Doctoral Dissertations


Lisa L. Grant

Keywords and Phrases

Algorithm; Graph Sparsification; Linear System; Matrix Preconditioning; Power System Simulation


"To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time.

This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included"--Abstract, page iv.


Crow, Mariesa

Committee Member(s)

Cheng, Maggie Xiaoyan
Ferdowsi, Mehdi
Kimball, Jonathan W.
He, Xiaoming


Electrical and Computer Engineering

Degree Name

Ph. D. in Electrical Engineering


Missouri University of Science and Technology

Publication Date

Spring 2017

Journal article titles appearing in thesis/dissertation

  • Computationally efficient solvers for power system applications
  • A chain method for preconditioned iterative linear solvers for power system matrices
  • Utilization of a chain linear solver for fast decoupled power flow


x, 66 pages

Note about bibliography

Includes bibliographic references (62-65).


© 2017 Lisa L. Grant, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11091

Electronic OCLC #