Convex Relaxations of Security Constrained AC Optimal Power Flow Under Uncertainty

Abstract

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.

Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems

“…The need for computationally more efficient convex relaxations of (chance-constrained) AC-OPFs was identified in [4], where we developed a SDP relaxation of the chanceconstrained AC-OPF based on rectangular and Gaussian uncertainty sets. Comparable instances to our case study may take up to 10 minutes to solve with the SDP relaxation (although the computational improvements proposed in [38] can reduce this time) whereas our proposed algorithm converges within 10.60 s. The solution time of the CC-SOC-OPF is mainly determined by the inner iteration loop for approximating the angle constraint (5), which accounts for 84% of the total solution time. More efficient approximations of the angle constraint, which can be implemented in an oneshot optimization, could significantly improve the performance of the proposed method.…”

Optimal Power Flow in Hybrid AC and Multi-terminal HVDC Networks with Offshore Wind Farm Integration Based on Semidefinite Programming

“…If the rank is bigger than 2, then the original solution couldn't be solved. From the paper [14], if the eigenvalue ratio between the largest eigenvalue and the third largest eigenvalue is bigger than 10 5 , then then rank of matrix WAC could be seen less than or equal to 2. After achieving the feasible matrices WAC and WDC with suitable ranks, the voltages could be recovered.…”

Efficient Database Generation for Data-Driven Security Assessment of Power Systems

“…The choice of R N −2 depends on the maximum number of steps κ max,N −2 of the directed walks during the N-2 security database generation. As we aim for avoiding duplicates but also for maximizing the number of unique OPs within Ω, a choice of R N −2 ≤ κ max,N −2 · min{α k } is recommended, where min{α k } is the minimum step size as defined in (18).…”

“…In a procedure similar to [18], we apply an iterative algorithm for the grid pruning: First, given η 1 initialization points, we solve (8) - (15) without considering contingencies, i.e. C = {0}.…”