Graph theory application to deregulated power system

This paper presents a methodology using graph theory to determine the specific generator contributions to different loads and the transmission system usage of different utilities. Starting from a power load flow solution, the method first identifies the buses as load buses or generation buses by getting the net power. Then a directed graph is formed with vertices representing buses and the edges representing transmission lines. Second, it constructs all possible directed and rooted subgraphs of the system from its generator vertices. Notice that the union of these subgraphs is the original directed graph. Using proportionality and average assumptions, it is possible to calculate the specific generator contributions to different loads and the transmission system usage of different utilities