  We consider the problem of designing (or augmenting) an electric power system
at a minimum cost such that it satisfies the N-k-e survivability criterion.
This survivability criterion is a generalization of the well-known N-k
criterion, and it requires that at least (1- e_j) fraction of the total demand
to be met after failures of up to j components, for j=1,...,k. The network
design problem adds another level of complexity to the notoriously hard
contingency analysis problem, since the contingency analysis is only one of the
requirements for the design optimization problem. We present a mixed-integer
programming formulation of this problem that takes into account both
transmission and generation expansion. We propose an algorithm that can avoid
combinatorial explosion in the number of contingencies, by seeking
vulnerabilities in intermediary solutions and constraining the design space
accordingly. Our approach is built on our ability to identify such system
vulnerabilities quickly. Our empirical studies on modified instances from the
IEEE 30-bus and IEEE 57-bus systems show the effectiveness of our methods. We
were able to solve the transmission and generation expansion problems for k=4
under 2 minutes, while other approaches failed to provide a solution at the end
of 2 hours.
