An investigation of the solution to the optimal power flow problem incorporating continuation methods

Abstract

This thesis analyzès and tests some néw solution techniques for the optimal power flow problem.This new methodology exploits a parametric technique, callp-d the continuation method, which is applied to different tasks in the solution procedure. In a first application, th'e continuation method l solves the-quadratic subp:t;oblems generàted sequentially by the optimal power This thesis first presents an analysis of the various structures used in optimal power flow algorithms. Then, having chosen and presented the structure of our algorithm, we analyze the quadratic subproblems generated by this algorithm for sorne of its more important tasks: minimum cost, minimum losses and load shedding. New rules are proposed to link the solutions of successive subproblems to erwure the convergence of the nonlinear problem.Then, as a final contribution to the theory, some extensions are suggested for the subproblems: among them are ramp constraints, bus incremental costs, and ~ provisioml for redf'spatching.Numerical simulations of the proposed optimal power flow algorithm using the minimum fuel cast task were performed 'on four test systems. with sizes•

A general parametric optimal power flow

“…Carpentier also published a very general paper conceming on-line operation of a power system, classifying and discussing important resuIts in the field [Carpentier, 1987]. Finally, a more recent paper by HuneauIt and Galiana [Huneault and Galiana, 1990] made a very thorough classification of the works published in the area until 1989. In addition, reviews regarding recent advances and trends in power system optimization and security control were published by Stott and colleagues [Stott et.…”

“…Since then, sustained research has been carried out in ED [Runeault andGaliana, 1990 andChowdhury andRahman, 1990]. In the c1assical load f10w formulation, the system incremental cost represents the minimal change in generation cost per unit change in the system total demand, with this demand located at the slack bus.…”

“…This can lead to difficulties for convergence. Many publications in linear programming applied to the OPF were presented between 1970 and 1980 [Huneault and Galiana, 1990], the best known being those of Stott and colleapes [Stott and Hobson, 1978 (a) and (h)]. In this work, a dual simplex approach is applied to the compact model of the linear active OPF.…”

Interior point based optimal voltage stability, oscillatory stability and ATC margin boundary tracing

“…Galiana et al [44][45][46][47][48] made significant contributions to the optimal power flow based on the homotopy type continuation method. It could trace the optimal solution along a certain load scenario with optimization formulated with power flow equations.…”

“…The above formulation is well established in the literature as an optimal power flow [45][46][47][48]. However our aim is to trace the voltage stability/oscillatory stability related margin boundaries that satisfy the optimal conditions defined in our problem simultaneously.…”