Measurement-Based Stiff Equation Methodology for Single Phase Transformer Inrush Current Computations

Łukasz Majka (), Bernard Baron and Paweł Zydroń ()
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Łukasz Majka: Department of Electrical Engineering and Computer Science, Faculty of Electrical Engineering, Silesian University of Technology, Akademicka Street 10, 44-100 Gliwice, Poland
Bernard Baron: Department of Drive Automation and Robotics, Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, Prószkowska Street 76, 45-272 Opole, Poland
Paweł Zydroń: Department of Electrical and Power Engineering, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, AGH University of Science and Technology, A. Mickiewicza Avenue 30, 30-059 Kraków, Poland

Energies, 2022, vol. 15, issue 20, 1-19

Abstract: The present paper describes the research on the mechanism of inrush current formation in a modern single-phase transformer, in which the insulation system must withstand the stresses arising during these transient states. A complete and measurement-verified method for determining the transformer inrush current waveforms and other signals (e.g., fluxes and voltages) is developed. This method makes it possible to determine a steady state solution. However, on account of the electromagnetic phenomena, the solving process is long. To analyze the transient dynamic response of the tested transformer, a nonlinear model was assumed, from which the stiff differential equations were derived. The simulation analyses were performed using dedicated software written in C# with the original implementation of the five-stage Radau IIA algorithm selected from the known variants of the Runge–Kutta implicit methods. The calculations were based on the measurement waveforms recorded during transient (switch-on) and steady-state states when the transformer was not loaded. The full magnetization curve of the core sheets of the tested transformer with an original implementation of the polynomial fitting mechanism was applied. As a representative example and for the purposes of experimental verification of numerical tests, the worst case scenario for switch-on of an unloaded transformer was applied (switch-on is performed when the supplied voltage is zero). Phenomena related to the obtained experimental results, such as saturation and hysteresis, are discussed as well.

Keywords: stiff nonlinear ordinary differential equations; Runge–Kutta implicit methods; circuit model of a single-phase transformer; hysteresis; parameter estimation; measurements; transient states (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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