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

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