  We propose a two-step algorithm for optimal controlled islanding that
partitions a power grid into islands of limited volume while optimizing several
criteria: high generator coherency inside islands, minimum power flow
disruption due to teared lines, and minimum load shedding. Several spectral
clustering strategies are used in the first step to lower the problem dimension
(taking into account coherency and disruption only), and CPLEX tools for the
mixed-integer quadratic problem are employed in the second step to choose a
balanced partition of the aggregated grid that minimizes a combination of
coherency, disruption and load shedding. A greedy heuristic efficiently limits
search space by generating starting solution for exact algorithm. Dimension of
the second-step problem depends only on the desired number of islands K instead
of the dimension of the original grid. The algorithm is tested on standard
systems with 118, 2383, and 9241 nodes showing high quality of partitions and
competitive computation time.
