A Conservative Graph-Theoretical-Based Framework for Solving Supply-to-Demand Matching and Transmission Line Usage Allocation Problems in Electrical Networks

Abstract

Power system operation and planning are greatly influenced by efficient matching of network demands with the available supply as well as allocation of network usage to the participants in a fairer manner. This has contributed a lot of challenge to an effective operation of modern power systems worldwide. This paper, therefore, presents an alternative approach of the graph theory-based method, which provides a simple but efficient solution to supply-to-demand matching as well as the network usage allocation problems for a secure and reliable operation of power systems most especially, during critical outages. The problems are formulated from the approach of the basic circuit theory and network topology perspectives. An Allocation Factor (AF) matrix, which captures the structural interconnections of various system components such as network nodes and transmission lines, is developed. The Generator Allocation Factor (GAF) matrix, which has the capability of matching the generation to load as well as solving transmission usage allocation problem within the power network, is then formulated using the developed AF matrix. The study uses a simple IEEE 5-bus system and the application is also extended to the practical system of the Nigerian 28-bus. The results show that the approach has the capability of matching the supply to demand plus losses in an efficient manner. The results obtained show the merit of the approach in solving the supply-to-demand matching and network usage allocation problems, most especially during critical outages, for efficient transmission pricing by the market regulators.