Related papers: Geometry of Injection Regions of Power Networks
We investigate the geometry of injection regions and its relationship to optimization of power flows in tree networks. The injection region is the set of all vectors of bus power injections that satisfy the network and operation…
The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the…
This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric…
The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive…
The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and…
We present a unified analytical framework within which power control, rate allocation, routing, and congestion control for wireless networks can be optimized in a coherent and integrated manner. We consider a multi-commodity flow model with…
The solvability set of a power network - the set of all power injection vectors for which the corresponding Power Flow equations admit a solution - is central to power systems stability and security, as well as to the tightness of Optimal…
A wind farm can provide reactive power at sub-transmission and transmission buses in order to support and improve voltage profiles. It is common for the reactive power capability of a wind farm to be evaluated as the sum of the individual…
Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper,…
A standard operational requirement in power systems is that the voltage magnitudes lie within prespecified bounds. Conventional engineering wisdom suggests that such a tightly-regulated profile, imposed for system design purposes and good…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
The classical optimal power flow problem optimizes the power flow in a power network considering the associated flow and operating constraints. In this paper, we investigate optimal power flow in the context of utility-maximizing demand…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
This note discusses an essentially decentralized interior point method, which is well suited for optimization problems arising in energy networks. Advantages of the proposed method are guaranteed and fast local convergence also for problems…
Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These…
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In…
The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly,…
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters…
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…