Related papers: Convex Relaxations in Power System Optimization: A…
To solve the AC optimal power flow problem, it is proposed in [1,2] that a convex conic approximation to branch flow model (BFM) can be obtained if we first eliminate phase angles of voltages and currents and then relax a set of equality…
In this letter, we propose a data-driven warm start approach, empowered by artificial neural networks, to boost the efficiency of convex relaxations in optimal gas flow. Case studies show that this approach significantly decreases the…
We use convex relaxation techniques to produce lower bounds on the optimal value of subset selection problems and generate good approximate solutions. We then explicitly bound the quality of these relaxations by studying the approximation…
The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing global optimality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF)…
This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP…
This article develops a strengthened convex quadratic convex (QC) relaxation of the AC Optimal Power Flow (AC-OPF) problem and presents an optimization-based bound-tightening (OBBT) algorithm to compute tight, feasible bounds on the voltage…
Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering…
We consider a class of optimal power flow (OPF) applications where some loads offer a modulation service in exchange for an activation fee. These applications can be modeled as multi-period formulations of the OPF with discrete variables…
The recent literature has discussed the use of the relaxed Second Order Cone Programming (SOCP) to formulate Optimal Power Flow problems (OPF) for radial power grids. However, if the shunt parameters of the lines, composing the power grid,…
We develop a new approach for construction of convex analytically simple regions where the AC power flow equations are guaranteed to have a feasible solutions. Construction of these regions is based on efficient semidefinite programming…
AC optimal power flow (AC OPF) is a fundamental problem in power system operation and control. Accurately modeling the network physics via the AC power flow equations makes AC OPF a challenging nonconvex problem that results in significant…
The relaxation systems are an important subclass of the passive systems that arise naturally in applications. We exploit the fact that they have highly structured state-space realisations to derive analytical solutions to some simple…
In this paper, we introduce the solver ConvexFlows for the convex flow problem first defined in the authors' previous work. In this problem, we aim to optimize a concave utility function depending on the flows over a graph. However, unlike…
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 existence of strictly positive lower bounds on voltage magnitude is taken for granted in optimal power flow problems. Nevertheless, it is not possible to rely on such bounds for a variety of real-world network optimization problems.…
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,…
We propose a branch flow model for the anal- ysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates…
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…
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…
The uncertainty of multiple power loads and renewable energy generations (PLREG) in power systems increases the complexity of power flow analysis for decision-makers. The chance-constrained method can be applied to model the optimization…