Semidefinite programming applied to electric power systems optimization

Abstract

Semidefinite programming is a convex optimization technique, that minimizes a linear objective function while constraining a symmetric matrix of variables to be positive semidefinite (i.e., all eigenvalues are constrained to be non-negative). Solution techniques for semidefinite programming guarantee global optimality in polynomial time, which cannot generally be achieved with traditional algorithms used in non-linear programming problems. When the semidefinite relaxation is "tight" (i.e., zero relaxation gap exists between solutions to the classical non-linear programming problem and the semidefinite relaxation), an optimal solution can be recovered. Conversely, when the semidefinite relaxation is not "tight" (i.e., the solution has non-zero relaxation gap), the solution from the semidefinite program provides a lower bound on the optimal objective value. On the other hand, optimization tools applied in electric power system area are becoming increasingly essential to support the complex task of efficiently providing electricity. The electric power system areas where these optimization tools are needed include power system operation, analysis, scheduling, and energy management. For these problems, is require the study of the objective function, decision variables and constraints of the resulting non-convex large-scale non-linear programming problems. In this sense, the semidefinite programming is presented as an efficient relaxation method to obtain optimal solutions of the theses non-linear programming problems in polynomial times.Therefore, from scientific and technological perspectives, the objective of this research project consists in developing optimization models based on semidefinite programming to solve planning and operation problems of the electric power systems. With respect to the international research center and supervisor, it can be highlighted that Dr. Bala Venkatesh, full professor at Ryerson University and Academic Director of the Centre for Urban Energy (CUE), leads a Canadian research group studying optimization applications for electrical energy systems, through of research project "Power Systems Analysis and Optimization". Thus, from the strategic viewpoint, these facts increase the chances of successfully accomplishing this project and of implementing a long-term scientific and technological collaboration between the universities, research centers and Brazilian and Canadian productive sectors. In fact, this long-term collaboration is the main strategic objective of this proposal. (AU)