Convex Relaxations of Security Constrained AC Optimal Power Flow under Uncertainty

Andreas Venzke, Spyros Chatzivasileiadis

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System operators have to ensure an N-1 secure operation, while dealing with higher degrees of uncertainty. This paper proposes a semidefinite relaxation of the chance and security constrained optimal power flow (SCOPF). Our main contributions are the introduction of systematic methods to obtain zero relaxation gap, providing a tractable chance constrained SCOPF formulation, and addressing scalability. We introduce a systematic procedure to obtain zero relaxation gap
using a penalty term on power losses. To achieve tractability of the joint chance constraint, a piecewise affine approximation, and a combination of randomized and robust optimization is used. To address scalability, we propose an iterative solution algorithm to identify binding constraints, and we apply a chordal decomposition of the semidefinite constraints. We demonstrate the performance of our approach on IEEE 24 and IEEE 118 bus system using realistic day-ahead forecast data and obtain tight near-global optimality guarantees.
Original languageEnglish
Title of host publicationProceedings of 20th Power Systems Computation Conference
Number of pages7
Publication date2018
ISBN (Print)9781910963104
Publication statusPublished - 2018
Event20th Power Systems Computation Conference - O’Brien Centre for Science at University College Dublin, Dublin, Ireland
Duration: 11 Jun 201815 Jun 2018
Conference number: 20


Conference20th Power Systems Computation Conference
LocationO’Brien Centre for Science at University College Dublin
Internet address


  • Chance constraints
  • Contingency filtering
  • Convex optimization
  • Security constrained optimal power flow


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