2020/2021

2020/2021

DM270

DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING

ELECTRICAL ENGINEERING

Sistemi elettrici

1°

Annual (28/09/2020 - 14/06/2021)

12

Italian

Base knowledge of electric and magnetic field in low frequency, elementary vector analysis and operators as curl, divergence and gradient.
In particular, the knowledge of vector operators for field analisys is needed.

Advanced knowledge of electric, magnetic and electromagnetic fields. Base knowledge of commercial codes for finite element simulations.
Knowledge of inverse problems and optimization methods.
Knowledge of technical European norms about environmental electromagnetic compatibility.

Vector fields
Basic operators and equations, electrostatic field, magnetostatic field, steady conduction field.

Analytical methods for solving boundary-value problems
Method of Green's function. Method of images. Method of separation of variables.

Numerical methods for solving boundary-value problems
Variational formulation in two-dimensional magnetostatics. Finite elements for two-dimensional magnetostatics. Finite elements for three-dimensional magnetostatics.

Time-varying electromagnetic field
Maxwell's equation in differential form. Poynting's vector. Maxwell's equations in the frequency domain. Plane waves in an infinite domain. Wave and diffusion equations in terms of vectors E and H.Wave and diffusion equations in terms of scalar and vector potentials. Electromagnetic field radiated by an oscillating dipole. Diffusione equation in terms of dual potentials. Weak eddy current in a conducting plane under AC conditions. Strong eddy current in a conducting plane under AC conditions. Eddy current in a cylindrical conductor under step excitation current. Electromagnetic field equations in different reference frames (a relativistic example and Galileian and Lorentzian transformations).

Computer aided design
Introduction to computer aided design by means of commercial software e.g. Magnet by Infolytica or Comsol Multiphysics. Finite element analysis of a simple case study.

Inverse problems
Direct and inverse problems. Well-posed and ill-posed problems. Fredholm's integral equation of the first kind. Under- and over-determined systems of equations. Least-squares solution. Classification of inverse problems.

Optimization
Solutions of inverse problems by the minimization of a functional. Constrained optimization. Multiobjective optimization. Gradient-free and gradient-based methods. Deterministic vs non-deterministic search. Numerical case studies.

Industrial electromagnetic compatibility
Field in low and high frequency, wave propagation, reflection and refraction. Near- and far-field. Biological effects of electromagnetic field. ICNIRP, Italian and European laws. Sources in low and high frequency. Antennas: properties (gain, directivity and polarization), kind of antennas, signal modulation. Theory of measurements of electric, magnetic and electromagnetic fields. Instruments for field measurements. Measurements of electromagnetic field radiated by microwave antennas and devices, radiofrequency antennas and fields produced by electric-power transmission plants.

The lectures are held with the help of blackboard and slide based presentations.
Finite element codes and Matlab programming are also used. These codes are made available to students.
For the Laboratory module measurements of electric and magnetic fields are done close to field sources.

Circuit and Fields, CAD modules: P. Di Barba, A. Savini, and S. Wiak. Field models in electricity and magnetism.. Springer, 2008.
Laboratory module: slides shown during the lectures.

The final examination consists of developing a finite element simulation. The progress of the work is discussed with the teacher.
For the CAD module, the final examination consists in solving an inverse problem. This work is discussed with the teacher.
For the Laboratory module, the final examination consists of a finite element simulation in order to asses the field measurements.