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The dynamic response of power grids to small events or persistent stochastic disturbances influences their stable operation. Low-frequency inter-area oscillations are of particular concern due to insufficient damping. This paper studies the…
Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite…
This paper proposes a hard-constrained unsupervised learning framework for rapidly solving the non-linear and non-convex AC optimal power flow (AC-OPF) problem in real-time operation. Without requiring ground-truth AC-OPF solutions,…
The optimal power flow (OPF) problem can be rapidly and reliably solved by employing responsive online solvers based on neural networks. The dynamic nature of renewable energy generation and the variability of power grid conditions…
Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms…
The future power grid may rely on distributed optimization to determine the set-points for huge numbers of distributed energy resources. There has been significant work on applying distributed algorithms to optimal power flow (OPF)…
This paper presents a scalable method for improving the solutions of AC Optimal Power Flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The focus of the paper is on…
As power systems become more complex and uncertain, low-voltage distribution networks face numerous challenges, including three-phase imbalances caused by asymmetrical loads and distributed energy resources. We propose a robust stochastic…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
Optimal Power Flow (OPF) is a very traditional research area within the power systems field that seeks for the optimal operation point of electric power plants, and which needs to be solved every few minutes in real-world scenarios.…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
We investigate the distributed DC-Optimal Power Flow (DC-OPF) problem for a dynamic and uncertain environment. The unpredictable supply of renewable resources and varying prices of the electricity market are a few factors responsible for…
Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient…
Nonlinear convex relaxations of the power flow equations and, in particular, the Semi-Definite Programming (SDP), Convex Quadratic (QC), and Second-Order Cone (SOC) relaxations, have attracted significant interest in recent years. Thus far,…
Typical formulations of the optimal power flow (OPF) problem rely on what is termed the "bus-branch" model, with network electrical behavior summarized in the Ybus admittance matrix. From a circuit perspective, this admittance…
Convex relaxations of the optimal power flow (OPF) problem provide an efficient alternative to solving the intractable alternating current (AC) optimal power flow. The conic subset of OPF convex relaxations, in particular, greatly…
We propose a data-driven method to solve a stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The objective is to determine power schedules for controllable devices in a power…
We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite…