Solving security constrained optimal power flow problems by a structure exploiting interior point method
- 283 Downloads
In this paper we present a new approach to solve the DC (n − 1) security constrained optimal power flow (SCOPF) problem by a structure exploiting interior point solver. Our approach is based on a reformulation of the linearised SCOPF model, in which most matrices that need to be factorized are constant. Hence, most factorizations and a large number of back-solve operations only need to be performed once. However, assembling the Schur complement matrix remains expensive in this scheme. To reduce the effort, we suggest using a preconditioned iterative method to solve the corresponding linear system. We suggest two main schemes to pick a good and robust preconditioner based on combining different “active” contingency scenarios of the SCOPF model. These new schemes are implemented within the object-oriented parallel solver (OOPS), a structure-exploiting primal-dual interior-point implementation. We give results on several SCOPF test problems. The largest example contains 500 buses. We compare the results from the original interior point method (IPM) implementation in OOPS and our new reformulation.
KeywordsSCOPF Interior point methods Structure exploitation iterative methods Preconditioner
We are grateful to the anonymous referees and the journal editors, whose many useful suggestions have significantly improved the paper.
- Altman A, Gondzio J (1999) Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization. Optim Methods Softw 11/12(1–4):275–302Google Scholar
- Carpentier J (1962) Contribution à à l’Étude du dispatching Économique. Bulletin de la Société Françise des Électricit 3:431–447Google Scholar
- Karoui K, Platbrood L, Crisciu H, Waltz R (2008) New large-scale security constrained optimal power flow program using a new interior point algorithm. In: Electricity market (EEM) 2008. 5th international conference on European, pp 1–6. doi: 10.1109/EEM.2008.4579069
- Kelley CT (1995) Iterative methods for linear and nonlinear equations. Frontiers in applied mathematics, vol 16. SIAM, PhiladelphiaGoogle Scholar
- Kirschen DS, Strbac G (2004) Fundamentals of power system economics. Wiley, HobokenGoogle Scholar
- Petra C, Anitescu M (2010) A preconditioning technique for Schur complement systems arising in stochastic optimization. Technical report of Argonne National Laboratory, Argonne, IL, to appear in computational optimization and applications, preprint ANL/MCS-P1748-0510Google Scholar
- Qiu W, Flueck A, Tu F (2005) A new parallel algorithm for security constrained optimal power flow with a nonlinear interior point method. In: Power engineering society general meeting, 2005, IEEE, vol 1, pp 447–453. doi: 10.1109/PES.2005.1489574
- Wright SJ (1997) Primal-dual interior-point methods. Society for Industrial and Applied Mathematics (SIAM), PhiladelphiaGoogle Scholar