Electrical Engineering

SALVATORE CELOZZI

The course deals with the fundamental principles and applications of the electrotechnics for the electrical engineering.

The course aims to present the methodologies for extracting equivalent circuits starting from the electric and magnetic field configurations typical of electrical engineering applications and to offer a complete picture of the analysis methodologies of linear, lumped parameter or distributed, in stationary or periodic sinusoidal regime.

In-depth knowledge of the principles and descriptive equations of the electromagnetic field is required, acquired by passing a university-level Physics course.

The stationary electric field. Maxwell's equations in static or quasi-static regime. The electric field: Coulomb forces, potential and electric field, electrostatic energy. Capacity. Dielectrics: polarization and dielectric strength. Characteristics of insulating materials. Gauss's law. Poisson and Laplace equations. Examples of electric fields in canonical configurations. Refraction laws of the electric field in the presence of a flat separation surface. Electrical imaging method for flat or cylindrical separating surfaces. The condenser. Energy associated with the electric field. Connection of capacitors. Coaxial cylinders. Uniformly charged cylindrical conductor. Two-wire line. Conductor on the ground. Partial capacities of a multi-conductor line on the ground. Partial capacities of the three-core cable. Effect of guard rope in overhead lines.
Current field. Resistivity of materials. Ohm's law. Current field in a homogeneous medium: sphere, thread-like source of finite dimensions. Resistivity as a function of temperature. Principle of continuity of current. Insulation resistance. Connection of resistors. Power. Kirchhoff's laws. Electrodes in the ground: sphere, hemisphere, cylindrical bar. Earth electrodes, step voltage.
The stationary magnetic field. Magnetic field. Biot-Savart law. Laplace force. Circulation law for the magnetic field. Magnetic induction in non-ferromagnetic materials. The divergence of B and the induction vector flux. The image method. Magnetomotive force. Electromotive force in the presence of magnetic induction. Second Maxwell equation. Energy associated with the magnetic field. Magnetic induction phenomena. Rotating coil in a magnetic induction field. Magnetic energy associated with thread-like circuits. Magnetic polarization. Dia-, para- and ferro-magnetism. Hysteresis loop. Soft, hard, amorphous magnetic materials. Permanent magnets. Magnetic circuits. Similarities and differences with respect to electrical circuits. Magnetic networks. Proper and mutual inductances of coupled wire-like circuits. Relationships between L and M. Magnetic energy as a function of L, M. Inductance of a coil on a core. Inductance of a two-wire line: internal and external inductance.
Analysis of lumped constant circuits.
Continuous regime. Generalized Ohm's law. Generators and users convention. Equations for mesh stresses. External characteristic of active electromotive force and current generator bipoles. Load adaptation. Equivalent (or input) resistance of a passive network. Transformation of active bipoles. Transformation of three-terminal passive networks. Tellegen's theorem, virtual powers. T. of effects superposition. Compensation theorem. T. of reciprocity. Thévenin and Norton theorems. Graph, tree and cotree of an electrical network. Analysis of a network using Kirchhoff's laws. The method of nodal potentials. The mesh current method. The controlled generators.
Sinusoidal periodic regime. Quantities in sinusoidal periodic regime, definitions. Symbolic method: algebraic operations, integral, derivative of f. sinusoidal. Powers in sinusoidal periodic regime: instantaneous, active, reactive, apparent. Impedance and admittance operators. Complex power. Powers in ideal resistive, capacitive, inductive components. Resistive-capacitive and resistive inductive series and parallel bipoles. Series and parallel R-L-C circuit. Resonance. Kirchhoff laws and Kennelly-Steinmetz theorem. Boucherot's theorem. Circuits with mutually coupled edges. Mesh method without mutually coupled sides, without or with non-transformable current generators. Mesh method with mutually coupled sides. Nodal potential method without or with emf generators not transformable. Power factor correction. Double ports, transfer matrix and reciprocity relationship. Cascade connection of double ports. Determination of the auxiliary constants of a double-port. No-load and short-circuit tests, equivalent circuits to the external terminals. Ideal transformer and equivalent circuit. Double-pole closed on impedance. Image impedance, iterative, characteristic.
Three-phase systems. Generation of a symmetric emf triple, properties and definitions in a three-phase system. Star or delta balanced load. Single-phase equivalent circuit. Unbalanced star loads (with or without neutral) or delta. Power in three-phase systems. Power factor correction. Aron's connection of power meters.
Notes on the non-sinusoidal periodic regime. Analysis methods. Definition of active power and apparent power. First order filters.
Analysis of circuits with distributed parameters. Limits of the concentrated constant formulation. Hypotheses underlying the telegraphers' equations. Solution of the equations. Wavelength. Standing waves. Transmission line closed on impedance, input impedance. Adaptation condition. Unidirectional propagation. Non-distortion condition. Line empty or short-circuited. Equivalent circuit according to Thévenin or Norton of a line. Powers in a distributed constant circuit. Equivalent circuit of a line. Non-dissipative line. Electrically short line. Voltage drop in the event of an electrically short line.

M. D’Amore, Elettrotecnica (2 volumi), ed. Siderea

Lessons and exercises are carried out in the classroom in a traditional way, on the blackboard.

Attendance is strongly recommended.

The exam consists of a written test and an oral test: the written test requires the numerical solution of 3 exercises, the oral includes three theory questions.
You are admitted to the oral exam with a grade greater than or equal to 18.
In the paper, one exercise is on electromagnetic fields (electrostatics, stationary electrokinetics or magnetostatics), two exercises focus on circuits in a sinusoidal periodic regime.
In both written and oral exams, the weight of the individual exercises or questions is the same (10 points per exercise or question).

Electrical imaging method for flat or cylindrical separating surfaces.
Two-wire line.
Conductor on the ground.
Partial capacities of a multi-conductor line on the ground.
Partial capacities of the three-core cable. Effect of guard rope in overhead lines.
Electrodes in the ground: sphere, hemisphere, cylindrical bar. Earth electrodes, step voltage.
Energy associated with the magnetic field.
Magnetic circuits.
Proper and mutual inductances of coupled wire-like circuits. Relationships between L and M.
Inductance of a two-wire line: internal and external inductance.
Tellegen's theorem, virtual powers. Compensation theorem.
T. of reciprocity.
Thévenin and Norton theorems.
Powers in sinusoidal periodic regime: instantaneous, active, reactive, apparent.
Series and parallel R-L-C circuit. Resonance.
Boucherot's theorem.
Circuits with mutually coupled edges.
Mesh method without mutually coupled sides, without or with non-transformable current generators. Mesh method with mutually coupled sides.
Nodal potential method without or with emf generators not transformable.
Power factor correction.
Double ports, transfer matrix and reciprocity relationship. No-load and short-circuit tests, equivalent circuits to the external terminals.
Ideal transformer and equivalent circuit.
Double-pole closed on impedance. Image impedance, iterative, characteristic.
Generation of a symmetric emf triple, properties and definitions in a three-phase system.
Star or delta balanced load.
Single-phase equivalent circuit.
Unbalanced star loads (with or without neutral) or delta.
Power in three-phase systems. Power factor correction. Aron advert.
Hypotheses underlying the telegraphers' equations. Solution of the equations.
Wavelength.
Transmission line closed on impedance, input impedance.
Unidirectional propagation.
Non-distortion condition.
Line empty or short-circuited.
Non-dissipative line.
Electrically short line.
Voltage drop in the event of an electrically short line.