ORIGINAL PAPER
Mathematical model and characteristics of dynamic modes for managing the asynchronous motors at voltage asymmetry
1
Management Department, AGH University of Science and Technology, Kraków, Poland
2
Institution of Social-Humanitarian Science, Dnipro University of Technology, Ukraine
3
Dnipro University of Technology, Ukraine
4
Universidad Nacional de San Agustin de Arequipa, Peru
5
South Ukrainian National Pedagogical University named after K. D. Ushynsky, Ukraine
Submission date: 2023-12-02
Final revision date: 2024-07-09
Acceptance date: 2024-07-29
Publication date: 2024-12-11
Corresponding author
Polityka Energetyczna – Energy Policy Journal 2024;27(4):39-58
KEYWORDS
asynchronous motormanagement of the voltage asymmetrygeneralised vectorsmathematical modeldynamic modes
TOPICS
Energy policyEcological, economic, social and legal aspects in energy systemsDevelopment of new energy technologiesEnergy systems modelling
ABSTRACT
The development of a comprehensive mathematical model depicting an asynchronous motor in generalised (resultant) vectors, accounting for voltage asymmetry, stands as a significant stride in this research endavour. This model serves as a powerful tool for conducting an exhaustive analysis of the motor’s characteristics in dynamic operational modes. Its unique capability lies in enabling a granular examination of the impact of both amplitude and phase asymmetry on the motor’s dynamic performance, thereby providing a nuanced understanding crucial for the effective management of asynchronous motors operating under the conditions of voltage asymmetry. In this pursuit, distinct models for an asynchronous motor are delineated separately for the direct and reverse sequence, conceptualised as two distinct machines integrated on a single shaft. Additionally, a unified model is presented, encapsulating the voltage equations along the α and β axes within the fixed coordinate system of the generalised machine. The empirical findings derived from this research present compelling insights into the behaviour of asynchronous motors in transient modes during direct starts under varying degrees of voltage asymmetry. These findings, summarised in a tabulated format, illustrate a clear correlation between the degree of voltage asymmetry and the subsequent reduction in motor performance indices. These findings not only enrich the theoretical understanding of asynchronous motor behaviour in the presence of voltage asymmetry but also lay a solid foundation for devising practical approaches to optimize their performance, further enhancing their operational efficiency and reliability.
METADATA IN OTHER LANGUAGES:
Polish
Model matematyczny i charakterystyki trybów dynamicznych do zarządzania silnikami asynchronicznymi
przy asymetrii napięcia
silnik asynchroniczny, zarządzanie asymetrią napięcia, wektory uogólnione, model, matematyczny, tryby dynamiczne
Opracowanie kompleksowego modelu matematycznego przedstawiającego silnik asynchroniczny w uogólnionych (wypadkowych) wektorach, uwzględniających asymetrię napięcia, stanowi znaczący krok w tym przedsięwzięciu badawczym. Model ten służy jako potężne narzędzie do przeprowadzania wyczerpującej analizy charakterystyk silnika w dynamicznych trybach pracy. Jego unikalna zdolność polega na umożliwieniu szczegółowego badania wpływu zarówno asymetrii amplitudy, jak i fazy na dynamiczną wydajność silnika, zapewniając w ten sposób niuansowe zrozumienie kluczowe dla skutecznego zarządzania silnikami asynchronicznymi pracującymi w warunkach asymetrii napięcia. W tym dążeniu odrębne modele silnika asynchronicznego są określane oddzielnie dla sekwencji bezpośredniej i odwrotnej, pojmowanej jako dwie odrębne maszyny zintegrowane na jednym wale. Dodatkowo przedstawiono ujednolicony model, obejmujący równania napięciowe wzdłuż osi α i β w stałym układzie współrzędnych uogólnionej maszyny. Wyniki empiryczne uzyskane w ramach tych badań przedstawiają przekonujące spostrzeżenia na temat zachowania silników asynchronicznych w trybach przejściowych podczas rozruchów bezpośrednich przy różnym stopniu asymetrii napięcia. Wyniki te, podsumowane w formie tabeli, ilustrują wyraźną korelację między stopniem asymetrii napięcia a późniejszym zmniejszeniem wskaźników wydajności silnika. Wyniki te nie tylko wzbogacają teoretyczne zrozumienie zachowania silnika asynchronicznego w obecności asymetrii napięcia, ale także stanowią solidną podstawę do opracowywania praktycznych podejść w celu optymalizacji ich wydajności, co dodatkowo zwiększa ich wydajność operacyjną i niezawodność.
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