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1
Content available Uncertainty of the magnetic flux linkage measurements performed by modified current decay test
Kowalik Z.
Archives of Electrical Engineering
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2017
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Vol. 66, nr 3
643--653
EN
The paper presents the estimation methodology for uncertainties of magnetic flux linkage measurements, when the flux linkage and current functions with respect to time are obtained instead of single values of these quantities. The computed uncertainties are then used to estimate the quality of an approximation of a current-flux characteristic in the mathematical model of an electrical machine when the approximation is based on the results of measurements.
2
Content available Measurement Results Based Approximation of the Nonlinear Flux-Current Characteristic of an Electromechanical Actuator
Kowalik Z.
Measurement Automation Monitoring
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2016
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Vol. 62, No. 2
49--54
EN
A Hamiltonian model of an electromechanical actuator requires approximation of its flux-current characteristic. It can be made using a simplicial approximation, which requires the sets of corresponding points in the spaces of currents and fluxes. These points can be chosen from the trajectories that describe the behaviour of the electromechanical system in these spaces. In the paper, a method of obtaining these trajectories by measurements is shown and four original methods of choosing points lying on them to construct the required points sets are presented. The sets are constructed so that they contain a possibly small number of points, but the approximation which is based on them is precise. The presented methods are used to approximate a flux-current characteristic of the prototype synchronous reluctance machine. The simulation results, computed using the models based on these approximations, are also presented and discussed. The best results are obtained by methods using the computed value of the magnetic field coenergy in the modelled machine.
3
Content available Aproksymacja charakterystyki strumieniowo-prądowej przetwornika elektromechanicznego wykorzystująca wyniki pomiarów
Kowalik Z.
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
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2016
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nr 2
60--63
PL
Hamiltonowski model przetwornika elektromechanicznego wymaga aproksymacji jego charakterystyki strumieniowo-prądowej. Można jej dokonać kawałkami afinicznie w oparciu o zbiory odpowiadających sobie punktów w przestrzeniach prądów i strumieni. W artykule przedstawiono cztery oryginalne metody konstrukcji tych zbiorów w oparciu o dane pomiarowe. Najlepsze rezultaty osiągnięto za pomocą metod wykorzystujących obliczoną wartość koenergii pola w maszynie.
EN
A Hamiltonian model of an electromechanical actuator requires an approximation of its flux-current characteristic. It can be made using a piecewise affine function, based on sets of corresponding points in the spaces of flux and current. In the paper four original methods of constructing these sets based on measurements results are presented. The best results are obtained using methods that incorporate the computed value of the magnetic field coenergy in the modeled machine.
4
Content available Tidal currents in the western Svalbard Fjords
Kowalik Z., Marchenko A., Brazhnikov D., Marchenko N.
Oceanologia
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2015
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No. 57 (4)
318--327
EN
The paper is focusing on the tides and on the strong tidal current generated in the western fjords of Svalbard. Numerical model is chosen as a tool to study the barotropic tides. Model results are compared against measured sea level and drifters. Numerical modeling and observation of tides point that the tidal amplitude does not change strongly in these fjords but the tidal currents are enhanced in several locations, namely at the entrance to the Dickson Fjord, in the narrow passages in proximity to Svea, and in the central part of Van Keulenfjorden. As the strongest currents have been found at the passages at Akseløya Island we have focused our research on this location. The narrow northern channel (Akselsundet) at Akseløya is the main waterway to Svea coal mines. Tidal currents computed and observed at the northern tip of Akseløya Island can reach amplitude from 2 to 3 m s−1. Observation of the deployed drifters and calculation of the seeded particles in the passage at Akseløya depicted a complicated pattern of eddies. The jet-like currents and eddies are quite different at the ebb and flood tide phases. As the Akseløya Island orientation relative to the shore is different for the flood and ebb waters the flow through Akselsundet is differently constrained by this geometry. The observations show that the oscillating tidal motion causes large excursions of the water particle. The drifters released in the passage during flood ended up trapped in the eddy on the eastern side of the island.
5
Content available remote Error analysis in mathematical model of electromechanical actuator using Hamiltonian equations
Burlikowski W., Kowalik Z.
Czasopismo Techniczne. Elektrotechnika
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2015
|
Y. 112, iss. 1-E
119--128
EN
This paper presents a methodology of error analysis in a mathematical model of an electromechanical actuator using Hamiltonian equations in the description of energy conversion. As the basic quantity in numerical algorithms, the coenergy of magnetic field Ecm is employed. The reason for the application of coenergy as a state function is the explicitness of its value for a given set of state variables, resulting from neglecting eddy currents and hysteresis phenomenon in the model.
PL
W artykule przedstawiono metodykę analizy błędu w modelu matematycznym przetwornika elektromechanicznego wykorzystującym równania Hamiltona w opisie przemiany elektromechanicznej. Jako podstawowej wielkości w algorytmie obliczeniowym użyto koenergii pola magnetycznego Ecm. Wykorzystano w tym celu jednoznaczność określenia wartości koenergii dla danej wartości zmiennych stanu, wynikającą z pominięcia w modelu prądów wirowych oraz zjawiska histerezy.
6
Content available Development of a topology-based current-flux characteristic approximation in a Hamiltonian model of a reluctance machine
Burlikowski W., Kowalik Z.
Archives of Electrical Engineering
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2015
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Vol. 64, nr 2
277--289
EN
The paper presents an algorithm for the construction of an approximation of a highly nonlinear current-flux characteristic of a synchronous reluctance machine. Such an approximation is required in a Hamiltonian model of an electric machine and the constructed approximation is suited to be used in such a model. It employs a simplicial approximation based on irregular points sets in the spaces of currents and fluxes. The sets are constructed by the iterative insertion of new points. Initially the sets contain an arbitrarily small number of elements. The insertion is based on an approximation error calculation. Based on the sets containing possibly small number of elements, the proposed procedure leads to smooth and precise approximation. Due to the nonlinearity of the approximated characteristics, ambiguities can occur. A method for the triangulation refinement of the sets of currents and fluxes that eliminates them is also presented. In the paper, a reluctance machine model using the constructed approximation is described and compared with a model using the approximation based on regular sets.
7
Content available remote Użycie aproksymacji symplicjalnej z nierównomiernym rozłożeniem wierzchołków do aproksymacji charakterystyki strumieniowo-prądowej silnika SynRM
Kowalik Z.
Prace Naukowe Politechniki Śląskiej. Elektryka
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2014
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z. 4
89--99
PL
Model hamiltonowski przetwornika elektromechanicznego wymaga aproksymacji jego charakterystyki strumieniowo-prądowej. Aproksymacji tej można dokonać, stosując aproksymację symplicjalną, która aproksymuje charakterystykę na podstawie zbiorów punktów w przestrzeniach prądów i strumieni. Aby aproksymacja była dokładna, ale zbiory zawierały małą liczbę punktów, punkty w zbiorach nie powinny być rozłożone równomiernie, ale zbiory powinny być zagęszczane w miejscach dużych nieliniowości charakterystyki strumieniowo-prądowej. W artykule opisano procedurę konstruowania zbiorów na podstawie obliczeń błędu aproksymacji. Aproksymację opartą na wygenerowanych zbiorach porównano z aproksymacją opartą na zbiorach równomiernych. W artykule porównano też zachowanie się uproszczonego modelu hamiltonowskiego maszyny SynRM dla obu tych aproksymacji.
EN
A Hamiltonian model of an electrical machine requires an approximation of its current-flux characteristic. Such an approximation can be performed with a use of symplicial approximation. Symplicial approximation is based on sets of points in currents and fluxes spaces. To obtain an accurate approximation with sets containing a small number of points, these points should not be distributed uniformly, but sets should be more dense in the areas, where approximated current-flux characteristic is highly nonlinear. In this paper a method of constructing these sets is described. A method is based on an approximation error calculation. Symplicial approximation based on constructed sets is compared to an approximation based on regular sets. In the paper a behavior of a Hamiltonian model of a SynRM machine working with two these approximations is also presented.
8
Content available remote Analiza błędu w modelu matematycznym przetwornika elektromechanicznego wykorzystującym równania Hamiltona
Burlikowski W., Kowalik Z.
Maszyny Elektryczne : zeszyty problemowe
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2014
|
Nr 4(104)
131--136
PL
W artykule przedstawiono metodykę analizy błędu w modelu matematycznym przetwornika elektromechanicznego, wykorzystującym równania Hamiltona w opisie przemiany elektromechanicznej. Jako podstawową wielkość w algorytmie obliczeniowym użyto koenergię pola magnetycznego Ecm. Wykorzystano w tym celu jednoznaczność określenia wartości koenergii dla danej wartości zmiennych stanu, wynikającą z pominięcia w modelu prądów wirowych oraz zjawiska histerezy.
EN
The paper presents a methodology of error analysis in mathematical model of an electromechanical actuator using Hamiltonian equations in the description of energy conversion. As the basic quantity in numerical algorithm the coenergy of magnetic field Ecm is employed. The reason for application of coenergy as a state function is the explicitness of its value for a given set of state variables, resulting from neglecting Eddy currents and hysteresis phenomenon in the model.
9
Content available remote The distribution and tapping tidal energy
Kowalik Z.
Oceanologia
|
2004
|
No. 46 (3)
291-331
EN
Tidal power along tidal shores has been used for centuries to run small tidal mills. Generating electricity by tapping tidal power proved to be very successful only in the last century through the tidal power plant constructed in 1967 in La Rance, France. This used a large barrier to generate the sea level head necessary for driving turbines. Construction of such plants evolved very slowly because of prohibitive costs and concerns about the environmental impact. Developments in the construction of small, efficient and inexpensive underwater turbines admit the possibility of small scale operations that will use local tidal currents to bring electricity to remote locations. Since the generation of such electricity is concerned with the tidal energy in local water bodies, it is important to understand the site-specific energy balance, i.e., the energy flowing in through open boundaries, and the energy generated and dissipated within the local domain. The question is how to tap the tidal energy while keeping possible changes in the present tidal regimes to a minimum. The older approach of constructing barrages may still be quite useful in some locations. The basics of such tidal power plants constructed in a small bay are analyzed in order to understand the principal parameter for tidal plant evaluation, i.e., the power produced. The new approach is to place turbines - devices similar to windmills - in the pathway of tidal currents. Theoretically, the amount of power available by such turbines for electricity generation is proportional to the water density and velocity cubed of the tidal flow. The naturally dissipated tidal power due to bottom friction forces is also proportional to the cube of the velocity. Because of this similarity, the exploitation of tidal energy can be directed to reinvesting the naturally dissipated power into tidal power for the generation of electricity. This approach to tidal power exploitation is better tuned towards preservation of the natural tidal regime. To answer the many questions related to tidal regime changes, it is important to develop a new branch of tidal dynamics which will help to better understand the interaction between a natural tidal regime and future changes caused by tapping into tidal energy.
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