* Knowledge of methods to perform circuit analysis in electrical engineering. * Ability to analyze electrical circuits operating under steady currents * Knowledge of criteria for use and application fields of the electrical machinery. * Knowledge of the principles of main electro-mechanical equipment and electrical machinery used in industrial * Ability to analyze and evaluate the performance of electric machines * Ability to make the choice of the appropriate electrical equipment to be included in mechanical systems.

Knowledge of linear algebra, knowledge of ordinary differential equations, complex numbers and basic concepts of electromagnetism with focus on static electric field, current field, steady electric current fields, magnetostatic fields and low frequency fields.

BASIC CIRCUIT THEORY -------------------------------------------- * Direct current -------------------------------------------- - Fundamental quantities: voltage and current - Kicrchhoff’s Laws - passive and active sign convention - Ideal two-terminal components: resistor, voltage and current source - Solution of the fundamental problem of circuit theory - Real generators - DC circuits with single source - Voltage and current divider - Series and parallel connection - star and delta connection - network theorems: superposition principle, Millman’s theorem, Thevenin’s equivalent circuit , Norton’s equivalent circuit, maximum power transfer -------------------------------------------- * Transient analysis -------------------------------------------- - Dynamic two-terminals: capacitor and inductor - RC and RL circuits - Solution of first order circuits with constant inputs -------------------------------------------- * Sinusoidal steady-state -------------------------------------------- - sinusoidal waveforms - phasors concept and relation with sinusoidal waveforms (summary of complex number algebra) - phasor diagram - topological and constitutive equations in phasor domain. Impedance definition. - series and paralell connection of impedances - generalization of principles and theorems in phasor domain - power in sinusoidal steady-state: real, reactive, complex and apparent power - Boucherot’s therem - Solution of AC circuit and power factor correction -------------------------------------------- * Three-phase circuits -------------------------------------------- - Three-phase sources and loads - line and phase quantities - Three-phase symmetric and balanced system - three-wire and four-wire three-phase systems - power in three-phase system: Aron connection - single phase equivalent circuit - energy method for the solution of three-phase systems - power factor correction - solution of not balanced three-phase systems (introduction) -------------------------------------------- * Frequency response -------------------------------------------- - multi-frequency generators - low-pass filter - high-pass filter - series resonance - parallel resonance ELECTRICAL MACHINES • Introduction and review of physics of electro-mechanical conversion: Ampere law. Magnetic flux. Lenz and Lorentz laws. • Materials employed for electrical machines: Soft and hard magnetic materials. Iron losses. Conductors and insulators. • Magnetic circuits: Electromagnet, Reluctance, Magnetic Circuit Model, Permanent magnets, Circuits with permanent magnets. • Thermal modelling of electrical machines: First-order thermal model. Thermal transients. Types of services. • Single-phase transformer: Realization aspects. Ideal transformer: working principle. Real transformer. Equivalent circuit. Equivalent circuit under sinusoidal supply. Vector diagram. Parameters identification: no load and short circuit tests. Voltage drop. Efficiency. Transformers in parallel. • Three phase transformer. Single-phase equivalent circuit. Nameplate data. Type of connection and group of the transformer. • DC machine (8 h). Realization aspects. Rotor. Working principle. Torque and emf generation. Machine equations. Equivalent circuit. Separately excited machine. Mechanical characteristic. Speed regulation. Series excited machine. Mechanical characteristic. Commutation. • Asynchronous machine. Rotating magnetic field. Realization aspects. Wounded rotor and cage rotor. Operating principles and comparison with the three-phase transformer. Energetic balance. Mechanical characteristic. Determination of parameters. Losses and efficiency. Speed regulation

* lectures and practice lessons about numerical solution of exercise are planned for each main topic. * Lab. experiences are planned for both basic circuit theory and electrical machinery. Labs are not evaluated by teachers, hence they do not influence the final score of the exam

The learning resources can be different depending on the teacher. Please refer to the Portale della didattica website for details. Generally speaking, lecture notes of the course and the entire video-recorded course of past years are available.

Lecture slides; Exercises; Exercise with solutions ; Video lectures (previous years);

Exam: Written test; Optional oral exam;

* The exam is made of two parts: a written and an oral exam. They are both mandatory. WRITTEN EXAM: * it includes two exercises of basic circuit theory and two exercises of electrical machinery * it lasts 2 hours at least. Some more time is provided according to the availability of the classroom. * A scientific calculator is allowed. * everything not explicitly allowed is to be considered forbidden * the maximum score of basic circuit theory and electrical machines is 15 pt for each part. The total maximum score is 30 pt. ORAL EXAM: * Students are allowed to sit the oral exam if the following conditions are satisfied: - total score (basic circuit theory + electrical machines) greater than or equal to 15 pt - score greater than or equal to 6pt for both basic circuit theory and electrical machines * Students are examined by one member of the commission only. The oral exam lasts, in average, 15 min. * All subjects in the program can be discussed at the oral exam * the maximum score is 30pt. The final score is the average between the score of the written exam and the score of the oral exam. PURPOSE OF THE EXAM: * the exam (written + oral) is organized to check the learning outcomes of the students with reference to the topics listed in the section "Expected Learning Outcomes".

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.