Modified Jacobi method for efficient multi-scenario load flow analysis

Faculty of Electrical Engineering and Information Technology, University of Zilina, Zilina, Slovakia

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 11 June 2026

Abstract

Ongoing changes in consumer behaviour and load composition in distribution networks are creating significant challenges for distribution system operators. The growing penetration of residential photovoltaic systems, increasing use of air conditioning and heat pumps, and the rapid rise of electric vehicles all contribute to substantial shifts in network operation. Addressing these developments requires detailed analysis of operating conditions in specific parts of the distribution system, as well as the development of optimization methods for coordinating and controlling loads and distributed energy resources. A major difficulty in analysing and predicting network behaviour is the highly stochastic nature of electrical loading. Consequently, network studies often rely on Monte Carlo simulations, while many optimization approaches employ evolutionary computational techniques. Both methods require repeatedly evaluating large numbers of distinct operating scenarios, resulting in substantial computational effort, especially when nonlinear load flow calculations are involved. This paper presents a modified Jacobi method capable of performing simultaneous load flow analysis across multiple scenarios. The implementation exploits vector operations and parallelization to significantly reduce computation time. Experimental results show that the proposed method decreases solution time by several orders of magnitude, with the greatest improvements achieved through GPU acceleration.