Solar-cell models need parameters that manufacturer datasheets do not provide. This paper tackles that gap by combining particle-swarm exploration with rat-search exploitation, aiming to avoid local minima while estimating three- and four-diode models.

Accurate solar-cell modeling matters for solar photovoltaic energy systems, but it has two stages: formulating mathematical expressions and estimating cell parameters. The cell can be represented with single-diode, double-diode, or three-diode models, and the selected model determines which parameters must be estimated.

The paper emphasizes that these models contain five, seven, and nine estimated parameters, respectively, so finding their optimal values is essential for matching physical solar-cell outputs. Existing approaches include Lambert W-functions, least squares, and curve fitting, but deterministic methods have restrictions linked to differentiability and convexity.

Because deterministic techniques are highly sensitive to the initial solution, they tend to arrive at a local minimum rather than the global optimum. Heuristic methods are presented as an alternative, and the block describes them as nature-derived, population-based methods that can produce more accurate and robust results.

The surveyed alternatives include particle swarm optimization, genetic algorithms, teaching–learning optimization, cuckoo search, artificial bee colonies, Rao-1, and the Jaya algorithm. The literature survey identifies local minima as a problem for swarm-based algorithms, and presents hybridization as a way to eliminate that problem and increase efficiency.

Against that background, the paper aims to use a new parameter-estimation algorithm for three- and four-diode solar photovoltaic-cell models. The three-diode solar photovoltaic cell offers high curve-fitting accuracy and can determine different components of the solar-cell current.

Its disadvantage is that the modeling is extremely complex. The block also states that this model simulates the current–voltage characteristics of large-area silicon solar cells. Compared with single-, double-, and triple-diode equivalent-circuit models, the four-diode model is described as more accurate for industrial solar photovoltaic cells, with less error between experimental and calculated data.

The four-diode model is more accurate for curve fitting and performs well under standard test conditions, but its disadvantage is a high level of complexity. For industrial applications larger than 155.2 square centimeters and with 17.1 percent efficiency, the block says that Idc1 and Idc2 are not sufficient to represent different solar-cell parameters.

An optimization technique helps identify unknown parameters from experimental current–voltage data for the real system. For the four-diode solar-cell model, the optimization vector contains series resistance, shunt resistance, photocurrent, four reverse-saturation-current terms, and four ideality factors.

The parameters are estimated to minimize the error between measured currents and calculated currents, while the rewritten equations define the objective function. The paper compares particle swarm optimization, rat search algorithm, sine-cosine algorithm, grey wolf optimizer, and cuckoo search approaches with the PSORSA hybrid algorithm.

The parameters of polycrystalline photovoltaic cells are optimized using three-diode and four-diode equivalent models. This comparison is used to introduce the hybrid PSORSA method. PSORSA combines two algorithms for increased efficiency, using particle swarm optimization to enhance the precision of results achieved by the rat search algorithm.

Particle swarm optimization performs the exploration part, while the rat search algorithm conducts the exploitation section. The block identifies a tendency of swarm-based algorithms to become stuck in local minima, and states that the hybrid method is not trapped in local minimums and is enhanced in accuracy.

The method is also described as improving speed, finding the global optimum within reasonable time, and requiring no large amount of computational power. Figure four presents the PSORSA workflow: it initializes parameters for PSO and RAT, updates each search agent’s position, and checks whether the stopping criteria are met.

If not, the hybrid process repeats; if so, it produces a final solution by updating the best search agent when the new solution improves on the previous one. This matters because PSO is used for exploration while RAT supports exploitation, helping the hybrid method address local-minimum stagnation.

To validate the new algorithm, five benchmark test functions are selected from CEC 2019. The dimensions of these features are thirty and fifty, and the functions are identified as f one through f five CEC functions. Tables three and four report average and standard deviations for five benchmark tests at dimensions of thirty and fifty, respectively.

The findings from those tables show that the suggested approach is more efficient than the others, offering lower mean and standard-deviation values than the rest. The block concludes that the proposed algorithm offers greater convergence rate, robustness, precision, and performance compared with the other algorithms.

The parameter-extraction study compares two panels from Nemy and Solar World: the monocrystalline JP270M60 panel rated at 270 watts and the polycrystalline SW80RNA panel. The JP270M60 panel from Nemy has voltage at maximum power of thirty-one point one zero volts, current at maximum power of eight point six eight amperes, open-circuit voltage of thirty-eight point six zero volts, and short-circuit current of nine point two zero amperes.

The SW80RNA panel has voltage at maximum power of 17.90 volts, current at maximum power of 4.49 amperes, open-circuit voltage of 21.90 volts, and short-circuit current of 4.78 amperes. Series resistance ranges from zero to zero point five ohms, shunt resistance from zero to one hundred ohms, and the four ideality factors from one to two.

Table six reports the fitted unknown parameters for a three-diode model under six algorithms: PSO, CSA, SCA, RSA, GWO, and PSORSA. It lists photovoltaic current, ideality factors, series and shunt resistance, three saturation-current terms, and RMSE, allowing the parameter sets and error values to be compared directly.

The reported RMSE values range from seven point three two times ten to the power of minus one to three point five four times ten to the power of minus eleven. Table 7 reports the estimated unknown parameters of a four-diode solar-panel model for six algorithms: PSO, CSA, SCA, RSA, GWO, and PSORSA.

It lists photovoltaic current, diode ideality factors, series and shunt resistance, four reverse-saturation currents, and the resulting RMSE, allowing the authors to compare both fitted model parameters and error values. The table matters because it provides the numerical basis for evaluating how these optimization methods characterize the solar-panel model.

For the Nemy monocrystalline panel, the paper discusses parameter extraction for both three-diode and four-diode models, with unknown parameters and root mean square error shown in Tables six and seven. The paper states that the hybrid algorithm is much better than the algorithm in this study, and that it is superior to the standalone algorithm in convergence time, reliability, and memory requirements.

The paper further states that the hybrid algorithm is more effective than the other standalone algorithms after the Friedman ranking test and Wilcoxon’s rank sum test. Figure five compares the root mean square error, or RMSE, for three-diode and four-diode solar-panel models in the mono-crystalline Nemy case.

The chart reports results for PSO, CSA, SCA, RSA, GWO, and PSORSA, with separate bars for each model. This visual matters because, together with Tables six and seven, it supports the authors’ assessment of parameter-extraction accuracy for the two model structures.

For the Solar World polycrystalline panel, the paper presents model-parameter analyses for three-diode and four-diode models, with unknown parameters and corresponding root mean square error in Tables ten and eleven. Figure six shows the root mean square error calculated for both models, and the paper states that the table and figure show the proposed hybrid algorithm outperforming the compared algorithm by a wide margin.

The paper also states that the hybrid algorithm outperforms the standalone algorithm in convergence time, reliability, and memory usage, with Friedman and Wilcoxon tests conducted afterward. Figure six reports the root mean square error, or RMSE, for three-diode and four-diode models across PSO, CSA, SCA, RSA, GWO, and PSORSA.

The chart provides a direct visual comparison of parameter-extraction error for the Solar World poly-crystalline panel, complementing the detailed values reported in the paper’s tables. This matters because RMSE quantifies how closely each model reproduces the observed solar-cell behavior.

Table 9 reports Wilcoxon rank-sum test values for PSORSA compared with three-diode and four-diode solar models, across PSO, CSA, SCA, RSA, and GWO. For the three-diode model, the reported values range from eight point six nine times ten to the power of minus twelve to nine point five four times ten to the power of minus twelve; for the four-diode model, they range from eight point three two times ten to the power of minus twelve to nine point five four times ten to the power of minus twelve.

The authors use these tests to support comparison of the hybrid algorithm with the standalone algorithms. The proposed PSORSA algorithm combines particle swarm optimization and rat search algorithm to balance exploration and exploitation, and it incorporates opposition-based learning to increase demographic diversity.

The study focuses on the Nemy JP270M60 and Solar World SW80RNA solar photovoltaic models, using three- and four-diode mathematical equivalent models. The paper’s central result is that PSORSA reports lower error and stronger comparative performance than the tested standalone algorithms for two solar-panel models, although the evidence is based on the paper’s stated benchmark and statistical comparisons.