Complex power tracing technique of load extraction using incidence matrix multiplication

In this paper, a complex power flow tracing technique based on the converged AC power flow solution is proposed to determine the participations of each load in line flows. This method is formulated by using mathematical derivations without topological analysis and proportional-sharing principle, where electrical circuit theories are satisfied. There four incidence matrixes found by the relationship of electrical circuit theories, and these matrixes will be integrated by matrix multiplication. With matrix formulations, this is an algorithm to find tracing components for line flows, generators and loads. Besides, the component of counter flows can also be found to show its effect on the line flow. This tracing technique can calculate power distributions of transmission network effectively, and can be easily integrated into the existent tariffs of charging for transmission services.