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

Qiong Zhang, Ph.D.

Committee Member

Sumit Paudyal, Ph.D.


convex programming, mixed-Integer programming, Photovoltaic, unbalanced distribution systems, volt var optimization


The distribution systems are increasingly challenged by the continued prevalence of distributed energy resources (DERs), signaling the need for new computational tools to systemize their involvement, coordinate their operation with existing control devices, and mitigate undesired actuation of expensive equipment. Co-optimized operation of the various control devices becomes possible with the advancement in the power system optimization algorithms and the increased deployment of advanced metering infrastructure, offering system awareness and two-way communication. The steady-state alternating-current optimal power flow (ACOPF) problem, being the most descriptive form of OPF, lies at the root of power system optimization, aiming to minimize an operating point subject to the system's physical and security constraints. The last fifteen years have witnessed some seminal convexifications of the ACOPF problem, offering more computational tractability when compared to the original non-convex ACOPF model and a more accurate representation of the physical model when compared to the linear OPF models. The existing literature has addressed a breadth of obstacles with particular relevance to the voltage/voltage ampere reactive power flow continuous and discrete models.

This research aims to build comprehensive computational methodologies that promote the accuracy of the convex distribution ACOPF (D-ACOPF) problem. Specifically, we propose to mitigate the trade-off between model precision and computational efficiency by encoding the precise mathematical models of the physical system and control devices, taking into account their limits and maintaining moderate actuation.

The first chapter serves as an introduction to the volt var control, the main components used in current distribution systems as well as the emergent challenges that face the conventional volt var control. The second chapter surveys and reviews the literature on the various modeling aspects of the model-based volt/var optimization (VVO). It begins by identifying the essential components of the optimization problem, namely, the objectives and constraints, and then compares and contrasts the current state-of-the-art while highlighting the need for new methodologies to overcome the modeling and computational bottlenecks to the existing volt/var scheduling problem.

The third chapter of this dissertation models a general off-line VVO problem for balanced distribution systems, relying on predicted load and generation profiles. We extend our research in the fourth chapter to consider the unbalances in the distribution system, which is of practical concern to the validity of the VVO dispatch. A methodology based on the generalized Benders decomposition (GBD) is proposed to incorporate the discrete devices into the D-ACOPF. Relying on predicted load and generation profiles, we explore the possibility of preventing excessive mechanical adjustments of tap changers to reduce higher maintenance costs.

It is a fact that only exact relaxations to the convex D-ACOPF problem are deemed feasible to the original non-convex problem. The exactitude of the solution is of paramount importance because it not only reflects the minimum operational objective that can be translated into financial savings, but provides the most realistic dispatch of control variables. Hence, inexact solutions are deemed less realistic. Although inevitably compromising the exactness, internalizing the distribution system's fundamental components into the D-ACOPF problem is of the essence for the solution quality and control dispatch viability. In the third part of this research, we propose to incorporate two improperly-constrained applications and a special objective function that initially render the problem inexact. Our contribution is to circumvent this conundrum and retrieve the exactness (AC feasibility) by utilizing the concept of convex iteration, in which the relaxation is strengthened iteratively. The simulations on various distribution feeders and comparative case studies with the literature evince the success of the proposed method for recovering exact solutions. Moreover, comparisons with existing methods demonstrate the global optimality of the solution with lower penalty weights.

The dissertation has resulted in two published conference papers, and two journal papers (one under revision and one submitted).