Fractional‐order dynamical model for electricity markets

Abstract

In this article, we use a generalized system of differential equations of fractional-order to incorporate memory into an electricity market model. By using this idea, essential information from the past, such as the behavior of market participants, namely, suppliers and consumers, can be used and have impact on future decisions. We construct the fractional-order dynamical model, study its solutions, and provide closed formulas of solutions. Finally, we provide an application by using the proposed formula of solutions as well as a numerical example which also compares the proposed model with a conventional, integer-order electricity market model. Results indicate that the inclusion of memory leads market participants to adopt a conservative behavior.

Robust fractional order singular Kalman filter

“…Analysis and design of fractional order singular (FOS) systems (also known as fractional descriptor models) have received increasing attention in the literature. These types of systems are frequently encountered in the modeling of biological systems, 1 power systems, 2 and electricity markets 3,4 . The FOS formulation not only includes the usual fractional state‐space system description but also describes some dynamical behavior of systems for which there is no state‐space formulation 5 …”

“…These types of systems are frequently encountered in the modeling of biological systems, 1 power systems, 2 and electricity markets. 3,4 The FOS formulation not only includes the usual fractional state-space system description but also describes some dynamical behavior of systems for which there is no state-space formulation. 5 Intensive studies have been carried out on FOS systems concerning solvability 6 and stability 7 properties thereof, and also observer design.…”

On the relations between a singular system of differential equations and a system with delays

“…Some interesting results have also been obtained for singular systems of equations evolving fractional operators, see [1,6,9,11,13,15,29,34]. This type of systems appear in control theory, see [3,10,33], and in several applications in electrical engineering such as the modeling of electrical circuits, see [20], electricity markets, see [14], and power system dynamics, see [28,32].…”