Magnetic Circuit Coupling Analysis of Voltage Transformer Based on ANSYS

A voltage transformer is a special transformer used to convert high voltage into low voltage. Under normal use conditions, the secondary voltage is substantially proportional to the primary voltage, and when the connection direction is correct, the phase difference between the secondary voltage and the primary voltage is close to zero. The primary winding of the voltage transformer is connected in parallel in the power system line, and the secondary winding is closed through the load (measuring instrument, relay, etc.).

This paper uses the internationally popular ANSYS large-scale general finite element analysis software to perform finite element analysis on voltage transformers. It has a rich and complete unit library, material model library and solver, which ensures that it can efficiently solve static, dynamic, vibration, linear and nonlinear problems of various structures, steady-state and transient thermal analysis and thermal-structural coupling problems, static and time-varying electromagnetic field problems, and multi-field coupling problems; its fully interactive pre- and post-processing and graphics software greatly reduces the workload of users in creating engineering models, generating finite element models, and analyzing and valuing calculation results; its unified and centralized database ensures reliable and flexible integration between various modules of the system; its DDA module realizes its effective connection with multiple CAD software products. The analysis process of ANSYS finite element analysis software includes three main steps: pre-processing, loading and solving, and post-processing. Pre-processing refers to the creation of solid models and finite element models. It includes creating solid models, defining unit properties, dividing meshes, and model correction. Loading can be applied to a solid model or a FEA model (nodes and elements), but no matter which loading method is used, ANSYS will convert the load to the finite element model before solving.

Before solving, the analysis data should be checked, and the solution results are saved in the database and output to the result file. ANSYS has two result post-processors: general post-processor and time-history post-processor. The former can only view the results of the entire model at a certain moment; the latter can view the results of the model at different time periods or sub-step histories, and is often used to process transient or dynamic analysis results. [1~5]

1 Finite element modeling and meshing

1.1 Finite element modeling

The voltage transformer is selected as a single-phase three-column structure, with a rated primary voltage of 35KV, a primary winding number of turns of 32126, a rated secondary voltage of 100V, a secondary winding number of turns of 92, a primary winding resistance of 8681 Ω, a secondary winding resistance of 0.097 Ω, and a rated frequency of 50HZ. A two-dimensional finite element analysis is performed on it.

Although all entities are three-dimensional, in actual calculations, we must first consider whether they can be simplified into 2D plane models, because 2D models are easier to build and faster to analyze. The 2D geometric model of the voltage transformer includes: primary coil, secondary coil, iron core and air. Figure 1 shows a single-phase three-column voltage transformer (1/2 model).

1.2 Unit selection

This magnetic field analysis specifically uses ANSYS/Multiphysics module, PLANE53 unit and CIRCU124 unit. PLANE53 unit is suitable for two-dimensional (planar and axisymmetric) magnetic field analysis. PLANE53 unit consists of 8 nodes, each node has 4 degrees of freedom: magnetic vector potential (AZ), time-integrated electric potential (VOLT), current (CURR) and electromotive force (EMF).

PLANE53 unit is based on the clear expression of magnetic vector potential and is applicable to the following low-frequency electromagnetic fields: magnetostatics, eddy currents (AC harmonic analysis and transient analysis), pressure-loaded electromagnetic fields (static, AC harmonic and transient analysis), and magnetic circuit coupling fields (static, AC harmonic and transient analysis). PLANE53 unit has nonlinear magnetic field analysis function and can input B-H curve or permanent magnet demagnetization curve. In PLANE53 unit, Maxwell force is added to the unit surface marked by the surrounded numbers through SF and SFE commands. The surface to calculate electromagnetic force is loaded by adding MXWF mark on its surface, and Maxwell stress tensor is calculated on these surfaces to obtain electromagnetic force.

CIRCU124 unit is a common circuit unit suitable for circuit simulation. CIRCU124 unit can also interface with electromagnetic finite element to simulate coupled electromagnetic-circuit field interaction. CIRCU124 unit has up to 6 nodes to define the circuit unit and each node has 3 degrees of freedom to simulate circuit response. For electromagnetic-circuit coupled fields, CIRCU124 unit can interface with PLANE53 unit (2D electromagnetic field analysis unit) and SOLID97 unit (3D electromagnetic field analysis unit). CIRCU124 unit is suitable for static, harmonic and transient analysis. CIRCU124 unit is defined by active and passive nodes. Active nodes are connected to the overall circuit diagram, and passive nodes are used internally by CIRCU124 unit and are not connected to the circuit.

1.3 Meshing

After building the geometric model, set the 2D magnetic field analysis unit PLANE53 unit type in the finite element model area. Set the real constants of the primary and secondary windings, and assign material properties to the core, coil, and air. Assign the defined material properties and unit types to each entity, and then you can mesh. Figure 2 shows the meshing diagram of the voltage transformer. Since the shape of this geometric model is very regular, free meshing can be used.

1.4 Magnetic Circuit Coupling Finite Element Analysis

After modeling and segmentation, circuit units are established: an independent voltage source (IVS) is established for the primary coil, a twisted coil unit (SCE) is established, the primary coil section composed of the PLANE53 unit is connected to the independent voltage source (IVS), and the unit attributes and real constants are set; a resistor (RES) is established for the secondary coil to simulate open circuit and short circuit conditions, a twisted coil unit (SCE) is established, the secondary coil section composed of the PLANE53 unit is connected to the resistor (RES), and the unit attributes and real constants are set. Then, the degrees of freedom are coupled and the node-based vector magnetic potential method is selected to analyze the voltage transformer model, and the boundary condition that the magnetic lines are parallel to the surface is applied. Figure 3 shows the model after coupling and loading the boundary conditions.

2 Solution and post-processing

2.1 Solution and post-processing of voltage transformer with no load

Input the command stream. After the solution is completed, in the post-processing, the real part voltrP and imaginary part voltiP of the primary voltage, as well as the real part voltrS and imaginary part voltiS of the secondary voltage are taken out through the *get command. The voltage error ERRPS= 0.6924163301469E-04 is taken out from the parameter list. The voltage error obtained by the traditional method in the example of this paper is 0.06%; the phase difference ERRF = 0.042′ is taken out. The phase difference obtained by the traditional method in the example is 0.17′. It can be seen that the voltage error calculated by ANSYS software is slightly smaller than the voltage error calculated by the traditional method. Figure 4 is a magnetic flux curve diagram when the circuit is open.

2.2 Solution and post-processing during short circuit

When the voltage transformer is working, the secondary winding is basically in an open circuit state and must not be short-circuited. To ensure the safety of equipment and personnel, the short-circuit current density on the secondary side of the voltage transformer cannot exceed 160A/mm2[1]. In post-processing, the real part currRP and imaginary part currIP of the primary current, as well as the real part currRS and imaginary part currIS of the secondary current are obtained through the *get command. The effective value of the primary current IP=1.11A and the secondary current IS=390.52A are taken from the parameter list and divided by the cross-sectional area of ​​the primary and secondary wires, respectively, to obtain the secondary short-circuit current density of 75.9 A/mm2. The secondary short-circuit current density calculated by the traditional method in the example is 77 A/mm2. It can be seen that the current density calculated by the ANSYS software is slightly smaller than the current density calculated by the traditional method. Figure 5 is a magnetic flux curve during short circuit.

3 Comparison and analysis of calculation results

Through the calculation and analysis of the above two cases, it can be seen that the voltage error and short-circuit current density calculated by ANSYS are smaller than the results calculated by traditional methods. This is mainly because some approximate formulas are used in the traditional method, and hysteresis and eddy current losses are not considered in the ANSYS calculation.

4 Conclusion

Using ANSYS to perform magnetic circuit coupling finite element analysis on a single-phase three-column voltage transformer can obtain detailed calculation result data, a vivid two-dimensional solid magnetic field distribution, and other related variable result descriptions. Compared with theoretical data, the results are more accurate, and the denser the grid division, the higher the calculation accuracy.

Innovation of the author of this article: This article realizes the magnetic circuit coupling analysis of single-phase three-column voltage transformer in ANSYS. By comparing with the data of theoretical calculation, the results are more accurate.