Around the world, countries are integrating photovoltaic generating systems to the grid to support climate change initiatives. However, solar power generation is highly uncertain due to variations in solar irradiance level during different hours of the day. Inaccurate modelling of this variability can lead to non-optimal dispatch of system resources. Therefore, accurate characterization of solar irradiance patterns is essential for effective management of renewable energy resources in an electrical power grid. In this paper, the Weibull distribution based probabilistic model is presented for characterization of solar irradiance patterns. Firstly, Weibull distribution is utilized to model inter-temporal variations associated with reference solar irradiance data through moving window averaging technique, and then the proposed model is used for irradiance pattern generation. To achieve continuity of discrete Weibull distribution parameters calculated at different steps of moving window, Generalized Regression Neural Network (GRNN) is employed. Goodness of Fit (GOF) techniques are used to calculate the error between mean and standard deviation of generated and reference patterns. The comparison of GOF results with the literature shows that the proposed model has improved performance. The presented model can be used for power system planning studies where the uncertainty of different resources such as generation, load, network, etc., needs to be considered for their better management.

In this article, we applied a new technique for solving the time-fractional coupled Korteweg-de Vries (KdV) equation. This method is a combination of the natural transform method with the Adomian decomposition method called the natural decomposition method (NDM). The solutions have been made in a convergent series form. To demonstrate the performances of the technique, two examples are provided.

In industrial devices like heat recovery systems, heat pumps, as well as symmetric and complex engineering systems, a nano fluid mixture is used. Regarding the nature of the energy sources (thermal or thermal and electrical), many physical systems could represent possible applications in manufactural activities. The presence of nanoparticles inside a solvent is of great interest in order to optimize the efficacy of the nano-technology systems. The present work deals with heat and mass transfer through a vertical channel where an alumina/water film mixture flows on one of its plates. For simulation, we use a numerical method under mixed convection during water/alumina nano fluid evaporation. We heat the flown plate uniformly while the other is dry and exchange heat with a constant coefficient. The gas mixture enters channel with a constant profile. Results show that an augmentation of the volume rate of the nanoparticle disadvantages evaporation if the heating is absent. Otherwise, if the heating exists, an increasing volume rate of the nanoparticle advantages evaporation. We found also that the film velocity behavior when the volume rate of the nanoparticle varies, independent of the heating.

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In this paper, the coupled system of Whitham–Broer–Kaup equations of the Caputo fractional derivative (CFD) is studied using the Sumudu decomposition method (SDM). Using different dispersion relations, these equations are needed to describe the properties of waves in shallow water. The current investigation for the future scheme includes convergence and error analysis. We use two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to ensure its accuracy. The numerical simulation is carried out to ensure the accuracy of the future technique. The obtained numerical and graphical results are presented, and the proposed scheme is computationally very accurate and simple to study and solve fractionally coupled nonlinear complex phenomena encountered in science and technology.