On period minimal pseudo-Anosov braids

A family of period minimal pseudo-Anosov braids, one for each pair of Farey neighbors in [0, 1/2], is described

Inexact Convex Relaxations for AC Optimal Power Flow: Towards AC Feasibility

Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted significant interest as in several instances they provably yield the global optimum to the original non-convex problem. If, however, the relaxation is inexact, the obtained solution is not AC-feasible. The quality of the obtained solution is essential for several practical applications of AC-OPF, but detailed analyses are lacking in existing literature. This paper aims to cover this gap. We provide an in-depth investigation of the solution characteristics when convex relaxations are inexact, we assess the most promising AC feasibility recovery methods for large-scale systems, and we propose two new metrics that lead to a better understanding of the quality of the identified solutions. We perform a comprehensive assessment on 96 different test cases, ranging from 14 to 3120 buses, and we show the following: (i) Despite an optimality gap of less than 1%, several test cases still exhibit substantial distances to both AC feasibility and local optimality and the newly proposed metrics characterize these deviations. (ii) Penalization methods fail to recover an AC-feasible solution in 15 out of 45 cases, and using the proposed metrics, we show that most failed test instances exhibit substantial distances to both AC-feasibility and local optimality. For failed test instances with small distances, we show how our proposed metrics inform a fine-tuning of penalty weights to obtain AC-feasible solutions. (iii) The computational benefits of warm-starting non-convex solvers have significant variation, but a computational speedup exists in over 75% of the cases

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

Power system security assessment methods require large datasets of operating points to train or test their performance. As historical data often contain limited number of abnormal situations, simulation data are necessary to accurately determine the security boundary. Generating such a database is an extremely demanding task, which becomes intractable even for small system sizes. This paper proposes a modular and highly scalable algorithm for computationally efficient database generation. Using convex relaxation techniques and complex network theory, we discard large infeasible regions and drastically reduce the search space. We explore the remaining space by a highly parallelizable algorithm and substantially decrease computation time. Our method accommodates numerous definitions of power system security. Here we focus on the combination of N-k security and small-signal stability. Demonstrating our algorithm on IEEE 14-bus and NESTA 162-bus systems, we show how it outperforms existing approaches requiring less than 10% of the time other methods require.Comment: Database publicly available at: https://github.com/johnnyDEDK/OPs_Nesta162Bus - Paper accepted for publication at IEEE Transactions on Power System