Search

In recent decades, because of the speedy progress of the smart grid and the deepening of the reforms of the energy system, demand-side users can contribute to the collaboration of the energy network, with the main right to public energy procurement and the main right to sell energy. The demand side of the smart grid and the open energy market provides users with more adoptions, and game theory is expected to become an important tool for optimizing multi-stakeholder decision-making and solving many problems in this area. In this regard, this review article first reviews the recent development of game theory application in modern power systems, in addition to discussing in detail the typical gaming behavior of the current energy demand side. Second, it focuses on the application of game theory mainly in three aspects: distributed energy users, high-energy energy users, and medium- and low-energy users. Game theory is used in optimizing the distributed energy coordination, optimizing the energy purchasing strategy, responding to the needs of commercial and residential users, and ensuring network communication. Later, a comprehensive analysis of recent trends in game theory application in power systems is carried out in detail.

This article extracts stochastic soliton waves for the perturbed nonlinear Schödinger’s equation (PNLSE) forced by multiplicative noise through the Itô sense by utilizing two unified solver methods. The presented solutions involve three types: rational function, trigonometric function, and hyperbolic function solutions. These stochastic solutions are critical for studying numerous complicated phenomena in heat transfer, new physics, and many other fields of applied science. We demonstrate the effect of multiplicative noise on the solution of the stochastic PNLSE, which have never been studied before. The study and acquired solutions clarify that the unified solver technique is sturdy and efficient. Finally, several 2D and 3D graphs for selected solutions are shown.

In a current article, two novel analytical approaches are compared for analytical analysis of wave like equations with variable coefficients, which describe the evolution of stochastic phenomena. One is the New Approximate Analytical Method which based on Caputo–Riemann operator with simple decomposition procedure. This new method directly provides a fractional order series form solution which fastly converge to exact form solution for integer order. The second is Mohand Variational Iteration Transform Method which base on iteration procedure with Mohand Transform. The Mohand Variational Iteration Transform Method provides series form solution without using any decomposition, discretization, and He’s polynomial. The solution in series form converges directly to the exact solution for integer orders. The comparative analysis validates that Mohand Variational Iterative Method has less computational work and simple procedure without using any decomposition, discretization, and He’s polynomial procedure as compared to New Approximate Analytical Method.