Sparse Tableau Formulation for Power System Networks and Its Application

Grid modeling for electric power systems optimization and control has long, well-studied history. Although many excellent texts and tutorials carefully describe such grid models, choices for mathematical power system representations are inevitably made in context of specific component technologies, operational objectives and computational tools. As the grid sees rapid changes in its network elements (e.g. FACT devices), operational objectives (e.g. integration of distributed energy resources) and computational tools (e.g. advanced optimization and control applications), approaches to grid modeling benefit from re-examination. To this end, this work focuses on developing grid models, which move from those classical concepts toward the most effective models and representations based on the multiport representations of components, and Sparse Tableau Formulation (STF) of network constraints. STF adopts a straightforward, algorithmic approach in network constraint formulation that clearly establishes the conceptual origin of each constraint (either KCL, KVL, or individual component behavior), and is well suited to facilitate research in grid optimization.;In this dissertation, we first discuss the standard AC optimal power flow (OPF) formulation in regard to computational time, robustness of convergence, and objective values, including such refinements as modeling of generator capability curves. These standard formulations widely use Nodal Analysis (and hence the Ybus nodal admittance matrix) to describe the network constraints on the problem, which requires the restrictive assumption of admittance representation for elements (i.e., the current flow through each element must be expressible as a function of its terminal voltage(s)). This observation is one of the factors motivating this work. From the initial contribution of resolving limitations imposed by Ybus, we adopt STF from standard circuit analysis in ways particularly suited to describe power system network constraints in optimization. This dissertation documents the STF approach in the context of the power system, and discusses its relationship to other modeling approaches. We then apply STF to formulate the OPF problem. We argue that this approach improves conceptual clarity in formulating constraints and improves fidelity in capturing physical behavior and engineering limits. With numerical examples, we demonstrate that STF provides computational speed comparable or superior to standard modeling approaches, while increasing flexibility.;Next, we demonstrate the very important practical advantage that STF can simply and directly represent circuit breaker actions in the security-constrained OPF (SCOPF). SCOPF problem is an extension of OPF with added constraints that ensure continued safe operation in the vent of individual component failures termed "contingencies.'' One of the challenges in the SCOPF is to formulate and impose appropriate constraints for all relevant power component outages to form the "contingency cases.'' Realistic representation of substations, including the information regarding circuit breaker configurations, is crucial for contingencies. However, this often challenges standard modeling approach based on the Ybus, which requires "topology processing.'' This imposes additional effort and time to represent contingency scenarios. In this thesis, we construct full nonlinear SCOPF problem with STF, showing its advantage of providing a uniform data structure for contingency analysis, and thus avoiding the need for topology processing.;In addition, motivated by recent advances in convex relaxations for the traditional Ybus-based OPF problem, we derive new convex relaxations suited to the STF formulation of the OPF problem. Two approaches are proposed, relaxing either node current variables or node admittance variables, and several techniques are suggested to improve the quality of relaxed solution.;In the final portion of this thesis, we employ STF to model transmission networks with high penetration of distributed energy resources (DERs) and Flexible AC Transmission System (FACTS) devices. This advanced modeling includes the detailed representation of substations to capture distribution network information with high penetration of DERs. This section also discusses modeling of the Unified Power Flow Controller (UPFC), an example of a particularly versatile FACTS device. It is shown that STF facilitates direct representation of physically relevant quantities as decision variables associated with these elements, thereby improving analysis of their impacts on transmission networks.