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Differential relaying is one of the most widely used techniques for protecting power transformers. The purpose of this paper is to discuss and cover a developed methodology for analyzing the signals obtained from the differential protection of power transformers.

The differential signal obtained from the protective relays of power transformers is analyzed in this paper, in order to establish a relation between time‐dependent symmetrical components and space vectors. As a result of the formulation of such a relation, specific patterns are obtained and classified for the plot of the space vector during fault and inrush conditions.

What was found in the course of the work? This will refer to analysis, discussion, or results. It has been found that the discrimination between inrush and fault conditions is possible by observing a characteristic asymmetry in the plots of the space vector. A method for dealing with the said asymmetries based on the absolute value of the space vector as obtained from the differential signal is proposed and discussed. The theoretical approaches given in the paper are further validated through finite element simulations and laboratory tests, which include linear and non‐linear loads, in order to account for more severe exploitation conditions.

A complete protective algorithm can be developed from the analysis of the methodology proposed, which avoids the spectral analysis, since the methodology is based in pattern analysis rather that in the latter technique.

The methodology provides faster identification of the fault during inrush condition, since the spectral analysis is prevented.

It may be stated that the major contribution of the paper is the methodology proposed for identifying internal faults in power transformers using pattern characterization of the plot of the space vector.

The purpose of this paper is to reduce the inrush current and dip in voltage for energy‐ saving purposes in relation to residential air‐conditioning systems.

The paper focuses on the experimental harmonic investigation of a window‐type residential AC unit line current under time‐based soft‐starting control strategy. The control strategy assumes that only source voltage and current measurements are available. The soft‐starter is based on power electronic devices controlled through a firing signal generated by a programmed microcontroller during the first 500 ms.

The harmonic content shows the effect of the soft‐starter in exciting high‐frequency components of the line current. Harmonics investigations show that the high frequencies – even or odd multiples – of the fundamental line frequency are all excited by the soft‐starter approach. Some of these frequencies may harm the life cycle of the air‐conditioner.

The real data harmonic analysis shows that the adopted approach excites the entire frequency spectrum of the signal. A better monitoring of the harmonics is required. A closed loop adaptive soft‐starting control may perform much better than a time‐based soft‐starting strategy.

The paper assesses the power quality related to time‐based soft‐starting strategy of a residential air‐conditioning system to reduce the inrush current and the dip in voltage, both with a serious effect on energy savings, especially when the AC load is around 65 per cent of the total power demand load.

Despite its well-founded criticism and lack of proper justification under core saturation conditions, the T-equivalent transformer model (Steinmetz scheme) is obviously championing in the literature. This educational paper aims to explain in a simple manner the limitations of the T-model of a low-frequency transformer and critically analyses some attempts to improve it.

Using a simplified examination of magnetic fluxes in the core and windings and using the modeling in ATPDraw, it is shown that transient transformer models with the indivisible leakage inductance allow circumventing the drawbacks of the T-model.

The authors show the absence of valid grounds for subdividing the leakage inductance of a transformer between its primary and secondary windings. The connection between the use of individual leakage inductances and inaccurate prediction of inrush current peaks is outlined as an important example.

The presented models can be used either as independent tools or serve as a reference for subsequent developments.

Over generations, the habitual transformer T-equivalent is widely used by engineers and Electromagnetic Transients Program experts with no attention to its inadequacy under core saturation conditions. Having studied typical winding configurations, the authors have shown that neither of them has any relation to the T-equivalent.

This educational paper will contribute to the correct understanding of the transients occurring in a transformer under abnormal conditions such as inrush current or ferroresonance events, as well as during an out-of-phase synchronization of step-up generator transformers.

This paper aims to propose a method of parametrizing topological transformer model at high flux densities in the core.

The approach proposed is based on terminal voltages and currents measured in a special purpose saturation test whose data are combined with typical saturation curves of grain-oriented electrical steels; the modeling is carried out in the ATPDraw program.

The authors corroborate experimentally the necessity of dividing the zero sequence impedance between all transformer phases and propose a method of the individual representation of the legs and yokes. This eliminates the use of nonexistent leakage inductances of primary and secondary windings.

The presented modeling approach can be used for predicting inrush current events and in the evaluation of the impact caused by geomagnetically induced currents (GICs).

The proposed approach is completely original and will contribute to a better understanding of the transients occurring in a transformer under abnormal conditions, such as inrush current events and GICs.

Two experts explain how to develop a common component for some sophisticated applications.

Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations leading to complicated analysis procedures. This study aims to propose an analytical-numerical method to accurately analyze the three-phase three-limb core-type transformer inrush current in different cases considering the nonlinear behavior of the iron core.

The proposed method focuses on acquiring equations for inrush current and also the magnetic core flux by the application of a simulation-based iterative approach. In this regard, multiple integral equations are solved taking the time intervals into account. Then several derivations and integrations of matrix terms are substituted into the obtained results so as to simplify the solution process.

The method provides notable enhancements in computation time and also excellent qualities of accuracy compared with conventional numerical methods.

The proposed method is simulated for two three-phase transformers via MATLAB software. The obtained simulation results have been also compared with experimental tests.

Actually, the analytical-numerical method is capable of computing higher number of iterations in a shorter time efficiently, while making use of the conventional numerical procedures may not result in expected convergences. The simulation results of the proposed analytical-numerical technique illustrate a close agreement with the experimental test, and hence, verify the method preciousness.

The purpose of this paper is to propose an accurate model for simulation of inrush current in power transformers with taking into account the magnetic core structure and hysteresis phenomenon. Determination of the required model parameters and generalization of the obtained parameters to be used in different conditions with acceptable accuracy is the secondary purpose of this work.

The duality transformation is used to construct the transformer model based on its topology. The inverse Jiles-Atherton hysteresis model is used to represent the magnetic core behavior. Measured inrush waveforms of a laboratory test power transformer are used to calculate a fitness function which is defined by comparing the measured and simulated currents. This fitness function is minimized by particle swarm optimization algorithm which calculates the optimal model parameters.

An analytical and simple approach is proposed to generalize the obtained parameters from one inrush current measurement for simulation of this phenomenon in different situations. The measurement results verify the accuracy of the proposed method. The developed model with the determined parameters can be used for accurate simulation of inrush current transient in power transformers.

A general and flexible topology-based model is developed in PSCAD/EMTDC software to represent the transformer behavior in inrush situation. The hysteresis model parameters which are obtained from one inrush current waveform are generalized using the structure parameters, switching angle, and residual flux for accurate simulation of this phenomenon in different conditions.

The purpose of this paper is to estimate that the start-up current parameters are stochastic or not. Electronic equipment in luminaries significantly improves their luminous efficiency, thereby increasing the energy efficiency of lighting installations. However, the use of electronics [e.g. electronic ballasts for discharge lamps or power supply units for light-emitting diode (LED) luminaries] may also cause some negative effects in lighting installations. One of such effects is large inrush current, which can greatly exceed the admissible line load and trigger the overcurrent protective devices.

The paper presents results of laboratory tests together with their statistical analysis of the inrush currents of lighting luminaires. Three road luminaires build in different technologies of similar power have been selected for the study. The theoretical distributions described by the analytical formulas matched the empirical distributions by using the MATLAB’ Statistical Toolbox.

As parameters that characterize short-time overcurrent at start-up are the maximum value of overcurrent amplitude in start-up moment (I_PIC), the duration of overcurrent in start-up moment (t_PIC) and melting integral MI. The aim of this statistical analysis of the selected parameter is to provide an overcurrent mathematical description allowing to estimate the probability of occurrence of values. For lighting luminaire fitted with magnetic ballasts, the parameters analyzed will randomly vary with the moment of power on. For electronic ballasts, the occurrence of this phenomenon depends on the adopted construction solution.

This will allow, for example, to estimate the probability of activation of protection device by comparing the value of the inrush current Joule’s integral MI with its value for the analyzed protection device. The proposed method may be useful for checking the selectivity of the protection devices in the lighting system.

The study enables application of a probabilistic model for analysis of inrush currents of lighting luminaire and predicting the possible consequences of their occurrence.

The theoretical method of converting the magnetic circuit into an electric circuit is mature, but the way to determine the inductances in the electric circuit is not reliable, especially for the core working in saturation status, and it is impossible to determine the inductances by the transformer terminal measurements, as the measurement information is not enough to determine a number of inductances. This paper aims to propose an approach of calculating the reluctances.

In this paper, an approach of calculating the reluctances is proposed based on the numerical simulation of magnetic field in transformer with different values of current excitation. The reluctance of a core segment or air region as a branch of magnetic circuit is obtained by the magnetic energy and magnetic flux. By this way, all the reluctances as function of flux can be determined, and then the inductances can be determined. The reluctances and equivalent electric circuit of three-phase integrative transformer is determined, and its validation is proved in the paper.

The single phase example shows that the proposed method has a good performances on analysis of the inrush current in deep saturation. The peak value of the inrush current derived from the proposed approach matches well with the results obtained by coupled circuit-FEM analysis, and the difference is about 4.8 per cent. For studies on dual models of single phase transformers, the leakage inductances have important effects on the peak value of the inrush current. The reluctances of three-phase transformer are calculated, and the equivalent circuit simulation results are slightly smaller than the coupled circuit-FEM simulation results.

Approach of calculating the reluctances based on the numerical simulation of magnetic field in transformer is proposed. The magnetic core and air space are divided into several segments, and the reluctance for each segment is calculated based on the energy in the region and the flux of the cross-sectional area. By applying various excitation currents, all the reluctances as function of flux can be determined, and then all the non-linear inductances including the non-linear leakage inductances are obtained. The proposed approach is reliable to determine a number of inductances in the dual electric circuit, especially for deep saturation status.

The purpose of this paper is the modelling and estimation of inrush currents while energising power devices under no load conditions. An analytical representation of the nonlinear B-H curve serves for considering the hysteresis behaviour in the numerical model.

The model is implemented into a standard finite element formulation to compute transient problems.

Inrush currents behave like faults in power distribution facilities. Its prior estimation helps to distinguish between operating conditions and faults.

The magnetic cores may become extremely magnetised. At such high material saturations, the material characteristics are not measurable accurately. Hence, the results depend on the extrapolation of the B-H curves.

The use of first-order reversal curves within the major hysteresis loops helps in a convenient way to estimate peak and shape of the inrush currents.