G.L. Araujo

Limiting efficiencies for photovoltaic energy conversion in multigap systems

Multigap systems are better matched to the suns spectrum than single gap systems and are, therefore, more efficient as photovoltaic converters. This paper reviews the different thermodynamic approaches used in the past for computing the limiting efficiency for the conversion of solar energy into work. Within this thermodynamic context, the limit ranges from 85.4% to 95.0% depending on the assumptions made. Detailed balance theory provides a more accurate model of the photovoltaic converter. It leads to a limit of 86.8% for a system with an infinite number of cells, as already pointed out by other authors. In this work, however, we use the concepts of angle and energy restriction to emphasize that this limit is independent of the light concentration. Systems with a finite number of cells are also studied and their limiting efficiency is found to be higher than previously reported. Data for AM1.5 Direct spectrum, never computed before, are included.

Absolute limiting efficiencies for photovoltaic energy conversion

The Detailed Balance Theory was used in the past by a number of authors to calculate the limiting efficiency of photovoltaic energy conversion. Values of 40.8% for optimum single gap devices and of 86.8% for infinite number of gaps were calculated for the maximum efficiencies of conversion of the radiation of the Sun, considered as a black body at a temperature of 6000 K. This work extends the generality of those results and introduces new refinements to the Theory: the cell absorptivity is justified to be equal to the emissivity under bias operation and under certain idealistic conditions, the optimization of the absorptivity is discussed and the concepts of solid angle and energy restriction are explained. Also, as a consequence of the review, new results arise: the maximum efficiency is found to be independent on the concentration and although the limiting efficiency of optimum devices is confirmed, the limiting efficiency previously established for non-optimum devices is found to have been underestimated under certain circumstances.

The effect of distributed series resistance on the dark and illuminated current—Voltage characteristics of solar cells

Distributed series resistance effects in solar cells are analyzed and the correctness of representing these by a lumped parameter is discussed for any conditions of bias and illumination. In addition to a general mathematical methodology, analytical expressions are derived to simplify the estimation of series resistance effects on the dark and illuminated<tex>J-V</tex>characteristics of the cell. The equivalent series resistance (r<inf>s</inf>) in the dark is found to decrease with current density<tex>J</tex>from<tex>r_{b} + r_{e}/3</tex>at small<tex>J</tex>to (<tex>r_{e} r_{b})^{1/2}</tex>at very high<tex>J</tex>, where r<inf>e</inf>and r<inf>b</inf>are the emitter layer and base region resistances, respectively. For illuminated conditions r<inf>s</inf>depends on<tex>J</tex>as well, being maximum near short-circuit and minimum near open-circuit; however, r<inf>s</inf>further depends on the photogenerated current J<inf>L</inf>: its short-circuit value increases with J<inf>L</inf>from<tex>r_{b} + r_{e}/3</tex>to<tex>r_{b} + r_{e}/2</tex>and the open-circuit value decreases with J<inf>L</inf>from<tex>r_{b} + r_{e}/3</tex>to<tex>(r_{e}r_{b})^{1/2}</tex>. The variability of r<inf>s</inf>is therefore related to the relative importance of r<inf>b</inf>and<tex>r_{e};r_{b}</tex>plays the role of attenuating this variability, a situation not well recognized previously. Previous theoretical and experimental work is critically reviewed throughout this paper.

A new method for experimental determination of the series resistance of a solar cell

A new method for determining the series resistance of a solar cell from illuminated<tex>I-V</tex>measurements is presented. The method, based on the computation of the area<tex>A</tex>, under the<tex>I-V</tex>curve, evaluates R<inf>s</inf>using the equation<tex>R_{s} = 2[V_{oc}/I_{sc} - A/_sc^2 - (mkT/q) (1/I_{sc})]</tex>This technique takes advantage of the special feature of integration as a procedure to smooth data errors. The R<inf>s</inf>obtained represents the resistive effects globally.

Determination of the two-exponential solar cell equation parameters from empirical data

Abstract The determination of the dark current-voltage two-exponential equation parameters of a solar cell from experimental data is presented. The approach used here is based on a least-squares technique for linear functions; this is possible because m 1 , m 2 and R s are considered as constant parameters while the standard deviation σ is calculated. After a matrix of σ values has been evaluated in this way the parameters corresponding to the minimum value of σ are chosen as those of the best fit. The technique is simple enough to be carried out using only a scientific pocket calculator.

Analytical expressions for the determination of the maximum power point and the fill factor of a solar cell

Simple approximate analytical expressions for calculating the values of current and voltage at the maximum power point and the fill factor of a solar cell are proposed. The ratios Im/IL and Vm/Voc, and hence the fill factor, are shown to depend on the two normalized parameters νoc = VocmkTe and νR = RSILmkTe which are closely related to the diode quality factor and the series resistance. The accuracy of the approach proposed here is fairly good for νR 15, for relative errors of less than 1%. These ranges for νR and νoc cover the real situations for most silicon and GaAs solar cells. The usefulness of the analytical expressions as indicators of the behavior of the cell is discussed, and the influence of the series resistance and the diode quality factor is emphasized. The application of these expressions to the determination of the series resistance and the diode quality factor is also discussed.

Mathematical analysis of the efficiency-concentration characteristic of a solar cell

Abstract A new general method of calculating the efficiency-concentration characteristic (including the direct determination of the maximum efficiency point) of a solar cell is presented. The method is valid for any model which describes the dark current density-voltage characteristic of the cell, including the common single-exponential and double-exponential models. For the single-exponential model, two simpler methods are derived: (a) a parametric method, which is both exact and analytical, and (b) an approximate method which provides a schematic representation of the efficiency-concentration characteristic and which can be extended to a double-exponential model. On the basis of this second method, the influence of the internal parameters of the solar cell on its behaviour under concentrated sunlight is discussed.

On the analytical determination of solar cell fill factor and efficiency

Abstract A comparison of several analytical, approximate expressions proposed by various authors to calculate the fill factor and the efficiency of a sol ar cell is presented. The comparison is referred to the conventional single-exponential solar cell model and it has been made by using a normalized nomenclature. The accuracy of the expressions has been examined as a function of the concentration factor and it is shown that the usefulness of the approximations decreases as the concentration factor increases. However, the loss in accuracy is different for each expression and, consequently, some of them can still be used for high concentration factors.

High efficiency photovoltaic conversion with spectrum splitting on GaAs and Si cells located in light confining cavities

A high-efficiency photovoltaic conversion system based on spectrum splitting of concentrated light to fall on GaAs and Si cells placed inside light confining cavities is described and experimental results are reported: 29.4% at 180 suns (near AM1.5 direct spectrum), 22% contributed by the GaAs cell. The short-circuit current gain derived from the use of the cavities is 7-8% (relative increase). However, the system is believed to have immediate potential to achieve as much as 32% efficiency. Benefits compared to systems based on stacked cells are pointed out: (a) conventional cells based on developed fabrication techniques can be used, with minor design changes, (b) cell design can be independently optimized with the aim of achieving maximum efficiency, (c) cells can operate at different concentrations, (d) electrical power can be extracted independently from each cell, and (e) it is easy to make the electrical connections to each cell.<<ETX>>

Efficiency of silicon and GaAs concentrator solar cells operated inside integrating cavity receivers

Abstract The theory for the general case of solar cells operating inside integrating cavity receivers is established. This is applied to the particular case of different configurations of silicon and GaAs cells. The results of the analysis show that a composite system of silicon and GaAs cells manufactured using relatively simple technology could reach an efficiency of 34%. The optimal configuration is that in which the GaAs cells are placed in the directly illuminated area of the receiver and the silicon cells are placed in the indirectly illuminated area of the receiver.