Finite Element Modelling for Electrical Energy Applications

This course consists of the following three blocks:

1) Block 1 (Week 1 and Week 2):

In this block, the finite difference method for the Poisson equation on the interval (Week 1) and the square (Week 2) will be discussed. The differential equation and the boundary conditions will be discretized on a mesh by a finite difference scheme. This will result in linear equations for the grid unknowns. A stencil notation for these linear equations will be introduced. A linear system will be formed and solved. The discrete solution will be visualized on the mesh. Properties of the discretization method and the linear system will be discussed.

2) Block 2 (Week 3 and Week 4):

In this block, the Galerkin finite element method for the one-dimensional (Week 3) and two-dimensional (Week 4) Poisson problem will be introduced. The problem in so-called strong form will be transformed into the problem in so-called weak or variational form. The problem in weak form will then be discretized in space using Lagrangian basis or shape functions. A linear system represents the Poisson equation on a discrete level will be assembled and solved. The finite difference and finite element solution methods will be compared.

3) Block 3 (Week 5, Week 6 and Week 7):

In this block, the application of the finite element will be extended to treat more complex problems. Partial differential equations for the scalar and vector potential for the magnetic flux or field will be derived from the Maxwell equations. More complex geometries that represent transformers, actuators or rotating extrical machines will be meshed using unstructured triangular meshes. The Maxwell equations will be discretized on these meshes. The discrete linear system will be assembled by a element-by-element procedure and solved. The computed vector potential solution will be processed to compute the magnetic flux and the magnetic field.