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Solving the power flow problem in a distributed fashion empowers different grid operators to compute the overall grid state without having to share grid models-this is a practical problem to which industry does not have off-the-shelf…
We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give linear-time algorithms to compute all non-dominated…
Neural warm starts can sharply reduce the number of Newton-Raphson iterations required to solve the AC power flow problem, but existing supervised approaches generalize poorly on heavily loaded instances near voltage collapse. We prove a…
Obtaining good initial conditions to solve the Newton-Raphson (NR) based ac power flow (ACPF) problem can be a very difficult task. In this paper, we propose a framework to obtain the initial bus voltage magnitude and phase values that…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric…
Bus admittance matrix is widely used in power engineering for modeling networks. Being highly sparse, it requires fewer CPU operations when used for calculations. Meanwhile, sparse matrix calculations involve numerous indexing and scalar…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface…
This work proposes a novel method for scaling multi-timestep security-constrained optimal power flow in large power grids. The challenge arises from dealing with millions of variables and constraints, including binary variables and…
This article studies a Newton-like method already used by several authors but which has not been thouroughly studied yet. We call it the robust-variance scoring (RVS) algorithm because the main version of the algorithm that we consider…
With the escalating frequency of extreme grid disturbances, such as natural disasters, comes an increasing need for efficient recovery plans. Algorithms for optimal power restoration play an important role in developing such plans, but also…
Phase reduction theory has been applied to many systems with limit cycles; however, it has limited applications in incompressible fluid systems. This is because the calculation of the phase sensitivity function, one of the fundamental…
Linear approximations of the AC power flow equations are of great significance for the computational efficiency of large-scale optimal power flow (OPF) problems. Put differently, the feasibility of the obtained solution is essential for…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…
Practical quantum computing applications to power grids are nonexistent at the moment. This paper investigates how a fundamental grid problem, namely DC power flow, can be solved using quantum computing. Power flow is the most widely used…
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…
Accurate and efficient power flow (PF) analysis is crucial in modern electrical networks' operation and planning. Therefore, there is a need for scalable algorithms that can provide accurate and fast solutions for both small and large scale…
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…