# Technical Papers and Presentations

#### Multigeometric Simulation of Transient Electromagnetic Processes in Branching Electric Lines

Shmelev, V.1, Dudnikov, E.2
1 VlSU
2 IRIAS

Multigeometry technology seems to be promising and effective for simulation of branching electric lines (electric networks) using FEMLAB package. In this report, we consider an example of such a system, composed of three straight-line segments of a two-wire line with various electromagnetic properties, which, when cascade-parallel connected, constitute a network system in the form of Y-branching with one input and two output lines.

EMF is connected at the input point of the system, with resistance loads being connected at the two output points. Behavior for each of the three two-wire lines is described by the standard system of telegraph equations. The task is to calculate the conditions (modes) for voltage wave advancing in the branching system and find output lines parameters for the case when the wave, reflected from the branching, is absent in the input line (network line consistency condition).

When using traditional approach to simulate this problem, one considers two-dimensional problem on plane and describes position of each two-wire line, each network segment, by two-dimensional coordinates. This leads to rather complicated problem, which can be solved in FEMLAB system in the Weak form.

In this report, we consider the solution of the stated problem using multigeometry. Each two-wire line is associated with one-dimensional problem with corresponding variables, initial and boundary conditions. To couple the problems, we specify the boundary condition with nonlocal coupling, corresponding to functioning of network branching. Thus, in this case we have three boundary problems with simple geometry and one nonlocal coupling boundary condition.

Simulation of the problem in FEMLAB system using multigeometry has demonstrated certain advantages of the proposed approach. The advantage becomes particularly evident as we increase the number of connected output lines, and also, when we consider networks with complicated structure, having many branching points and many wires in the lines. The network line consistency condition can be obtained by plugging into the branching point a special transformer with three windings and adjusting the required parameters of the transformer. This case can also be investigated using the multigeometry approach.

Branching power network simulation using multigeometry can be applied to solve a wide set of real-world problems in telecommunications, power supply, power industry, and mechatronics.