An Optimization Model for Harmonic Parameters Estimation of Transmission Lines Using Phasor Measurements

Transmission line parameter estimation is a critical issue for power system operation and planning studies. With the advent of synchrophasor technology, numerous new methods have been developed using PMUs (Phasor Measurement Units) based on real-time measurements from the sending and receiving ends of a transmission line. Typically, the equivalent PI section of the line is determined for the fundamental frequency only. For other harmonic orders, impedances can be measured at specific points in the electric network using a frequency scan approach. However, few studies have focused on the separate estimation of all longitudinal resistances, reactances and shunt admittances for higher harmonic orders. This paper presents a novel approach to this long-standing issue by formulating an optimization problem, where the least squares equation is minimized, subject to inequality constraints associated with the harmonic impedances of a transmission line, modeled with a quadrupole representation. The proposed optimization method allows for the estimation of line impedance parameters with reduced errors for all harmonic orders considered in the analysis. Computational simulations are carried out to demonstrate the applicability of the method, using different line models including a real Brazilian transmission line, and the impact of instrument transformers on the estimated results is also assessed.