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

Nasir Ghani, Ph.D.

Committee Member

Fangxing Li, Ph.D.

Committee Member

Qiong Zhang, Ph.D.


Dynamic mode decomposition, eigenvalues analysis, inverter, oscillation, synchronous generator


The complexity of dynamical analysis has been growing to suffice the understanding and modeling of dynamical systems. Besides its nonlinearity and high-dimensionality, the dynamics of power systems contain uncertainty that complicates its analysis. Recently, dynamical modeling has been categorized into three types: white-box, black-box, and gray-box. White-box modeling has the accessibility of all system components. Black-box modeling has the observability of the system measurements without knowing the actual system. Gray-box modeling has the observability of the system measurements with the reachability to some of the system components. The scope of this dissertation focuses on black-box and gray-box models to achieve practical system and parameter identification of power system applications.

Dynamic Mode Decomposition (DMD) is a black-box method that has been proposed by the fluid community. It is a free-equation model identification technique and it has proven its practicality in various fields including brain modeling, fluid experiments, video separation, flows around a train, and financial trading strategies. Our work reviews the DMD algorithm and implements it for mode identification and signal reconstruction in three power system-related applications: RLC circuit dynamics, phasor measurement unit (PMU) measurements of an unknown system, and AC voltage waveform polluted by harmonics. In the first two applications, we compare DMD with Eigensystem Realization Algorithm (ERA) and present that the two methods have the same accuracy level. The last application shows that DMD can also work as fast Fourier transformation (FFT), which can identify harmonics and their magnitudes in the analyzed system.

The standard DMD is unable to identify real-world measurement data captured by phasor measurement units (PMUs) because they are noisy. In our research, we enhance DMD performance by data stacking that increases the rank of the data matrix. Correspondingly, DMD accurately identifies the system eigenvalues and eigenvectors. The eigensystem components reveal the details of the dynamics and reconstruct the signals in the time-evolving format. While data stacking raises the computation cost, we further implement a randomization technique for DMD to radically reduce the size of the data matrix. The randomized DMD (rDMD) has high accuracy and efficiency. Our work shows that the identified mode shapes (eigenvectors) of the DMD/rDMD can recognize the oscillation mode type whether it is local or interarea. PMU data from three real-world oscillation events are used for demonstration. Also, we compare both DMD and rDMD with the classical identification methods including Prony, Matrix Pencil, and Eigensystem Realization Algorithm.

The second part of this dissertation focuses on gray-box dynamical modeling for parameter identification. The two classical parameter identification methods are the prediction error method (PEM) and the similarity matrix technique. These methods are nonlinear and require a good initial guess of parameters that must be in the domain of convergence. Recently, two new methods have been developed by the system identification community. These methods start from the two conventional methods, make computing improvement by taking into consideration the low-rank characteristic of data, and formulate the estimation problems as rank-constraint optimization problems. Furthermore, the rank-constraint optimization problems are converted to difference of convex programming (DCP) problems and solved by convex iteration. The new convexification technique leads to more accurate parameter estimation. Our work presents the four methods and implements the problem formulations and solving algorithms for synchronous generator and inverter-based resource (IBR) dynamic model parameter estimation.