Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment
Autor: | García Blanco, Raquel, Borzacchiello, Domenico, Chinesta, Francisco, Díez, Pedro |
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Přispěvatelé: | Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental, Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
Jazyk: | angličtina |
Rok vydání: | 2017 |
Předmět: |
Engineering
Civil Engineering Multidisciplinary Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC] Computer Science Software Engineering Engineering Marine Engineering Manufacturing Engineering Mechanical Energia elèctrica -- Distribució -- Models matemàtics Electric power distribution--Mathematical models Engineering Industrial Engineering Ocean Enginyeria elèctrica::Distribució d’energia elèctrica [Àrees temàtiques de la UPC] Engineering Aerospace Engineering Biomedical |
Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Scipedia Open Access Scipedia SL Recercat. Dipósit de la Recerca de Catalunya instname |
Popis: | This is the peer reviewed version of the following article: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems. |
Databáze: | OpenAIRE |
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