2023/02/17 by Ruohan Wang, Zhiyong Sun, Wang, Ruohan +1 · 1 citation
Engineering · Mathematics · #Distributed #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Graph theory and applications #Low-power high-performance VLSI design #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Parallel #Social and Information Networks (cs.SI) #Systems and Control (eess.SY) #VLSI and FPGA Design Techniques #and Cluster Computing (cs.DC) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2302.08896
openalex publication_date 2023/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Electrical grids are large-sized complex systems that require strong computing power for monitoring and analysis. Kron reduction is a general reduction method in graph theory and is often used for electrical circuit simplification. In this paper, we propose a novel formulation of the weighted Laplacian matrix for directed graphs. The proposed matrix is proved to be strictly equivalent to the conventionally formulated Laplacian matrix and is verified to well model a lossless DC power flow network in directed graphs. We as well present significant properties of the proposed weighted Laplacian and conditions of Kron reduction in directed graphs and in lossless DC power flow networks. The reduction method is verified via simulation models of IEEE-3, IEEE-5, IEEE-9, IEEE-14, and IEEE RTS-96 test systems.