-Final2.pdfSustainable Energy Science and Engineering CenterPerformance FactorsPV Technology – Efficiency, crystalline silicon, thin film etc. PV System Tilt -latitudeOrientation –south facingTracking System -noneSystem location – insolation and utility ratesSustainable Energy Science and Engineering CenterEnergy EconomicsLife Cycle Cost of a Energy System1. Acquisition Costs2. Operating Costs3. Maintenance Costs4. Replacement CostsRefer all costs to the time of acquisition.Sustainable Energy Science and Engineering CenterSimple Payback PeriodSimple payback = Extra first cost / Annual savingsEx: Energy efficient washer that cost an extra $500 and which saves $ 100/year in electricity would have a simple payback of about 5 years. This method does not consider the longevity of the system. It generally makes an investment look worse than it is. Initial simple rate of return = Annual savings / Extra first costThis is the inverse of a simple payback period and it makes the investment look good with a 20% initial rate of return in the above example. It is a convenient indicator of “minimum threshold”. If an investment has an initial rate of return below the threshold, there is no need to proceed any further.Sustainable Energy Science and Engineering CenterTime Value of MoneyInflation rate - iDiscount rate - d (relates to the amount of interest that can be earned on principal that is saved)Where dis the percentage rate expressed as a fraction - 100d % per yearInitial amount of money = NoNumber of years = nThe final value of investment= NN(n) = No(1+d)nSustainable Energy Science and Engineering CenterInitial cost of the item: CoInflation rate : 100i %Cost of the item after nyears:C (n) = Co(1+i)nTime Value of MoneySustainable Energy Science and Engineering CenterPresent WorthPresent Worth Factors and Present Worth:Present worth factor, Pr is defined byFor an item to be purchased n years later, the present worth is given byPW = (Pr) CoPr =1+ i1+ d⎛ ⎝ ⎜ ⎞ ⎠ ⎟ nSustainable Energy Science and Engineering CenterPresent worth of a recurring expense:Example: Diesel fuel of a diesel generator or yearly maintenance costs of a systemThe costs are incurred at the beginning of each year The present worth is: LetPW = Co+ Co1+ i1+ d⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + Co1+ i1+ d⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2+ Co1+ i1+ d⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3+ ............+ Co1+ i1+ d⎛ ⎝ ⎜ ⎞ ⎠ ⎟ n−1x =1+i1+ d⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Present WorthSustainable Energy Science and Engineering CenterPW = C01+ x + x2+ ........+ xn−1()11− x=1+ x + x2+ x3+ .............= xii=