Research on Magnetic Characteristics and Short-Circuit Force of 3D Wound Core Transformer

The problem of eddy current loss in power transformers directly affects the technical economy of the transformer, which is a problem that cannot be ignored in the design and calculation of power transformers. Studying how to reduce the eddy current losses caused by leakage magnetic fields is a difficult point in transformer design. The load loss of low-voltage foil copper windings in a 10 kV/400 kVA 3D wound core transformer is calculated, and the three-dimensional finite element models of the transformer are established by Using Magnet software and COMSOL Multiphysics software, and the calculation results are compared. At the same time, the short-circuit force of foil windings is shown in the simulation. The results show that the three-dimensional finite element models are correct.


Introduction
Compared with three-phase planar stacked core transformers, 3D wound core transformers have the advantages of a balanced magnetic circuit and low shake and noise, and have been widely used in lowvoltage distribution grids and other occasions in recent years.By winding the electrical steel strip, an iron core frame with an approximate semi-circular section is obtained, and three iron core frames of the same size are spliced in pairs to form a triangular three-dimensional structure of iron core [1].This core structure greatly reduces the core loss compared with the traditional stacked core, but due to its special structure, its central core column saturation magnetic density is not large, so it is mostly used in distribution transformers.
In terms of the winding selection of distribution transformers, foil windings occupy an important place in the field of distribution transformers due to their high degree of mechanization and good winding filling coefficient [2].With the continuous improvement of transformer performance indicators, in the field of high-efficiency and energy-saving distribution transformers, especially in the range of 400 kVA~6300 kVA capacity, to meet the no-load loss and load loss required by the standard, the use of foil winding for low-voltage winding is almost an inevitable choice.
Therefore, in the 3D wound core transformer loss, especially the load loss, the eddy current loss of the low-voltage foil winding cannot be ignored, but most of the current methods are analysed by the finite element method [3][4], and only a complex two-dimensional or three-dimensional model of the winding can be established in terms of power frequency and simulated and analysed, which greatly increases the time cost.
Under short-circuit conditions, the winding will bear huge electromotive force and mechanical force, which may cause the deformation of windings, which will lead to the destruction of the winding insulation or the reduction of the mechanical strength of windings.Therefore, studying the test method of short-circuit mechanical force of transformer winding, improving the test accuracy of short-circuit mechanical force of transformer windings, and improving the calculation method of short-circuit mechanical force of transformer windings is conducive to improving the short-circuit resistance of the transformer [5].
[1] established a two-dimensional equivalent modelling method for finite element analysis of a threedimensional core transformer, which is convenient for the calculation of transformer core working characteristics.Compared with a three-dimensional FEM model, this method can shorten simulation time by 96.66% and reduce memory usage by 92.93%.
[2-4] established two-dimensional and three-dimensional finite element models of copper foil windings and analysed their current distribution and temperature rise through electromagnetic field simulation.
[6] proposed a three-dimensional eddy current field modelling method that applies to wound core transformers by correcting the traditional anisotropic equivalent conductivity formula.

Three-dimensional Simulation of Load Loss
The establishment of load loss models for windings can be traced back to the 19th century [7,8], and the discussion of it has continued to the present day, especially since a big number of power electronic devices have been introduced into the power system, making the loss effects of high-frequency voltage and current more prominent.Therefore, it is necessary to establish a loss model which has more accuracy to describe its effect.
According to the model, considering one layer of any transformer foil winding, the leakage flux passing through the winding space through this layer will produce eddy currents in the conductor of this layer, thereby increasing the resistance of that layer.The leakage flux in this layer will also cause the storage of magnetic energy.This stored magnetic energy is related to the leakage inductance of the transformer.Therefore, the leakage flux in this layer determines the AC resistance and leakage inductance of this layer.
The leakage flux is related to the total current between the layer of magnetic excitation and the zero magnetic excitation surface, as shown in Figure 1, which displays the magnetomotive force of the foil coil.In the case of power frequency 50 Hz, this paper analyses and calculates the low-voltage winding of a 10 kV/400 kVA 3D wound core transformer, which adopts a copper foil structure, and the specific parameters are shown in Table 1 According to the core and coil drawings, establish a 1/2 model.To calculate the eddy current loss of the copper foil, the A phase low-voltage lead establishes a spiral coil according to the number of turns of the copper foil, calculates the low-voltage eddy current loss, the high-voltage winding gives the rated current, and the low-voltage winding is short-circuited.The final model structure is shown in Figure 2.  The high-voltage coil adopts current source excitation, the excitation current is the rated current, and the low-voltage coil is short-circuited.
The model magnetic field energy storage was 15.16 J, the short-circuit impedance calculated by the energy method was 3.82%, the design value was 3.86%, the deviation was -1.04%<±10% and the impedance was low, and the experimental value was 3.95%.
The flux density distribution cloud diagram is shown in Figure 4: According to the calculation results, it is calculated that the magnetic density of the main airway modelling of the simple winding of the 3D wound core transformer under the load condition is 0.0622 T, and the direct loss of the winding is 1992.8W.

Three-dimensional Simulation of Winding Force
For transformers, the mechanical stress in the winding caused by electromagnetic force is very huge, and the contact pressure between the outer layer of the winding wire insulation paper and the gasket increases, which will lead to the damage of the insulation paper and the failure of the insulation, thereby causing short-circuit discharge and even causing the transformer to explode [5].
According to the three-dimensional model established in the previous section, the short-circuit force distribution of low-voltage foil winding under the 3D wound core short-circuit condition can be obtained as shown in Figure 6:

Conclusion
In this paper, a three-dimensional simple and complex winding model of a 10 kV/400 kVA 3D wound core transformer is established by COMSOL Multiphysics and Simcenter Magnet software, and simulation analysis is carried out to obtain the transformer load loss and winding short-circuit force distribution.By comparing the simulation results with the experiments, the accuracy of the 3D model is verified.

Figure 1
Figure 1 Distribution of magnetomotive force of foil coil

Figure 2
Figure 2 Load loss model of 3D wound core transformerThe simulation software uses Simcenter Magnet, and the meshing of the transformer load loss model is shown in Figure3, using nonlinear time-harmonic field calculation.

Figure 3
Figure 3 Model mesh diagram

Figure 4 Figure 5
Figure 4 Magnetic flux density distribution diagramAccording to the simulation calculation results, the eddy current loss of the low-voltage winding is 761.97162W, the direct loss of the winding is 1990.017832W, the eddy current loss of the high-voltage winding is 44.64241184W, considering the lead loss of 100 W, and the load loss when other additional loss coefficients are 1.02 is about 2954.5645W, which is less than the first-level energy consumption requirement value of 3070 W and the measured value of 3015 W.While Magnet is modelling and simulating complex coils, this paper also established a threedimensional model of simple windings in COMSOL and simulated the loading conditions of the 3D wound core.The magnetic flux density distribution cloud diagram is shown in Figure5:

Figure 6
Figure 6 Distribution of winding short circuit force