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A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems
TLDR
This paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.
Implementation of a Large-Scale Optimal Power Flow Solver Based on Semidefinite Programming
TLDR
A semidefinite programming relaxation of the OPF problem is presented that incorporates multiple generators at the same bus and parallel lines and provides three advances to existing decomposition techniques: a matrix combination algorithm that further decreases solver time, a modification to anexisting decomposition technique that extends its applicability to general power system networks, and a method for obtaining the optimal voltage profile.
Examining the limits of the application of semidefinite programming to power flow problems
TLDR
This paper investigates an SDP approach utilizing modified objective and constraints to compute all solutions of the nonlinear power flow equations, and suggests SDP's promise as an efficient algorithm for identifying large numbers of solutions to the power flow equation.
Sparsity-Exploiting Moment-Based Relaxations of the Optimal Power Flow Problem
Convex relaxations of non-convex optimal power flow (OPF) problems have recently attracted significant interest. While existing relaxations globally solve many OPF problems, there are practical
The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms
TLDR
This IEEE PES Task Force report proposes a standardized AC-OPF mathematical formulation and the PGLib-OPf networks for benchmarking AC-opF algorithms and a motivating study demonstrates some limitations of the established network datasets in the context of benchmarking ASF algorithms.
Moment-based relaxation of the optimal power flow problem
TLDR
This paper investigates "moment-based" relaxations of the OPF problem developed from polynomial optimization theory, finding moment relaxations are generally tighter than relaxations employed in previous research, thus resulting in global solutions for a broader class of OPF problems.
Approximate Representation of ZIP Loads in a Semidefinite Relaxation of the OPF Problem
Recent research has applied semidefinite programming (SDP) to the optimal power flow (OPF) problem. Extending SDP formulations to include the ZIP load model, which consists of constant impedance,
A Survey of Relaxations and Approximations of the Power Flow Equations
TLDR
This monograph provides the first comprehensive survey of representations in the context of optimization of the power flow equations, categorized as either relaxations or approximations.
Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables
TLDR
The Lasserre hierarchy is generalized from real to complex to numbers in order to enhance its tractability when dealing with complex polynomial optimization and the notion of hyponormality in operator theory is provided to provide a finite convergence criterion which generalizes the Curto-Fialkow conditions of the real Lasser re hierarchy.
A Sufficient Condition for Power Flow Insolvability With Applications to Voltage Stability Margins
For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic
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