Course detail

Electrical Machines

FEKT-BPA-ESBAcad. year: 2023/2024

The basic laws and equations used in the theory of electrical machines. Magnetic circuits of electrical machines. The basic voltage equations, equivalent circuit diagrams, phasor diagrams, the basic electrical connections of electrical machines. Energy and power flow diagrams, losses and efficiency. Torque equation. Electrical machines performance. Nonsymmetrical loading. Basic characteristics of electrical machines.

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Offered to foreign students

The home faculty only

Entry knowledge

Student should be able to
- explain and define basic terms electromagnetic field, electric field, magnetic field, circuits with lumped and distributed parameters,
- solve DC, AC and magnetic circuits,
- solve three phase AC circuits,
- define the terms work and energy,
- describe and explain basic properties soft and hard magnetic materials.

Rules for evaluation and completion of the course

Control tests - 20 points
Exercises and Laboratory exercises - 10 points
Final Exam - 70 points 


To acquaint the students with the principle of operation and performance of transformers, induction machines, DC machines and synchronous machines. The theoretical knowledge are proved in laboratory excerscises.
Subject graduate should be able to
- describe main parts of electric machines,
- know classes of insulation and electrical machines costruction,
- describe construction of transformer,
- explain transformer losses,
- explain single and multiphase transformer operation,
- calculate parameters of transformer equivalent circuit from no-load and short – circuit tests,
- draw and explain phasor diagrams of transformer at no load, at short circuit and generally loaded.
- transformer winding connection and phasor diagram for different hour angle,
- explain and calculate transformer voltage regulation,
- describe and explain construction and principle of operation of induction machine with wound rotor and with squirrel cage,
- describe revolving magnetic field generation,
- define basic kinds of AC machine windings,
- sketch curve of magnetic field of AC winding distributed in more slots,
- draw equivalent induction machine circuit diagram, derive torque equation and draw torque - speed characteristic ,
- describe connection of induction motor into public utility network and speed control,
- describe construction and principle of operation of single phase induction motor,
- describe principle operation and construction of nonsalient synchronous machine,
- draw simplified circuit diagram, derive torque equation and draw phasor diagram,
- explain synchronous generator operation with isolated load and with public utility network, use phasor diagram for explanation,
- explain synchronous compensator principle of operation,
- describe DC machine construction and principle of operation,
- describe basic types of DC machine windings,
- derive torque and induced voltage equations,
- explain properties of DC motors and generators,
- describe construction and explain principle of operation of AC single phase commutator machines.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

FITZGERALD, A.E., KINGSLEY, Charles, UMANS, Stephen D. Electric Machinery. 6th edition. McGraw-Hill, 2002. 704 p. ISBN 978-0073660097. (EN)

Recommended reading

Not applicable.


Classification of course in study plans

  • Programme BPA-ELE Bachelor's

    specialization BPA-PSA , 2. year of study, summer semester, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


1. Introduction and motivation
    Magnetism - repetition and solving magnetic circuits.
2. Transformer - design, working principle and ideal transformer.
3. Transformer - Real transformer, substitution scheme, basic equations.
4. Transformer - Three phase transformers, winding connection and parallel operation.
5. Torque production, generation of spinning magnetic field and windings of AC electrical machines.
6. Asynchronous machine - Design, principle of operation, alternate circuit.
7. Asynchronous machine - phasor diagram and operating characteristics.
8. Asynchronous machine - starting three-phase asynchronous motors from the mains, speed control and single-phase asynchronous machines.
    Synchronous machine - Principle of operation, design, phasor diagrams.
9. Synchronous machine - Theory of smooth rotor machine. Moment characteristics, synchronous machine operating into independent load and in parallel with the grid.
10. Synchronous machine - Synchronous machines with salient poles and permanent magnets.
11. DC machine - Principle of operation and design, derivation of basic equations.
12. DC machine - Operating characteristics of DC machines in steady state.
13. Electric machines in electrification of transport - Overview of modern trends.  




Fundamentals seminar

8 hours, compulsory

Teacher / Lecturer


      Week - description

      2.  N1 - Magnetic circuits.
      3.  N2 - Transformers.
      5.  KT1 - Magnetic circuits and transformers.
      6.  N3 - Torque production, magnetic field torque generation and windings of AC electrical machines.
      7.  N4 - Asynchronous machine.
      10. N5 - Synchronous machine.
      11. KT2 - Asynchronous and synchronous machines.

      Where: N - numerical exercise, KT - control test.




      Laboratory exercise

      18 hours, compulsory

      Teacher / Lecturer


          Week - description

          1. Principles of safety at work in the laboratory. Familiarization with the laboratory - practice wiring.

          4.  L1 - Transformers: replacement parameters, loading and transformer efficiency.
          8.  L2 - Asynchronous motor - torque characteristics.
          9.  L3 - Asynchronous motor - distribution of losses and calculation of parameters of the replacement scheme.
          12. L4 - DC machine.
          13. Spare laboratory 

          Where: L - laboratory exercise