The course, divided into two parts, aims to provide: - The main concepts about analysis of electrical and magnetic circuit with particular attention to aspects of DC and low frequency; - Methodological bases for understanding the operating principles and key operational concepts of electromechanical equipment and in general a rational, proper and safe use of electrical equipment; - The operating principles and tools to evaluate the performance of the main electrical machinery, in view of their application in industrial processes

Knowledge of methods to perform circuit analysis in electrical engineering. Knowledge of the principles of main electro-mechanical equipment and electrical machinery used in industrial Knowledge of criteria for use and application fields of the electrical machinery. Ability to analyze electrical circuits operating under steady currents 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 ordinary differential equations, complex numbers and basic concepts of electromagnetism

Introduction to Electrical Engineering Lectures PART I: PRELIMINARIES (6h) Basic definitions (2h) • models • electrical engineering and lumped circuit models: hypotheses • electrical components and terminals, two-terminal components • current e ammeter • voltage and voltmeter • passive and active sign convention • electrical power (wattmeter) and energy, passivity Topology (1h) • operative definitions: node, branch, loop, mesh, graph • Kirchhoff’s current law (surface, node) • Kirchhoff’s voltage law (closed path, mesh) Two-terminal components and constitutive equations (2h) • constitutive equations • classifications: control type, linearity, time invariance • passive elements 1. resistor (resistance, conductance), short circuit, open circuit, ideal switch 2. electric energy and capacitor 3. magnetic energy and inductor • active elements 1. voltage generator 2. current generator Solution of the fundamental problem of circuit theory (1h) • definition • linearly independent equations: KCL, KVL constitutive equations • method of sparse tableau • adynamic networks (algebraic equations), dynamic (differential equations), order of a network PART II: ADYNAMIC CIRCUITS (8h) Special methods for the solution of electrical circuits (8h) • equivalence principle • series and parallel connection 1. definitions 2. series of resistors and voltage division 3. parallel of resistors and current division 4. examples 5. series of generators 6. parallel of generators • star and delta connection • superposition principle (proof) • Millman’s theorem (proof) • Thevenin’s equivalent circuit (proof) • Norton’s equivalent circuit (proof) • Tellegen’s theorem • Maximum power transfer PARTE III: DYNAMIC CIRCUITS (16h) Transient analysis (4h) • constitutive equations of capacitor and inductor • series and parallel connection of capacitors and inductors • solutions of differential equations with constant coefficients: outline 1. associated homogeneous equations 2. particular solution 3. initial conditions • first order differential equations 1. free and forced evolution 2. transient and permanent evolution • RC circuit • RL circuit • Solution of first order circuits with constant inputs (Thevenin, Norton) • switches Sinusoidal steady state (8h) • (summary of complex number algebra) • sinusoidal waveforms • phasor of a sinusoidal waveform • properties of phasors • topological and constitutive equations in phasor domain • impedance, admittance and generalized Ohm’s law • generalization of principles and theorems in phasor domain • maximum power transfer in AC • phasor diagram • frequency response • power in sinusoidal steady state 1. instantaneous power 2. real and reactive power 3. complex and apparent power • Boucherot’s law • power factor correction of inductive single-phase loads • non sinusoidal periodic regime Three-phase circuits (4h) • origin • definition: balanced and unbalanced three phase circuits, line (line-to-line) phase (line-to-neutral) voltages • star and delta connected loads • series and parallel connection of loads • single phase equivalent circuit • power • power factor correction: star and delta connection of capacitors • connection of single-phase loads to three-phase circuits • suitability of three-phase systems 1. cost effectiveness 2. constant instantaneous power Practice lessons Practice # 1 KVL and KCL Constitutive equations General solution of electric circuits Practice # 2 Evaluation of equivalent resistances Solution of circuits by using voltage and current division Practice # 3 Use of superposition principle Thevenin and Norton equivalent circuits Millman’s theorem Practice # 4 Transient analysis Practice # 5 Sinusoidal steady state analysis of circuits in phasor domain Practice # 6 Sinusoidal steady state: method of power balance Practice # 7 Analysis of three-phase circuits Electrical Machines Lectures Introduction (1 h) • Ampere law. Magnetic flux. Lenz and Lorentz laws. Fundamental laws. Materials (3 h) • Soft and hard magnetic materials. Iron losses. • Conductors and insulators. Magnetic circuits (3 h) • Electromagnet. Magnetic reluctance. • Permanent magnets. • Circuits with permanent magnets. Thermal aspects (2 h) • Simplified thermal model. Thermal transients. • Types of services. Transformer (9 h) • Realization aspects. Ideal transformer: working principle. • Real transformer. • Equivalent circuit • Equivalent circuit under sinusoidal supply. Vector diagram. • Equivalent circuit parameters: no load and short circuit tests • Voltage drop. Efficiency • Parallel. • Three phase transformer Asynchronous machine (8 h) • Rotating magnetic field • Realization aspects. Wounded rotor and cage rotor • Working principle. Comparison with transformer • Energetic balance. • Mechanical characteristic. • Determination of parameters. • Losses and efficiency • Speed regulation 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. Practice lessons Magnetic circuits (2 h) Numeric examples Thermal aspects (2 h) Numerical evaluation of the temperature in the machines. Transformer (5 h) Determination of parameters of the equivalent circuit Operation with load connected Three phase transformer Asyncronous machine (6 h) Determination of parameters. Determination of parameters and working conditions DC machine (4 h) Evaluation of torque and power in separately excited machines Evaluation of torque and power in series excited machines

Introduction to Electrical Engineering The lectures are given in the traditional mode by using the blackboard. Practice lessons consist in the numerical solution of exercises proposed by the lecturer. Electrical machines The lectures will be held with the use of powerpoint slides previously transferred to the students. Practice lessons will consist in the solution of numerical exercises.

Introduction to Electrical Engineering • Canova, Gruosso, "Introduction to Electrical Circuits", Progetto Leonardo, 2008 • Giorgio Rizzoni, "Principles and Applications of Electrical Engineering", 5/e, McGraw-Hill, 2007 Additional resources: slides of prof. Repetto course, available on the official website. Note: I recommend to take your own notes during class hours and metabolize the subject using the textbooks and slides as learning aids. Electrical machines • Ned Mohan, "Electric machines and drives: a first course", Wiley, 2012 • Slides of the course, available on the Portale della Didattica website. • Exercises to be solved in the classroom.

Modalitΰ di esame: Prova scritta (in aula); Prova orale obbligatoria;

Exam: Written test; Compulsory oral exam;

... The two modules have a common exam made of two parts. The written exam consists in the solution of four exercises, two each module, in approximately two hours. Topics of the exercises are: analysis of circuits in steady state (DC and AC), transients, single and three phase circuits, magnetic circuits, evaluation of the working conditions of transformers, asynchronous and DC machines. It is possible to use a scientific calculator and the official formula sheet uploaded on the course website. Candidates with positive scores (≥ 18/30, with a minimum of 8 in each of the 2 subjects) have access to the mandatory oral examination, consisting in the discussion of the exercises, and in theoretical questions on the main subjects of the course. A collection of past exams with solutions is available on the course website.

Gli studenti e le studentesse con disabilitΰ o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unitΰ Special Needs, al fine di permettere al/la docente la declinazione piω idonea in riferimento alla specifica tipologia di esame.