Photovoltaic generation of electrical power

Transcript

1 Photovoltaic generation of electrical power The photovoltaic device: working principle and efficiency limits Effects of internal resistance, light intensity and temperature variation Solar spectrum and semiconductor properties

2 Neutral n-region E o Neutral p-region Long λ Drift Diffusion Medium λ Short λ L e Back electrode Finger electrode L h l n Depletion region W l p V oc The principle of operation of the solar cell (exaggerated features to highlight principles) 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

3 With different wavelengths Different absorption coefficient Different quantum efficiency Different photon energy The energy per absorbed photon doesn t change

4 Photon energy (ev) Ge In 0.7 Ga 0.3 As 0.64 P α (m -1 ) Si GaAs InP In 0.53 Ga 0.47 As a-si:h Wavelength (μm) Absorption coefficient (α) vs. wavelength (λ) for various semiconductors (Data selectively collected and combined from various sources.) Each semiconductor has a critical wavelength, over which photons are not absorbed λ 0 = hc/e g

5 I (ma) 20 Dark 0 I ph V oc 0.6 V Light 20 Twice the light Typical I-V characteristics of a Si solar cell. The short circuit current is I ph and the open circuit voltage is V oc. The I-V curves for positive current requires an external bias voltage. Photovoltaic operation is always in the negative current region S.O. Kasap, Optoelectronics (Prentice Hall)

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7 Short circuit Energy bands diagram is similar to that of thermal equilibrium of a non biased pn junction. The Fermi level is the same through the device Neglecting the internal ohmic losses and recombination, the external current I sc is equal to the photogenerated current

8 Open circuit At open circuit, without external current flow, photo generated electrons accumulate in the n region, which is negatively charged. Same for the holes in the p region The open circuit potential difference V oc has the same signe of the voltage applied to a forward biased pn junction The built in potential barrier is lowered. At the equilibrium photogenerated current is equal to the diffusion current flowing in the diode It is important to notice that V oc is always smaller that V bi

9 Diode connected to an external load The photogenerated currents flows in part in in the external load and in part through the diode The voltage applied to the external load is less than the open circuit V oc The amount of current flowing in the load depend on photogenerated voltage and load resistance It is important to notice that V l is always smaller that V oc

10 Illuminated junction with a load resistor The photocurrent lasts the time needed for the electron and hole to cross the depletion layer W and reach the neutral regions When the drifting hole reaches the p-type region it recombines with an electron entering the p side form the negative electrode, that is from the power supply When the drifting electron reaches the n-type neutral region, an electron leaves the n- side into the positive electrode The photocurrent depends on the number of eh pairs generated and the drift velocities of the carriers across the depletion layer

11 I (ma) Light I V V oc 0.6 V I R V I sc = I ph 10 Slope = 1 / R I P I-V for a solar cell under an illumination of 600 Wm -2. Operating Point The Load Line for R = 30 ž (I-V for the load) 20 (a) (b) (a) When a solar cell drives a load R, R has the same voltage as the solar cell but the current through it is in the opposite direction to the convention that current flows from high to low potential. (b) The current I and voltage V in the circuit of (a) can be found from a load line construction. Point P is the operating point (I, V ). The load line is for R = 30 ž S.O. Kasap, Optoelectronics (Prentice Hall)

12 Optimum load Power transferred to the load in zero for infinite (open circuit) and zero (short circuit) load resistance There is an intermediate load resistance (optimum load) which optimizes the output power Optimum load depends on the cell characteristics and illumination

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14 Fill factor Fill factor is the ratio between the maximum power transferred to the load and the product of open circuit voltage and short circuit current Fill factor depends on the shape of cell characteristic, which is mostly related to internal ohmic losses

15 Energy per photon maximum value E m E m is the energy per photon which can be transferred to the load in optimal conditions The corresponding conversion efficiency is η = E m /hν NOTE: this is the efficiency after the photon absorption. It doesn t include the absorption probability which is measured by the quantum efficiency the conversion efficiency affects the voltage and the quantum efficiency affects the current of the generator

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17 Energy per photon maximum value E m E m = ev l < ev oc < ev bi < E g < hν

18 High energy photons A photon, in order to be absorbed by the semiconductor, must have an energy at least equal to the energy gap All the energy in excess is lost as thermal energy of the lattice and is lost for photovoltaic conversion Electron, in a very short time, are found in the lowest energy states of the CB, from were are driven by the built in field. Same for the holes The maximum energy per photon which can be converted is therefore a function of the energy gap and NOT of the energy of the photons

19 Change of characteristic with illumination intensity

20 Optimum load dependence from illumination Half illumination might provide a quarter of power if load is not adapted Red square is ¼ of the orange MPPT electronic is needed (maximum power point tracking)

21 Variation of V oc with T V oc = kt/e ln(i ph /i 0 ) i 0 ~ n i2 =N c N v exp(-e g /kt) e/k V oc /T = ln(i ph /i 0 ) e/k ( V oc2 /T 2 -V oc1 /T 1 ) = ln (i 01 /i 02 ) ~ ln (n i12 /n i22 ) ln (n i12 /n i22 ) = E g /k (1/T 2-1/T 1 )

22 Variation of V oc with T e/k ( V oc2 /T 2 -V oc1 /T 1 ) = E g /k (1/T 2-1/T 1 ) V oc2 = V oc1 (T 2 /T 1 ) + E g /e (1 - T 2 /T 1 ) V oc2 = E g /e - T 2 /T 1 (E g /e - V oc1 )

23 Temperature dependence strong implicit temperature dependence of the saturation current I s the temperature dependence of I s is dominated by the strong dependence of the equilibrium minority-carrier concentrations on temperature I s approximately doubles every 6 C in silicon

24 Variation of V oc con T polycrystalline silicon

25 Effects of temperature on photovoltaic efficiency Characteristics depend on operating conditions A test condition must be defined Standard Test Condition (STC): the irradiation is 1000 W/m2, the spectrum Air Mass (AM) 1.5 and the cell temperature 25ºC

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27 PV concentrated systems

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29 Series resistance effects Finger electrodes Bus electrode for current collection n p Finger electrodes on the surface of a solar cell reduce the series resistance 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

30 Neutral n-region Depletion region Neutral p-region Finger electrode R s Back electrode R p R L Series and shunt resistances and various fates of photegenerated EHPs S.O. Kasap, Optoelectronics (Prentice Hall)

31 I ph R s A I I d I ph Rp V R L Solar cell B Load The equivalent circuit of a solar cell 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

32 Ohmic losses

33 R s = 50 Ω V oc V 5 R s = 0 R s = 20 Ω I sc I ph 10 I (ma) The series resistance broadens the I-V curve and reduces the maximum available power and hence the overall efficiency of the solar cell. The example is a Si solar cell with n 1.5 and I o ma. Illumination is such that the photocurrent I ph = 10 ma S.O. Kasap, Optoelectronics (Prentice Hall)

34 Celle moduli - pannelli

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37 I ph R s I/2 A I/2 R s I d I I d I ph V R L I ph B Two identical solar cells in parallel under the same illumination and driving a load R L. Power (mw) Voltage (V) 1999 S.O. Kasap, Optoelectronics (Prentice Hall) cell cells in parallel 20 Current (ma) Current vs. Voltage and Power vs. Current characteristics of one cell and two cells in parallel. The two parallel devices have R s /2 and 2I ph S.O. Kasap, Optoelectronics (Prentice Hall)

38 Esempio: serie di 36 celle

39 Solar radiation Solar spectrum and intensity Semiconductor absorption and conversion efficiency Optimun gap

40 Solar radiation The radiative surface of the sun, or photosphere, has an average temperature of about 5800 Kelvins. The total quantity of energy emitted from the sun's surface is approximately 63,000,000 Wm -2

41 Solar constant calculation average Earth-sun distance of million kilometers

42 Variazione stagionale della distanza terra sole Solar constant at 1 AU: 1371 W/m 2 Maximum solar energy flux (winter solstice): 1428 W/m2 Minimum solar energy flux (summer solstice): 1316 W/m2

43 Solar Constant : 1368 W/m 2

44 Che frazione raggiunge la terra? Parte della radiazione viene riflessa, parte diffusa e parte trasmessa

45 AM0 h 0 Atmosphere h θ α α Earth AM1 AM(sec θ) Tilted PV device Direct Diffuse (a) (b) (a) Illustration of the effect of the angle of incidence θ on the ray path length and the definitions of AM0, AM1 and AM(sec θ). The angle α between the sun beam and the horizon is the solar latitude (b) Scattering reduces the intensity and gives rise to a diffused radiation 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Il valore di m nella espressione Air mass m (AMm) è definito come rapporto tra il cammino effettivamente percorso in atmosfera h ed il cammino più breve h 0, quindi m=h/h 0.= 1/sinθ dove θ è l angolo di osservazione del sole (zenith). Per un angolo di circa 40 si ha m = 1.5 (AM1.5). A questo valore corrisponde una intensità integrata sulla superficie terrestre di 925 Wm -2, usualmente approssimato con 1kWm -2, sommando sia il contributo diretto che quello diffuso (AM1.5G). Il contributo diretto (AM1.5D) dipende dalla nuvolosità, umidità, e altre caratteristiche dell atmosfera. In una giornata limpida vale Wm -2

46 Parte della radiazione viene assorbita, modificando lo spettro

47 Spectral Intensity W cm -2 (μm) Black body radiation at 6000 K AM0 AM Wavelength (μm) The spectrum of the solar energy represented as spectral intensity (I λ ) vs wavelength above the earth's atmosphere (AM0 radiation) and at the earth's surface (AM1.5 radiation). Black body radiation at 6000 K is shown for comparison (After H.J. Möller, Semiconductors for Solar Cells, Artech House Press, Boston, 1993, p.10) 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

48 Solar spectrum shown as number of photons per energy interval vs energy

49 Maximun conversion efficiency vs Eg A material with small Eg absorbs more photons per second second and generates a higher photocurrent A material with small Eg has a smaller Em per photons and generates a smaller output voltage Generated power is the product of current and voltage, and is represented by the rectangle shown in the figure. There is an optimum value of Eg that gives the maximum output power Conversion efficiency is the ratio between the area of the rectangle and the total area under the curve. Maximun value is approximately 30-35% for a single cell conversion This efficiency limit is a consequence of solar spectrum and semiconductor physics.

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53 A higher total efficiency can be obtained with a series of cells made of semiconductor with different gaps First cell has the highest Eg. It absorbs high energy photons and is transparent to lower energy, which are absrobed by subsequent cells The cell absorption must be balanced in order to have the same photocurrent for all the cell. The voltages are summed A device of this kind is much more expensive

54 Example of multilayer cell

55 Examples of material employed in multi-cell concentrated PV systems

56 Cella concentrata a mille soli

57 Efficienza massima Limite teorico cella ideale (AM1.5) Singola giunzione non concentrata: 31% Singola giunzione 1000 soli: 37% Doppia giunzione 1000 soli: 50% Tripla giunzione 1000 soli: 56% V.M.Andreev et al.: Photovoltaic conversion of concentrated sulight, J.Wiley&Sons 1997

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59 Potenza ed energia La potenza massima producibile da un pannello si esprime in kw p ed è misurata in condizioni standard L energia prodotta si esprime in kwh/anno e dipende dall irraggiamento solare, quindi dalla latitudine e dalla stagione

60 Irraggiamento solare Variazione dell irraggiamento Stagionale Con la latitudine

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65 La radiazione solare giornaliera media mensile per metro quadrato nella località in oggetto viene determinata mediante la tabella VIII della norma UNI 10349, relativamente alla zona di appartenenza (Napoli [54]):

66 Potenza ed energia prodotte Per passare dalla potenza in kwp (misura standard che prescinde dalle condizioni di illuminazione) alla energia espressa in kwh (che dipende dall irraggiamento solare) è necessario tener conto della latitudine e del numero di ore di luce durante l anno Ad esempio un sistema da 1kWp produce: 1800 kwh/year in Southern California 850 kwh/year nel nord della Germania kwh in India e Australia (in un anno ci sono 8760 ore)

67 Costi e ricavi Il costo di acquisto dei pannelli è legato ai watt di picco installati (kwp) Il costo è solo di impianto. I costi annui dipendono dal ammortamento Il ricavo annuo del sistema è legato valore dell energia prodotta, misurato in kwh/y La convenienza dipende dall irraggiamento, dal costo del kwh e dalle politiche di finanziamento