The module aims at presenting the main methods for the analysis of electric circuits. The module also includes the basics of power systems and electric machines.

D1 - Knowledge and comprehension ability
By the end of the course, students will gain the background of electric linear circuits, power systems, and electric machines.

D2 - Ability of applying knowledge and comprehension
The student will be able to analyze an electric circuit. The student will be also able to design a simple power system.

D3 - Autonomy of assessment
The student will be able to assess how to correctly model an electric circuit. The student will also be able to choose the correct electric machine for the specific application.

D4 - Communication ability
The student will be able to describe the way an electric circuit works. The student will also be able to properly describe the operation of a power system and of an electric machine.

D5 – Learning skills
By the end of the course, students will have developed critical thinking abilities which are essential to the understanding of more complex circuits and power systems.

Basic math skills: systems of linear equations, complex numbers, derivatives and integrals.

Energy transition:
Transition from conventional to renewable energy sources. Electrification of the final energy consumption.

Topology and circuits:
Transit time and lumped element model. Basic electrical quantities and sign conventions. Ideal conductors. Nodes, branches, meshes. Kirchhoff’s laws. Equations of a circuit. Conservation of power.

Basic circuit elements:
Classification. Ohm’s and Joule’s laws. Inductors and capacitors. Short-circuit and open circuit. Ideal voltage and current sources. Parallel and series connections. Star delta transformation. Equivalent representations. Real voltage sources.

Circuit analysis:
Voltage and current-divider circuits. Superposition in circuits. Thévenin’s, Norton’s and Millman’s theorems. Tableau analysis. Node-voltage method.

First-order transient analysis:
First order RL and RC circuits: natural and step response.

Sinusoidal steady-state analysis:
Sinusoidal steady-state analysis. Phasors and Steinmetz’s transformation. Impedance and reactance. Introduction to filters. Instantaneous, active, reactive and complex powers. Power triangle and power factor. Boucherot’s theorem and power factor correction.

Three-phase circuits:
Balanced three-phase voltage sources. Three-phase quantities. Balanced and unbalanced loads. Single-phase equivalent circuit. Neutral conductor and 4-wire systems. Power factor correction.

Production, transmission, distribution and consumption of electrical energy:
DC and AC, single and three-phase systems. Structure of electric power systems. Smart grid and renewable energy sources. The role of the direct current (DC), storage systems and e-vehicles.
Electrical conductors and devices:
Design of electrical conductors: insulation, ampacity and voltage drop. Current overloads, short circuits and overvoltage. Electrical devices: automatic and differential switches, relay, fuses, contactors, disconnectors.

Electrical safety:
Low voltage conventional safety curve. Protections against direct and indirect contacts. Low voltage systems: TT, TN, IT.

Photovoltaic systems:
The role of photovoltaics in the energy transition. Photovoltaic modules, inverters and photovoltaic generators. Solar irradiation and yield. Economic analysis.

Electronic converters:
Classification and applications. Power switches. Rectifiers and inverters.

Energy storage:
Peak shaving and time shift. Storage systems. Lithium-ion battery model.

Electric machines:
Classification. Principles of electromechanical energy conversion. Ideal and real transformers, equivalent circuit. Induction machines and synchronous machines: working principles, equivalent circuits and mechanical characteristics.

R. Perfetti. Circuiti elettrici, Zanichelli
M. Repetto e S. Leva. Elettrotecnica, Città Studi Edizioni
F. Ciampolini. Elettrotecnica generale, Pitagora Editrice
F. Grimaccia e altri. Elettrotecnica – Esercizi e temi d’esame svolti, Società Editrice Esculapio
A. Losi e G. Casolino. Progettazione degli impianti elettrici di bassa tensione, Pearson
V. Carrescia. Fondamenti di sicurezza elettrica, Edizioni TNE
Guide blu numero 1 - Edifici civili, numero 2 – Strutture commerciali, numero 3 – Cantieri edili, numero 5 – piccola industria, Edizioni TNE
V. Bearzi. Manuale di Energia Solare, Tecniche Nuove

Energy transition:
Transition from conventional to renewable energy sources. Electrification of the final energy consumption.

Topology and circuits:
Transit time and lumped element model. Basic electrical quantities and sign conventions. Ideal conductors. Nodes, branches, meshes. Kirchhoff’s laws. Equations of a circuit. Conservation of power.

Basic circuit elements:
Classification. Ohm’s and Joule’s laws. Inductors and capacitors. Short-circuit and open circuit. Ideal voltage and current sources. Parallel and series connections. Star delta transformation. Equivalent representations. Real voltage sources.

Circuit analysis:
Voltage and current-divider circuits. Superposition in circuits. Thévenin’s, Norton’s and Millman’s theorems. Tableau analysis. Node-voltage method.

First-order transient analysis:
First order RL and RC circuits: natural and step response.

Sinusoidal steady-state analysis:
Sinusoidal steady-state analysis. Phasors and Steinmetz’s transformation. Impedance and reactance. Introduction to filters. Instantaneous, active, reactive and complex powers. Power triangle and power factor. Boucherot’s theorem and power factor correction.

Three-phase circuits:
Balanced three-phase voltage sources. Three-phase quantities. Balanced and unbalanced loads. Single-phase equivalent circuit. Neutral conductor and 4-wire systems. Power factor correction.

Production, transmission, distribution and consumption of electrical energy:
DC and AC, single and three-phase systems. Structure of electric power systems. Smart grid and renewable energy sources. The role of the direct current (DC), storage systems and e-vehicles.
Electrical conductors and devices:
Design of electrical conductors: insulation, ampacity and voltage drop. Current overloads, short circuits and overvoltage. Electrical devices: automatic and differential switches, relay, fuses, contactors, disconnectors.

Electrical safety:
Low voltage conventional safety curve. Protections against direct and indirect contacts. Low voltage systems: TT, TN, IT.

Photovoltaic systems:
The role of photovoltaics in the energy transition. Photovoltaic modules, inverters and photovoltaic generators. Solar irradiation and yield. Economic analysis.

Electronic converters:
Classification and applications. Power switches. Rectifiers and inverters.

Energy storage:
Peak shaving and time shift. Storage systems. Lithium-ion battery model.

Electric machines:
Classification. Principles of electromechanical energy conversion. Ideal and real transformers, equivalent circuit. Induction machines and synchronous machines: working principles, equivalent circuits and mechanical characteristics.

Lessons and exercises. Part of the materials is provided using the Moodle platform. Photovoltaic laboratory.

The examination consists of a written assessment and an oral exam. Only students who pass the written examination (minimum marks: 18/30) can participate in the oral exam.
The written examination consists of a multiple-choice questionnaire (using the Moodle platform) and a set of exercises, which one can access if the questionnaire is passed.
The final mark will be a calculation of the arithmetic mean of the written and the oral examination. Up to 3/30 can be added to the average depending on level of competence demonstrated during the oral examination.

This module deals with the following goals of the UN Agenda 2023 for sustainable development:
7, 9, 11, 12, 13