# Application of Symmetric Conditions in the Simulation of High Voltage Power Transmission Models

The height of the power transmitting towers is usually in the range of 10m to 40m and the separation between two consecutive towers is about 200m to 400m. In addition, the area of the ground that needs to be considered in the simulation is large. Therefore, Finite Element Method (FEM) is not suitable for simulation of this application. Whereas Boundary Element Method (BEM) is best suited for these open region problems. This paper refers to the 3D Electric Field Solver COULOMBâ„¢ for the simulation method and presented results. The BEM method is based on the discretization of Maxwellâ€™s equations in integral form. BEMâ€™s distinctive strength lies in its ability to achieve a high degree of precision both locally and across the entirety of the problem domain. Though the BEM method is suitable for open region problems, it requires a computing machine with large RAM and CPU power to obtain a fast solution. Hence it is important to develop a BEM formulation that can utilize the mirror symmetry and/or angular symmetry and/or linear periodicity and/or angular periodicity in the model. In this paper, we confine ourselves to the application of symmetric conditions only.

In many High Voltage Power Transmission models, there exists a mirror symmetry about a plane. In such models, Symmetric Conditions can be applied to reduce the model size to half. This will reduce the solution time by one-fourth of the time taken for the full model without losing accuracy. Moreover, the time taken will be less to prepare the reduced model to solve. In the COULOMBâ„¢ program, Symmetric Conditions can be applied only to the principal planes: X=0, Y=0, and Z=0. Therefore, the model may need to be displaced accordingly. In COULOMBâ„¢, Symmetric Conditions about the three Principal planes can be applied simultaneously. However, itâ€™s noteworthy that Power Transmission models typically exhibit symmetry about one plane or, at most, two planes. In Fig. 1(a) a transmitting tower holding the power lines by two insulating strings is shown. For estimating the E-fields at the insulators and on the associated corona rings it is not necessary to model all the details of the tower. Hence the tower shown in Fig. 1(a) is modeled as a solid vertical block. This model has mirror symmetry about the X=0 plane. Therefore, the model is cut by X=0 plane and the half in the X 0 the region is retained

[Fig. 1(b)]. By applying symmetric conditions about one principal plane, the RAM requirement will be reduced by one-fourth and the solution time reduced by more than half a full model takes. In Fig. 2, electric field arrow plot on the surface of the circular corona ring is shown.

In the model shown in Fig. 3, there exists mirror symmetry about X=0 and Z=0 principal planes. By applying symmetric conditions about two principal planes, the RAM requirement is reduced by one-sixteenth and the solution time is reduced by more than one-fourth of the full model.

Read full article in T&D Consulting, Engineering & Construction Special Edition 2023