The coupling of single-carrier network into multicarrier energy systems (MES) has recently become more important. Conventional single-carrier steady-state load flow models are not able to capture the full extent of the coupling. Different models for multi-carrier networks have been proposed, either based on the energy hub concept or using a case specific approach. However, the effect of the coupling on solvability and well-posedness of the integrated system of non-linear equations has not been discussed. Using a general load flow model on a small example MES, this paper discusses the problems arising due the coupling of single-carrier networks, and provides guidelines to obtain a solvable steady-state load flow model for MES.
The load flow equations express the balance of power in an electrical power system. The power generated must equal the power consumed. In the AC time-harmonic case, the load flow equations are non-linear in the voltage phasors associated with the nodes in the network. The development of future power systems urgently requires new, highly efficient and robust load flow solvers. In this contribution we aim at making the following three scientific contributions. We first show that the use of a globalization procedure is required to ensure the convergence of a Newton load flow simulation of a stressed network. Such operational conditions are more likely to occur in the future. We subsequently show that the use of an inexact Newton-Krylov method results in faster computations. We employ Quotient Minimal Degree (QMD) as a matrix reordering method, incomplete LU factorization (ILU) as a preconditioner, Generalized Minimal Residual (GMRES) as a Krylov acceleration, and the Dembo-Steihaus strategy to defined the accuracy of the linear solver at each Newton iteration. We finally show the results of iterative solution algorithms that allow to exploit the decomposition of a network into subnetworks. Decompositions with and without overlapping nodes are tested.
This paper verifies a mathematical model that is developed for the open source CFD-toolbox OpenFOAM, which couples turbulent combustion with conjugate heat transfer. This feature already exists in well-known commercial codes. It permits the prediction of the flame's characteristics, its emissions, and the consequent heat transfer between fluids and solids via radiation, convection, and conduction. The verification is based on a simplified 2D axisymmetric cylindrical reactor. In the first step, the combustion part of the solver is compared against experimental data for an open turbulent flame. This shows good agreement when using the full GRI 3.0 reaction mechanism. Afterwards, the flame is confined by a cylindrical wall and simultaneously conjugate heat transfer is activated and analysed. It is shown that the combustion and conjugate heat transfer are successfully coupled.
Isogeometric Analysis (IgA) can be considered as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. The development of efficient solvers for discretizations arising in IgA is a challenging task, as most (standard) iterative solvers have a detoriating performance for increasing values of the approximation order p of the basis functions. Recently, p-multigrid methods have been developed as an alternative solution strategy. With p-multigrid methods, a multigrid hierarchy is constructed based on the approximation order p instead of the mesh width h (i.e. h-multigrid). The coarse grid correction is then obtained at level p = 1, where B-spline basis functions coincide with standard Lagrangian P 1 basis functions, enabling the use of well known solution strategies developed for the Finite Element Method to solve the residual equation. Different projection schemes can be adopted to go from the high-order level to level p = 1. In this paper, we compare a direct projection to level p = 1 with a projection between each level 1 ≤ k ≤ p in terms of iteration numbers and CPU times. Numerical results, including a spectral analysis, show that a direct projection leads to the most efficient method for both single patch and multipatch geometries.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.