A sequential ℓ<inf>1</inf> quadratic programming method for robust nonlinear optimal power flow solution

Abstract

Large-scale nonlinear optimal power flow (OPF) problems have been solved lately by primal-dual interior point (IP) methods. In spite of their success, there are many situations in which IP-based OPF programs can fail to find a solution. On the other hand, with power systems operating heavily loaded there is an increasing need for globally convergent OPF solvers. Trust region schemes have been used to enforce convergence, but they are by nature computationally expensive. This paper aims at developing a trust region OPF algorithm less expensive than the one proposed by Sousa et al. The major difference lies in how they handle inconsistent constraints in the solution of the trust region subproblems. The algorithm proposed here employs a sequential ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> quadratic programming (S ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> QP) approach, while the one of Sousa et al. employs the Byrd-Omojokun technique. Thus, rather than solving two quadratic programming (QP) problems per iteration as in the Byrd-Omojokun technique, the Sℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> QP approach solves a single, but slightly larger, QP problem. The developed algorithm is tested on the IEEE test systems of up to 300-bus, with all QP problems solved by primal-dual IP algorithms. The numerical results indicate that the Sℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> QP method is competitive in processing time when compared to the Byrd-Omojokun approach.