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Power Generation from Renewable Energy Sources Fall 2012 Instructor: Xiaodong Chu Email：[email protected] Office Tel.: 81696127 Flashbacks of Last Lecture • A photon with short enough wavelength and high enough energy can cause an electron in a photovoltaic material to break free of the atom that holds it • If a nearby electric field is provided, those electrons can be swept toward a metallic contact where they can emerge as an electric current • Photovoltaics use semiconductor materials to convert sunlight into electricity Flashbacks of Last Lecture • Photons with enough energy create hole–electron pairs in a semiconductor • Photons can be characterized by their wavelengths or their frequency as c where c is the speed of light (3 × 108 m/s), v is the frequency (hertz), λ is the wavelength (m), and E h hc where E is the energy of a photon (J) and h is Planck’s constant (6.626 × 10−34 J-s) Flashbacks of Last Lecture • Assuming a standard air mass ratio AM 1.5, 20.2% of the energy in the spectrum is lost due to photons having less energy than the band gap of silicon (hν < Eg), and another 30.2% is lost due to photons with hν > Eg • The remaining 49.6% represents the maximum possible fraction of the sun’s energy that could be collected with a silicon solar cell under 50% Flashbacks of Last Lecture • The voltage–current characteristic curve for the p–n junction diode is described by the following Shockley diode equation I d I 0 (e qvd / kT 1) where Id is the diode current in the direction of the arrow (A), Vd is the voltage across the diode terminals from the p-side to the n-side (V), I0 is the reverse saturation current (A), q is the electron charge (1.602 × 10−19C), k is Boltzmann’s constant (1.381 × 10−23 J/K), and T is the junction temperature (K) Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • Consider what happens in the vicinity of a p–n junction when it is exposed to sunlight Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • If electrical contacts are attached to the top and bottom of the cell, electrons will flow out of the n-side into the connecting wire, through the load and back to the p-side Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • A simple equivalent circuit model for a photovoltaic cell consists of a real diode in parallel with an ideal current source • The ideal current source delivers current in proportion to the solar flux to which it is exposed I I SC I d I SC I 0 (e qV / kT 1) Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • There are two conditions for the actual PV and for its equivalent circuit: – The current that flows when the terminals are shorted together (the short-circuit current, ISC) – The voltage across the terminals when the terminals are left open (the open-circuit voltage, VOC) Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • For the short-circuit condition Id 0 – and I I SC • For the open-circuit condition I 0 – and V VOC I kT I SC ln 1 0.0257 ln SC 1 (at 25o C) q I0 I0 Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • Example 8.3 of the textbook: you should master it! Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • There are situations when a more complex PV equivalent circuit is needed, e.g., consider the impact of shading – The simple equivalent circuit suggests that no power will be delivered to a load if any of its cells are shaded, but the situation is not quite as bad as that Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • For a PV equivalent circuit that includes some parallel leakage resistance Rp, the ideal current source ISC in this case delivers current to the diode, the parallel resistance, and the load V I ( I SC I d ) RP Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • At any given voltage, the parallel leakage resistance causes load current for the ideal model to be decreased by V/Rp Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • An even better equivalent circuit will include series resistance as well as parallel resistance • Consider the original PV equivalent circuit has been modified to include some series resistance, RS – Some of this might be contact resistance associated with the bond between the cell and its wire leads, and some might be due to the resistance of the semiconductor itself Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • Start with the simple equivalent circuit I I SC I d I SC I 0 (e qV / kT 1) and add the impact of Rs, Vd V I RS to give q(V I RS ) I I SC I 0 exp 1 kT Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • At any given current, the original PV I –V curve shifts the voltage to the left by V = IRS Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • Generalize the PV equivalent circuit by including both series and parallel resistances q(V I RS ) V I RS I I SC I 0 exp 1 kT RP Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • Under the standard assumption of a 25◦C cell temperature V I RS I I SC I 0 e38.9(V IRS ) 1 RP • Applying Kirchhoff’s Current Law to the node above the diode, we can write I SC I I d I P Photovoltaic Materials and Electrical Characteristics–A Generic Photovoltaic Cell • Rearranging, and substituting the Shockley diode equation at 25◦C gives I I SC I 0 (e38.9Vd 1) Vd RP • With an assumed value of Vd in a spreadsheet, current I can be found from the above equation • Voltage across an individual cell can be found from V Vd IRS Photovoltaic Materials and Electrical Characteristics– From Cells to Modules to Arrays • The basic building block for PV applications is a module consisting of a number of pre-wired cells in series, all encased in tough, weather-resistant packages – A typical module has 36 cells in series and is often designated as a “12V module” even though it is capable of delivering much higher voltages than that – Large 72-cell modules are now quite common, some of which have all of the cells wired in series, in which case they are referred to as 24-V modules – Some 72-cell modules can be field-wired to act either as 24-V modules with all 72 cells in series or as 12-V modules with two parallel strings having 36 series cells in each Photovoltaic Materials and Electrical Characteristics– From Cells to Modules to Arrays • Multiple modules can be wired in series to increase voltage and in parallel to increase current, the product of which is power • An important element in PV system design is deciding how many modules should be connected in series and how many in parallel to deliver whatever energy is needed • Such combinations of modules are referred to as an array Photovoltaic Materials and Electrical Characteristics– From Cells to Modules to Arrays • When photovoltaics are wired in series, they all carry the same current, and at any given current their voltages add as • we can find an overall module voltage Vmodule by multiplying the number of cells in the module n. Vmodule n(Vd IRS ) Photovoltaic Materials and Electrical Characteristics– From Cells to Modules to Arrays • Modules can be wired in series to increase voltage, and in parallel to increase current • Arrays are made up of some combination of series and parallel modules to increase power • For modules in series, the I –V curves are simply added along the voltage axis Photovoltaic Materials and Electrical Characteristics– From Cells to Modules to Arrays • For modules in parallel, the same voltage is across each module and the total current is the sum of the currents Photovoltaic Materials and Electrical Characteristics– From Cells to Modules to Arrays • When high power is needed, the array will usually consist of a combination of series and parallel modules for which the total I –V curve is the sum of the individual module I –V curves • There are two ways to imagine wiring a series/parallel combination of modules – The series modules may be wired as strings, and the strings wired in parallel – The parallel modules may be wired together first and those units combined in series Photovoltaic Materials and Electrical Characteristics– From Cells to Modules to Arrays Photovoltaic Materials and Electrical Characteristics–The PV I –V Curve Under Standard Test Conditions • Consider the I –V characteristic curve of the module as well as the I –V characteristic curve of the load Photovoltaic Materials and Electrical Characteristics–The PV I –V Curve Under Standard Test Conditions Photovoltaic Materials and Electrical Characteristics–The PV I –V Curve Under Standard Test Conditions • The fill factor is the ratio of the power at the maximum power point to the product of VOC and ISC Fill factor (FF) Power at the MPP V I R R VOC I SC VOC I SC Photovoltaic Materials and Electrical Characteristics–The PV I –V Curve Under Standard Test Conditions • Since PV I –V curves shift all around as the amount of insolation changes and as the temperature of the cells varies, standard test conditions (STC) have been established to enable fair comparisons of one module to another • Those test conditions include a solar irradiance of 1 kW/m2 (1 sun) with spectral distribution, corresponding to an air mass ratio of 1.5 (AM 1.5) • The standard cell temperature for testing purposes is 25◦C (it is important to note that 25◦ is cell temperature, not ambient temperature) Photovoltaic Materials and Electrical Characteristics–Impacts of Temperature and Insolation • Manufacturers will often provide I –V curves that show how the curves shift as insolation and cell temperature changes Photovoltaic Materials and Electrical Characteristics–Impacts of Temperature and Insolation • As insolation drops, short-circuit current drops in direct proportion • Decreasing insolation also reduces VOC, but it does so following a logarithmic relationship that results in relatively modest changes in VOC Photovoltaic Materials and Electrical Characteristics–Impacts of Temperature and Insolation • As cell temperature increases, the open-circuit voltage decreases substantially while the short-circuit current increases only slightly • Photovoltaics, perhaps surprisingly, therefore perform better on cold, clear days than hot ones Photovoltaic Materials and Electrical Characteristics–Impacts of Temperature and Insolation • Cells vary in temperature not only because ambient temperatures change, but also because insolation on the cells changes • Since only a small fraction of the insolation hitting a module is converted to electricity and carried away, most of that incident energy is absorbed and converted to heat