Special Trans Function Theory Research Articles

Mathematical modeling of solar cells: novel approaches based on Special Trans Function Theory

Mathematical modeling of solar cells: novel approaches based on Special Trans Function Theory

Analytical modeling of novel equivalent circuits of double diode solar cell circuits using a special transcendental function approach.

Solar photovoltaic (PV) cell modeling is crucial to understanding and optimizing solar energy systems. While the single-diode model (PVSDM) is commonly used, the double-diode model (PVDDM) offers improved accuracy at a reasonable level of complexity. However, finding analytical closed-form solutions for the current-voltage (I-U) dependency in PVDDM circuits has remained a challenge. This work proposes two novel configurations of PVDDM equivalent circuits and derives their analytical closed-form solutions. The solutions are expressed in terms of the Lambert W function and solved using a special transcendental function approach called Special Trans Function Theory (STFT). The accuracy of the proposed equivalent circuits is demonstrated on two solar cells/modules, RTC-F and MSX-60, showing equal or better performance than the standard PVDDM equivalent circuit. Further testing on a commercial solar panel under different irradiance and temperature conditions confirms the applicability of the proposed models. To address the parameter estimation problem, a novel metaheuristic algorithm, the chaotic honey-badger algorithm, is developed and evaluated. The results obtained validate the accuracy and practicality of the proposed PVDDM equivalent circuit configurations.

Analytical solutions using special trans functions theory for current–voltage expressions of perovskite solar cells and their approximate equivalent circuits

Perovskite solar cells (PSC) have been recognized as devices with a constant increase in power conversion efficiency, confirming this promising technology’s upward trend. This paper deals with the mathematical modeling of current voltage and inverse voltage-current relationships of PSCs, in which standard equivalent circuits, as well as approximate equivalent circuits where series or parallel resistance is neglected, are investigated. Analytical solutions for voltage-current and current–voltage dependencies are derived for all investigated circuits. Furthermore, analytical solutions for short-circuit current and open-circuit voltage are derived. All nonlinear formulations of these dependencies are solved by applying special trans function theory. This paper proposes an enhanced algorithm called the Chaotic African Vultures Optimization Algorithm (Ch-AVOA) for PSC’s parameter estimation. The proposed algorithm is compared with other algorithms in terms of the convergence speed to the global solution and other statistical test measures to validate the algorithm’s efficiency.

On the exact analytical formula for dimensionless injection rate in CO2 storage based on Special Trans Functions Theory

On the exact analytical formula for dimensionless injection rate in CO2 storage based on Special Trans Functions Theory

Single Diode Solar Cells-Improved Model and Exact Current-Voltage Analytical Solution Based on Lambert's W Function.

There are three standard equivalent circuit models of solar cells in the literature—single-diode, double-diode, and triple-diode models. In this paper, first, a modified version of the single diode model, called the Improved Single Diode Model (ISDM), is presented. This modification is realized by adding resistance in series with the diode to enable better power loss dissipation representation. Second, the mathematical expression for the current–voltage relation of this circuit is derived in terms of Lambert’s W function and solved by using the special trans function theory. Third, a novel hybrid algorithm for solar cell parameters estimation is proposed. The proposed algorithm, called SA-MRFO, is used for the parameter estimation of the standard single diode and improved single diode models. The proposed model’s accuracy and the proposed algorithm’s efficiency are tested on a standard RTC France solar cell and SOLAREX module MSX 60. Furthermore, the experimental verification of the proposed circuit and the proposed solar cell parameter estimation algorithm on a solar laboratory module is also realized. Based on all the results obtained, it is shown that the proposed circuit significantly improves current–voltage solar cell representation in comparison with the standard single diode model and many results in the literature on the double diode and triple diode models. Additionally, it is shown that the proposed algorithm is effective and outperforms many literature algorithms in terms of accuracy and convergence speed.

Current-voltage curves of planar heterojunction perovskite solar cells – Novel expressions based on Lambert W function and Special Trans Function Theory

IntroductionAt the present time, much attention has been focused on new types of solar cells, called perovskite solar cells. They are highly efficient devices with more than 25% power conversion efficiency. However, perovskite solar cell performance has not yet been fully explored. ObjectivesWe aimed to mathematically investigate the analytical modeling of current–voltage curves of planar heterojunction perovskite solar cells using Perovich Special Trans Function Theory (STFT). Furthermore, we proposed novel analytical closed-form solutions for short-circuit current and open-circuit voltage of these cells in terms of STFT. We evaluated the safety for laying the theoretical foundation by comparing the accuracy of the proposed expressions by the known methods. MethodsA novel hybrid metaheuristic algorithm, called particle swarm optimization (PSO) – evaporation rate water cycle algorithm (ERWCA), is proposed to determine equivalent circuit parameters of the perovskite solar cell. A novel objective function is introduced for estimating the parameters for that purpose too. ResultsIt was shown that STFT is very applicable and efficient for representing current–voltage expressions of perovskite solar cells. STFT provides a more accurate solution and requires fewer order members than the solutions provided by the conventional Taylor series. Based on these expressions and numerical calculations, it is verified that the characteristic values ​​of variables (short-circuit current, no-load voltage, efficiency, and fill factor) were not accurately calculated in the literature. Also, parameters of equivalent circuits of these cells were not accurately estimated. The equivalent circuit parameters were determined using the algorithm proposed in this work, which fit the verified values ​​of characteristic quantities much better than the literature. ConclusionThis work lays the foundation for developing the planar-structured perovskite solar cell models, in which the proposed estimation method and expressions are highly effective and provide excellent results.

Towards accurate calculation of supercapacitor electrical variables in constant power applications using new analytical closed-form expressions

Supercapacitor (SC) is one of the most trending energy storage solutions. The SCs equivalent circuit models have been extensively applied to energy management because of their accuracy and simplicity. However, there is a difficulty in solving the conventional differential equation-based model used to characterize the electrical behavior of SCs operating in constant power applications. Hence, numerical or metaheuristic techniques have been used in the literature to derive SC's internal voltage at any time. In this work, a thorough mathematical analysis that enables a precise calculation of the electrical variables implied in the charge/discharge processes of SCs operated at constant power as a function of time is presented. First, the transcendental discharge voltage expression of SCs operating at constant power is formulated, and then it was solved using the Special Trans Function theory (STFT). The precision of calculation of the method used for solving the transcendental expression is presented and discussed. Second, the transcendental voltage of charging expression of SCs operating at constant power as a function of time is also formulated, and then it was solved using Lambert W equation. Third, a comparison of different methods for solving mentioned equations is presented. Fourth, the electrical variables involved in the charge/discharge processes of SCs – voltage, current, power, energy, state of charge, and power loss are investigated. Furthermore, the results obtained for the variation of parameters and their operating conditions demonstrate the proposed equations’ applicability and accuracy. Finally, the results obtained validate that the closed-form expressions suggested in this paper are accurate and straightforward, which can contribute to proper modeling, investigation, sizing, regulation, and control of constant power SCs in modern energy systems.

Some applications of special trans function theory in physics

The Karolyhazy uncertainty relation is the statement that if a device is used to measure a length $l$, there will be a minimum uncertainty $\delta l$ in the measurement, given by $(\delta l)^3 \sim L_P^2\; l$. This is a consequence of combining the principles of quantum mechanics and general relativity. In this note we show how this relation arises in our approach to quantum gravity, in a bottom-up fashion, from the matrix dynamics of atoms of space-time-matter. We use this relation to define a space-time-matter foam at the Planck scale, and to argue that our theory is holographic. By coarse graining over time scales larger than Planck time, one obtains the laws of quantum gravity. Quantum gravity is not a Planck scale phenomenon; rather it comes into play whenever no classical space-time background is available to describe a quantum system. Space-time and classical general relativity arise from spontaneous localisation in a highly entangled quantum gravitational system. The Karolyhazy relation continues to hold in the emergent theory. An experimental confirmation of this relation will constitute a definitive test of the quantum nature of gravity.

Experimental Testing and Analytical Solution by Means of Lambert W-Function of Inductor Air Gap Length

In this paper the exact analytical closed form solutions for inductor air gap length have been presented. To be specific, in a mathematical sense, the dependence between the air gap length, inductance and other constructional parameters of inductor is nonlinear, i.e. transcendental. In this paper that nonlinear equation is solved in two manners – by using the Lagrange inversion theorem of the Lambert W function or by using its asymptotic formula and by using Special Trans Functions Theory. The numerical results obtained by using these methods, are mutually compared in terms of the calculation error. In order to prove the validity of the mathematical dependence between the inductance, air gap length, and the other constructional parameters, two inductors have been created. The measured results of inductance and air gap length are compared with the corresponding results obtained by the calculations. Very good agreement is shown between the measured and the calculated value of both the air gap length and the inductance value.

Concerning an analytical solution of some families of Kepler’s transcendental equation

The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.

Concerning a novel mathematical approach to the solar cell junction ideality factor estimation

The problem of finding an analytical solution of the solar cell junction ideality factor n is studied in some detail, by the Special Trans Functions Theory (STFT). The advanced STFT iterative method just as the structure of the theoretical derivation is presented, while proofs and numerical results confirm the validity and base principle of the STFT. In addition, the obtained results are compared with the calculated values of other methods for alternative proving its significance. Undoubtedly, the proposed novel STFT exact analytical approach implies qualitative improvement of the conventional analytical and numerical methods.

On the exact analytical solution of some families of equilibrium critical thickness transcendental equations

The problem of finding an exact analytical closed-form solution of some families of transcendental equations, which describe the equilibrium critical thickness of misfit dislocation generation in epitaxial thin films, is studied in some detail by the Special Trans Functions Theory (STFT). A novel STFT mathematical approach with an analytical closed-form solution is presented. Structure of the STFT exact solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. The proposed STFT analytical approach shows qualitative improvement in theoretical sense (a novel gradient coefficient genesis), and, in accuracy when compared to the conventional analytical and numerical methods.

Exact Analytical Solution for Organic Solar Cells Showing S-Shaped J-V Characteristics Using Special Trans Function Theory (STFT)

Many organic solar cells exhibit anomalous kinks showing S-shaped J-V behaviour. This atypical behaviour may be electrically modelled by including a second diode (D 2 ) with opposite current characteristics together with a shunt resistance to that of the conventional solar cell diode (D 1 ). In this communication, we present an exact analytical expression for the cell’s output voltage as an explicit function of its terminal current by the application of special trans function theory (STFT) for the S-shaped J-V characteristics model. The explicit nature of the proposed solution avoids approximations and numerical iterations. The differentiability of the trans function in STFT facilitates the analytical analysis of the problem. The evolution of the S-shaped J-V characteristics and the fill factor (FF) is also deliberated by varying different parameters to validate the proposed analytical solution.

An Exact Analytical Method for Calculating the Parameters of a Real Solar Cell Using Special Trans Function Theory (STFT)

An exact analytical method using special trans function theory (STFT) is presented to calculate the parameters of a real solar cell. Calculated values are compared with other methods. Various characteristic curves are also drawn using the analytical expressions to validate this approach. The effect of the parasitic resistances in the fill factor is studied in detail. Relative percentage accuracy of STFT method is also calculated to show the significance of the method over other methods.

Concerning exact analytical STFT solutions to some families of inverse problems in engineering material theory

The problem of finding the exact analytical closed-form solution of some families of transcendental equations, which describe two different physical phenomenon, thermionic emission and electrical conductivity in semiconductors, is studied, in some detail, by the Special Trans Functions Theory (STFT). The mathematical genesis of the analytical closed-form solution is presented, and the structure of the theoretical derivation, proofs and numerical results confirm the validity and base principle of the STFT. Undoubtedly, the proposed analytical approach implies the qualitative improvement of the conventional analytical and numerical methods.

An inverse problem of temperature estimation for the combination of the linear and nonlinear resistances

The subject of the theoretical analysis presented in this paper is an analytical approach to the temperature estimation, as an inverse problem, for different thermistors – linear resistances structures: series and parallel ones, by the STFT - Special Trans Functions Theory (S.M. Perovich). The mathematical formulae genesis of both cases is given. Some numerical and graphical simulations in MATHEMATICA program have been realized. The estimated temperature intervals for strongly determined values of the equivalent resistances of the nonlinear structures are given, as well.

On the Exact Analytical Solutions of Certain Lambert Transcendental Equations

The subject matter of this paper is the Special Trans Functions Theory (STFT) in finding the exact analytical closed form solutions (the new special tran functions) of certain Lambert transcendental equations. Note that these Lambert transcendental equations frequently appear in applied physics and engineering domain. The structure of the theoretical derivations, proofs, and numerical results confirms validity and basic principles of the STFT. Undoubtedly, the proposed exact analytical approach implies the qualitative improvements of the conventional methods and techniques.

Determination of the solar cell junction ideality factor using special trans function theory (STFT)

This paper presents the use of properties of special trans function theory (STFT) for determining the ideality factor of real solar cell. The extracted values are compared with the calculated values obtained by other methods for proving its significance.

On the analytical solution of some families of transcendental equations

The problem of finding the exact analytical closed-form solution of some families of transcendental equations is studied, in some detail, by the Special Trans Function Theory (STFT). The mathematical genesis of the analytical closed-form solution is presented, and the structure of the theoretical derivation, proofs and numerical results confirm the validity and base principle of the STFT. Undoubtedly, the proposed analytical approach implies the qualitative improvement of the conventional analytical and numerical methods.