Newton- Raphson Method and Algorithm in the Extraction for the Parameters of Solar Cell

Clean, quiet, and widely available, solar energy may be harnessed for use in power generation via the solar thermal process or converted directly into electricity by a photovoltaic system. Even while solar photovoltaic systems have seen rapid expansion in recent decades, their low efficiency and reliance on favorable weather conditions mean that researchers need to find new ways to make the most of the energy they generate. Because of this, The accuracy of simulation is highly dependent on PV factors that are not published in manufacturers' data sheet, therefore modelling the proposed photovoltaic (PV) system before actual installation is necessary to offer accurate forecasts for planning reasons. Several methods for extracting PV parameters have been published and categorized, including analytical methods, numerical methods, and evolutionary methods. Analytical methods rely on mathematical equations to find answers; they are fast, produce answers that are close to correct, take less time to compute, and may be found with as little as one round of iteration. In the instance of the Rp-model, which includes five unknowns, however, they may not be able to find a solution since there are too many parameters that are not known. A numerical extraction strategy based on some methodology may be used to fit the spots on the PV characteristic curve. The method is comprehensive in that it considers every value along the characteristic curve, it yields more precise results than the analytical approach. Numerical methods like Newton Raphson have the basic drawbacks of requiring a large amount of computation for convergence and producing unreliable results as the number of parameters to be evaluated grows and as close approximation of initial circumstances is needed. The inaccuracies in estimating PV parameters using analytical or iterative approaches may be mitigated by using Evolutionary algorithms instead. Inspired by the natural processes of evolution, evolutionary algorithms make incremental improvements over time. Now, standard evolutionary methods like artificial bee colony (ABC), particle swarm optimization (PSO), genetic algorithm (GA), simulated annealing (SA), etc. are used for parameter extraction of PV modules. Perovskite, a mineral discovered by a Russian mineralogist named L.A. Perovski, with the formula ABX3. The six X anions in the octahedral position stabilise the smaller B cation, whereas the twelve X anions in the cubo-octahedral site support the larger Acation. Oxide perovskites, because to their ferroelectricity or superconductivity, have been the focus of the majority of the study. Halide perovskites were largely disregarded till it was discovered that they underwent a semiconductor-to-metal transition when their dimensionality was increased via stacking organometal halide perovskites. There were shifts in electrical characteristics as well as a narrowing of

Tummala, Ayyarao (2020) If you want to know how well your solar photovoltaic power system is doing, you'll need a mathematical model with very specific characteristics. This technical paper introduces a novel method for precisely predicting solar PV system characteristics. In contrast, nonlinear equations are solved using the NR approach in order to compute the objective function. Most algorithms estimate parameters using an objective function that ignores nonlinearities in I-V characteristics and is thus very inaccurate. The accuracy of such models may be too low for use in critical situations. The work presented here formulates an objective function that, when applied to the corresponding PV models, results in more precise parameters without ignoring nonlinearities. Parameters for the SDM, DDM, and PV module are estimated using the suggested technique. Results from various state-of-the-art algorithms are compared with the proposed QANO method to gauge its effectiveness. The suggested technique outperforms the majority of currently available algorithms, with an RMSE of 7.7300630E-04 for SDM and 7.5248E-04 for DDM, respectively. Nunes, Hugo & Pombo, José & Mariano, Silvio & Calado, Maria Do Rosário. (2020) When metaheuristics are used, the output current is calculated using LWF and NRM, which are examples of indirect techniques, rather than the most popular way in the literature, the output current can be solved in a straightforward manner (DirectSolve). To do this, we estimated the PV parameters of the single-diode model using the GSK optimization method (SDM). In the study, both typical and experimentally measured datasets were included, as were a variety of operational settings. When taking into account LWF or NRM, the findings produced from both the indirect and direct methods were shown to be accurate and reliable. When comparing computational efficiency, LWF was 0.11 percentage points better than NRM on average. DirectSolve was, on average, 35% less accurate than indirect methods. Results demonstrated that LWF and NRM provide highly comparable performances in estimating PV parameters, with only minor differences in computing costs. Gnetchejo, Patrick & Salomé, Ndjakomo & Dadje, Abdouramani & Ele, Pierre. (2021) Standard PV cells cannot be designed without first extracting relevant parameters. Heuristic algorithms have been shown to be the most efficient approach for determining the values of parameters. This paper's goal is to demonstrate that integrating heuristics algorithms with the Newton Raphson technique significantly improves the reliability of the obtained outcomes. The optimal constitutive parameters may be extracted with the use of a suggested artifact approach based on data from a control center simulation of a drone squadron. At the of the top 10 heuristic methods currently available for PV estimate is performed. In addition, the convergence of algorithms under varying current-voltage characteristics is explored. This research indicates the greatest formulation accuracy and sheds insight on the key distinctions between the two formulations. Exact PV module parameters were extracted from the findings obtained from seven examples addressed in this research, using a combination of the Newton Raphson performance approach and Drone Squadron optimisation. Analyzing the point count, we find that fewer points on the I-V axis leads to faster convergence and better accuracy from the algorithm. On the other hand, if these data points are sparse, the algorithm will be hampered in its ability to provide desirable outcomes.

Reza, M. Nahid & Mominuzzaman, Sharif (2018) Parameters in the equivalent circuit are crucial for modeling the behavior of a perovskite solar cell in order to find the optimal operating conditions. Extraction of these characteristics for perovskite solar cells is currently a topic of little scientific interest. Using the Newton-Raphson technique, the authors of this paper extract the device characteristics of a perovskite solar cell that incorporates carbon nanotubes. These factors are used to investigate the cell structure and the impact of inserting carbon nanotubes into various layers of the perovskite solar cell.

Electronic equivalent circuit of a solar cell is shown in Figure 1 (neglecting Rs and Rsh).

Based on this equivalency, we can get the complete equation for the current in the solar cell by using Kirchhoff's current law (KCL). I= Iph-ID (1)

(2) (3)

where: I0, Iph, I measured in Ampere: the current in the cell, the photocurrent, and the reverse saturation current. In addition, the thermic voltage= 26 mV and the cell voltage's VPV are provided. Recombination factor about (1

(5)

Put Eq. 4 in Eq. 5 yield

(6)

Where: Is reverse saturation current=10-12 A. In a similar vein, VD=Vpv=V. Obtaining the numerical roots of Vpv requires the derivative of Eq. 6.

The Newton–Raphson technique is an iterative procedure that begins with a first estimation of the value of the function f(x) to be estimated. To acquire this technique, we use the Taylor series expansion in (x- x0) as shown below. Let's pretend the first estimate is quite close to the correct root. In this case, the difference between (x - x0) is small enough that only the first terms matter term.

(7)

Equation (7) and the accompanying picture (9) may be used to provide numerical and visual representations of this (7).

(8)

The Newton Raphson Method is guaranteed to converge for the interval [a,b] that contains the root of f(x) if f(x) and f'(x) are continuous in this interval and f()= 0, where is the root of f(x). For the purpose of solving Eq. 6, the following approach is proposed utilizing NRM.

Technique 1 (NRM) and the suggested method have been utilized to evaluate and contrast the various numerical methods of iterations (2SM). Along with showing how well the new approach works, we also solved Eq. 6 to check for numerical consistency and stability. Some iteration is used to analyze the obtained findings.

The manufacturer lists the following features of the photovoltaic module's technical specifications: As shown in Figure 3, a photovoltaic module's maximum power (PMP) is achieved when its maximum power current (IMP) and maximum power voltage (VMP) are both measured. The open circuit voltage VOC is measured when the module is not under any load, and the short circuit current (ISC) is measured when the module is shorted.

Tables with varied values of load resistance of the proposed circuit show the results of nonlinear Eq. 6 in the PV single diode model is solved using NRM and 2SM, two numerical approaches.

In Table 1, with an initial value of x0=1, it is fascinating to see that the NRM technique converges to the root 0.922423135 at the 9th iteration, whereas the suggested method in Eq. 6 converges to the same approximate root 0.922423135 at the 7th iteration. The PV parameters derived using NRM and 2SM are shown in Figure 4.

Since the results achieved by the proposed strategy are closer to the original approximation, it works better with this kind of model. It is well known that the best approximation to an exact root is generally closer to the beginning value. Additionally, the suggested approach 2SM seems to need less rounds. The following outcomes were found after testing the Octave-built program:

Several educated estimates were made throughout the simulation runs, some of which eventually led to a solution and others which did not. As can be seen in Tables 3 and 4, fewer iterations were produced when the original estimate was closer to the root.

A simulation of the related curves was performed using the data in table 4. In Figure 5 and Figure 6, we see the link between current and voltage in both the actual world and in a computer simulation. The simulated curves can be shown to pass through all five of the problem's initial points, indicating that they are a close approximation to the true curve. The connection between power and voltage is seen in Figures 7 and 8. The simulated curves are similar in form to the actual curve and can be seen to have reached the locations of greatest power.

Knowledge of the desired approximation value is required for success with the Newton Raphson approach, since the first estimate must be quite near to the actual answer for the procedure to work. The Jacobian matrix that is calculated at each iteration must satisfy this condition, therefore understanding it is crucial.

We can say that non-linear equation of a solar cell was solved numerically using two-step and Newton's techniques. Different levels of the load resistance are used to test the procedures, and they have shown to be effective. Since approximative answers may be generated with just a few calculations using MATLAB, the computational procedure in these approaches is straightforward. This method is therefore quite effective. The success of the suggested strategy is determined on the value of x0 chosen at the outset. The parameters calculated from the VxI curve using the method proposed in this research matched the actual curve obtained from the solar module well. The Newton Raphson approach may be used to solve issues involving nonlinear equations in a wide range of scientific disciplines. However, as shown in this study, convergence cannot be attained without prior knowledge of a range of values near to the solution. In conclusion, this study provides a quick and easy mathematical

1. Tummala, Ayyarao. (2020). Parameter estimation of solar PV models with quantum-based avian navigation optimizer and Newton–Raphson method (Accepted). Journal of Computational Electronics. 21. 10.1007/s10825-022-01931-8. 2. Nunes, Hugo & Pombo, José & Mariano, Silvio & Calado, Maria Do Rosário. (2020). Newton-Raphson method versus Lambert W function for photovoltaic parameter estimation. 1-6. 10.1109/EEEIC/ICPSEurope54979.2020.9854525. 3. Gnetchejo, Patrick & Salomé, Ndjakomo & Dadje, Abdouramani & Ele, Pierre. (2021). A combination of Newton-Raphson method and heuristics algorithms for parameter estimation in photovoltaic modules. Heliyon. 7. e06673. 10.1016/j.heliyon.2021.e06673. 4. Sriabisha, R. & Hariharan, R.. (2020). High efficiency perovskite solar cell. Materials Today: Proceedings. 33. 10.1016/j.matpr.2020.05.031. 5. Reza, M. Nahid & Mominuzzaman, Sharif. (2018). Extraction of Equivalent Circuit Parameters for CNT incorporated Perovskite Solar Cells Using Newton-Raphson Method. 10.1109/ICECE.2018.8636738. 6. P. Rodrigues, J. R. Camacho, and F. B. Matos ―The application of Trust Region Method to estimate the parameters of photovoltaic modules through the use of single and double exponential models‖, in International Conference on Renewable Energies and Power Quality (ICREPQ), 2011. 7. P. Rodrigues, ―The extraction of parameter of photovoltaic panels from the solution of a non-linear equation system through thrust region techniques‖. MSc Dissertation. Universidade Federal de Uberlândia, Uberlândia, Minas Gerais, Brazil, 2012, 117p. (In portuguese) 8. Shivananda Pukhrem,―A Photovoltaic Panel Model in Matlab/Simulink‖, Wroclaw University of Technology (2013). 9. R. Zilles, W. N. Macêdo, M. A. B. Galhardo and S. H. F. Oliveira, ―Photovoltaic systems connected to the grid‖, Workshop Texts, 2012, 208p. (In portuguese) 10. J.T. Pinho, and M.A. Galdino, ―Photovoltaic Systems Engineering Manual‖, CEPEL-

Research Scholar, Shri Krishna University, Chhatarpur M.P.