Security-constrained economic dispatch using dual quadratic programming

Abstract

This paper presents a procedure for efficiently handling real power transmission constraints on branch flows and inter-area exchanges to supplement the classic economic dispatch (ED) formulation. A sequential quadratic programming (SQP) method is employed to solve the resulting non-linear programming problem. Each quadratic subproblem is approached by a dual programming technique — a dual feasible starting point is obtained by relaxing transmission limits; constraint violations are then enforced using the dual quadratic algorithm by Goldfarb and Idnani. The Hessian matrix of the Lagrangian function is approximated by a diagonal matrix thus keeping the objective function of each quadratic subproblem separable. Two versions of the proposed procedure exploit different assumptions in the evaluation of the sensitivities of the slack bus balance equation and of transmission constraints. For comparison purposes, the exact model of the security-constrained economic dispatch (SCED) is solved using a standard SQP algorithm taken from the NAG library. Tests on a CIGRE sample network and on actual medium and large-scale systems show that feasible and nearly optimal solutions of the SCED problem can be obtained. The proposed method presents limited computation times and a sufficiently good accuracy; it can be profitably employed whenever computation speed and algorithmic robustness are important issues as in real time operation to update the trajectories of thermal generations, as well as in system planning and hydro-thermal co-ordination studies.