Implementation of fractional-order electromagnetic potential through a genetic algorithm

Several phenomena present in electrical systems motivated the development of comprehensive models based on the theory of fractional calculus (FC). Bearing these ideas in mind, in this work are applied the FC concepts to define, and to evaluate, the electrical potential of fractional order, based in a genetic algorithm optimization scheme. The feasibility and the convergence of the proposed method are evaluated.

Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

Strategic Bidding in Electricity Markets: An agent-based simulator with game theory for scenario analysis

Electricity markets are complex environments, involving a large number of different entities, with specific characteristics and objectives, making their decisions and interacting in a dynamic scene. Game-theory has been widely used to support decisions in competitive environments; therefore its application in electricity markets can prove to be a high potential tool. This paper proposes a new scenario analysis algorithm, which includes the application of game-theory, to evaluate and preview different scenarios and provide players with the ability to strategically react in order to exhibit the behavior that better fits their objectives. This model includes forecasts of competitor players’ actions, to build models of their behavior, in order to define the most probable expected scenarios. Once the scenarios are defined, game theory is applied to support the choice of the action to be performed. Our use of game theory is intended for supporting one specific agent and not for achieving the equilibrium in the market. MASCEM (Multi-Agent System for Competitive Electricity Markets) is a multi-agent electricity market simulator that models market players and simulates their operation in the market. The scenario analysis algorithm has been tested within MASCEM and our experimental findings with a case study based on real data from the Iberian Electricity Market are presented and discussed.

Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.