Diagonal Density: Optimization Technique for Consecutive Numbering in Synthetic Power Grids

This paper presents a novel reordering algorithm based on graph bandwidth minimization for the renumbering of synthetic power grids. As power grids evolve into complex networks, effective methodologies for their analysis and management become essential. The proposed algorithm aims to achieve near-consecutive numbering of buses, enhancing the computational efficiency of the bus admittance matrix and improving system dynamics and vulnerability assessments. A new metric, diagonal density, is introduced to measure the distribution of non-zero entries in the adjacency matrix, facilitating the optimization process. The study demonstrates that maximizing diagonal density is particularly effective for low and medium-sized synthetic power grids. Simulations reveal that the average degree of the grids does not significantly impact diagonal density or execution time, while degree distribution plays a crucial role in achieving optimal solutions. The findings indicate that the bandwidth minimization problem is less effective for radial distribution grids, highlighting the need for tailored approaches in different grid structures.