Improved spectral clustering for multi-objective controlled islanding of power grid

We propose a two-step algorithm for optimal controlled islanding that partitions a power grid into islands of limited volume while optimizing several criteria: maximizing generator coherency inside islands, minimizing power flow disruption due to teared lines, and minimizing load shedding. Several spectral clusterings 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 heuristics efficiently limits search space by generating the starting solution for the 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 the standard systems with 118, 2383, and 9241 nodes showing high quality of partitions and competitive computation time.