### Electrical Machines and Transformers Theory

#### Course Description

Power transformers and inductors. Introduction to general theory of electrical machines. General model of an electrical machine. Conditions for electromechanical energy conversion. Single-phase and multi-phase rotating field. Winding function and inductances. Utilization of complex space vectors. Transformation of coordinates, method of symmetrical components. Two-axis theory of electrical machines. Equivalent electrical circuits and mathematical models of power transformers, induction and synchronous machines. Steady states and transient states of transformers and electrical machines. Mathematical models of AC electrical machines derived from the general theory. Asymmetric working conditions of electrical machines.

#### General Competencies

Detailed knowledge of the theory of electrical machines and transformers. Capability of solving complex problems related to electrical machines in steady state and transient states, as the elements of a power system or an industrial plant. The ability to determine parameters for mathematical models of transformers and rotating machines.

#### Learning Outcomes

1. describe basic components of electrical rotating machines and transformers
2. distinguish between static and dynamic parameters of machines
3. derive basic mathematical forms according to theory of general machinery
4. use a general model of the machine for various types of electrical machinery
5. show the latest trends in the construction of electric machines and transformers
6. analyze the impact of machine parameters on the dynamic behavior
7. relate the behavior of dynamic phenomena with sizes of parameters

#### Forms of Teaching

Lectures

Lectures take place in two cycles, the first 7 weeks at 3 hours and another 6 weeks at 3 hours.

Exercises

Exercises take place in the first and second cycle of every other week for 2 hours (6*2),

Consultations

Possible after each lecture and exercises

Internship visits

1. Končar - Power transformers 2. Končar - Distribution and special transformers 3. Končar - Instrument transformers 4. Končar - Generators and motors

Continuous Assessment Exam
Mid Term Exam: Written 50 % 35 % 0 %
Final Exam: Written 50 % 35 %
Final Exam: Oral 30 %
Exam: Written 50 % 60 %
Exam: Oral 40 %

#### Week by Week Schedule

1. Basic physical principles of transformers, magnetic circuit, main and leakage flux, magnetization current, inductances, equivalent circuits
2. Winding and core construction, scaling laws applied to transformers, output characteristics, winding connections, autotransformer, parallel connection, losses and efficiency, heating, standards
3. Introduction to general theory of electrical machines
4. Machine windings, linear current density, air gap magnetomotive force and flux density, pulsating and rotating magnetomotive force
5. Winding factors, three-phase and multi-phase rotating field, induced voltage, higher harmonics in rotating field and induced voltage
6. Torque of an AC machine, electromagnetic and reluctance torque, criterions for existence of permanent electromechanical conversion
7. Winding functions, calculation of inductances in the case of smooth and salient air gap, display of three-phase quantities using complex space vectors
8. Mid-term exam
9. Voltage equations of an induction machine displayed using complex vectors, two-axis model, transformation of coordinates between coordinate systems rotating at various speeds, power balance and calculation of the induction machine torque
10. Induction machine steady-state model, utilization of per-unit system, general and derived forms of the equivalent circuit
11. Induction machine under variable voltage and frequency, utilization of the model for the cases of scalar and field oriented control, doubly-fed wound field induction machine
12. Voltage equations of a synchronous machine displayed using complex vectors, two-axis model of a synchronous machine, calculation of the synchronous machine torque, steady-state model, vector diagram, per-unit system
13. Synchronous machine connected to the power grid in the generating and motoring regime, actual and apparent induced voltage, armature reaction, active and reactive power control
14. Working principle of synchronous permanent magnet motors, induced voltage, inductances, phasor diagram, conditions for achieving maximum torque, characteristic current, torque characteristic, field weakening regime, torque pulsations and methods for their suppression
15. Final exam

#### Study Programmes

Electrical Engineering Systems and Technologies (profile)
Theoretical Course (1. semester)

#### Literature

Harlow, James H. (2001.), Transformers, CRC Press LLC
Z.Sirotić, Z.Maljković (1996.), Sinkroni strojevi, Element, Zagreb
M.Jadrić, B.Frančić (2004.), Dinamika električnih strojeva, Graphis, Zagreb
R.Wolf (1995.), Osnove električnih strojeva, Školska knjiga
P. Vas (1992.), Electrical Machines and Drives, Clarendon Press - Oxford
(.), Analysis of Electric Machinery and Drive Systems P. C. Krause, O.Wasynczuk, S. D. Sudhoff Wiley-IEEE Press 2002,

#### General

ID 86532
Winter semester
5 ECTS
L1 English Level
L1 e-Learning
45 Lectures
12 Exercises
0 Laboratory exercises
0 Project laboratory