Related papers: A differential analysis of the power flow equation…
We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to…
The impact of different linearisation and iterative solution strategies for fully-coupled pressure-based algorithms for compressible flows at all speeds is studied, with the aim of elucidating their impact on the performance of the…
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…
Networks with phase-valued nodal variables are central in modeling several important societal and physical systems, including power grids, biological systems, and coupled oscillator networks. One of the distinctive features of phase-valued…
Alternating current optimal power flow (ACOPF) problems are nonconvex and nonlinear optimization problems. Utilities and independent service operators (ISO) require ACOPF to be solved in almost real time. Interior point methods (IPMs) are…
We introduce a general framework for flow problems over hypergraphs. In our problem formulation, which we call the convex flow problem, we have a concave utility function for the net flow at every node and a concave utility function for…
Power flow analysis is used to evaluate the flow of electricity in the power system network. Power flow calculation is used to determine the steady-state variables of the system, such as the voltage magnitude/phase angle of each bus and the…
With the proliferation of distributed generation into distribution networks, the need to consider fault currents in the dispatch problem becomes increasingly relevant. This paper introduces a method for adding fault current constraints into…
Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce…
Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which…
The alternating current optimal power flow (ACOPF) problem is central to modern power system operations, determining how electricity is generated and transmitted to maximize social welfare while respecting physical and operational…
Solving the AC optimal power flow problem (AC-OPF) is critical to the efficient and safe planning and operation of power grids. Small efficiency improvements in this domain have the potential to lead to billions of dollars of cost savings,…
The energy transition is driving the integration of large shares of intermittent power sources in the electric power grid. Therefore, addressing the AC optimal power flow (AC-OPF) effectively becomes increasingly essential. The AC-OPF,…
This paper addresses the challenges of embedding common droop control characteristics in ac-dc power system steady-state simulation and optimization problems. We propose a smooth approximation methodology to construct differentiable…
Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the…
Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory.
We present a massively parallel solver that accelerates DC loadflow computations for power grid topology optimization tasks. Our approach leverages low-rank updates of the Power Transfer Distribution Factors (PTDFs) to represent substation…
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…
Balanced steady operation state in power networks changes over time. Traditional power flow algorithm is focused on the steady operation state under a certain time point and calculates the corresponding voltage and power distributions for…
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,…