Related papers: Convex Relaxations and Linear Approximation for Op…
This work considers the task of finding an AC-feasible operating point of a severely damaged transmission network while ensuring that a maximal amount of active power loads can be delivered. This AC Maximal Load Delivery (AC-MLD) task is a…
The optimal power flow (OPF) problem is one of the most fundamental problems in power system operations. The non-linear alternating current (AC) power flow equations that model different physical laws (together with operational constraints)…
The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the…
Determining contingency aware dispatch decisions by solving a security-constrained optimal power flow (SCOPF) is challenging for real-world power systems, as the high problem dimensionality often leads to impractical computational…
This letter investigates properties of the second-order cone relaxation of the optimal power flow (OPF) problem, with emphasis on relaxation tightness, nodal voltage angles recovery, and alternating-current-OPF feasibility in meshed…
The DistFlow model accurately represents power flows in distribution systems, but the model's nonlinearities result in computational challenges for many applications. Accordingly, a linear approximation known as \mbox{LinDistFlow} (and its…
Given an affine space of matrices $\mathcal{L}$ and a matrix $\Theta\in \mathcal{L}$, consider the problem of computing the closest rank deficient matrix to $\Theta$ on $\mathcal{L}$ with respect to the Frobenius norm. This is a nonconvex…
This paper presents a method to obtain a convex inner approximation that aims to improve the feasibility of optimal power flow (OPF) models in distribution feeders. For a resistive distribution network, both real and reactive power effect…
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 relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…
This paper studies the throughput maximization problem for a three-node relay channel with non-ideal circuit power. In particular, the relay operates in a half-duplex manner, and the decode-and-forward (DF) relaying scheme is adopted.…
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is…
This paper introduces a new model for highly accurate distribution voltage solutions, coined as a parameterized linear power flow model. The proffered model is grounded on a physical model of linear power flow equations, and uses…
A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…
Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in…
Combined heat and power dispatch promotes interactions and synergies between electric power systems and district heating systems. However, nonlinear and nonconvex heating flow imposes significant challenges on finding qualified solutions…
Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear…
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…