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Abstract Solving nonlinear equation systems (NESs) requires locating different roots in one run. To effectively deal with NESs, a multi-population cooperative teaching–learning-based optimization, named MCTLBO, is presented. The innovations of MCTLBO are as follows: (i) two niching technique (crowding and improved speciation) are integrated into the algorithm to enhance population diversity; (ii) an adaptive selection scheme is proposed to select the learning rules in the teaching phase; (iii) the new learning rules based on experience learning are developed to promote the search efficiency in the teaching and learning phases. MCTLBO was tested on 30 classical problems and the experimental results show that MCTLBO has better root finding performance than other algorithms. In addition, MCTLBO achieves competitive results in eighteen new test sets.

The accuracy of unknown parameters determines the accuracy of photovoltaic (PV) models that occupy an important position in the PV power generation system. Due to the complexity of the equation equivalent of PV models, estimating the parameters of the PV model is still an arduous task. In order to accurately and reliably estimate the unknown parameters in PV models, in this paper, an enhanced Rao-1 algorithm is proposed. The main point of enhancement lies in i) a repaired evolution operator is presented; ii) to prevent the Rao-1 algorithm from falling into a local optimum, a new evolution operator is developed; iii) in order to enable population size to change adaptively with the evolutionary process, the population size linear reduction strategy is employed. To verify the validity of ERao-1 algorithm, we embark a study on parameter estimation of three different PV models. Experimental results show that the proposed ERao-1 algorithm performs better than existing parameter estimation algorithms in terms of the accuracy and reliability, especially for the double diode model with RMSE 9.8248E-04, three diode model with RMSE 9.8257E-04 for the R.T.C France silicon cell, and 2.4251E-03 for the three diode model of Photowatt- PWP201 cell. In addition, the fitting curve of the simulated data and the measured data also shows the accuracy of the estimated parameters.

Photovoltaic (PV) parameter extraction plays a key role in establishing accurate and reliable PV models based on the manufacturer's current-voltage data. Owning to the characteristics such as implicit and nonlinear of the PV model, it remains a challenging and research-meaningful task in PV system optimization. Despite there are many methods that have been developed to solve this problem, they are often consuming a great deal of computing resources for more satisfactory results. To reduce computing resources, in this paper, an advanced differential evolution with search space decomposition is developed to effectively extract the unknown parameters of PV models. In proposed approach, a recently proposed advanced differential evolution algorithm is used as a solver. In addition, a search space decomposition technique is introduced to reduce the dimension of the problem, thereby reducing the complexity of the problem. Three different PV cell models are selected for verifying the performance of proposed approach. The experimental result is firstly compared with some representative differential evolution algorithms that do not use search space decomposition technique, which demonstrates the effectiveness of the search space decomposition. Moreover, the comparison results with some reported well-established parameter extraction methods suggest that the proposed approach not only obtains accurate and reliable parameters, but also uses the least computational resources.