Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2018/2019
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Docente Di Gerlando Antonino
Cfu 10.00 Tipo insegnamento Monodisciplinare

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

Obiettivi dell'insegnamento

The methods and procedures are studied for the design and the electromagnetic and thermal check of the static and rotating electrical machines.

The considered machines are those of the four most common ones, that is transformers, induction machines, synchronous and d.c. commutator machines, with some suitable variants, such as special transformers and permanent magnet a.c. and. d.c. rotating machines (of brush and brushless type).

The analyzed topics are those of specific interest for the designer. However, they are useful also for readers interested in “inside” understanding of the electrical machines and also for who needs to evaluate the equivalent model parameters of the machines, in order to analyze and to control their operation.

As concerns the calculation approach point of view, the analytical treatments are favoured, suited to point out the dependence on the constructional parameters and on the electrical and magnetic loadings, by developing and using the classical sizing equations.

The use of analytical and numerical techniques are described for the basic sizing and the detailed design of components and for the evaluation of their performances, characteristic curves and related electrical parameters. The employment of calculation algorithms is illustrated, using design sheets for sizing and FEM codes for the check evaluations: the use of free student versions of tools are favoured (MathCad Prime Express, Maxwell Ansoft 2D).

Risultati di apprendimento attesi

Knowledge and understanding

Following the getting through of the exam, the student gains the following skills:

  • he knows the fundamentals, the general aspects, the theory elements and the basic ideas for the electrical machines sizing;
  • he knows the appropriate terms and the main elements of static and rotating electrical machines design;
  • he knows the sizing equations and the scaling laws linking power and main sizes of similar machines series;
  • he knows the meaning, the list and the calculation procedure of the rated and nameplate quantities of each kind of electrical machines;
  • he knows the link among the loadings and the electromagnetic and thermal limits of the used materials and of insulation and cooling systems of the electrical machines;
  • he understands the adopted approximations in the design models and he knows how to estimate their parameters.

Ability to apply knowledge and understanding

Moreover, following the getting through of the exam, the student:

  • is able to use the acquired knowledge to evaluate the main sizes of the electrical machines and all the operation and costructional quantities of the preliminary design;
  • is able to identify the main parameters and variables linking the design and the performances of an electrical machine;
  • is able to choose the parametric ratios involved in the sizing equations and in the expressions of the parameters to obtain performances close to the specifications;
  • is able to adapt, to modify and to use worksheets for the design analysis and the check evaluations of the various kinds of electrical machines;
  • is able to use FEM tools for the evaluation of leakage reactances, additional losses in the windings, check of the dielectric field and of the local saturation levels.

Autonomy of judgment

During the exam, the student should show he has suitably refined an autonomous ability of judgment about the adequacy of the approach adopted for the solution of a problem, choosing the corrective actions to be employed in order to improve the design results.

Communication skills

Moreover, the student is able to communicate the design results with effectiveness, pointing out the main consequences on the performances of the analyzed electrical machine.

Learning skills

At last, the student has the opportunity to furtherly develop the acquired knowledge and methodologies, through autonomous activities carried out within the M. Sc. thesis activity.

Argomenti trattati

Topic 1: general aspects; conductive materials (circular and rectangular wires: standard sizes); insulating materials; soft laminated and solid magnetic materials; permanent magnets (PM) and their features (grades; B-H plane parameters; operating point; temperature dependence and irreversible demagnetization risks); losses and heating: core losses, ohmic and eddy current losses, cooling aspects, duty types.

Topic 2: transformers: magnetic dispositions (single-phase, shell type, three and five limb cores); winding structures; pulse stress and insulation protection; sizing of standard and special transformers (zig-zag windings, autotransformers, three-winding transformers); leakage reactance evaluation for concentric and double concentric windings, zig-zag connection, three-winding transformers; dissymmetry aspects and their effects on losses, reactances, electro-dynamical stress.

Topic 3: windings for a.c. rotating machines and fields in the air gap: m.m.f.s, fluxes and e.m.f.s; main, fundamental and harmonic fields; slot harmonic fields; cartesian and Goerges m.m.f. diagrams; winding types (with integer and fractional slots/(pole-phase)), their representation and electromagnetic properties; surface and linear current density and their relations; sizing equations; cages: bar and ring currents; construction features and operating aspects (shaft currents, Carter factor, leakage reactance and its contributions, main and parasitic torques).

Topic 4: induction machines: equivalent circuit and parameter transportation factors; disturbances due to harmonic fields (parasitic torques and noise); simple, deep bar and multiple bar cages; wound rotor types; parameter evaluation and calculation of the torque-speed characteristic curves; performances and figures of merit; p.u. values; design and check aspects.

Topic 5: synchronous machines: wound rotor types (isotropic and salient-pole; evaluation of the field m.m.f. in loaded operation); PM types (a.c. brushless: types of rotors, PM dispositions –surface, buried –, PM materials and geometry); no-load and loaded operation; cogging and torque ripple at load; characteristic curves and phasor diagrams determination, taking or not saturation into account; armature reaction and related parameters; design and check calculations.

Topic 6: d.c. machines: commutator types, with field current or PM excitation; d.c. brushless machines; armature reaction and commutation aspects; winding data and design choices; sizing evaluations; magnetization characteristic curve; checks regarding commutation and auxiliary pole. 


Among the important pre-requisites, there are the following knowledge items:

  • the structure of the static and rotating electrical machines and the principles of operation;
  • the equivalent circuit of the electrical machines and their use for the performance evaluation;
  • the procedures for the determination of the operation characteristics of the electrical machines;
  • the test procedures of the electrical machines.

Modalità di valutazione

The examination is oral, it consists of three questions and it regards the subjects developed during lessons and throughout the practice activities.

During the examination, the following skills are evaluated in the description of the topics:

  • ability to organize the description of assigned topic in a tidy and logic sequence;
  • ability to focus the presentation on the priority aspects of the topic considered;
  • level of critical in-depth knowledge of the topic under discussion;
  • quality of the exposition: property of language, ability of analytical manipulation to develop demonstrations, ability to interact with the conversation partners during the discussion of the topic;
  • knowledge of the order of magnitude of the main quantities and parameters involved in the expressions concerning operation, sizing and check of electrical machines.


Risorsa bibliografica obbligatoriaTeaching material for this course is available on the Polimi Beep Portal https://beep.metid.polimi.it/

The available material includes: Lecture Notes: "Construction and Design of Electrical Machines", by F. Correggiari, A. Di Gerlando, G.M. Foglia; practice lessons notes; slides used for presentations

Risorsa bibliografica facoltativaJ. Harlow, Electric Power Transformer Engineering, Editore: CRC Press, Anno edizione: 2012, ISBN: 978-1-4398-5636-9

3rd Edition

Risorsa bibliografica facoltativaJ. Pyrhonen, T. Jokinen, V. Hrabovcova, Design of Rotating Electrical Machines, Editore: Wiley and sons, Anno edizione: 2008, ISBN: 978-0-470-69516-6
Risorsa bibliografica facoltativaI. Boldea, S. Nasar, Induction Machine Design Handbook, Editore: CRC Press, Anno edizione: 2010, ISBN: 978-1-4200-6668-5

2nd Edition

Risorsa bibliografica facoltativaD. Hanselman, Brushless PM Motor Design, Editore: Magna Physics Pub., Anno edizione: 2006, ISBN: 1-881855-15-5

2nd Edition

Risorsa bibliografica facoltativaJ. Gieras, M. Wing, PM Motor Technology, Design and Applications, Editore: Marcel Dekker, Anno edizione: 2002, ISBN: 0-8247-0739-7

2nd Edition

Risorsa bibliografica facoltativaJ.R. Hendershot, T.J.E. Miller, Design of brushless permanent-magnet machines, Editore: Motor Design Books, Anno edizione: 2010, ISBN: 978-0-9840687-0-8

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
schedaincarico v. 1.6.5 / 1.6.5
Area Servizi ICT