Paradigm and Paradox in Topology Control of Power Grids

Abstract

Corrective Transmission Switching can be used by the grid operator to relieve line overloading and voltage violations, improve system reliability, and reduce system losses. Power grid optimization by means of line switching is typically formulated as a mixed integer programming problem (MIP). Such problems are known to be computationally intractable, and accordingly, a number of heuristic approaches to grid topology reconfiguration have been proposed in the power systems literature. By means of some low order examples (3-bus systems), it is shown that within a reasonably large class of "greedy" heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence based on a large number of simulations using using IEEE 118-bus systems indicates that among three heuristics, a globally greedy heuristic is the most computationally intensive, but has the best chance of reducing generation costs while enforcing N-1 connectivity. It is argued that, among all iterative methods, the locally optimal switches at each stage have a better chance in not only approximating a global optimal solution but also greatly limiting the number of lines that are switched. arXiv:1803.05852v2 [cs.SY]

Power Grid Decomposition Based on Vertex Cut Sets and Its Applications to Topology Control and Power Trading

“…To test the validity of the grid decomposition based on vertex cut set, a new topology control heuristic was proposed and tested on the IEEE 118-bus test systems. The so called Local Greedy Heuristic is the same as the Standard Greedy Heuristic in [12] except that the switchable lines are limited to the neighboring area of the congested line, i.e the congested sub-grid obtained by the grid decomposition algorithm shown in Fig. 4.…”

“…The Standard Greedy Heuristic redoes the DCOPFs for each allowable line outage and then select the single line outage that leads to maximum savings in each iteration. Please refer [12] for more details.…”

“…In all of these studies, simulations show that significant savings are indeed possible from transmission switching. While optimality for this NP-hard problems is ever elusive, theorems together with simulation results on a set of iterative heuristics in [12], nevertheless, offer some justification that, with similar searching space, the locally optimal switching at each stage of an iterative heuristic has the best chance in reducing generation cost while enforcing connectivity.…”