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This paper presents possibilities offered by a diagnostic system called FeD. The system is completely original; it has been developed by the authors on the basis of Arduino platform. The system has been designed to perform and record measurements and to carry out different numerical operations. The real-time function for several operations is incorporated in this system. The necessary input data for the system consist of the electrical voltage waveforms only. Rescaled voltage quantities can be displayed, measured, recorded or computed in any chosen way. The system has been developed particularly for measurements and computations in the ferroresonant circuits. The strongest part of the system is its versatility. It works with a standard PC and supports a universal connection (USB standard). This is undeniably a cost-wise solution. Driving and control of the system functions are carried out using the authors' original software implemented in SciLab environment. This is free software, similar to and compatible with other existing CAD programs such as Octave and MATLAB. The obtained data, scripts and results can be freely transferred between them. The program is equipped with a transparent GUI. The need of constructing a special system to diagnose the ferroresonant circuit has emerged during earlier ferroresonance analyses and computations. Every ferroresonant circuit requires specific kind of diagnostics to estimate and display its base features in order to determine the best scientific approach to the problem. The ferroresonance phenomenon belongs to the domain of nonlinear problems. Its analysis requires excellent skills in mathematics and physics as well as computer science. Moreover, this subject also requires specialized engineering knowledge, particularly in the field of power engineering and power system equipment. Modern mathematical models and analyses used in ferroresonant computations are quite accurate; however, in case of a common user, they are often difficult to understand or implement. This paper provides full description of construction, features and test results of the developed hardware/software system designed for diagnostics of ferroresonant circuits. The test circuit case study has been performed in the entire power supply range. Results of measurements and computations as well as screenshots captured from authors' original software are shown in different figures. The developed software and recorded data have been finally used in modeling and further simulations. During this, the application of the fractional derivative iron core coil model to ferroresonance analysis has been shown. The waveforms obtained from computer simulations have been compared with those obtained from measurements performed in the test circuit.

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.

The methodology and test results of a three-phase three-column transformer with a Dy connection group are presented in this paper. This study covers the dynamics of events that took place in the first period of the transient state caused by the energizing of the transformer under no-load conditions. The origin of inrush currents was analyzed. The influence of factors accompanying the switch-on and the impact of the model parameters on the distribution and maximum values of these currents was studied. In particular, the computational methods of taking into account the influence of residual magnetism in different columns of the transformer core, as well as the impact of the time instant determined in the voltage waveform at which the indicated voltage is supplied to a given transformer winding, were examined. The study was carried out using a nonlinear model constructed on the basis of classical modeling, in which hysteresis is not taken into account. Such a formulated model requires simplification, which is discussed in this paper. The model is described using a system of stiff nonlinear ordinary differential equations. In order to solve the stiff differential state equations set for the transient states of a three-phase transformer in a no-load condition, a Runge–Kutta method, namely the Radau IIA method, with ninth-order quadrature formulas was applied. All calculations were carried out using the authors’ own software, written in C#. A ready-made strategy for energizing a three-column three-phase transformer with a suitable pre-magnetization of its columns is given.

The modeling of a ferromagnetic core coil magnetic hysteresis has been considered. The measurement basis consisted of waveforms that have been recorded for various levels of the iron core saturation levels. The investigated models included classical cases as well as models including a nonlinear fractional coil. The possibilities of solutions for transient problems including such models have been recalled. The details of the estimation process have been described next, where each model evaluation made use of an original methodology dealing with periodic steady states. The influence of the model response on parameter changes has also been studied. Further on the parameter estimation procedure has been described, and the results for the various models have been presented.