Stochastic Optimal Selection and Analysis of Allowable Photovoltaic Penetration Level for Grid-Connected Systems Using a Hybrid NSGAII-MOPSO and Monte Carlo Method

Abstract

Generally, the main focus of the grid-linked photovoltaic systems is to scale up the photovoltaic penetration level to ensure full electricity consumption coverage. However, due to the stochasticity and nondispatchable nature of its generation, significant adverse impacts such as power overloading, voltage, harmonics, current, and frequency instabilities on the utility grid arise. These impacts vary in severity as a function of the degree of penetration level of the photovoltaic system. Thus, the design problem involves optimizing the two conflicting objectives in the presence of uncertainty without violating the grid’s operational limitations. Nevertheless, existing studies avoid the technical impact and scalarize the conflicting stochastic objectives into a single stochastic objective to lessen the degree of complexity of the problem. This study proposes a stochastic multiobjective methodology to decide on the optimum allowable photovoltaic penetration level for an electricity grid system at an optimum cost without violating the system’s operational constraints. Five cutting-edge multiobjective optimization algorithms were implemented and compared using hypervolume metric, execution time, and nonparametric statistical analysis to obtain a quality solution. The results indicated that a Hybrid NSGAII-MOPSO had better convergence, diversity, and execution time capacity to handle the complex problem. The analysis of the obtained optimal solution shows that a practical design methodology could accurately decide the maximum allowable photovoltaic penetration level to match up the energy demand of any grid-linked system at a minimum cost without collapsing the grid’s operational limitations even under fluctuating weather conditions. Comparatively, the stochastic approach enables the development of a more sustainable and affordable grid-connected system.