Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Electrical Engineering

Major Professor

Lingling Fan, Ph.D.

Committee Member

Zhixin Miao, Ph.D.

Committee Member

Fangxing Li, Ph.D.

Committee Member

Qiong Zhang, Ph.D.

Committee Member

Yasin Yilmaz, Ph.D.


Eigenvalue Identification, Observability, PMU Measurements, PMU Placement, Power System Oscillations


Phasor measurement units (PMUs) have been put into power grid for real-time monitoring. This research investigates the PMU data for steady state estimation and dynamic model estimation. It focuses on three main research areas to enhance the security of the power system monitoring. First, optimal PMU placement (OPP) problem is developed to minimize the number of PMUs required for the system to be completely observable using mixed integer linear programming and nonlinear programming. Second, PMU measurements are ranked for oscillation monitoring based on two approaches: oscillation mode observability and Prony analysis. Further, the principles, multi-channel data handling, and noise resilience techniques of three eigenvalue identification methods used in power systems: Prony analysis, Matrix Pencil (MP), and Eigensystem Realization Algorithm (ERA) are examined.

The first part of this research discusses the optimal PMU placement (OPP) problem to find the optimal number of PMUs to make the system fully observable. Two different formulations are presented for modeling power grid observability to solve the OPP problem: mixed integer linear programming (MILP) and nonlinear programming (NLP). For each formulation, modeling of power flow measurements, zero injection, limited communication facility, single PMU failure, and limited channel capacity is studied. MILP zero injection formulation is improved to solve the redundant observability and optimality limitations. A new formulation for nonlinear programming-based PMU placement considering zero injection measurement is proposed. A comparison between MILP and NLP formulations is conducted to show the advantages and disadvantages of each formulation.

The second part of this research is to rank PMU measurements for oscillation monitoring based on two approaches: oscillation mode observability and Prony analysis. In the first approach, the system model is assumed known and the critical oscillation mode observability of different measurements are compared. In the second approach, the dynamic model of the system is not known. Prony analysis is employed to identify critical oscillation modes based on PMU measurements. Measurements at different locations are compared for their characteristics in Prony analysis. Specifically, singular values of Hankel matrices are compared. The two approaches lead to the same conclusion. Their internal connection is presented in this research. As a step further, sensitivity analysis of model order assumption and noise level in Prony analysis is conducted to show singular values of Hankel matrices can indeed serve as indicators of the quality of oscillation monitoring.

In addition, power system eigenvalues from PMU measurement data are identified using Prony analysis, matrix Pencil (MP), and Eigensystem Realization Algorithm (ERA). This part sheds insight on the principles of the three methods: eigenvalue identification through various Hankel matrix formulation. Further, multiple channel data handling and noise resilience techniques are investigated. In the literature, singular value decomposition (SVD)-based rank reduction technique has been applied to MP and resulted in a reduced-order system eigenvalue estimation and an excellent noise resilient feature. In this part of the research, ERA is refined using the SVD-based rank reduction to achieve a superior performance. Moreover, a reduced-order Prony analysis method is invented. With the proposed technique, Prony analysis can not only give reduced-order system eigenvalues, but also become noise resilient.

This dissertation has been resulted in three conference papers (two published and one accepted) and two journal papers (one published and one in revision process). The future work of this dissertation will examine the dynamic parameter estimation technique using the measurement-based methods. Using the PMU data and measurement-based methods of the system identification can provide an accurate dynamic parameter estimation without prior information of the system transfer function. Generator parameters such as inertia constant, damping coefficients, and regulation speed constant can be estimated.

Included in

Engineering Commons