Related papers: Construction of power flow feasibility sets
Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper…
There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow…
We study inverse statistical mechanics: how can one design a potential function so as to produce a specified ground state? In this paper, we show that unexpectedly simple potential functions suffice for certain symmetrical configurations,…
We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It…
Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the optimal power flow (OPF) problem. Meanwhile, convex relaxed power flow equations are also prerequisites for efficiently solving a wide…
It is well known that closed-form analytical solutions for AC power flow equations do not exist in general. This paper proposes a multi-dimensional holomorphic embedding method (MDHEM) to obtain an explicit approximate analytical AC…
With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC…
In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. Part II of this paper explores further implications of the results in Part…
Motivated by the minimax concave penalty based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions…
Power system security assessment methods require large datasets of operating points to train or test their performance. As historical data often contain limited number of abnormal situations, simulation data are necessary to accurately…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derived a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model…
Linear active-power-only DC power flow approximations are pervasive in the planning and control of power systems. However, these approximations fail to capture reactive power and voltage magnitudes, both of which are necessary in many…
We study an extended trust region subproblem minimizing a nonconvex function over the hollow ball $r \le \|x\| \le R$ intersected with a full-dimensional second order cone (SOC) constraint of the form $\|x - c\| \le b^T x - a$. In…
This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…
Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or other operational objectives are optimized. Due to the non-convexity of the set of feasible OPF operating points, it is…
This paper presents an algorithm for restoring AC power flow feasibility from solutions to simplified optimal power flow (OPF) problems, including convex relaxations, power flow approximations, and machine learning (ML) models. The proposed…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
This paper focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with high integration of renewables, where adjustments of the real and reactive output powers from renewable…
This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…