  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.
