# Improved Spectral Clustering for Multi-Objective Controlled Islanding of Power Grid

## TL;DR

This paper introduces a two-step spectral clustering algorithm for controlled islanding in power grids, optimizing for coherency, disruption, and load shedding with improved efficiency and scalability.

## Contribution

It presents a novel two-step approach combining spectral clustering and mixed-integer quadratic programming for better power grid partitioning.

## Key findings

- High-quality partitions on standard systems
- Reduced computational time compared to existing methods
- Effective handling of large-scale power grids

## Abstract

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.