Pré-despacho hidrotérmico de potência ativa e reativa via método dos Pontos Interiores e coordenadas retangulares

Abstract

Hydro-thermal scheduling of active e reactive power generation using rectangular form and Interior Points Method This article presents the mathematical formulation of the active and reactive power generation pre-dispatch problem, whose objective function is the minimization of thermal plant costs and transmission losses. Bus voltages are represented in rectangular coordinates, transmission limits are imposed through linearized constraints and the optimization problem is solved by the Primal Dual Interior Point Method. The efficiency of the formulation is analyzed in a 5 buses example and an equivalent of the Paraná system composed of 291 buses. RESUMOEste artigo apresenta a formulação matemática de um problema de pré-despacho de geração de potência ativa e reativa no qual a função objetivo engloba minimização dos custos de usinas térmicas e minimização das perdas elétri-cas na transmissão. A representação do fasor tensão é feita em coordenadas retangulares, consideram-se os limites de transmissão utilizando a formulação linearizada e o problema de otimização é resolvido pelo Método de Pontos Interiores versão Primal-Dual. A eficiência da formulação é testada utilizando-se o sistema de 5 barras e o sistema de 291 barras que representa o sistema elétrico reduzido do estado do Paraná.

Multiperiod Optimum Power Flow for Active Distribution Networks With Provisioning of Ancillary Services

“…The formulation proposed for the present work was based on [21] that minimizes the system power losses and costs in a hydrothermal pre-dispatch problem, implementing an MPOPF solved using Interior Points Method with a Primal-Dual Version. Works developed by [25] follow the same approach considering it for a distribution system with the insertion of distributed energy resources as distributed generation, batteries, and electric vehicles.…”

“…The active and reactive power injections are represented as a function of x and a [21]: P(x,a) and Q(x,a), respectively. The active and reactive power balance equations are:…”

“…In sequence, the Karush-Kuhn-Tucker (KKT) conditions that express the first optimality conditions of the optimization problem are resolved by the application of Newton's method to obtain the solution of the non-linear equations (KKT). This method was selected due to its good performance obtained to solve traditional OPF [21], [25].…”

“…In addition, operational constraints are defined by equalities and inequalities expressions representing the operative limits of the grid and the considered equipment. The MPOPF is solved by the Interior-Points Method [18]- [21] in a Primal-Dual version completely implemented in Python language, without use any solver.…”