Diagnostic approach in assessment of a ferroresonant circuit

Abstract

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.

Supercapacitor fractional model − DAQ-based measurements of frequency characteristics and error computation

“…Fractional calculus has many other applicationsalso in other fields, like control systems [7]. In circuit theory some studies have shown its usefulness when modelling coils with ferromagnetic cores [8,9,10]. As for the elements of fractional calculus, there are many definitions of derivatives and integrals [11].…”

Diagnosis of a ferroresonance type through visualisation

“…Through an adjustment of the source voltage level one can intentionally induce a ferroresonance phenomenon in the circuit. The FeD system [5] was used to acquire the voltages and current waveforms of all circuit components ( Fig. 1.…”

“…During the measurements the ferromagnetic core coil has reached its saturation region conditions. The flux linkage, a quantity not measurable directly, was obtained on the basis of its definition as a time integral of the voltage across the coil [5].…”

“…Among recognized tools dedicated to study the nonlinear and dynamic systems, a diagnostic approach to the ferroresonance is optimal with 2D/3D phase plane analyses supported by Poincaré maps [5,8]. Such solution with upgrades was proposed in this paper to correctly classify the ferroresonance type that has occurred in the test circuit.…”

Optimization for Software Implementation of Fractional Calculus Numerical Methods in an Embedded System

“…Apart from classic examples like the modeling of viscoelastic materials [ 4 ] and the diffusion process [ 5 , 6 ], it was also found to be useful in economics for modeling of financial systems and economic growth [ 7 , 8 ], in medicine and biomedical engineering for disease analysis, drug modeling and administration, and signal acquisition [ 9 , 10 , 11 , 12 , 13 ], in computer science [ 14 ] for the development of neural networks with memory effects, and other applications with time-varying values of fractional-orders [ 15 ]. Only in the field of electrical engineering do some recent advances involve mathematical descriptions of supercapacitors [ 16 , 17 ], lithium-ion batteries with nonlinear capacities [ 18 ], and nonlinear coils in a ferroresonant circuit [ 19 ]. In control engineering, the algorithms of fractional-order controllers have received much interest, in particular, the fractional-order PID controller [ 20 , 21 , 22 ].…”