Generators and Transformers

Course Description

Types, main parts, basic construction, applications of transformers and synchronous generators. Mathematical models, equivalent circuits and phasor diagrams of transformers and synchronous generators. No load, short circuit, load, and parallel operation of transformers. Winding connections. Transformer heating and cooling. Autotransformer. Operation of a synchronous generator online. Power chart. V curves and power factor control curves. Swedish and American diagram. Generators for small power plants and wind farms. Excitation systems. Laboratory measurements of transformer parameters, generator synchronization to the grid, active and reactive power management.

Learning Outcomes

  1. List and describe the main parts of transformers and generators
  2. Derive and explain equations describing basic physical models of transformers and generators
  3. Apply physical models to analyze the operation of transformers and generators online
  4. To apply theoretical knowledge in laboratory conditions

Forms of Teaching


classical lectures using blackboard in combination with PowerPoint slides


solving numerical examples related to the content of the lectures

Partial e-learning

posting study materials and communicating with students through the course website

Field work

a visit to factories that produce transformers and electrical machines


laboratory exercises using transformers, electrical machines, and accompanying power supply and measuring equipment for the purpose of practical demonstration and confirmation of the acquired theoretical knowledge

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 50 % 15 % 50 % 15 %
Mid Term Exam: Written 40 % 30 % 0 %
Final Exam: Written 40 % 30 %
Final Exam: Oral 25 %
Exam: Written 50 % 60 %
Exam: Oral 25 %

Week by Week Schedule

  1. Transformers: basic principle of operation of transformers, equivalent circuit and voltage equations, construction of windings and core
  2. Transformers: main and leakage flux, magnetization current, inductances, no-load and short-circuit test, determination of the equivalent circuit parameters, winding and core losses, stray losses
  3. Transformers: inrush current, scaling laws, parallel connection, connection groups, external characteristics, voltage drop
  4. Transformers: autotransformer, intrinsic rated power, efficiency, heating and cooling
  5. Transformers: insulation system, short-circuit forces and mechanical stress
  6. Transformers: instrument and special transformers, fundamentals of transformer protection, diagnostics and monitoring
  7. Synchronous generators: basic principle of operation of synchronous machines, division according to types and construction, windings
  8. Midterm exam
  9. Synchronous generators: vector-phase diagram, equivalent circuit, d-q reference frame, no-load and short-circuit test, equivalent circuit parameters
  10. Synchronous generators: synchronization, operation on power grid, generator stability, power and torque characteristics
  11. Synchronous generators: field current under load, Swedish diagram
  12. Synchronous generators: PQ diagram of a turbogenerator, PQ diagram of a hydrogenerator
  13. Synchronous generators: types of excitation systems, island operation, synchronous wound field motors
  14. Synchronous generators for wind farms and small hydroelectric power plants
  15. Final exam

Study Programmes

University graduate
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(.), D. Žarko, Z. Maljković, Osnove transformatora, skripta, FER Zagreb, 2016.,
(.), M. Vražić, Sinkroni stroj, skripta, FER Zagreb, 2012.,
(.), Stephan J. Chapman, Electric Machinery Fundamentals, McGraw-Hill International Edition, 2004.,
(.), John J. Winders, Jr., Power Transformers Principles and Applications, Marcel Dekker, Inc., 2002.,
(.), Ion Boldea, Synchronous Generators, CRC Press, 2006.,

For students


ID 222522
  Summer semester
L3 English Level
L1 e-Learning
45 Lectures
15 Exercises
13 Laboratory exercises

Grading System

85 Excellent
70 Very Good
60 Good
50 Acceptable