University of Zagreb. Faculty of Electrical Engineering and Computing. Department of Energy and Power Systems.
Abstract
U radu je dat pregled modela linearnih i nelinearnih električnih elemenata sa naglaskom na modelu transformatora u postojećim bibliotekama dvaju poznatih programa: EMTP-ATP-a i MATLAB/PSB-a. Identificirani su uzroci postojanja numeričkih oscilacija i totalne numeričke nestabilnosti u transformatora sa negativnom reaktancijom namota analizom svojstvenih vrijednosti matrica sustava. Pokazan je originalni način modeliranja nelinearnih elemenata u proračunima niskofrekvencijskih prijelaznih pojava u transformatorima. Izgrađen je algoritam baziran na hiperstabilnoj backward differentiation formulas-BDFp p-tog reda numeričkoj metodi za proračune niskofrekvencijskih prijelaznih pojava u jednofaznim i trofaznim transformatorima. Pokazane su prednosti razvijenog algoritma u pogledu eliminiranja efekta “prebačaj” i mogućnosti reduciranja ili izbjegavanja numeričkih oscilacija i totalne numeričke nestabilnosti u proračunima niskofrekvencijskih prijelaznih pojava u jednofaznim i trofaznim transformatorima. Izgrađen je model dinamičke histerezne petlje sa prednostima u odnosu na postojeći model Hysteretic Inductor-Type 96 u EMTP-u. Također su provedena eksperimentalna mjerenja prijelaznih pojava uklapanja i ferorezonancije kod jednofaznog transformatora kao i uklapanja kod trofaznog trostupnog transformatora. Rezultati pokusa vrlo dobro se slažu s rezultatima proračuna razvijenog programa.In this work is presented the model of linear and nonlinear electrical elements with accent on transformer model in existing well-known software libraries: EMTP-ATP and MATLAB/PSB. Causes of existance of numerical oscillations and total numerical instability in transformers with negative winding reactance are identified by analysis of eigenvalues of system matrix. Original method of nonlinear elements modeling in calculation of low frequency transients in transformers is showed in this work. The algorithm based on hyper stable backward differentiation formulas-BDFp p-th order numerical procedure for calculation of low frequency transients in single-phase and three-phase transformers is developed additionally. The advantages of developed algoritham in a way of elimination of overhooting effect and possibility of reduction or avoiding numerical oscillations and total numerical instability in low frequency transients calculations in single-phase and three-phase transformers are presented. Model of dynamic hysteretic loop with advantages in comparison with existing Hysteretic Inductor-Type 96, EMTP model is developed. Experimental measurements of transients: switching-on and ferroresonance in single-phase transformer and switching-on in three-phase transformer are obtained. Measurements obtained in the experiment confirmed calculation results of developed software
