Independent Component Analysis-Based Harmonic Transfer Impedance Estimation for Networks with Multiple Harmonic Sources

This paper presents a novel methodology to estimate the harmonic transfer impedances in electric power systems with multiple harmonic sources (HSs). The purpose is to determine the responsibility of each HS for the total harmonic distortion at a specific bus within the system, addressing a critical issue in the power quality field. To achieve this objective, it is necessary to estimate not only the individual HS, but also the transfer impedances between each source and the bus under analysis (BUA). Most methods for solving this problem are based on proper network modeling or restrict variations in harmonic sources to a single source at a time. The proposed methodology has overcome this limitation. For this, synchronized current and voltage phasors are measured at the BUA. Once the measurements are gathered, the Independent Component Analysis (ICA) method is applied to estimate the Norton equivalent. The harmonic transfer impedance (HTI) is then determined using the information provided by the ICA. To enhance the accuracy of HTI estimation, three procedures are employed for data mining the parameters provided by ICA over time to generate a well-conditioned system. Once the HTI is satisfactorily determined, the individual harmonic contributions (IHCs), i.e., the harmonic responsibility, can be estimated accurately. The effectiveness and performance of the method are demonstrated based on computational simulations using distribution and transmission systems. Additionally, the methodology is validated with real data collected from a Brazilian transmission system monitored by synchronized power quality measurement units. Simulated results show that the Total Vector Error (TVE) is less than 0.4%, and for the field data test, the TVE is less than 2%.