Doctoral Dissertations

Keywords and Phrases

Optimal power flow; QC relaxation; Coordinate transformation


"Motivated by the potential for improvements in electric power system economics, this dissertation studies the AC optimal power flow (AC OPF) problem. An AC OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. The difficulty of an AC OPF problem is strongly connected to its feasible space's characteristics. This dissertation first investigates causes of nonconvexities in AC OPF problems. Understanding typical causes of nonconvexities is helpful for improving AC OPF solution methodologies.

This dissertation next focuses on solution methods for AC OPF problems that are based on convex relaxations. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This dissertation proposes several improvements to strengthen QC relaxations of OPF problems. The first group of improvements provides tighter envelopes for the trigonometric functions and product terms in the power flow equations. Methods for obtaining tighter envelopes includes implementing Meyer and Floudas envelopes that yield the convex hull of trilinear monomials. Furthermore, by leveraging a representation of line admittances in polar form, this dissertation proposes tighter envelopes for the trigonometric terms. Another proposed improvement exploits the ability to rotate the base power used in the per unit normalization in order to facilitate the application of tighter trigonometric envelopes.

The second group of improvements propose additional constraints based on new variables that represent voltage magnitude differences between connected buses. Using 'bound tightening' techniques, the bounds on the voltage magnitude difference variables can be significantly tighter than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can improve the QC relaxation"--Abstract, page iv.


Crow, Mariesa

Committee Member(s)

Molzahn, Daniel K.
Shamsi, Pourya
Ferdowsi, Mehdi
Kimball, Jonathan W.
Long, Suzanna, 1961-


Electrical and Computer Engineering

Degree Name

Ph. D. in Electrical Engineering


Missouri University of Science and Technology

Publication Date

Spring 2020

Journal article titles appearing in thesis/dissertation

  • Empirical investigation of non-convexities in optimal power flow problems
  • Improving QC relaxations of OPF problems via voltage magnitude difference constraints and envelopes for trilinear monomials
  • Comparison of various trilinear monomial envelopes for convex relaxations of optimal power flow problems
  • Tightening QC relaxations of AC optimal power flow problems via complex per unit normalization
  • Tightening QC relaxations of OPF problems by independently rotating the trigonometric terms


xiii, 163 pages

Note about bibliography

Includes bibliographic references.


© 2020 Mohammad Rasoul Narimani, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11687

Electronic OCLC #