Tracing Reactive Power Flows and Allocating Transmission Lines Losses: An Analytical Method

This paper proposes a new efficient method for solving the reactive power tracing problem in a transmission system. Based on the operating point obtained by an ac power flow computation, a novel model is first introduced to represent the lines, which generate reactive power, for considering them as separate reactive power sources. This model converts the study system to a system in which each line has only reactive loss. Thereafter, new matrices named outflow-line and inflow-line are created for the modified system. By using the properties of these matrices, four other matrices, which establish the relationship between the lines' reactive power flows and reactive power productions (consumptions) of the sources (loads), are derived. These matrices are applied to calculate the contribution of each source or load to the reactive power flow and loss of each line, and determine the share of each source in the reactive power consumed by each load. An illustrative example is used to elaborate the computing process of the proposed method. Comparison with some earlier methods indicates the validity of the proposed method.