Related papers: Solving the Convex Flow Problem
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. We show that in the case when the flow is a monotonically…
We consider the robust version of a multi-commodity network flow problem. The robustness is defined with respect to the deletion, or failure, of edges. While the flow problem itself is a polynomially-sized linear program, its robust version…
The optimal power flow (OPF) is an optimization model dedicated to the development of computational tools used for the planning and operation of electric power systems (EPS). In this work, based on the polar formulation, an extended convex…
The concave utility in the Network Utility Maximization (NUM) problem is only suitable for elastic flows. However, the networks with the multiclass traffic, the utility of inelastic traffic is usually represented by the sigmoidal function…
Given a graph with non-negative edge weights, there are various ways to interpret the edge weights and induce a metric on the vertices of the graph. A few examples are shortest-path, when interpreting the weights as lengths; resistance…
Maxflow is a fundamental problem in graph theory and combinatorial optimisation, used to determine the maximum flow from a source node to a sink node in a flow network. It finds applications in diverse domains, including computer networks,…
In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond…
Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC…
This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced…
This paper investigates the uncertain power flow analysis in distribution networks within the context of renewable power resources integration such as wind and solar power. The analysis aims to bound the worst-case voltage magnitude in any…
In this paper, we propose a graph neural network architecture to solve the AC power flow problem under realistic constraints. To ensure a safe and resilient operation of distribution grids, AC power flow calculations are the means of choice…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
Solving the non-convex optimal power flow (OPF) problem for large-scale power distribution systems is computationally expensive. An alternative is to solve the relaxed convex problem or linear approximated problem, but these methods lead to…
This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces new valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing…
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 studies a variant of the minimum-cost flow problem in a graph with convex cost function where the demands at the vertices are functions depending on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches for…
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…
Many optimization problems in power transmission networks can be formulated as polynomial problems with complex variables. A polynomial optimization problem with complex variables consists in optimizing a real-valued polynomial whose…
Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We…