Optimization and Engineering

, Volume 16, Issue 1, pp 49–71 | Cite as

Solving security constrained optimal power flow problems by a structure exploiting interior point method

Article

Abstract

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.

Keywords

SCOPF Interior point methods Structure exploitation iterative methods Preconditioner 

Notes

Acknowledgments

We are grateful to the anonymous referees and the journal editors, whose many useful suggestions have significantly improved the paper.

References

  1. Alsac O, Stott B (1974) Optimal load flow with steady-state security. IEEE Trans PAS 93(3):745–751. doi: 10.1109/TPAS.1974.293972 CrossRefGoogle Scholar
  2. Alsac O, Bright J, Prais M, Stott B (1990) Further development in lp-based optimal power flow. IEEE Trans Power Syst 5(3):697–711CrossRefGoogle Scholar
  3. 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
  4. Capitanescu F, Glavic M, Ernst D, Wehenkel L (2007) Interior-point based algorithms for the solution of optimal power flow problems. Electr Power Syst Res 77(5–6):508–517. doi: 10.1016/j.epsr.2006.05.003 CrossRefGoogle Scholar
  5. Carpentier J (1962) Contribution à à l’Étude du dispatching Économique. Bulletin de la Société Françise des Électricit 3:431–447Google Scholar
  6. Dommel H, Tinney W (1968) Optimal power flow solutions. IEEE Trans PAS 87:1866–1876CrossRefGoogle Scholar
  7. Golub GH, van Loan CF (1983) Matrix computations. North Oxford Academic, OxfordMATHGoogle Scholar
  8. Gondzio J, Grothey A (2009) Exploiting structure in parallel implementation of interior point methods for optimization. Comput Manag Sci 6(2):135–160CrossRefMATHMathSciNetGoogle Scholar
  9. 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
  10. Kelley CT (1995) Iterative methods for linear and nonlinear equations. Frontiers in applied mathematics, vol 16. SIAM, PhiladelphiaGoogle Scholar
  11. Kirschen DS, Strbac G (2004) Fundamentals of power system economics. Wiley, HobokenGoogle Scholar
  12. 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
  13. 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
  14. Quintana V, Torres G, Medina-Palomo J (2000) Interior-point methods and their applications to power systems: a classification of publications and software codes. IEEE Trans Power Syst 15(1):170–176. doi: 10.1109/59.852117 CrossRefGoogle Scholar
  15. Stott B, Jardim J, Alsaç O (2009) DC power flow revisited. IEEE Trans Power Syst 24:1290–1300CrossRefGoogle Scholar
  16. Trodden PA, Bukhsh WA, Grothey A, McKinnon KIM (2013) MILP formulation for controlled islanding of power networks. Int J Electr Power Energy Syst 45(1):501–508CrossRefGoogle Scholar
  17. Wei H, Sasaki H, Yokoyama R (1996) An application of interior point quadratic programming algorithm to power system optimization problems. IEEE Trans Power Syst 11(1):260–266. doi: 10.1109/59.486104 CrossRefGoogle Scholar
  18. Wright SJ (1997) Primal-dual interior-point methods. Society for Industrial and Applied Mathematics (SIAM), PhiladelphiaGoogle Scholar
  19. Zimmerman RD, Murillo-Sanchez CE, Thomas RJ (2011) MATPOWER: steady-state operations, planning and analysis tools for power systems research and education. IEEE Trans Power Syst 26(1):12–19CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.Argonne National LaboratoryLemontUSA

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