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The dynamic response of power grids to small disturbances influences their overall stability. This paper examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes ${cal H}_2$-norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. The efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.
In recent years, the power systems research community has seen an explosion of novel methods for formulating the AC power flow equations. Consequently, benchmarking studies using the seminal AC Optimal Power Flow (AC-OPF) problem have emerged as the
This paper considers the robust ${cal D}$-stability margin problem under polynomic structured real parametric uncertainty. Based on the work of De Gaston and Safonov (1988), we have developed techniques such as, a parallel frequency sweeping strategy
In the design flow of integrated circuits, chip-level verification is an important step that sanity checks the performance is as expected. Power grid verification is one of the most expensive and time-consuming steps of chip-level verification, due t
In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their universal applic
Distribution grids constitute complex networks of lines often times reconfigured to minimize losses, balance loads, alleviate faults, or for maintenance purposes. Topology monitoring becomes a critical task for optimal grid scheduling. While synchrop