Planejamento da expansão de sistemas de transmissão de energia elétrica baseado na relaxação sigmoidal de variáveis de decisão binárias e análise de sensibilidade por multiplicadores de Lagrange

Abstract

This paper presents the development of a heuristic algorithm to solve the Transmission System Expansion Planning (TSEP) problem. The binary decision variables associated with the decision to build transmission lines in the PEST problem are modeled by the image of a sigmoidal function, transforming the original Mixed Integer Nonlinear Programming (MINLP) problem into an equivalent Nonlinear Programming (NLP) problem whose local optima coincide with the feasible region of the original problem, allowing the use of commercial NLP solvers. In the proposed heuristic algorithm, the final investment plan is obtained after successive PEST resolutions with the sigmoidal relaxation of the binary expansion decision variables, followed by the accommodation of the relaxed solution into a mixed integer solution based on local sensitivity analysis by Lagrange multipliers. Moreover, reference data from the National Electric Energy Agency (ANEEL) are used to define the unit cost of expansion of the candidate transmission lines. The effectiveness of the developed heuristic algorithm is demonstrated through its application to Garver 6-bus, 24-bus IEEE and 46-bus South Brazilian systems.