Tomas Markvart

Sizing of hybrid photovoltaic-wind energy systems

A procedure is described which determines the sizes of the PV array and wind turbine in a PV/wind energy hybrid system. Using the measured values of solar and wind energy at a given location, the method employs a simple graphical construction to determine the optimum configuration of the two generators that satisfies the energy demand of the user throughout the year.

Light harvesting for quantum solar energy conversion

Abstract Despite wide structural and functional differences, the laws that govern quantum solar energy conversion to chemical energy or electricity share many similarities. In the photosynthetic membrane, in common with semiconductor solar cells, the conversion process proceeds from the creation of electron–hole pairs by a photon of light, followed by charge separation to produce the required high-energy product. In many cases, however, mechanisms are needed to enhance the optical absorption cross-section and extend the spectral range of operation. A common way of achieving this is by light harvesting: light absorption by a specialised unit which transfers the energy to the conversion apparatus. This paper considers two examples of light harvesting — semiconductor solar cells and the photosynthetic apparatus — to illustrate the basic operation and principles that apply. The existence of a light harvesting unit in photosynthesis has been known since the early 1930s but details of the process — relating, in particular, to the relationship between the structure and spectral properties — are still being unravelled. The excitation energy carriers are excitons but the precise nature of the transport — via the solid state Frenkel–Peierls variety or by Forsters resonant energy transfer — is still subject to debate. In semiconductor solar cells, the energy of the absorbed photon is collected by minority carriers but the broad principles remain the same. In both cases it is shown that the rate of energy conversion is described by a law which parallels the Shockleys solar cell equation, and the light harvesting energy collection is subject to reciprocity relations which resemble Onsagers reciprocity relations between coefficients which couple appropriate forces and flows in non-equilibrium thermodynamics. Differences in the basic atomic make-up in the two systems lead to different energy transport equations. In both cases, however, similar mathematical techniques based on Greens functions can be used to advantage. The Greens function provides a convenient vehicle for the determination of the probability of energy collection — known as the trapping probability in the photosynthetic unit. Using the reciprocity relation, both quantities are shown to be closely related to the distribution of the energy carriers in the dark. The collection probability can then be discussed in detail, by solving the semiconductor device equations in the case of solar cell, and by linking the Greens function formalism to the random walk model in the case of the photosynthetic unit. The concept of resonant energy transfer is beginning to enter the arena of solid-state optoelectronics. It is an aim of this paper to show that similar phenomena — which exist in the domain of bioenergetics — can throw new light on a range of energy transfer and collection processes that are of considerable importance in many modern optoelectronic devices.

Detailed balance method for ideal single-stage fluorescent collectors

It is shown that fluorescent collectors where radiation is confined with the use of selective reflectors can be modeled as converters of blackbody radiation. By decreasing the temperature and frequency of the radiation, the effective etendue of the emitted beam can be reduced substantially in the conversion process without violating the second law of thermodynamics. This type of collector can, in principle, achieve surprisingly high efficiencies: the output from a silicon solar cell operating with an ideal collector can exceed 90% of the output from a directly illuminated solar cell.

THE CARNOT FACTOR IN SOLAR-CELL THEORY

In a two-level system the open circuit voltage or difference between the electro-chemical potentials at the contacts, is related to the energy gap Eg by a Carnot factor;V=(1-Ts/Tp)Eg.Here, Ts and Tp are the absolute temperatures of the ambient (surroundings) and of the incident black-body radiation (pump), respectively. A simple two-step statistical thermodynamic argument is given here which makes this result plausible. Its standing in a more general context is also discussed.

Modelling battery charge regulation for a stand-alone photovoltaic system

Abstract A new model for the charge and discharge characteristics of a lead–acid battery is presented which aims to model the effect on capacity of variable charge and discharge rates. This model has been implemented using the circuit simulator PSPICE, and is used to investigate the effect of the charge controller strategy on the performance of a stand-alone PV system. It is shown that a simple limit on charging voltage is probably adequate to achieve a high state of charge, although a two-level regulator may be needed to maintain battery condition. The benefits of maximum power point tracking are also investigated.

Relationship between dark carrier distribution and photogenerated carrier collection in solar cells

The Greens function formalism is used to obtain new theoretical results which establish a simple and quantitative relationship between the spatial dependence of solar cell parameters in the dark and under illumination. It is shown, in particular, that the minority-carrier collection efficiency is equal to a suitably normalized excess minority carrier concentration in the dark.

The chemical potential of light in fluorescent solar collectors

The energetic aspect, discussed by the means of the chemical potential, involved into the absorption and radiation processes occurring in the operation of fluorescent solar collectors is of interest in this publication. The chemical potential of the fluorescent light incident on the solar cell is characterized by studying the fluorescence spectrum emitted by a special type of fluorescent collector, where absorption and fluorescence take place in a liquid medium, in effect a liquid fluorescent collector. It is shown that photon reabsorption (known also as photon recycling) gradually brings the emitted photon flux into thermal equilibrium with the collector. The fluorescence photon distribution is then characterized by a specific temperature, obtained from the Kennard–Stepanov law, and a chemical potential given by the generalized Planck’s law. We find that the chemical potential of the fluorescent light incident on the solar cell is nearly equal to the thermodynamical limits imposed by a detailed balance a...

Photon frequency management for trapping & concentration of sunlight

This paper considers a range of techniques which – within the realm of classical optics – can be used to enhance light capture as a first step in photovoltaic energy conversion. Examples include a simple case of downshifting, fluorescent collectors which reduce the size of a light beam, and a novel form of light trapping to increase the path length of light within the solar cell. The results are discussed using a thermodynamic framework where the energy exchange with an absorbing/fluorescent medium allows the entropy of the captured photon gas to be lowered, reducing the etendue of the emitted beam. We show that frequency management represents a powerful tool, allowing enhancement in light trapping above the Yablononovitch limit, leading to potentially highly efficient but very thin crystalline silicon solar cells.

Photon reabsorption in fluorescent solar collectors

Understanding photon transport losses in fluorescence solar collectors is very important for increasing optical efficiencies. We present an analytical expression to characterize photon reabsorption in fluorescent solar collectors, which represent a major source of photon loss. A particularly useful universal form of this expression is found in the limit of high reabsorption, which gives the photon reabsorption probability in a simple form as a function of the absorption coefficient and the optical etendue of the emitted photon beam. Our mathematical model predicts fluorescence spectra emitted from the collector edge, which are in excellent agreement with experiment and provide an effective characterization tool for photon transport in light absorbing media.

Photogenerated carrier collection in solar cells in terms of dark carrier distribution: three dimensions

A relationship between the collection efficiency and the normalized excess minority carrier distribution under forward bias in the dark, which was recently derived using the Greens function technique for a one-dimensional (1-D) quasi-neutral region of a solar cell, is generalized here to three dimensions. The link with other reciprocity theorems is also briefly discussed.