pv conversion

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Conversia fotovoltaica a energiei solare 1. Radiatia solara Intr-o prima aproximare se poate cansidera ca soarele actioneaza ca un emitator perfect de radiatie (corp negru). Astfel, rezulta ca fluxul energiei medii incidente pe o unitate de suprafata perpendicular ape directia radiatiei, cunosuta ca constanta solara: In general, puterea totala care provine de la o sursa de radiatie si care este receptionata pe o unitate de suprafata, este denumita iradianta. Temperatura corpului negru al radiatiei solare cu suprafata S poate fi dedusa din legea lui Stefan-Boltzmann si un factor geometric simplu ce reprezinta distanta de la pamant la soare si raza soarelui: Conceptual de radiatie a corpului negru face posibila utilizarea legii de radiatie a lui Planck referitor la fluxul de fotoni receptionati de unitatea de arie a unei suprafete plane intr-un interval de : La incidenta radiatiei solare cu atmosfera terestra o parte este indepartata prin imprastiere difuza sau absorbtie de catre moleculele de aer, nouri si particule de materie aflate in mod obisnuit in aerosoli. Radiatia care nu este reflectata sau imprastiata parazit si care intalneste suprafata direct de la dicul solar, numit radiatie directa sau The radiation that is not reflected or scattered and reaches the surface directly in line from the solara sau fascicol. Radiatia parazita care intalneste pamantul se numeste radiatie difuza. Oricare radiatie poate ajunge la un receptor dupa reflectarea de la pamant, si care este denumita Albedo. Radiatia totala care consta din aceste 3 componente este denumita globala. Cantitatea de radiatie care atinge pamantul este, desigur una extrem de variabila. In plus, variatia anticipata zilnica si anuala datorita deplasarii aparente a soarelui, precum si variatiile intamplatoare cauzate de conditiile climatice (cer acoperit cu nori) precum si prin componentele generale ale atmosferei. Din aceasta cauza, proiectul unui sistem fotovoltaic bazat pe achizitia datelor masurate in imediata apropiere a locului de amplasare instalatiei. Un concept care caracterizeaza efectul unei atmosfere curate asupra luminii solare este masa aerului, egala cu lungimea relativa a parcursului direct al fascicolului prin atmosfera. O zi de vara senina la nivelul marii, radiatia de la soare in pozitia corespunzatoare zenitului si masa aerului 1 (AM1); in alte circumstante, masa de aer este 1/cos θ , in care θ reprezinta unghiul de zenit. Efectul atmosferei (dependenta de masa aerului) asupra spectrului solar este reprezentat in figura de mai jos:

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Page 1: PV Conversion

Conversia fotovoltaica a energiei solare1. Radiatia solaraIntr-o prima aproximare se poate cansidera ca soarele actioneaza ca un emitator perfect de radiatie (corp negru). Astfel, rezulta ca fluxul energiei medii incidente pe o unitate de suprafata perpendicular ape directia radiatiei, cunosuta ca constanta solara:

In general, puterea totala care provine de la o sursa de radiatie si care este receptionata pe o unitate de suprafata, este denumita iradianta. Temperatura corpului negru al radiatiei solare cu suprafata S poate fi dedusa din legea lui Stefan-Boltzmann si un factor geometric simplu ce reprezinta distanta de la pamant la soare si raza soarelui:

Conceptual de radiatie a corpului negru face posibila utilizarea legii de radiatie a lui Planck referitor la fluxul de fotoni receptionati de unitatea de arie a unei suprafete plane intr-un interval de :

La incidenta radiatiei solare cu atmosfera terestra o parte este indepartata prin imprastiere difuza sau absorbtie de catre moleculele de aer, nouri si particule de materie aflate in mod obisnuit in aerosoli. Radiatia care nu este reflectata sau imprastiata parazit si care intalneste suprafata direct de la dicul solar, numit radiatie directa sau The radiation that is not reflected or scattered and reaches the surface directly in line from the solara sau fascicol. Radiatia parazita care intalneste pamantul se numeste radiatie difuza. Oricare radiatie poate ajunge la un receptor dupa reflectarea de la pamant, si care este denumita Albedo. Radiatia totala care consta din aceste 3 componente este denumita globala. Cantitatea de radiatie care atinge pamantul este, desigur una extrem de variabila. In plus, variatia anticipata zilnica si anuala datorita deplasarii aparente a soarelui, precum si variatiile intamplatoare cauzate de conditiile climatice (cer acoperit cu nori) precum si prin componentele generale ale atmosferei. Din aceasta cauza, proiectul unui sistem fotovoltaic bazat pe achizitia datelor masurate in imediata apropiere a locului de amplasare instalatiei. Un concept care caracterizeaza efectul unei atmosfere curate asupra luminii solare este masa aerului, egala cu lungimea relativa a parcursului direct al fascicolului prin atmosfera. O zi de vara senina la nivelul marii, radiatia de la soare in pozitia corespunzatoare zenitului si masa aerului 1 (AM1); in alte circumstante, masa de aer este 1/cos θ , in care θ reprezinta unghiul de zenit. Efectul atmosferei (dependenta de masa aerului) asupra spectrului solar este reprezentat in figura de mai jos:

Spectrul extra terestru, notat cu AM0, este important in aplicatii cu satelit al celulelor solare. AM1.5 reprezinta un spectru solar tip la suprafata pamantului intr-o zi senina, care cu iradianta totala de 1 kW/m 2, este utilizata la calibrarea celulelor si modulelor solare. In locul iradiantei proiectarea sistemului fotovoltaic (in principal a celor autonome) in mod obisnuit se bazeaza pe radianta solara zilnica: energia receptionata de o suprafata unitara intr-o zi. Fluxul de energie totale incidente pe pamant este egala cu S inmultita cu aria discului care reprezinta radiatia soarelui pe pamant. Fluxul mediu incident pe unitatea de suprafata se obtine

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atunci prin impartirea acestui numar la suprafata totala a pamantului. Avand in vedere ca 30% din radiatia incidenta imprastiata si reflectata in spatiu, radiatia medie solara zilnica G pe pamant este

Acest numar va fi comparat cu valorile observate. In figura de mai jos se reprezinta radiatia solara zilnica pe un plan orizontal pentru 4 locatii reprezentative, de la padurile tropicale la tarile din nordul Europei. Radiatia solara este cea mai mare in aria desertului continental in jurul latitudinii de 250 N si 250 S, si scade spre ecuator din cauza norilor, precum si spre poli din cauza elevatiei solare scazute. Regiunile ecuatoriale sufera mici variatii sezoniere, in contrast cu latitudinile mai ridicate acolo unde rapoartele vara/iarna sunt mari.

2. Convertor cu 2 nivele cuantice de energieConsideram un model simplificat al procesului de conversie a energiei care reprezinta principiile, si anume balanta echilibrata intre energia luminii absorbite si energia libera furnizata utilizatorului. Partea principala a sistemului de conversie este un absorbator de lumina cu 2 stari cuantice, acolo unde absorbtia unui foton a radiatiei luminoase stimuleaza ca un electron sa treaca din starea normala intr-o stare excitata. Viteza de excitatie reprezinta o combinatie a 2 procese, iluminarea (inclusiv tranzitiile cu viteza g) si excitatia termica, cu viteza go. Durata de viata a starii excitate cu considerarea tranzitiilor la starea normala va fi notata cu .

Fie (1-q) si p probabilitatile ca absorbatorul sa fie intr-o stare normala si respectiv excitata. Cantitatea q poate fi interpretata ca probabilitatea de ocuparea unui gol din starea normala. Vitezele de excitare si de dezexcitare sunt:

La echilibrul termic atunci cand g=0, viteza de generare termica este egala cu viteza de excitare, iar g o se poate exprima in functie de valorile de echilibru a lui po si qo la temperatura ambianta T:

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Ceea ce reprezinta o alta cale de a scrie faimoasa relatie a lui Einstein intre coeficientii A si B. Procesele de conversie este modelat prin adaugarea altor 2 stari: un rezervor de electroni (care accepta un electron de la starea excitata) si un rezervor de goluri (care accepta un 'gol' de la starea normala sau, cu alte cuvinte, doneaza un electron starii normale). In regim stabilizat, viteza de extragere a energiei (notata K) este egala cu viteza de transfer a electronilor si a golurilor la rezervoare, care pe rand, trebuie sa fie egale cu viteza neta de excitatie.

In unele aplicatii, viteza K poate fi viteza unei reactii fotochimice de oxidare si reducere care actioneaza printr-un transfer de electroni de la cuplajul de oxidare si reducere 1 (notat D-/D, unde simbolizeaza electronul donator) catre cuplajul 2 (A-/A, unde A reprezinta electronul acceptor):

Termenii G si R corespund reactiei directe si inverse. Intr-o celula solara, viteza K este in legatura cu curentul in circuitul extern I, astfel:

unde q (>0) reprezinta sarcina electrica a electronului. Energia libera pe electron in cele 2 rezervoare (cu alte cuvinte, potentiale chimice) notate cu µe si µh. la echilibrul termic µe = µh desi in general, µe si µh nu vor fi egale, si poate extrasa o cantitate de lucru mecanic extern egal cu ∆µ = µ e - µh prin transferul unui electron de la rezervorul de electroni la cel cu goluri. Acest transfer de electroni modeleaza o reactie chimica de oxidare si de reducere, sau asa cum vom vedea mai tarziu, curentul electric printr-un circuit extern.

Daca tranzitia intre cele 2 nivele cuantice si rezervoare sunt reversibile pentru extragerea energiei maxime, energia libera a electronului in starile normale si excitate sunt egale cu µe si µh, and iar populatiile p si 1-q urmeaza distributia Fermi-Dirac:

Primii 2 factori pot devenii relevanti in cazul iluminarii foarte puternice dar in cazul unei excitatii modeste, care in acest caz conduce la p,q << 1 fapt ce conduce la:

Sub considerente termodinamice, atunci cand viteza de reactie este nula (K=0), diferenta intre potentialelor termice devin:

Daca celula este iluminata de radiatia unui corp negru la temperatura Ts, viteza de excitatie poate fi obtinuta in mod analog, inlocuid in ecuatiile de mai sus temperatura ambianta T cu temperatura de radiatie Ts.

Cu alte cuvinte, energia maxima generata este egala cu banda de energie ∆E inmultita cu eficienta Carnot, diminuata prin radiatia solara ce provine de la discul solar sub unghiul solid ωs. The model that we have just

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described can be generalised to include the situation where the electron transfer from the hole to electron reservoir takes place in an electric field with electrostatic potential ψ which has the value ψe in the electron reservoir and ψh in the hole reservoir. The conversion equation (12) then remains in force but the chemical potential difference ∆µ =µe - µh must be replaced by the difference ∆φ of electrochemical potentials φe = µe - qψe and φh = µh - qψh.. This will be particularly relevant in the case of solar cell which will be discussed in Sec. 4. We shall see that if the rates K are replaced by the appropriate electrical currents and ∆φ by qV = q(ψe - ψh) = ∆ψ, where V is the voltage at the terminals of the cell, Eq. (12) becomes the Shockley's ideal solar cell equation. In addition to semiconductor solar cells, the two level converter serves as a model for a number of other quantum solar energy conversion systems. Two of these are briefly discussed below.The primary photochemical reaction in photosynthesisThe fundamental photosynthetic reaction can be represented by electron transport across the photosynthetic membrane. The reaction is responsible for the formation of highenergy chemical products and, in some organisms, electrostatic potential can also form across the membrane. The electron transport takes place in the photosynthetic reaction centre - a protein complex which binds components of the electron transport chain shown in Fig. 3.3. The primary electron donor (usually denoted by P) is a chlorophyll (or bacteriochlorophyll) dimer. The electron transport then proceeds through a number of intermediaries to a quinone molecule Q. Electron excitation by light from the ground state of P to an excited state P* is followed by electron transfer to Q, creating the reduced form Q-. The reduced quinone Q- is subsequently oxidised to Q by an extraneous electron acceptor, the ground state of the primary donor is replenished by an electron, and the electron transfer cycle can start again. The link to the two level quantum energy converter is apparent from Fig. 3.3 b which can be used to estimate thermodynamic limits on the conversion efficiency (Ross and Calvin, 1967).

Fig. 3.3 A schematic diagram of the photosynthetic reaction centre in purple bacteria (a). The electron transport can be modelled in a simplified manner by a scheme shown in (b). In reality, the primary donor P is rarely excited directly by the incident light but the excitation proceeds via an ‘antenna’ of accessory bacteriochlorophyll molecules which transfer the excitation energy to P by resonant energy transfer.Dye sensitised solar cells. Invented by Michael Grätzel and his group at the Ecole Polytechnique Fédérale de Lausanne in the early 1990s, these cells were arguably the first photochemical solar cells that operate on a similar principle as the photosynthetic conversion system. Molecules of Ru-based dye, deposited on very small (‘nanocrystalline’) particles of titanium dioxide act as the absorber in the quantum energy converter (Fig. 3.4). Electrons, supplied to the ground state of the dye from a liquid redox iodine/ iodide electrolyte are transferred, upon photoexcitation, from the excited state of the dye to the conduction band of TiO2 (Fig. 3.5). In effect, the mono-molecular dye layer ‘pumps’ electrons from one electrode (liquid electrolyte) to the other (solid titanium dioxide). The use of nanocrystalline TiO2 particles coated by the dye ensures high optical absorption, resulting in almost all light within the spectral range of the dye being absorbed by a coating not more than few angstroms thin.

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Fig. 3.5 The energy diagram of the electron flow in the dye sensitised cell. The ground, excited and oxidised states of the dye molecule are denoted by S, S* and S+, respectively. After A. Mc Evoy, Electrochemical photovoltaics, p. 247 in: T. Markvart, Solar Electricity (see bibliography).

4. Celule solare cu semiconductoria. Functionarea celulei solare

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Functionarea celulei solare cu semiconductori poate fi ilustrata prin exemplificarea unei jonctiuni p-n supusa iluminarii. Jonctiunea p-n reprezinta in mod efectiv interfata intre semiconductori de tip n si p: cu alte cuvinte, semiconductori dopati cu electroni si goluri in exces introduse prin adaus de impuritati. Caracteristica fundamentala a jonctiunii este data de prezenta unui camp electric puternic, indicate prin panta laturilor de conductie si banda de valenta in regiunea de jonctiune:

La echilibru, potentialele electrochimice pe cele 2 laturi ale jonctiunii, sunt egale si nu exista un curent electric. Supus radiatiei solare, sunt generate perechi de electron-goluri prin semiconductor, si separate ulterior de campul electric al jonctiunii. Printr-o judecata rapida se vede ca jonctiunea p-n devine un convertor cuantic, cu zona de energie interzisa a semiconductorului Eg jucand rolul de energie de excitare ∆E. Inlocuid ∆µ cu qV si vitezele K prin curentii electrici I

Fotocurentul generat Iℓ este egal cu curentul produs prin celula la scurcircuit (V=0). Tensiunea la mers in gol Voc (cand I=0) se poate obtine usor intr-un mod similar cu ∆µK=0:

Caz in care nu este generata putere. Puterea maxima P produsa de dispozitive de conversie se obtine intr-un punct de pe caracteristica in care produsul IV este unul maxim (aria cea mai mare a dreptunghiului). Definim factorul de umplere:

Diferenta principala intre o celula solara cu semiconductori si convertorul cu 2 nivele este de natura absorbtiei optice al semiconductorului care apare intr-un domeniu spectral mai corect intr-o linie spectrala ingusta. Mai mult decat atat, o placa suficient de subtire poate absorbii toti fotonii cu energie in exces din banda interzisa a semiconductorului Eg. Neglijind reflexia si presupunand ca toti electronii si golurile fotogenerati sunt colectati pentru a genera putere, curentul fotogenerat fiind:

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Observam ca curentul scade cu cresterea benzii interzise pornind de la faptul ca pentru benzile interzise mai largi Note that the current (20) decreases with increasing bandgap since for larger bandgaps, fewer photons have energies in excess of Eg and can be absorbed by the semiconductor. The open circuit voltage of an ideal solar cell can be obtained in a similar manner as in the thermodynamic argument used to obtain ∆µK=0 in Eq. (16). Since absorption takes place over a broader energy range than the room-temperature photon

emission, a term can be added to improve the accuracy, giving

Figures 4.3 and 4.4 compare the theoretical predictions with the open circuit voltage and short circuit of the best cells made from different materials. It is seen that the observed values of short circuit current for several materials almost reach the theoretical maximum. This corresponds to a virtually 100% quantum yield – in other words, almost every photon gives rise to an electron in the external circuit. The open circuit voltage is more sensitive to nonradiative recombination (to be discussed below) and the observed values are slightly lower, although the difference in the case of crystalline materials is still less than 20%.

Fig. 4.3 The measured short circuit current for various materials compared with the maximum theoretical value (full line). Full and empty symbols correspond to crystalline and thin film materials, respectively.

Fig. 4.4 The measured open circuit voltage for various materials compared with the maximum theoretical value. Full and empty symbols correspond to crystalline and thin film materials, respectively. The quantity of greatest interest is the efficiency which can be obtained from (18) and (20) with the use of the fill factor (19) which can be determined numerically as the solution of

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where voc=Voc/kT and vm=Vm/kT. The maximum theoretical efficiency is shown as a function of the bandgap in Fig. 4.5 (Shockley and Queisser, 1961). The bandgaps of the principal photovoltaic materials (to be discussed below) are also shown. The curve marked ‘one sun’ corresponds to the usual terrestrial conditions, approximating the solar radiation by the black body spectrum with temperature Ts = 6000K. To a good accuracy, this curve can be obtained with the use of the open circuit voltage given by Eq. (21). The curve marked ‘concentrated sunlight’ is plotted under conditions when solar radiation is focused with lenses or mirrors, enhancing the efficiency. This can be seen from the voltage equation (21) where, under maximum concentration, the second term effectively drops out.

Practical devicesSolar cells are now manufactured from a number of different semiconductors which are summarised below. In addition, there is considerable activity to manufacture commercially the dye sensitised solar cells which were discussed briefly in Sec. 3.• Crystalline silicon cells dominate the photovoltaic market. To reduce the cost, these cells are now often made from multicrystalline material, rather than from the more expensive single crystals. Crystalline silicon cell technology is well established. The modules have long lifetime (20 years or more) and their best production efficiency is approaching 18%.• Amorphous silicon solar cells are cheaper (but also less efficient) type of silicon cells, made in the form of amorphous thin films which are used to power a variety of consumer products but larger amorphous silicon solar modules are also becoming available.• Cadmium telluride and copper indium diselenide thin-film modules are now beginning to appear on the market and hold the promise of combining low cost with acceptable conversion efficiencies.• High-efficiency solar cells from gallium arsenide, indium phosphide or their derivatives are used in specialised applications, for example, to power satellites or in systems which operate under high-intensity concentrated sunlight. The structure of a typical silicon solar cell is illustrated in Fig. 4.6. The electrical current generated in the semiconductor is extracted by contacts to the front and rear of the cell. The top contact structure which must allow light to pass through is made in the form of widelyspaced thin metal strips (usually called fingers) that supply current to a larger bus bar (Transparent conducting oxide is also used on a number of thin film devices). The cell is covered with a thin layer of dielectric material - the antireflection coating, ARC – to minimise light reflection from the top surface.

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The energy conversion process in solar cells is very different from the operation of the classical heat engine, and it is instructive to consider the limitations and losses that occur in more detail. The fundamental mechanisms responsible for losses in solar cells are apparent from the discussion of solar cell operation earlier in this section: heat is produced on carrier generation in the semiconductor by photons with energy in excess of the bandgap, and a considerable part of the solar spectrum is not utilised because of the inability of a semiconductor to absorb the below-bandgap light. These losses can be reduced, but only going over to more complex structures based on several semiconductors with different bandgaps. A device called tandem cell, for example, represents effectively a stack of several cells each operating according to the principles that we have just described. The top cell is made of a high-bandgap semiconductor, and converts the short-wavelength radiation. The transmitted light is then converted by the bottom cell. This arrangement increases considerably the achievable efficiency: high efficiency space cells operating at close to 30% are now commercially available. There are also amorphous silicon cells where a double or triple stack is used to boost the low efficiencies of single-junction devices and reduce the degradation which is observed in these materials.

Other losses reduce the typical efficiency of commercial devices to roughly 50% of the achievable maximum (Fig. 4.7), somewhat less in thin-film devices. A ubiquitous loss mechanisms present in all practical devices is non-radiative recombination of the photogenerated electron-hole pairs. Such recombination is most common at impurities and defects of the crystal structure, or at the surface of the semiconductor where

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energy levels may be introduced inside the energy gap. These levels act as stepping stones for the electrons to fall back into the valence band and recombine with holes. An important site of recombination are also the ohmic metal contacts to the semiconductor. Measures taken to minimise the recombination losses include careful processing to maintain long minority-carrier lifetime, and protecting the external surfaces of the semiconductor by a layer of passivating oxide to reduce surface recombination. The contacts can be surrounded by heavily-doped regions acting as "minority-carrier mirrors" which impede the minority carriers from reaching the contacts and recombining. The losses to current by recombination are usually grouped under the term of collection efficiency: the ratio between the number of carrier generated by light and the number that reaches the junction. Considerations of the collection efficiency affect the design of the solar cell. In crystalline materials, the transport properties are usually good, and carrier transport by simple diffusion is sufficiently effective. In amorphous and polycrystalline thin films, however, electric fields are needed to pull the carriers. The junction region is then made wider to absorb the main part of the photon flux. Other losses to the current produced by the cell arise from light reflection from the top surface, shading of the cell by the top contacts, and incomplete absorption of light. The last feature can be particularly significant for crystalline silicon cells since silicon – being an indirect-gap semiconductor - has poor light absorption properties. Measures which can be taken to reduce these losses include the use of multi-layer antireflection coatings, surface texturing to form small pyramids, and making the back contact optically reflecting. When combined with a textured top surface, this geometry results in effective light trapping which provides an good countermeasure for the low absorptivity of silicon. Top-contact shading is reduced in some cells by forming these contacts in narrow laser grooves, or all the contacts can be moved to the rear of the cell. Another common loss in commercial cells involves ohmic losses in the transmission of electric current produced by the solar cell, usually grouped together as a series resistance, which reduce the fill factor of the cell. The principal characteristics of different types of cell in or near commercial production are summarised in Table

We have already seen earlier in this section that, in addition to crystalline silicon, much effort is focused on the manufacture of thin-film devices which have lower material requirements. We have also seen, on the example of dye sensitised solar cell, that photovoltaic materials are no longer restricted to semiconductors. Furthermore, there is considerable research activity into purely molecular materials. A number of research groups have demonstrated solar cells based on conducting polymers, often in combination with fulerene derivatives as electron acceptors to create the p-n junction. There is much to look forward to if their success matches the achievements of the LED technology.5. ISSUES IN SYSTEM DESIGNFor practical use, solar cells are laminated and encapsulated to form photovoltaic modules. These are then combined into arrays, and interconnected with other electrical and electronic components – for example, batteries, charge regulators and inverters – to create a photovoltaic system. A number of issues need to be resolved before an optimum system design is achieved. These issues include the choice between a flat plate or concentrating system, and whether fixed tilt will be used or the modules will ‘track’ the sun. Answers to these questions will vary depending on the solar radiation at the site of the installation and its variation during the year (see Fig. 2.1). Specific issues also relate to whether the system is to be connected to the utility supply (the ‘grid’) or is intended for stand-alone operation. Most photovoltaic arrays are installed at fixes tilt and, wherever possible, oriented towards the equator. The optimum tilt angle is usually determined by the nature of the application. Arrays which are to provide maximum generation over the year (for example, some grid-connected systems) should be inclined at an angle equal to the latitude of the site. Stand-alone systems which are to operate during the winter months have arrays inclined at a steeper angle of latitude + 15o. If power is required mainly in summer (for example, for water pumping and irrigation), the guide inclination is latitude – 15o. The amount of solar energy captured can be increased if the modules track the sun. Full two-axis tracking, for example, will increase the energy available by almost 40% over a non-tracking array fixed at the angle of latitude - at the expense, however, of increased complexity. Single axis tracking is simpler but yields a smaller gain. Tracking is particularly important in systems which use concentrated sunlight. These systems can partially offset the (high) cost of solar cells by the use of inexpensive optical elements (mirrors or lenses). The cells, however, then usually need to be cooled and it should also be borne in mind that only the direct (beam) solar radiation can be concentrated to a significant degree, thus reducing the available

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energy input. This effectively restricts the application of concentrator systems to regions with high amounts of solar radiation and clear skies. There is a considerable difference between the design of stand alone and grid connected systems. Much of the difference stems from the fact that the design of stand-alone systems endeavours to make the most of the available solar radiation. This consideration is less important when utility supply is available, but the grid connection imposes its own particular issues which must be allowed for in the system design.4.1 Stand-alone systemsPV systems are ideally suited for applications in isolated locations. An important parameter in these application is the required security of supply. Telecommunication and systems used for marine signals, for example, need to operate at a very high level of reliability. In other applications, the user may be able to tolerate lower reliability in return for a lower system cost. These considerations have an important bearing on how large PV array and how large energy storage (battery) should be installed, in other words, on system sizing. Among the variety of sizing techniques, sizing based on energy balance provides a simple and popular technique which is often used in practice. It gives a simple estimate of the PV array necessary to supply a required load, based on an average daily solar irradiation at the site of the installation, available now for many locations in the world. Choosing the month with the lowest irradiation (usually December in northerly latitudes), one can determine the solar radiation incident on the inclined panel, and the array size can be found from the energy balance equation:

where the Daily solar radiation should be equated to the Peak Solar Hours in Fig. 2.1 Equation (23) specifies how many PV modules need to be installed to supply the load under average conditions of solar irradiation. The battery size is then estimated ‘from experience’ – a ‘rule of thumb’ recommends, for example, installing 3 days of storage in tropical locations, 5 days in southern Europe and 10 days or more in the UK. Other sizing methods include the elegant random walk method (Bucciarelli,1984) which treats the possible states of charge of the battery as discrete numbers which are then identified as sites for a random walk. Each day, the system makes a step in the ransom walk depending on solar radiation: one step up if it is ‘sunny’ and one step down if it is ‘cloudy’. Bucciarelli (1986) subsequently extended this method to allow for correlation between solar radiation on different days. These and other more complex sizing techniques have been summarised by Gordon (Gordon, 1987).4.2 Grid-connected systemsGrid connected systems have grown considerably in number since the early 1990s spurred by Government support programmes for ‘photovoltaics in buildings’ in a number of countries, led initially by Switzerland and followed by more substantial programmes in Germany and Japan. One feature that affects the system design is the need for compliance with the relevant technical guidelines to ensure that the grid connection is safe; the exported power must also be of sufficient quality and without adverse effects on other users of the network. Many of the grid connection issues are not unique to photovoltaics. They arise from the difficulties trying to accommodate ‘embedded’ or distributed generators in an electricity supply system designed around large central power stations. It is likely that many of these features of grid connection will undergo a review as electricity distribution networks evolve to absorb a higher proportion of distributed generators: wind farms, co-generation (or CHP) units, or other local energy sources. The electricity supply system in twenty or thirty years time might be quite different from now, and new and innovative integration schemes will be needed to ensure optimum integration. Photovoltaic generators are likely to benefit from these changes, particularly from the recent advances in the technology of small domestic size co-generation units (micro-CHP) which have a good seasonal synergy with the energy supply from solar sources, and can share the cost of the grid interface. An example of how elegant architecture can be combined with forward looking engineering is offered by the Mont-Cenis Energy Academy at Herne-Sodingen (Fig. 5.1). This solar-cell clad glass envelope at the site of a former coal mine provides a controlled Mediterranean microclimate which is powered partly by 1 MWp photovoltaic array and partly by two co-generation units fuelled by methane released from the disused mine. To ensure a good integration into the local electricity supply, the generators are complemented by a 1.2MWh battery bank. In addition to the Academy, the scheme also export electricity and heat to 250 units in a nearby housing estate and a local hospital. The Mont-Cenis Academy is a fine flag-carrier for photovoltaics and new energy engineering –without a doubt, similar schemes will become more prolific as photovoltaics and energy efficient solutions become the accepted norm over the next few decades.

Theoretical limits of photovoltaic solar energy conversion1. CURRENT-VOLTAGE CHARACTERISTICSIn Fig. 1(a) (Landsberg, 1995) a positive applied voltage moves the current carriers so as to produce a conventional current density (current divided by the cross-sectional area, A say) which flows to the right-hand side. This means electron vacancies (“holes”) move to the right as they are positively charged, and electrons to the left as they carry a negative charge. Further, we see that a positive applied voltage yields an easy current flow, i.e. a bigger current density, while the same voltage applied in the opposite direction produces a smaller current density. Our structure has therefore a rectifying property for the current, which is not

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displayed by a simple resistance, say. The two directions are referred to as 'forward' and 'reverse', and the structure is a rectifier, which is in this case a p-n junction. In the figure J0 is the saturation current density, which is found for reasonably large reverse voltages. For even larger voltages (not shown) the current grows again and the system suffers eventually an electrical breakdown.

Fig. 1. Schematic current-voltage characteristics of a p-n junction: (a) in the dark, (b) under illumination.In the presence of light, sunlight in the case of a solar cell, the whole characteristic is displaced rigidly (in the simplest picture) by an amount equal to the light-induced current density JL, as shown in curve (b). Two new characteristic quantities occur now: the 'open-circuit' voltage Voc, produced in the absence of a current, and the 'short-circuit' current density Jx. Short-circuit means of course that there is then no voltage across the cell. The current AJSC multiplied by a voltage gives an electrical power as in Ohm's law. In fact, 0.5 A Jsc Voc is a rudimentary measure of the power output of which the cell is capable. It is favoured by (i) a small reverse current density and (ii) a good carrier generation. So far we have considered a unit to which a voltage is applied. In a solar cell, however, the voltage which is developed is generated inside the cell by the electrons and holes which are no longer in equilibrium when the radiation falls on the cell.2. THEORETICAL EFFICIENCIESTo obtain photovoltaic efficiencies we have to introduce the energy gap Eg across which incidentphotons can excite the electrons of a semiconductor. They leave behind holes, as already discussed.The electrons and holes are separated in space by the internal electric field of the p-n junction. Thisyields a photo-voltage and a photo-current.What is the best value of Eg? If it is zero, all photons can contribute to the photo-current whichbecomes maximal. The photo-voltage is however zero. A bigger gap stops some photons fromproducing electron-hole pairs and the photo-current is thereby reduced, while the photo-voltage isincreased. Between the limits for the conversion efficiency (η = 0 for Eg = 0 and η = 0 as Eg tends toinfinity) there must lie a value of Eg for which η is maximal - see Fig. 2. This curve assumes a normalsolar temperature of about 6000 K and maximum concentration (46500 suns) of the radiation andassuming that the sun surrounds the cell hemispherically. It gives a (theoretical) optimum efficiencyof 44% which corresponds to a band-gap of 2.2 kTp, where Tp is the temperature of the sun (“p” standsfor “pump”). This efficiency reduces to about 30% for one sun. Actual efficiencies are of coursesmaller. They lie near or below 30%, and an improvement by each fraction of one percent results froma real struggle! (de Vos 1992, Sieniutycz and de Vos 2000, Würfel 2000, Kabelac 1994).

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Fig. 2. Energy conversion efficiency as a function of band gap, assuming the pump (i.e. the sun)at 6000 K surrounds the converter.3. SOME WAYS OF INCREASING EFFICIENCIESThe (theoretical) overestimate of the efficiencies is in part due to the neglect of the naturalrecombination of electrons and holes which takes place anyway in the presence of a current. It leadsto the loss of some electron-hole pairs which can then, not contribute to the current. Thus energy,which should aid the current, is given to the lattice by electron-phonon collisions and to otherelectrons by the Auger effect (electron-electron collisions). However, the good news is that higherefficiencies can be obtained by having several materials with decreasing energy gaps in series. Thesesystems are called tandem cells. Experimentally one can have so far at most four or five in series.Photons which pass through the first cell (because its energy gap is too big to excite an electron-holepair), are in this arrangement able to create a pair in the next cell, which has a smaller gap. This is inprinciple continued down a series of cells to smaller and smaller gaps. The theory can be worked outfor an infinite number of tandem cells. This procedure clearly makes better use of the higher energyphotons, for if they merely gave up the gap energy to create ONE electron-hole pair, then theremaining energy would go to heat up the lattice, instead of adding to the solar current.Another way of imagining a use for the higher energy photons is to trace the result if they producemore than one electron-hole pair. This process is called impact ionization, and it takes place in a cellin any case. Instead of producing an electron-hole pair with the energy which is left over beingeventually dissipated as heat, it leads to a second electron-hole pair being produced, thus increasingthe solar current instead of heating up the sample. This leads to a modification of the theory, and amaximum efficiency can be estimated if this phenomenon is fully exploited. Again one may allow aninfinite number of impact ionizations.Additional electron-hole pairs can also be produced by the re-absorption of emitted photons (“photonrecycling”). This is, another process which takes place automatically in a cell. These two extremecases, the infinite tandem cell and unlimited impact ionizations, lead, remarkably, to similar values ofthe theoretical maximum efficiency. For one sun illumination it is of the order of 61%-68%, and it isabout 86%-88% for maximal solar concentration, depending on the method of calculation. The resultis higher than the value of 44% of section 2, reflecting the improvements resulting from the tandemconnection and/or the impact ionizations. Nothing like these values have been obtained

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experimentally, of course, but they give an indication of what can still be aimed at; for a review, andfor a list of about 100 theoretical and experimental efficiencies, see Landberg and Badescu (1998).The experimental results are the lower ones in this list. Even for monochromatic irradiation theefficiency drops already to 45%. This is a favourable case, since to design a cell for what is in effectjust one narrow frequency range is so much more straightforward than to cater for the whole of thesolar spectrum.For a two-stage GaAs/GaSb tandem cell with a concentration ratio of C = 50 suns one can achieve thevery respectable efficiency of 34%. The value for an InP/GaInAs cell has been reported at 32%. Forsmall area GaAs/GaInAsP tandem cells at C =39.5 one has found 30%. For unconcentrated radiationone can reach 25% for a GaInP/GaAs/Ge cell. So one can give many values for the efficiency(Landsberg and Badescu, 1998). Note that the maximum concentration is about 46500 suns. Insatellites solar cells represent a small fraction of the total expense, so that expensive cells can here beused. But among additional considerations: one needs in these cases a long life and good radiationresistance. A major market share has been secured by GaAs-Ge monojunctions, and one is lookingforward to 25% efficient triple junctions', 40% cells are envisaged in the more distant future. In thesespace cells one can tolerate a medium beginning-of-life efficiencies provided they deteriorate onlymarginally to end-of-life efficiencies by virtue of good irradiation stability.4. THE HETEROJUNCTION WITH AUGER EFFECTSRecall that in radiative studies one should include with radiative emission also absorption ofradiation, since one cannot occur without the other. In fact, they are related by the important principleof detailed balance. lf one applies this idea to impact ionization one tends an analogous symmetry.One would expect electron-hole recombination with the energy set free being given to, say, aconduction band electron. This removes particles which might contribute to the solar current and, likeradiative recombination, it is detrimental. This recombination, named after Pierre Auger, is thedetailed balance analogue of impact ionization, and should therefore be included in a theory whichtakes account of impact ionization, though this has not always been done. In our work in this area wehave always insisted on using a probability P(E) that an electron which has the energy E to impactionise will actually do so. This introduces unfortunately another parameter, but a simple theory servesas a guide to its value. In a simple model we find theoretically that for P = 1 the efficiency of a cell islowered by 5% if Auger recombination is included, but only by 3% if both Auger recombination andimpact ionization are covered. The theory introduces quite a few parameters, apart from the obviousones like diffusion coefficients, effective densities of states, lifetimes of electrons and holes, etc. Forthere are threshold parameters for Auger recombination since a partner electron, making a transitionbetween bands, cannot do so from the bottom of the band owing to constraints of energy andmomentum conservation.A broad conclusion is that band-band Auger effects shift the optimum energy gaps of bothheterojunction materials to higher values, but this is opposed by impact ionization. Favourable solarcell efficiencies may be expected for good impact ionization, low radiative and Auger recombinationand thin active layers. Specific designs of cascaded cells may get further improved results (Andreev,1999, and Aroutiounian et al., 2001).5. THERMOPHOTOVOLTAICSThe average energy of absorbed sold photons is normally of the order of 1.9 eV, whereas thesemiconductor band gap is typically 1 eV. This leaves an average of 0.9 eV per incident photon to beabsorbed by the lattice as heat, and therefore essentially wasted. This waste is decreased if the solarradiation is first taken up by an intermediate absorber whose temperature is less than the solartemperature and which acts now as a “low-temperature sun”. The 0.9 eV average energy loss is nowdecreased and the overall conversion is increased. In this so-called thermophotovoltaic conversion theaverage energy of the photons emitted by the absorber, and then of course absorbed by the cell, is lessthan 1.9 eV and implies a smaller heat loss by thermalisation. This leads to improved efficiencies.6. CONCLUDING REMARKSIt is worth noting that it has been estimated that the energy payback time of a solar cell is of the order3 to 4 years and in its lifetime a cell may produce something in the order of 10 times its cost ofproduction (Knapp and Jester, 2001). This shows that it can be a satisfactory device on purelyeconomic grounds.