Paradigm and Paradox in Topology Control of Power Grids
For power grid operators, this work provides guidance on heuristic selection for topology control, though the theoretical result is limited to a specific class of heuristics.
The paper shows that no greedy heuristic for corrective transmission switching outperforms others across all grid topologies (3-bus example), but statistical evidence on IEEE 118-bus systems indicates a globally greedy heuristic best reduces generation costs while enforcing N-1 connectivity, albeit with higher computational cost.
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.