Controlled islanding is a part of frequency stabilization strategy in power grids. It implies partitioning a grid into independent islands in case of massive failures to minimize accident aftermaths, prevent cascading blackouts and keep critical infrastructure alive. To achieve these goals slow coherence of generators must be avoided in the islands formed. Also, line switch off distortion and load shedding must be minimized. Existing approaches account for just one or two of these factors. We propose a two-step islanding algorithm that balances multiple criteria: slow coherence of generators, minimal line switching-off distortion, island size, and minimum load shedding. The mathematical challenge is high dimension (up to 10^4 nodes in a grid) and dependence of cost function on power flow directions (so, spectral clustering is inapplicable).
Several hierarchical spectral clustering schemes are used at the first step to cut the problem dimension (caring for coherence and distortion only), and CPLEX tools for the mixed integer quadratic problem are employed at the second step to choose a balanced partition of the aggregated grid that minimizes a combination of coherence, distortion and load shed (approximated by power imbalance). The problem dimension on the second step depends only on the desired number of islands K but not on the dimension of the initial grid. A greedy heuristic generates a starting solution for the branch and bound scheme assuring high performance of the second step. The algorithm was compared with the basic one-step hierarchical clustering scheme on example grids with 118, 2383, and 9241 nodes, showing good performance (10% average improvement of the cost function) with modest increase in computation time (
