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.

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.