Grouping of $N-1$ Contingencies for Controller Synthesis: A Study for Power Line Failures

The problem of maintaining power system stability and performance after the failure of any single line in a power system (an "N-1 contingency") is investigated. Due to the large number of possible N-1 contingencies for a power network, it is impractical to optimize controller parameters for each possible contingency a priori. A method to partition a set of contingencies into groups of contingencies that are similar to each other from a control perspective is presented. Design of a single controller for each group, rather than for each contingency, provides a computationally tractable method for maintaining stability and performance after element failures. The choice of number of groups tunes a trade-off between computation time and controller performance for a given set of contingencies. Results are simulated on the IEEE 39-bus and 68-bus systems, illustrating that, with controllers designed for a relatively small number of groups, power system stability may be significantly improved after an N-1 contingency compared to continued use of the nominal controller. Furthermore, performance is comparable to that of controllers designed for each contingency individually.