Related papers: Locating Power Flow Solution Space Boundaries: A N…
The primary goal of Optimal Power Flow (OPF) is to optimize the operation of a power system while meeting the demand and adhering to operational constraints. This paper presents a new approach for AC OPF. First, the approach constructs a…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
This paper establishes a sufficient condition for guaranteeing power flow solvability in distribution grids with inverter-based resources (IBRs) operating under IEEE 1547 compliant Volt-Var control. While designed to improve voltage…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start…
In this paper, we consider a chance-constrained formulation of the optimal power flow problem to handle uncertainties resulting from renewable generation and load variability. We propose a tuning method that iterates between solving an…
This paper aims to systematically and comprehensively initiate a foundation for using concepts from computational differential geometry as instruments for power flow computing and research. At this point we focus our discussion on the…
This chapter presents recent solutions to the optimal power flow (OPF) problem in the presence of renewable energy sources (RES), {such} as solar photo-voltaic and wind generation. After introducing the original formulation of the problem,…
Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the…
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…
This note discusses an essentially decentralized interior point method, which is well suited for optimization problems arising in energy networks. Advantages of the proposed method are guaranteed and fast local convergence also for problems…
The Optimal Power Flow (OPF) problem is pivotal for power system operations, guiding generator output and power distribution to meet demand at minimized costs, while adhering to physical and engineering constraints. The integration of…
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,…
We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…
In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
The increasing scale and nonlinearity of modern energy and power system problems pose significant challenges to classical numerical solvers. In parallel, advances in quantum and quantum-inspired hardware are expected to improve scalability…
A proven methodology to solve multiphase flows is based on the one-fluid formulation of the governing equations, which treats the phase transition across the interface as a single fluid with varying properties and adds additional source…