Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2018/2019
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 093586 - ELECTRIC POWER SYSTEMS
Docente Berizzi Alberto
Cfu 10.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The course is meant to provide the basic analytical and computational tools to reach a complete and deep understanding of the planning and operation of large power system, including controls, starting from the basic knowledge acquired during the basic electrical courses and from some basic concepts of numerical analysis.

The course will show how the different electrical components and machines interact to each other resulting in a system, whose behaviour can be complex to understand and control. A thorough understanding of the main phenomena (that would include multi-physic aspects) is the target of the course; this will make it possible for the student to face the challenges of his/her future job and to find out solutions to known and less known power system problems. 

Another goal is the acquisition of a common technical and scientific terminology, which will make it possible for the student to read and understand both technical and scientific documents. 

The course will make use of teaching methods based on the "learning by problems" approach, in order to make it possible for the student to tackle practical, although reduced in size, problems related to power system dynamic and control. 

Risultati di apprendimento attesi

M.Sc. students in electrical engineering after following and passing Electric Power Systems will be able

  1. To make use of the system knowledge acquired to have a general insight of the power system behaviour, both from the steady-state and the dynamic point of view,
  2. to discuss in technical and scientific meetings about power system related issues,
  3. to read and understand specialized documents related to planning and operation of power systems, to roughly identify problems and solutions (DdD1 and 2). 

The students will be able to identify necessary data and to elaborate them to obtain results using simple commercial software and to discuss critically results, providing directions to the solution and obtaining sensitivities on the parameters.

Assessment of the proposed solutions is also a part of the knowledge provided by the course.

A couple of projects assigned during the course will make it possible for the student to experience the mechanisms of team working and will improve abilities related to communication and public presentation skills, thanks to the presentations that some of them will have to make to the rest of the class (DdD4). 


Students are expected to spend five to seven hours on average per week outside of class on this course to read the textbook, review the class material, and work on projects.

I do not take attendance and you are free to attend or not attend class as you choose.

Argomenti trattati

The course is organized in theoretical and numerical tutorials: during theoretical classes, models and methodologies will be taught and some simple numerical examples will be developed; during numerical tutorials, some more complex and elaborate examples will be explained, based on real reduced systems, actual problems and experiences coming from the experience.

A couple of project will be assigned to students and will have to be developed and solved in small teams (learning by problems). All projects will be checked by Teaching Assistants and a yes/no decision will be made about the projects that will allow/prevent the authors about the possibility to give the exam. The best projects will be presented by the Authors to the rest of the class and discussed during lessons.


The program is as follows: 

  1. Introduction to electric systems: definitions, typical structures, statistics, current challenges.
  2. Steady – state operation of power systems: Y matrix, Power flow computations and solution methods: Gauss, Gauss-Seidel, Newton-Raphson, Carpentier, Fast Decoupled Load Flow, DC Power Flow.
  3. Security analysis, sensitivities.
  4. Short-circuit currents computation of large power systems: positive/negative/zero sequence circuits, computation of faulted state: currents, voltages. Matrix approach. Single line to ground, double line to ground, line to line faults, three phase faults. Series faults and interruptions. 
  5. Protection systems: definitions and devices. Protection of power system elements: network elements, power station components. 
  6. State estimation for transmission systems: linear and non linear approaches. Numerical problems of state estimation.
  7. Dynamics of power systems: Definitions and stability.
  8. Large perturbation Angle stability: equal-area criterion, simulation methods. Critical clearing time. 
  9. Small perturbations angle stability: Single machine infinite bus systems, large systems. Eigenvalues and eigenvectors of the state matrix and their meaning, participation factors and modes of oscillation. Role of Power System Stabilizers. Examples.


Basic knowledge of Electrotechnics and power systems is required: models, methods to study linear and nonlinear circuits, etc.

Basic knowledge of power flow modelling is also considered as acquired: models of lines, 2 and 3 winding transformers, auto transformers, phase shifters, tap changers, generators, including simple dynamic models. In particular, referring to book Power Systems Analysis and Design, Chapters 1, 2, 3, 5.15.5, 5.6, 5.7 wil be considered as pre-requirements to follow the course. The same subjects could also be studied on book Power System Analysis, Chapters 1, 2, 6.8, 6.9.

Also, numerical analysis skills are appreciated: in particular, solution of linear and non linear systems, and differential equations; eigenanalysis. 

Modalità di valutazione

As a prerequisite for the exam, the project assigned during the course will have to be developed in team and checked by Teaching Assistants. All projects will be checked and only teams with passed projects will be allowed to give the exam. A couple of them will have to present their project to the rest of the class and to discuss results. 

The exam is a written test divided in two sections; each one has an impact of 50% on the overall mark.

The first section is made by a few numerical exercises (usually 4-5) related to the subjects of the course, aimed at checking the understanding of the main problems, assumptions, methodologies and fields of application, as well as knowledge of the numerical values of actual variables in power systems.

The second part consists of few questions on the theoretical subjects explained during the theoretical lectures. They can be either multiple answer questions, true/false questions or complete proof as explained during classes. In particular, for open questions, the student will have to critically elaborate on the subject requested, using the correct notation and terminology, highlighting assumptions and restrictions of the methodologies, drawing clear conclusions and limitations. 

All topics explained during classes might be subject for questions during the exam.

The value associated to each question is clearly indicated in the text, in order to allow the student to self-evaluate.

All examples of the past exams are available in the Beep application of the Politecnico di Milano, together with their solution.

All cheating will be reported directly to the university.  You are welcome and encouraged to discuss material with your colleagues, when and where it is appropriate, but copying, stealing papers, etc. are considered dishonest and will be prosecuted.

Risorsa bibliografica facoltativaJ. Duncan Glover, Mulukutla S. Sarma, Thomas Overbye, Power Systems Analysis and Design, Editore: Cengage, Anno edizione: 2012, ISBN: 978-8131516355
Risorsa bibliografica facoltativaJohn J. Grainger, William D. Stevenson, Power System Analysis, Editore: Mcgraw Hill Book Co, ISBN: 978-0070612938
Risorsa bibliografica facoltativaRoberto Marconato, Electric power systems, Editore: CEI, Anno edizione: 2004, ISBN: 9788843200252
Risorsa bibliografica facoltativaP.Kundur, Power System Stability and Control, Editore: McGraw Hill, ISBN: 0-07-035958-X
Risorsa bibliografica obbligatoriaSlides of the professor https://beep.metid.polimi.it

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
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