New reactive power flow tracing and loss allocation algorithms for power grids using matrix calculation

A novel simple method is suggested in this paper to evaluate the contributions of the sources (including the generators and branches' charging capacitances) or the loads to the branches' reactive flows and losses separately as well as to calculate the sources' shares in providing the loads' reactive powers. In the method, the study system is first converted to the system, each branch of which only has reactive loss, using a new technique for modeling the generating branches based on the AC load flow results. The properties of two new matrices (i.e. injection-bus and absorption-bus matrices), which are constituted for the obtained system, are then used to derive three other matrices. These matrices, which express reactive power productions of the sources in terms of reactive power consumptions of the demands (viz. the loads and branches' losses) and vice versa, contain the intended contributory factors. Three-bus system is applied to demonstrate the computing process of the method whereas several IEEE systems are used to show its capability to implement on the transmission systems with arbitrary topologies and sizes. Some advantages of the method compared to the earlier methods are also illustrated.