Lecture 2b Photovoltaic (PV) cell model • • • • Single diode based model I-V and P-V characteristics Effect of different parameters PLECS model Photovoltaic cell Load n-type p-type contacts • PV cells consist of p-type and n-type semiconductors (silicon being the dominant at present) forming a p-n junction • Metal strips for contact with external circuit • Anti-reflective coating Raja Ayyanar , ASU PV cell operation (1/2) Load n-type p-type contacts • Absorption of photons (light) generates electron-hole pairs leading to light-generated current • Light generated carriers are separated by the electric field at the p-n junction preventing recombination and enabling current flow through external circuit Raja Ayyanar , ASU PV cell operation (2/2) - n-type Load p-type + contacts • Voltage generated by photovoltaic effect – the light-generated carriers result in forward bias of the junction • Current in the external circuit is the difference of the light-generated current and the forward bias current PSERC Academy videos: http://youtu.be/rjLd6eJYMsI http://youtu.be/RRebGefCFps Also refer to http://pveducation.org/pvcdrom for more detailed discussions Raja Ayyanar , ASU Ideal PV cell model ๐ผ ๐ผ๐ ๐ผ๐โ + ๐ To Load • Ideal PV cell is modeled as a solar-irradiance-dependent current source, ๐ผ๐โ in parallel with a diode • The current in the external circuit is the difference between the photon current and the forward-biased diode current • Good compromise between model accuracy and model complexity (compared to, for example, two-diode models) with non-idealities included later • Useful for understanding V-I characteristics, designing MPPT algorithms, study of partial shading, design of power converters Raja Ayyanar , ASU Diode equation + ๐ผ๐ ๐๐ - ๏ฆ qVd ๏ถ I d ๏ฝ I o ๏ง e a k T ๏ญ 1๏ท ๏ง ๏ท ๏จ ๏ธ T ๏ญ Temperature in K q ๏ญ charge of an electron in Coulombs 1.602 ๏ด 10-19 ๏จ ๏ฉ k ๏ญ Boltzman constant (1.38 ๏ด 10-23 j/K) I o ๏ญ dark or reverse saturation current of diode at T a ๏ญ diode ideality factor, normally between 1 and 2 Raja Ayyanar , ASU Diode equation- reverse saturation current + ๐ผ๐ ๐๐ - 10 ๏ฆ qVd ๏ถ I d ๏ฝ I o ๏ง e a k T ๏ญ 1๏ท ๏ง ๏ท ๏จ ๏ธ 5 Id( Vd) (A) 0 I o ๏ญ dark or reverse saturation current of diode at T 5 • ๐๐ ๐ ๐๐๐ ๐๐ ๐ is 25.84 mV at 300K and a = 1 Raja Ayyanar , ASU 1 ๏ฎ10 0.4 0.6 8 Id( Vd) 0 (A) 1 ๏ฎ10 8 ๐ผ๐ ≈ 15 ๐๐ด 0.15 is called the ‘thermal voltage, ๐๐กโ ’ and 0.2 Vd (V) • ๐ผ๐ is an important characteristic of a given diode; higher material quality relates to smaller ๐ผ๐ • ๐ผ๐ increases significantly with temperature; for silicon cells near room temperature, ๐ผ๐ doubles for every 100C rise in temperature 0 0.1 0.05 Vd (V) 0 0.05 Ideal PV cell model ๐ผ + ๐ผ๐ ๐ผ๐โ ๐ To Load - I ๏ฝ I ph ๏ญ I o (e qV akT ๏ญ 1) I ph ๏ญ Photon current at a given irradiance and given T V ๏ญ Voltage across the diode Raja Ayyanar , ASU Photon current dependencies I ๏ฝ I ph ๏ญ I o (e qV akT ๏ญ 1) I ph ๏ญ Photon current at a given irradiance and given T • Magnitude of photon depends on the irradiance level, light spectrum, and the characteristics of the cell • Short circuit current which is a direct measure of the photon current is specified at standard test conditions (STC) which is 1000 W/m2 , module temperature of 25oC and air mass AM = 1.5 • Magnitude of photon current (short circuit current) is directly proportional to the irradiance – e.g., 20% lower irradiance results in 20% lower photon current • Change in photon current with temperature is not very significant – about 0.05% increase per oC rise for silicon Raja Ayyanar , ASU Series resistance • Series resistance RS models the combined resistances of contacts, metal grids, and p and n layers ๐ ๐ ๐ผ + ๐ผ๐ ๐ผ๐โ ๐ - I ๏ฝ I ph ๏ญ I o (e Raja Ayyanar , ASU q (V ๏ซ I RS ) akT ๏ญ 1) To Load Shunt resistance • RSh models the leakage current of p-n junction • Typically RSh is a large value, with low values representing defective cells • Impact (on power loss) more pronounced at low irradiance levels Complete PV cell model ๐ ๐ + ๐ผ๐ ๐ผ๐โ ๐ผ ๐ ๐โ ๐ To Load I ๏ฝ I ph ๏ญ I d ๏ญ I Rsh I ๏ฝ I ph ๏ญ I o (e Raja Ayyanar , ASU q (V ๏ซ I RS ) akT ๏ฆ V ๏ซ I RS ๏ถ ๏ญ 1) ๏ญ ๏ง ๏ท ๏จ RSh ๏ธ I-V characteristics in dark and light conditions ๐ผ + ๐ผ๐ ๐ผ ๐ผ๐ ๐๐ + ๐ Increasing irradiance No light ๏ฆ qVd ๏ถ akT ๏ง Id ๏ฝ Io e ๏ญ 1๏ท ๏ง ๏ท ๏จ ๏ธ I o ๏ญ dark saturation current of diode at T ๐ ๐ผ๐โ - - + ๐ผ๐ ๐ผ = − ๐ผ๐ ๐ผ ๐ผ = ๐ผ๐โ − ๐ผ๐ ๐ผ ๐ผ๐ Vd 0 Id ( Vd ๏ฌ 300 ) Id ( Vd ๏ฌ 300 ) 0 Vd Raja Ayyanar , ASU ๐๐ Vd ๐ 0 ๐ Id ( Vd ๏ฌ 300 ) L O A D I-V characteristics of a single PV cell ๐ผ (๐ด) short circuit current, ๐ผ๐ ๐ open circuit voltage, ๐๐๐ ๐ (๐) Raja Ayyanar , ASU Short circuit current ๐ผ = ๐ผ๐ ๐ • With small values of ๐ ๐ , ๐ผ๐ ๐ = ๐ผ๐โ , and it is the maximum possible current from the PV cell • ๐ผ๐ ๐ depends on • Solar irradiance level and spectrum of light • Area of solar cell (in commercial silicon cells, ๐ผ๐ ๐ is roughly 30-35 mA/cm2 ) • Characteristics of material • For modeling, ๐ผ๐ ๐ can be considered to vary linearly with irradiance level • ๐ผ๐ ๐ variation with temperature can be usually neglected (0.05% increase for every oC) Raja Ayyanar , ASU Open circuit voltage • • • • Maximum possible voltage from PV cell with zero external current ๐๐๐ depends on the quality of the material (low value of ๐ผ๐ ) Typical values for polycrystalline: 600 mV per cell ๐๐๐ is a strong function of temperature with a high negative temperature coefficient • Roughly - 0.35%/oC or about -2.2 mV/ oC • ๐๐๐ increases slightly with irradiance Raja Ayyanar , ASU Effect of irradiance 1000 W/m2 ๐ผ (๐ด) 750 W/m2 500 W/m2 250 W/m2 open circuit voltages, ๐๐๐ ๐ (๐) Raja Ayyanar , ASU ๐ผ (๐ด) Effect of temperature Higher T Lower T (STC) โ๐ ≈ 25โ ๐ (๐) • The most dominant effect of temperature is on the open circuit voltage, ๐๐๐ with a temperature coefficient of about - 0.35%/oC or about -2.2 mV/ oC Example commercial PV cell – STP245 • ๐ผ๐ ๐ increases slightly since the band gap of the material decreases slightly with temperature and for a given irradiance more electron-hole pairs created(0.05%/oC) Raja Ayyanar , ASU Effect of series resistance ๐ ๐ ๐ 1 ๐ ๐ ๐ 3 ๐ ๐ ๐ 2๐ ๐ 1 ๐ ๐ 1 2 ๐ 3 ๐ ๐ 2 ๐ ๐ 4 ๐ผ (๐ด) ๐ ๐ 1 ๐ ๐ 4 > ๐ ๐ 3 > ๐ ๐ 2 > ๐ ๐ 1 ๐ (๐) I ๏ฝ I ph ๏ญ I o (e q (V ๏ซ I RS ) akT ๏ญ 1) • Terminal voltage at which the current begins to drop rapidly becomes progressively lower as ๐ ๐ increases (e.g., 0.45 V instead of 0.55 V), since ๐๐ = ๐ + ๐ผ๐ ๐ • Impact at low voltage is not significant for typical values of ๐ ๐ since ๐ + ๐ผ๐ ๐ is still low • ๐ ๐ determines the slope near ๐๐๐ which can be used to determine ๐ ๐ from datasheets Raja Ayyanar , ASU Effect of shunt resistance ๐ผ (๐ด) 1000 W/m2 ๐น๐๐ = ๐๐๐ ๐ด ๐น๐๐ = ๐๐ ๐ด ๐น๐๐ = ๐ ๐ด ๐น๐๐ = ๐ ๐ด ๐ (๐) • Low values of shunt resistance leading to higher power loss indicates process defects or device degradation • ๐ ๐ โ determines the slope near ๐ = 0 which can be used to determine ๐ ๐ โ from datasheets • Impact (on efficiency) more severe at low irradiance Raja Ayyanar , ASU Effect of shunt resistance: low irradiance ๐ผ (๐ด) 250 W/m2 ๐น๐๐ = ๐๐๐ ๐ด ๐น๐๐ = ๐๐ ๐ด ๐น๐๐ = ๐ ๐ด ๐น๐๐ = ๐ ๐ด ๐ (๐) Raja Ayyanar , ASU Effect of ideality factor ๐ผ (๐ด) Smaller ๐ −โ higher MPP ๐ = ๐. ๐ ๐ = ๐. ๐ ๐ = ๐. ๐ ๐ (๐) • Ideality factor ‘a’ is measure of the material quality – lower values reflect better material, smaller dark saturation current and higher power output • ๐ ranges from 1 to 2 • Impact is mainly near the maximum power point and can be used to estimate ๐ from datasheet Raja Ayyanar , ASU P-V (power-voltage) characteristics ๐๐๐ 9 ๐ผ๐ ๐ ๐ผ๐๐ 4 ๐ผ ๐ฃ๐ . ๐ 1000 8 3.5 7 3 ๐ ๐ฃ๐ . ๐ 6 ๐ฐ (๐จ) I ( Vd ) W/m2 5 2.5 ๐๐๐2 500 W/m2 2 ๐ท (๐พ) P ( Vd ) 4 1.5 3 1 2 0.5 1 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ๐ (๐) V ( Vd ) ๏ฌ V ( Vd ) Imp ๏ฝ 7.95 ๐๐๐ : Maximum power ๐๐๐ : Voltage at maximum power ๐ผ๐๐ : Current at maximum power 0.4 0.45 ๐๐๐ 0.5 0.55 ๐๐๐2 0 0.65 0.6 ๐๐๐ • MPPT (maximum power point tracking) to ensure that the operation is always at the ๐๐๐ Raja Ayyanar , ASU Fill factor ๐๐๐ , ๐ผ๐ ๐ ๐๐๐ , ๐ผ๐๐ 5 8 Curr ent (A ) 2.5 4 P ow er (W ) ๐๐๐ 6 2 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0 0.65 Voltage (V) ๐น๐๐๐ ๐๐๐๐ก๐๐, ๐น๐น = ๐๐๐ ๐ผ๐๐ ๐๐๐ ๐ผ๐ ๐ • Low values of fill factor represent higher losses in parasitic resistances and other non-idealities Raja Ayyanar , ASU For the example above, 0.498 × 7.95 ๐น๐น = = 0.75 8.33 × 0.622 P ๏จ0 ๐(๐) Simulation results: P-V at different irradiance levels ๐ (๐) Raja Ayyanar , ASU Effect of temperature Lower T Higher T โ๐ ≈ 25โ • The dominant effect of temperature is the increase in reverse saturation current , ๐ผ๐ • Significantly reduces open circuit voltage, ๐๐๐ and maximum power - 0.35%/oC or about -2.2 mV/ oC in ๐๐๐ and about -0.45 %/oC in ๐๐๐ Raja Ayyanar , ASU (STC) Example commercial PV cell – STP245 PLECS model of a PV cell I ๏ฝ I ph ๏ญ I o (e q (V ๏ซ I RS ) akT ๏ฆ V ๏ซ I RS ๏ถ ๏ญ 1) ๏ญ ๏ง ๏ท R ๏จ ๏ธ Sh ๐ผ + To ๐ load Io(T) I o (e Raja Ayyanar , ASU q Vd akT ๏ญ 1) PLECS model to get I-V and P-V characteristics Voltage source swept From 0 to VOC PLECS Demo Raja Ayyanar , ASU