Module: Introduction to Electrical Engineering Knowledge of methods to perform circuit analysis in electrical engineering. Ability to analyze electrical circuits operating in DC Ability to analyse electrical circuits operating in transient conditions Ability to analyse electrical circuits operating in AC Ability to analyse three-phase circuits Module: Electrical Machines Knowledge of the principles of main electro-mechanical equipment and electrical machinery used in industrial environment Knowledge of criteria for use and application fields of the electrical machinery 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.

Module: Introduction to Electrical Engineering Knowledge of ordinary differential equations, complex numbers and basic concepts of electromagnetism Module: Electrical Machines Knowledge of the content of Introduction to Electrical Engineering module

Module: 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 Module: 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

Module: 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. Module: 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.

Module: 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. Module: 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.

Exam: Optional oral exam; Computer-based written test using the PoliTo platform;

The modules are integrated and coordinated, thus there is a common exam with the following assessment methods and criteria. Description The exam has a written and an oral part. The written exam is delivered using the Exam platform provided by Polito, integrated with the proctoring tool Respondus. It is also possible to give an optional oral exam, according to the rules described below. The written exam will be given at the scheduled date and time, as communicated to students and will consist of two parts: Introduction to Electrical Engineering and Electrical Machines. Each part has a maximum score of 16 points. Each part has * 4 multiple-choice quizzes: 0.75 points per questions, -0.25 penalty points for errors * 4 short numerical quizzes: 1.25 points per questions, 5% of numerical tolerance allowed on the result * Solution of a written exercise with multiple questions: 8 total points. The written exercise is a classical exercise and must be solved on A4 pages, scanned or photographed and uploaded on the Exam platform in digital format. Duration The duration of each module is 50 minutes. There will be a break between the two parts. As an example: * Start Introduction of Electrical Engineering: 8:00am * End Introduction of Electrical Engineering: 9:15am * Max duration 50 minutes (increased to 65 for students with special needs) * Start Electrical Machines: 9:15pm * End Electrical Machines: 10:30pm * Max duration 50 minutes (increased to 65 for students with special needs) Permissible and non-permissible aids During the exam it is possible to use * a scientific calculator * pen, pencil, drafting instruments * blank A4 sheets (max of 3 pages) for the written exercise to be scanned and uploaded as previously described) * The exam is a “closed book” examination: no book or formula sheet is admitted. * Everything that is not officially allowed, must be considered as a non-permissible aid. Cheating is a serious academic offense. Students discovered engaging in such behavior during the exam shall earn a failing grade and their case shall be reported to the Academic authorities for further disciplinary actions. Grading The exam is failed if any of the following is verified * total score (Introduction to Electrical Engineering and Electrical Machines) lower than 16 points * partial score (Introduction to Electrical Engineering or Electrical Machines) lower than 7 points The total score of the two parts will be limited to 30 points in case of higher score. Oral Exam Candidates with a positive total score have access to the optional oral examination that consists of a 1 or 2 questions related to the course program of both modules. In this case, the final score is the mean value of the written and oral exam. To access the written and oral exam, it is necessary to independently apply through the official registration website. The oral exam will be given remotely, with the teleconference tool communicated to the students a few days in advance or in person, according to the University rules. The oral exam is * mandatory for students with a non sufficient total score (16 or 17 points) * mandatory in case of doubts regarding the written exam In these cases the Students will be informed a few days after the written test * upon request of the Students A few days after the written exam the grades will be notified and students will be requested to fill out a form with the following choices * I accept the grade of the written exam * I ask to give an oral exam * I withdraw my exam (in this case a fail grade will be registered)

Exam: Optional oral exam; Computer-based written test using the PoliTo platform;

The modules are integrated and coordinated, thus there is a common exam with the following assessment methods and criteria. To guarantee a uniform evaluation of the students, the blended exam is identical to its online version. It is however possible to give the optional oral exam in person, according to the University rules. Description The exam has a written and an oral part. The written exam is delivered using the Exam platform provided by Polito, integrated with the proctoring tool Respondus. It is also possible to give an optional oral exam, according to the rules described below. The written exam will be given at the scheduled date and time, as communicated to students and will consist of two parts: Introduction to Electrical Engineering and Electrical Machines. Each part has a maximum score of 16 points. Each part has * 4 multiple-choice quizzes: 0.75 points per questions, -0.25 penalty points for errors * 4 short numerical quizzes: 1.25 points per questions, 5% of numerical tolerance allowed on the result * Solution of a written exercise with multiple questions: 8 total points. The written exercise is a classical exercise and must be solved on A4 pages, scanned or photographed and uploaded on the Exam platform in digital format. Duration The duration of each module is 50 minutes. There will be a break between the two parts. As an example: * Start Introduction of Electrical Engineering: 8:00am * End Introduction of Electrical Engineering: 9:15am * Max duration 50 minutes (increased to 65 for students with special needs) * Start Electrical Machines: 9:15pm * End Electrical Machines: 10:30pm * Max duration 50 minutes (increased to 65 for students with special needs) Permissible and non-permissible aids During the exam it is possible to use * a scientific calculator * pen, pencil, drafting instruments * blank A4 sheets (max of 3 pages) for the written exercise to be scanned and uploaded as previously described) * The exam is a “closed book” examination: no book or formula sheet is admitted. * Everything that is not officially allowed, must be considered as a non-permissible aid. Cheating is a serious academic offense. Students discovered engaging in such behavior during the exam shall earn a failing grade and their case shall be reported to the Academic authorities for further disciplinary actions. Grading The exam is failed if any of the following is verified * total score (Introduction to Electrical Engineering and Electrical Machines) lower than 16 points * partial score (Introduction to Electrical Engineering or Electrical Machines) lower than 7 points The total score of the two parts will be limited to 30 points in case of higher score. Oral Exam Candidates with a positive total score have access to the optional oral examination that consists of a 1 or 2 questions related to the course program of both modules. In this case, the final score is the mean value of the written and oral exam. To access the written and oral exam, it is necessary to independently apply through the official registration website. The oral exam will be given remotely, with the teleconference tool communicated to the students a few days in advance or in person, according to the University rules. The oral exam is * mandatory for students with a non sufficient total score (16 or 17 points) * mandatory in case of doubts regarding the written exam In these cases the Students will be informed a few days after the written test * upon request of the Students A few days after the written exam the grades will be notified and students will be requested to fill out a form with the following choices * I accept the grade of the written exam * I ask to give an oral exam * I withdraw my exam (in this case a fail grade will be registered)