Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Electrical and Computer Engineering

First Advisor

Dr. Yuan Liao


Accurate value of transmission line parameters is important for power system protection applications, especially for distance relays whose zone settings are based on positive sequence line impedance. The research is devoted to estimating transmission line positive-sequence parameters from synchronized or unsynchronized measurements of voltage and current phasors that are obtained at both terminals of the line. The positive sequence parameters including series impedance and shunt admittance can be linearly estimated. The linear least square algorithm has been derived in this dissertation for different transmission line configurations. The algorithm is able to handle both synchronized and unsynchronized measurements and deal with potential synchronization errors by explicitly modeling the synchronization angle. Sample results are reported to demonstrate the effectiveness of the proposed method.

Three types of transmission line models depending on line length (long, medium and short) are studied in this dissertation. Chapter 3 uses unsynchronized data for the long transmission line. The derived method can detect the unsynchronized angle and estimate the positive sequence of long line parameters. The proposed method is examined with negative impacts such as errors on currents and voltages data. These errors are added randomly to one set each time to test the robustness of the developed algorithm.

The medium transmission line algorithm derivation is presented in chapter 4. This chapter uses a linear least square to estimate the lumped parameters of a medium transmission line. The two different transmission line circuits are used to model the medium line. The first circuit is a single transmission line with two nodes and is used to evaluate the developed algorithm. The second circuit is a double transmission line. These two lines can have the same or different line parameters or line length. The developed algorithm shows that the proposed method achieves highly accurate results for the estimation of positive sequence line parameters.

The short transmission line is studied in chapter 5. The short transmission line uses less data than the long or medium lines because in this model the shunt capacitance is omitted. Thus, the linear estimation yields highly accurate results. Case studies are considered to test the robustness of this developed method.

The line temperature mainly affects the series resistance, and the developed algorithms in previous three chapters can accurately estimate the transmission line parameters. To simplify the real-time estimation of line resistance and temperature, the series inductance, and shunt capacitance can be treated as constant and known values. Chapter 6 provides such studies of estimating resistance by treating inductance and capacitance as known values.

Digital Object Identifier (DOI)