Sergey E. Zirka

The paper is devoted to the modeling of a three-phase, three-legged transformer under no-load and inrush current conditions. To simplify the study, transformer simulations are carried out in the ATPDraw environment, which now incorporates a dynamic hysteresis model (DHM). The main distinction of the DHM-based transformer models proposed from existing analogues lies in their ability to replicate transformer behavior over an extended range of excitation voltages. In addition to the use of the DHM, this improvement is achieved by reproducing a variable nature of equivalent air gaps at core joints. Two model versions with variable core gaps differ in whether they account for or disregard magnetic anisotropy of the core steel. Both these experiment-oriented models were fitted accurately to the same measured data by using individual flux–current characteristics of their gaps. In such a way, we have demonstrated the difficulties in distinguishing between effects caused by the core gaps and magnetic anisotropy in practical transformer modeling. By extending the method of variable core gaps to inrush currents modeling, residual fluxes in the core and current peaks were replicated accurately. The results simulated with the topological models presented are in a good agreement with measurements performed on a 300 kVA Yyn 11.350/0.235 kV transformer.

The work proposes a method of reproducing the no-load losses and currents of large five-legged transformers with the use of their transient models. This aim is achieved by employing topological transformer models based on a dynamic hysteresis model (DHM) and taking into account equivalent transformer capacitances. It is proposed to reproduce initially the measured total losses by using DHM means, and then to determine an equivalent per phase capacitance value that provides a best possible coincidence of calculated and measured current waveforms.

This paper is devoted to improvements of the low-frequency topological model of a three-legged stacked-core transformer. It is shown that $B-H$ hysteresis loops employed in the transformer model and $\Psi -i$ curves measured at transformer terminals are quite different in shape. A distinction is made between transformer modeling at moderate and deep saturations, separated conditionally by the level of technical saturation (near 2 Tesla) typical for grain-oriented steels. In the former case, in addition to the magnetic coupling of different phase windings through the core, an important part is played by air gaps at core joints. It is found that the effective gap length depends on the instantaneous magnetic flux and this dependence is proposed to implement by a variable inductance. It is shown that regardless of the core saturation depth, an important role in the transformer modeling belongs to the distribution of the zero-sequence path between all three phases. In addition to accurate replications of the special purpose saturation test, the modeled results are in a close agreement with positive- and zero sequence data measured on a 50 kVA transformer, as well as with the measured inrush currents.

The paper analyses a high-speed solenoid valve (HSV) whose core and moving armature are massive elements characterized by strong eddy currents, hysteresis and saturation. The feedback control employed in obtaining a predetermined non-sinusoidal current in the core coil necessitates the use of a high-frequency PWM-like voltage with parameters varying in a manner unknown in advance during the uninterrupted transient. In view of the known difficulties in using finite-element solvers, physical Cauer circuits are found to be a reliable engineering alternative. The use of the duality transformation is proposed to obtain a pure electric model of the core and armature. As a preliminary result, it is found that a threefold reduction in eddy-current loss is achieved by using the slotted core. The results obtained with the model are in a reasonable agreement with the experimental magnetizing current and the armature movement during successive valve operations.

The paper further develops a modeling concept of three-phase, three-legged transformer with tank walls represented as a distributed parameter structure. The circuital models proposed replicate accurately all possible zero-sequence impedances and losses of a three-winding transformer. Several model versions are compared to each other and to a conventional topological model with respect to their transient behavior during inrush and short circuit events, and in the presence of geomagnetically induced current (GIC). It was found that in all the cases considered, except that with a large GIC, all the models yield similar results. The reliability of the models is due to the representation of the tank walls behavior in a physical way, allowing one to observe the field distribution over the wall thickness as a function of transformer excitation. The modeled results are in a close agreement with positive and zero sequence data measured on a 25 MVA transformer as well as with inrush current test on a 300 kVA unit.

Purpose: The purpose of this study is to develop a topological model of a three-phase, three-limb transformer for low-frequency transients. The processes in the core limbs and yokes are reproduced individually by means of a dynamic hysteresis model (DHM). A method of accounting for the transformer tank with vertical magnetic shunts at the tank walls is proposed and tested on a 120 MVA power transformer. Design/methodology/approach: The model proposed has been implemented independently in a dedicated Fortran program and in the graphical pre-processor ATPDraw to the ATP version of the electromagnetic transient program. Findings: It was found that the loss prediction in a wide range of terminal voltages can only be achieved using a DHM with variable excess field component. The zero sequence properties of the transformer can be accurately reproduced by a duality-derived model with Cauer circuits representing tank wall sections (belts). Research limitations/implications: In its present form, the model proposed is suitable for low-frequency studies. Its usage in the case when transformer capacitances are involved should be studied additionally. Practical/implications: The presented model can be used either as an independent tool or serve as a reference for subsequent simplifications. Social/implications: The model proposed is aimed at meeting the needs of electrical engineering and ecology-minded customers. Originality/value: Till date, there were no experimental data on zero-sequence behavior of three-phase, three-limb transformer with vertical magnetic shunts, so no verified transient model existed. The model proposed is probably the first that matched this behavior and reproduced measured no-load losses for a wide voltage range.