In this work, a mathematical model of a three-phase nonlinear transformer is suggested. The model enables simulating the transformer operation with allowance for its nonlinearity and covers needs of the relay protection. Our model has been developed on the basis of a mathematical model with phase coordinates, where differential equations are composed by the Kirchhoff’s phase-voltage law. Based on this model, we first compose a mathematical model for simulating steady-state operation modes of a transformer, taking into account the asymmetry and nonlinearity of its ferromagnetic core. In this model, the initial values of inductances and mutual inductances of loops are determined from the main phase inductance calculated by the experimentally found no-load current, and their current values are determined from the currents in windings and the magnetic fluxes in legs of the transformer core. The magnetic fluxes are calculated by the nodal-pair method. This improved mathematical model is verified through a comparison between the calculated harmonic components of the phase currents and the experimental results. The harmonic components are calculated with the use of Fourier expansion of the calculated phase currents. Their experimental values are determined with a spectrum analyzer. The calculated and experimental harmonic components of the currents of phase A during no-load and rated-load operation of the transformer are tabulated. The comparison of these results shows that the mathematical model of a three-phase transformer we suggest makes it possible to simulate currents in transformer windings under steady-state operation modes with accuracy acceptable for relay protection.

The design features of high-power ore furnaces are the transformer’s secondary winding made of 4–8 isolated splits and a busbar assembly made of the same number of paired bifilar bus tubes, spaced 20–40 mm apart. Only an arc fault (AF) can occur between paired bus tubes in such an assembly, during which the assembly with currents of 35–150 kA can be completely destructed. To protect against AFs, these bus tubes are wrapped in several layers of gluey fiberglass cloth. However, such cloth is abraded under the impact of airborne abrasive dust particles during furnace operation, and coal dust in the air creates the conditions for an AF. A new current protection with a magnetic current transformer (MCT), which prevents busbar assembly destruction, is suggested. Its design is based on the analysis of the distribution of busbar assembly magnetic fields. The choice of MCT position is justified, and parameters of its windings are determined; MCT construction and fastening are described, and a technique for reliable MCT output signal transmission under strong magnetic fields and with a specified protection threshold is suggested. These protections are currently the simplest and cheapest tool for preventing the complete destruction of an expensive busbar assembly in events of AFs during it.

High-power ore furnaces mainly use single-phase transformers supplied by phase-to-phase voltage with the secondary winding made in the form of four to eight isolated splits and a high-voltage busbar assembly made of the same number of pairs of tube buses. Due to these design features, turn-to-turn faults are the main faults in the primary winding of the transformer, and flexible coupling breaks and arc faults in splitting circuits prevail in the high-voltage system. This is why current and gas protections are currently used to protect transformers against short circuits. However, current protections are insensitive to turn faults, and the gas protection response time can be long since it strongly depends on the oil temperature. High-current systems are protected from arc faults only by insulating tube buses. However, this insulation is gradually destroyed under the impact of abrasive dust in the air, and the presence of coal dust in the air creates conditions for arc faults. There is no protection against breaks in the circuits of pairs of tube buses. The extent of damage in a transformer and its high-current system due to the faults can be significantly reduced by using new protection devices based on the measurements of the longitudinal and transverse asymmetry of the stray magnetic fields of the protected transformer. To implement these protections, this article suggests a method for protecting a transformer and a high-current system using magnetic current transformers (MCTs). The number and points for MCT winding coils are determined through the analysis of their EMF values versus their positions relative to the windings of the transformer operating under different modes. The results serve as the basis for the protection circuit design; the protection response threshold is calculated, the protection operation is described, and the results of the experiment are given.

One of the most common damage to the windings of three-phase transformers are loop closures. Traditional current protections have low sensitivity to them, and gas protections are not able to protect «dry» transformers. Unconventional protections on magnetic current transformers are devoid of these disadvantages. However, the implementation of such protections is impossible without calculating the MTT EMF in an arbitrary transformer operation mode, the magnitude of which is determined by the magnitude of the axial component of the magnetic field scattering of the transformer coils. Their mathematical modeling is a difficult task and does not allow taking into account the nonlinearity of this transformer. This can be avoided if the ELCUT software package is used to simulate this axial component of the magnetic scattering field of the transformer windings. Based on its use, a method is proposed for modeling the effective value of the EMF induced in the MTT windings located in the places proposed in the considered protection device of a linear three-phase transformer using the ELCUT software package. The adequacy of the results of modeling the magnetic fields of scattering of transformer windings is assessed by comparing the measured and calculated MTT EMF. Recommendations for taking into account the nonlinearity of this transformer are given.