Monitoring a PGD solver for parametric power flow problems with goal‐oriented error assessment

• Published in: International journal for numerical methods in engineering 2017-08, Vol.111 (6), p.529-552
• Main Authors: García‐Blanco, R., Borzacchiello, D., Chinesta, F., Diez, P.
• Format: Article
• Language: English
• Subjects: Accuracy; Algebra; Computer programs; Distribució; Distribució d’energia elèctrica; Electric power distribution; Energia elèctrica; Enginyeria elèctrica; Error analysis; error assessment; Estimates; Matemàtiques i estadística; Mathematical models; Models matemàtics; Nested loops; Parametric analysis; parametric power flow; Permissible error; Power flow; power losses; proper generalized decomposition; reduced order models; Àlgebra; Àrees temàtiques de la UPC
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.5470

Summary 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. Copyright © 2016 John Wiley & Sons, Ltd.