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EN
Transformers are the main element of the power system. Their reliable operation affects the efficiency of energy supply. Each transformer should be subjected to periodic diagnostic tests. Frequency response analysis (FRA) is a non-destructive diagnostic method that detects deformations in windings. The paper presents research on the influence of the measuring setup on the efficiency of detecting various windings deformations in the transformer, which showed that the capacitive interwinding test setup is more sensitive than standard end-to-end test setup.
PL
Głównym elementem systemu elektroenergetycznego są transformatory. Ich niezawodna praca wpływa na jakość dostaw energii. Każdy transformator powinien być poddawany okresowym badaniom diagnostycznym. Analiza odpowiedzi częstotliwościowej (FRA) jest bezinwazyjną metodą do wykrywania odkształceń uzwojeń. W pracy przedstawiono badania wpływu układu pomiarowego na efektywność wykrywania różnych deformacji uzwojeń w transformatorze. Badania przeprowadzone w układzie międzyuzwojeniowym pojemnościowym wykazują skuteczność wykrywania deformacji lepszą niż w standardowym układzie pomiędzy końcami uzwojenia.
PL
Artykuł omawia możliwość zastosowania wykresów polarnych do analizy danych pomiarowych odpowiedzi częstotliwościowej uzwojeń transformatorów. Zaprezentowano dane pochodzące z eksperymentu polegającego na wprowadzaniu do transformatora defektów i rejestrowaniu odpowiedzi w dwóch różnych konfiguracjach pomiarowych. Najlepsze efekty uzyskano prezentując na wykresach polarnych dane różnicowe zmierzone w układzie międzyuzwojeniowym pojemnościowym.
EN
The paper describes the possibility of using polar plots to the analysis of measurement data of transformer windings frequency response. There is presented data from the experiment based on introduction into transformer faults and measurements of the response in two measurement setups. The best effects were achieved for presentation on the polar plots differential data measured in the interwinding capacitive test configuration.
EN
The diagnostics of power transformers is a very fast developing branch. Due to increasing average age of assets and changes in asset management strategies, nowadays companies introduce asset management based on technical condition. One of important methods used for diagnostics of a transformer’s active part is Frequency Response Analysis (FRA). It allows determination of mechanical condition of windings, their displacements, deformations and electric faults, as well as some problems with internal leads and connections, core and bushings. In the FRA measurements of many power transformers there can be observed a first resonance, which position on frequency axis and damping factor seems to be similar for primary and secondary windings. The authors are going to explain this strange phenomenon, not depending on inductance of the winding being measured.
PL
W zakresie częstotliwości do 10 kHz rdzeń transformatora ma decydujący wpływ na kształt charakterystyki częstotliwościowej uzwojenia. Przedstawiono metodę modelowania uwzględniającą laminację rdzenia oraz jego konduktywność. W podanym zakresie częstotliwości występuje rezonans powodowany obecnością innych, w danej chwili niepodlegających pomiarowi, uzwojeń. Pokazano prosty sposób uwzględnienia wpływu tych uzwojeń w modelu o stałych skupionych.
EN
In the frequency range up to 10 kHz transformer’s core has a principal influence on the shape of the frequency response of the winding. The paper presents a modeling method taking into account the core lamination and its conductivity. In the given frequency range there can be found a resonance caused by the presence of others windings, at the moment not being measured. A simple way to take into account the impact of these windings in the lumped parameter model is shown.
EN
One of important methods used for diagnostics of a transformer’s active part is Frequency Response Analysis (FRA). It allows to determine the mechanical condition of windings, their displacements, deformations and electric faults, as well as some problems with internal leads and connections, core and bushings. Still pending problem is interpretation of measurements results. One of approaches is application of computer modeling to simulate various failure modes and connected with them changes in FRA response. The paper presents two types of models, one based on lumped parameters with RLC elements, and one based on distributed parameters with TLM method. Both methods give similar results, comparable to real measurements of simulated coil.
EN
The diagnostics of power transformers is a very fast developing branch, due to increasing average age of assets and changes in asset management strategies, nowadays companies introduce asset management based on technical condition. One of important methods used for diagnostics of a transformer’s active part is Frequency Response Analysis (FRA). It allows determination of mechanical condition of windings, their displacements, deformations and electric faults, as well as some problems with internal leads and connections, core and bushings. For the aim of windings impedance modeling the RLC models are applied. The idea of lumped parameters models was presented in [6]. The new universal model basing on circuit solution is developed in this paper. Lumped parameters used are calculated with finite element method and Maxwell package. The examples of models created for simple windings were compared to real measurements.
EN
The diagnostics of power transformers is a very fast developing branch, due to increasing average age of assets and changes in asset management strategies, nowadays companies introduce asset management based on a real technical condition. One of important methods used for diagnostics of a transformer’s active part is Frequency Response Analysis (FRA). It allows determination of mechanical condition of windings, their displacements, deformations and electric faults, as well as some problems with internal leads and connections, core and bushings. For the aim of windings impedance modeling the RLC models are applied. The idea of lumped parameters models was presented in [6]. The new universal model basing on circuit solution is developed in this paper. Lumped parameters used in calculations are obtained with finite element method and Maxwell package. The examples of models created for simple windings were compared to real measurements.
PL
W artykule przedstawiono metodę modelowania odpowiedzi częstotliwościowej uzwojenia transformatora wykorzystującą elementy linii długiej. Uzyskane wyniki symulacji porównano z pomiarem przeprowadzonym na rzeczywistym fragmencie uzwojenia, uzyskując zbliżony kształt przebiegu odpowiedzi częstotliwościowej. Nowa metoda, po uzyskaniu odpowiednio dużej dokładności obliczeń, umożliwi dokładne odwzorowanie rzeczywistych przebiegów.
EN
The paper presents the method for frequency response simulation based on transmission line elements. The results obtained from simulation were compared to data measured on a disc taken from the real winding. It was found that both curves were similar. The new method, when improved with higher accuracy of calculations, will allow exact simulations of the real frequency responses.
EN
The diagnostics of power transformers is a very fast developing branch, due to increasing average age of assets and changes in asset management strategies, nowadays companies introduce asset management based on technical condition. One of important methods used for diagnostics of a transformer’s active part is Frequency Response Analysis (FRA). It allows determination of mechanical condition of windings, their displacements, deformations and electric faults, as well as some problems with internal leads and connections, core and bushings. For the aim of windings impedance modeling the transmission-line models are applied. The idea of TLM was presented in [1], While the length of transformer wires is comparable to wave length at high frequency, such approach is reasonable. The paper presents examples of models created for simple windings.
EN
The diagnostics of power transformers is a very fast developing branch, due to increasing average age of assets and changes in asset management strategies, nowadays companies introduce asset management based on technical condition. One of important methods used for diagnostics of a transformer’s active part is Frequency Response Analysis (FRA). It allows determination of mechanical condition of windings, their displacements, deformations and electric faults, as well as some problems with internal leads and connections, core and bushings. For the aim of windings impedance modeling the transmission-line models are applied. The idea of TLM was presented in [1]. While the length of transformer wires is comparable to wave length at high frequency, such approach is reasonable. The paper presents examples of models created for simple windings.
EN
In last years, the methods for material structure recognition using the modern CAD technology have made remarkable progress in achieving automatically optimum designs. The recognition and optimization of structure, are done in order to fine tune the optimum layout. For this aim, the measurements of desired field quantity for sufficient number of points have to be undertaken. Next, the inverse task, consisting in fact of repeated forward tasks, should be conducted.
PL
W ostatnich latach metody rozpoznawania struktury materiału z wykorzystaniem nowoczesnych metod komputerowych poczyniły znaczny postęp. Celem rozpoznawania struktury materiału przewodzącego jest optymalizacja jego kształtu lub ocena stanu tej struktury pod kątem obecności pęknięć i defektów. Punktem wyjścia jest dokonanie odpowiedniej liczby pomiarów pola magnetycznego nad powierzchnią przewodzącą a następnie przeprowadzenie zadania odwrotnego wyznaczenia struktury materiału przewodzącego. (Zadania odwrotne pola elektromagnetycznego wykorzystujące analizę wrażliwości w dziedzinie czasu).
EN
This work deals with the inverse problem associated to 3D crack identification inside a conductive material using eddy current measurements. In order to accelerate the time-consuming direct optimization, the reconstruction is provided by the minimization of a last-square functional of the data-model misfit using space mapping (SM) methodology. This technique enables to shift the optimization burden from a time consuming and accurate model to the less precise but faster coarse surrogate model. In this work, the finite element method (FEM) is used as a fine model while the model based on the volume integral method (VIM) serves as a coarse model. The application of the proposed method to the shape reconstruction allows to shorten the evaluation time that is required to provide the proper parameter estimation of surface defects.
PL
W artykule przedstawiono badania dotyczące wpływu zwarć w uzwojeniach transformatora na rejestrowaną odpowiedź częstotliwościową – metodą FRA (Frequency Response Analysis). Zwarcia mają duży wpływ na kształt krzywej FRA w zakresie częstotliwości charakteryzującym obwód magnetyczny, co pozwala jednoznacznie identyfikować powstanie zwarcia. Dodatkowo w zakresie wyższych częstotliwości występują zmiany zależne od miejsca i skali zwarcia, na podstawie których możliwe jest dokładne określenie położenia i rozmiaru tego defektu. Prace eksperymentalne i modelowe wskazują, że jest możliwe przeprowadzenie analizy wyników pomiarowych FRA pod tym kątem.
EN
The paper presents research on influence of short-circuits in transformer windings on frequency response measured with FRA method (Frequency Response Analysis). Short-circuits have significant influence on the shape of FRA curve in frequencies responsible for magnetic circuit, which allows clear identification of short-circuit presence. In addition in higher frequencies range there are changes dependent on the location and scale of short-circuit, which can help to determine size and location of defect. Experimental studies and computer modeling showed that it is possible to conduct analysis of measurement results in this direction.
EN
Semi-discrete method is known since 80's. The method provides analytical solution in time, so the time-stepping may be omitted. Comparing to usual finite elements in time, this method seems not to be numerically effective, because produced matrices are dense. From this reason, it was rather rarely used. But now, carrying out sensitivity analysis with adjoint models [1, 2] we have to obtain the solutions in forward and backward time. The both time points should coincide with each other. For space discretization we use finite elements, as usual. The semi-discrete method allows us to determine analytically the continuous solution for any given time of analysis. In this work we show evaluation of this method for different kind of excitation shapes.
EN
The diagnostics of power transformers is very important in order to plan repairs and replacements of aged population of transformers operated in Poland and Europe. One of these methods is Frequency Response Analysis - FRA. It can detect any mechanical changes in active part of transformer, which may even lead to serious faults of units in service. As the method is based on comparison of measured curves, which are not always available from previous measurements the computer modeling was applied to create models of windings’ response. The paper presents examples of models created for simple windings and also for real transformer with some deformations of windings simulated.
EN
Semi-discrete method was described already in the earlier works of Zienkiewicz. Because of poor numerical efficiency it was rather rarely used. But now, carrying out sensitivity analysis with adjoint models [1,2] we have to obtain the solutions in forward and backward time. The both time points should coincide with each other. In our earlier works, the FE-time-stepping scheme was exploited. The proposed semi-discrete method allows us to obtain time-domain solution without time-stepping. For space discretization we use finite elements, as usual. The semi-discrete method allows us to determine analytic and continuous solution for any given time of analysis. In this work we consider only axial- symmetric models containing linear and isotropic media.
EN
Sensitivity analysis determines the dependence of global or local electromagnetic quantities on geometrical or physical parameters expressed in the form of an objective function. The final aim of the field calculation methods is generally the design of an electromagnetic device. Solution of inverse problem on the basis of the finite elements method (FEM) makes the optimal shape design possible, as well as the identification of material cracks and flaws inside the conducting materials with the help of the eddy-current method. These tasks can be defined similarly for recognition of the spatial distribution of material parameters. The recognition takes place in iterative manner, basing on gradient information derived from the sensitivity analysis. The work deals with sensitivity evaluation in conjunction with finite element algorithms. It will be shown that the sensitivity analysis necessary to solve an inverse problem, requires only a low additional calculation cost.
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