Related papers: Semi-implicit Continuous Newton Method for Power F…
We introduce Newton-ADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then…
We propose a semismooth Newton method for non-Newtonian models of incompressible flow where the constitutive relation between the shear stress and the symmetric velocity gradient is given implicitly; this class of constitutive relations…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…
Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation,…
Conventional AC Power Flow (ACPF) solvers like Newton-Raphson (NR) face significant computational and convergence challenges in modern, large-scale power systems. This paper proposes a novel, two-stage hybrid method that integrates a…
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 work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
High percentage penetrations of renewable energy generations introduce significant uncertainty into power systems. It requires grid operators to solve alternative current optimal power flow (AC-OPF) problems more frequently for economical…
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…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Power grid operators typically solve large-scale, nonconvex optimal power flow (OPF) problems throughout the day to determine optimal setpoints for generators while adhering to physical constraints. Despite being at the heart of many OPF…
Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…
The stability of classical semi-implicit scheme, and some more advanced iterative schemes recently proposed for Numerical Weather Prediction (NWP) purpose is examined. In all these schemes, the solution of the centred-implicit non-linear…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
This paper focuses on power flow analysis through the lens of the Newton flow, a continuous-time formulation of Newton's method. Within this framework, we explore how quantized-state concepts, originally developed as an alternative to time…
When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we…
This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…