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Convex Relaxations of Optimal Power Flow Problems: An Illustrative Example
Daniel K. Molzahn, Ian A. Hiskens
Recently, there has been significant interest in convex relaxations of the optimal power flow (OPF) problem. A semidefinite programming (SDP) relaxation globally solves many OPF pr…
Recent Advances in Computational Methods for the Power Flow Equations
Dhagash Mehta, Daniel K Molzahn, Konstantin Turitsyn
The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonli…
Toward Topologically Based Upper Bounds on the Number of Power Flow Solutions
Daniel K Molzahn, Dhagash Mehta, Matthew Niemerg
The power flow equations, which relate power injections and voltage phasors, are at the heart of many electric power system computations. While Newton-based methods typically find…
Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization
Daniel K. Molzahn, Cédric Josz, Ian A. Hiskens +1
The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been…
Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization
Cédric Josz, Daniel K. Molzahn
We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to sol…
A Laplacian-Based Approach for Finding Near Globally Optimal Solutions to OPF Problems
Daniel K. Molzahn, Cédric Josz, Ian A. Hiskens +1
A semidefinite programming (SDP) relaxation globally solves many optimal power flow (OPF) problems. For other OPF problems where the SDP relaxation only provides a lower bound on t…