Related papers: Construction of power flow feasibility sets
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)…
Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment…
This paper proposes a convex optimization based method that either locates all real roots of a set of power flow equations or declares no real solution exists in the given area. In the proposed method, solving the power flow equations is…
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 presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…
Electric power grids regularly experience uncertain fluctuations from load demands and renewables, which poses a risk of violating operational limits designed to safeguard the system. In this paper, we consider the robust AC OPF problem…
This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance…
The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…
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…
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained…
The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such…
An important monitoring task for power systems is accurate estimation of the system operation state. Under the nonlinear AC power flow model, the state estimation (SE) problem is inherently nonconvex giving rise to many local optima. In…
Certifying power flow solvability is important for reliable power system operations under volatile operating conditions, but solving power flow equations repeatedly can be costly and may encounter convergence issues. In this paper, we…
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…
The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and…
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…
We investigate the constraints on power flow in networks and its implications to the optimal power flow problem. The constraints are described by the injection region of a network; this is the set of all vectors of power injections, one at…
We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility…
We propose an iterative method of energy flow shaping in the focal region with the amplitude, phase and polarization modulation of incident light. By using an iterative optimization based on the diffraction calculation with help of the fast…