Estimation of transmission line parameters by using two least‐squares methods

Abstract

Abstract This work proposes two new approaches based on the ordinary least‐squares method and the total least‐squares method to estimate the parameters of a balanced three‐phase transmission line using voltage and current measurements from phasor measurement unit. First, a new model for the steady‐state phasorial equations of a medium‐length transmission line is proposed. Then, the noises acting upon each measurement on the ordinary least‐squares setup are considered, and for the total least‐squares setup, noise acting upon the observation matrix in order to account for model uncertainties and non‐linearities is also considered. The methods are tested in simulation data of a real medium‐size transmission line.s The main goal is to compare both methods and show their complexities. The results show good performances for both methods and, indeed, the total least‐squares setup had better performance than other reported total least‐squares estimators, which use a different phasorial set of equations and oversimplified noise modelling. It is concluded that for the ordinary least‐squares, the solution is well known and its behavior is predictable. While for the total least‐squares, the solution requires more sophisticated methods of matrix decomposition and its behavior is not as predictable. Therefore the implications of these new approaches, where new considerations about the modelling of the noises are made and where a new phasorial set of equations is used are significant, given that the many works in the literature make use of these common‐place tools.

Keywords

• Interpolation and function approximation (numerical analysis)
• Linear algebra (numerical analysis)
• Current measurement
• Power transmission lines and cables
• Power system measurement and metering