Tema 4.2 (2013)Apunte Catalán
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4.1. Fundamentals of solar cells
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4.1. Fundamentals of solar cells
4.1.2. Solar radiation
4.1.3. Basic operation principles of solar cells
4.1.4. Characteristic parameters of solar cells
4.1.5. Equivalent circuit of a solar cell
4.1.6. Solar cell state‐of‐the‐art
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The market for photovoltaics is rapidly expanding. As prices fall, the number of
installed systems will continue to increase.
Typical applications of photovoltaics: ‐ PV power plants ‐ Residential ‐ Utilities interactive or grid connected ‐ Remote Power ‐ Space applications T4 (2) - 5 4.1.2. Solar Radiation FISE Electromagnetic spectrum =c/f Solar radiation spectrum T4 (2) - 6 4.1.2. Solar Radiation FISE Main Parameters Spectral Irradiance : I () or Power Spectral density: () Is defined as the power received by a unit surface area in a wavelength differential d . The units are W/ m2 nm.
Irradiance I (or G) Is defined as the integral of the Spectral irradiance extended to all wavelength range of interest. The units are W/m2 ( power density).
Radiation H Is defined as the time integral of the irradiance extended over a given period of time, so the Radiation units are units of energy .
Spectral irradiance W/m2mm I Irradiance W/m2 2 I I d 1 I Radiation kWh/m2‐day t2 H I dt H t1 It is common to find radiation data in J/m2‐day, if a day integration period of time is used, or most often the energy is given in kWh/m2‐day, kWh/m2‐month or kWh/m2‐year depending on the time slot used for the integration of the Irradiance. FISE 4.1.2. Solar Radiation T4 (2) - 7 4.1.2. Solar Radiation T4 (2) - 8 Solar radiation and PV map Spain (kWh/m2‐year) FISE Reference Spectrums Reference Solar Spectrum: AIR MASS x (AM x) θz x = 1/ cos θz AM0, Spatial Applications AM1, x=1, θz=0 AM1.5 G, Earth Applications (global tilt) x=1.5, θz= 48.19° ( Tilt surface 37° ) • T4 (2) - 9 4.1.2. Solar Radiation FISE AM 1.5 Standard Reference Spectrum: The solar spectral irradiance distribution (diffuse and direct) incident at sea level on a sun‐facing 37 degree tilted surface from horizontal. The atmospheric conditions for AM 1.5 are: precipitable water vapor 14.2 mm, total ozone 3.4 mm, turbidity (base e, l=0.5 μm) 0.27 • Standard Test Conditions (STC): Conditions under which a module is typically tested in a laboratory: (1) irradiance intensity of 1000 W/ m2, (2) AM1.5 standard reference spectrum, and (3) cell or module temperature of 25 ± 2 degrees C.
FISE 4.1.3. Basic Operation Principles of solar cells T4 (2) - 10 How solar cell powers an external load When light shines on the crystal and electron‐hole pairs are created, the electrons travel through the load to recombine with the holes.
As long as light is shining on the crystal, the process is repeated: (1) energy from the light is absorbed by electrons and they are freed from their resting state (2) electrons are drawn across the junction in the crystal which only permits movement in one direction (3) the electrons move through an externally‐connected load to recombine with the holes they left behind FISE 4.1.3. Basic Operation Principles of solar cells T4 (2) - 11 When Light Strikes Silicon When light shines on a crystal of pure silicon (A‐B), particles called "electrons" are ejected from silicon atoms and move about the crystal somewhat randomly (C) The place the electron came from is called a "hole". It takes energy from the light to eject the electron from its normal resting place, and energy is released when the electron returns to an atom that is missing an electron, and recombines with a hole (D).
FISE 4.1.4. Characteristic Parameters of solar cells Current‐Voltage characteristics ‐I Dark I‐V: qV enKT IL=0 I Id (V) Io 1 Illumination I‐V: I = IL ‐ Id (V) n is the ideality factor T4 (2) - 12 FISE 4.1.4. Characteristic Parameters of solar cells Maximum power point, MPP Voc=nVT ln(IL/Io+1) T4 (2) - 13 Open circuit Voltage Vm Power Isc=I(V=0)=IL Im MPP Short circuit Current FISE Current 4.1.4. Characteristic Parameters of solar cells Current‐Voltage characteristics T4 (2) - 14 4.1.4. Characteristic Parameters of solar cells FISE T4 (2) - 15 Fill Factor (FF) and Conversion Efficiency () P m Pin VmIm Current‐Voltage characteristic A ( )d 0 Isc Im MPP I V FF m m IscVoc FISE Vm Voc IscVoc FF Pin 4.1.4. Characteristic Parameters of solar cells Current‐voltage characteristics Temperature dependence Irradiance dependence Current (A) Irradiance increases Voltage (V) T4 (2) - 16 4.1.5. Equivalent circuit of a solar cell FISE T4 (2) - 17 Solar Cell, electric model II Rs, Rp : Power losses Rs + Id I L V Rp Rs : Front contact ( V>>) - Rp : cell borders ( V <<) IRs V I Rs VnV T I IL I o e 1 Rp FISE IL = f( I, T) Id = f ( Io, n, T) 4.1.6. Solar cell state‐of‐the‐art Best laboratory solar cell conversion efficiencies Current commercial monocristaline PV cells reach 20% of conversion efficiency UPC c‐Si solar cell: 21.5 % !!! T4 (2) - 18 T4 (2) - 19 4.2. Components of PV systems FISE 4.2. Components of PV systems 4.2.1. Assembly of solar cells to form arrays 4.2.2. Standard PV Modules 4.2.3. Interconnection of Modules 4.2.4. Batteries FISE 4.2.1. Assembly of solar cells to form arrays PV module PV generator PV cell Cells are assembled into modules... … and modules are assembled into arrays (PV generator) T4 (2) - 20 FISE T4 (2) - 21 4.2.1. Assembly of solar cells to form arrays Series Connection of solar cells • Solar cells in series Isc = Isc1 = Isc2 = Isc (worst cell) Voc = Voc1 + Voc2 The limit of the output current available in a series connection of solar cells is imposed by the worst solar cell FISE I=I1=I2 + V1 + V2 - + V=V1+V2 Load - I T4 (2) - 22 4.2.1. Assembly of solar cells to form arrays Shunt connection of solar cells 1 2 I=I1+I2 • Solar cells in parallel Isc = Isc1 + Isc2 Voc = Voc1 = Voc2 = Voc (worst cell) The limit of the output voltage available in a shunt connection of solar cells is imposed by the worst solar cell Load I1 + V=V1=V2 I2 - FISE 4.2.1. Assembly of solar cells to form arrays T4 (2) - 23 FISE 4.2.2. Standard PV modules T4 (2) - 24 Photovoltaic modules are composed of combinations of parallel and series connections of solar cells and eventually bypass diodes T4 (2) - 25 4.2.2. Standard PV modules FISE PV module: Ns solar cells in series in a string Np solar cell strings in parallel VM NsV VocM NsVoc IM NpI IscM NpIsc Rs M Solar Cell Rs Ns Rs Np + Id V Rp I L - Rp IL Isc I Isc I0 (e V IRs nVT 1) IM IscM I0 (e Np Np VM IM Np RsM Ns Np Ns T4 (2) - 26 4.2.2. Standard PV modules FISE PV Module equation IM IscM I0 (e Np Np Solar Cell in open circuit: VM IM RsM Ns Ns nVT IM IscM IscM (e Np Np Np 1) VM IM RsM Ns Ns nVT (e VocM nVT Ns 1) Isc I0 (e Voc nVT 1) IscM I0 Np (e VocM nVT Ns 1) neglecting the two unity terms IM IscM (1 e 1) nVT VM IM RsM VocM nVT Ns ) Current‐voltage characteristic of the PV module 1) 4.2.2. Standard PV modules FISE T4 (2) - 27 Temperature effects on the PV module equation Tcell = Ta + 0.035 G STC : IscMr , VocMr IscM } G is the irradiance in W/m2 STC are the standard test conditions under which a module is typically tested Ta, Tcell are the ambient and solar cell temperatures I IscMr G scM (Tcell Tr ) 1000 T I V VocM VocMr ocM (Tcell Tr ) VT ln scM T IscMr FISE 4.2.2. Standard PV modules T4 (2) - 28 FISE 4.2.2. Standard PV modules T4 (2) - 29 FISE 4.2.2. Standard PV modules T4 (2) - 30 FISE 4.2.3. Interconnection of Modules T4 (2) - 31 Module Generator Scaling procedure: Array of NsG modules in series and NpG in parallel FISE I G = N pG I M V G = N sG V M 4.2.3. Interconnection of Modules PV Generator Maximum Power Point : ( VmG, ImG ) I mG G dI scM N pG I mMr Gr dT VmG I I mM N sG N sVT ln1 scM I scM M means Module m means maximum power point (Tcell Tr ) VocM e N sVT 1 I R mM sM T4 (2) - 32 4.2.4. Batteries FISE T4 (2) - 33 Lead‐acid batteries are most commonly used energy storage elements for stand‐ alone photovoltaic systems: ‐ Low cost per Kw∙h.
‐ Weight doesn't matter.
‐ Widely distributed, can take advantage of other industries.
In some cases, as in PV low power applications, nickel‐cadmium batteries can be a good alternative to lead‐acid batteries despite their higher cost.
Lead‐acid batteries are formed by two plates, positive and negative, immersed in a dilute sulphuric acid solution. The positive plate, or anode, is made of lead dioxide ( PbO2 ) and the negative plate, or cathode, is made of lead (Pb). 4.2.4. Batteries FISE Lead‐acid battery Total reaction at the battery PbO 2 Pb 2 H 2 SO 4 disch arg e ch arg e Battery Operation modes 3 saturation 2 .5 overcharge 2 Voltage [V] discharge charge underdischarge 1 .5 1 0 .5 0 0 5 10 15 20 Tim e [h] 25 30 35 2 PbSO 4 2 H 2 O T4 (2) - 34 T4 (2) - 35 4.2.4. Batteries FISE Lead‐acid battery main parameters 1 ‐ Battery Nominal Voltage, Vbat 2 ‐ Charge or Discharge rate: Defined as the relationship between the nominal capacity of the battery and the charge/discharge current values. In the case of a discharge, the discharge rate is the time needed for the battery to discharge at a constant current. 3 ‐ Nominal Capacity: Total charge that can be obtained in a given period of time at a given temperature.
Cx for a discharge in x hours (Units in A∙h or W∙h): 50 Cx(Wh) = Cx(Ah) Vbat(V) 42 Ah I (A) 40 C1 = 42 Ah I1= 42 A 30 20 10 100 Ah 0 1 3 5 7 9 11 13 15 17 C20 = 100 Ah I20= 5 A 19 (hours) Battery capacity variation in function of discharge rate 4.2.4. Batteries FISE T4 (2) - 36 3 ‐ The state of charge , SOC: Ratio of the battery available charge at a given time divided by the maximum capacity.
SOC = Q/ C 0 ≤ SOC ≤ 1 SOC(%) = Q/ C 100 4 ‐ Depth of discharge DOD = 1‐SOC ...