Theoretical Electrical Engineering
Original title in Czech: Teoretická elektrotechnikaFaculty: FEECAbbreviation: DKC-TEEAcad. year: 2020/2021
Type of study programme: Doctoral
Study programme code: P0714D060005
Degree awarded: Ph.D.
Language of instruction: Czech
Accreditation: 28.5.2019 - 27.5.2029
Mode of study
Standard study length
doc. Ing. Petr Drexler, Ph.D.
doc. RNDr. Martin Kovár, Ph.D., prof. Ing. Karel Bartušek, DrSc., prof. Ing. Lubomír Brančík, CSc., doc. RNDr. Dana Hliněná, Ph.D., doc. Ing. Jan Mikulka, Ph.D.
prof. Ing. Jan Macháč, DrSc., prof. RNDr. Martin Knor, Ph.D., prof. RNDr. Ondřej Kalenda, Ph.D.
Fields of education
The doctoral study program "Theoretical Electrical Engineering" is focused on the preparation of high-qualified scientific and research specialists in various areas of theoretical electrical engineering. Particularly, in the theory and applications of electromagnetism, electrical circuits, electro/magnetic measurement methods and signal processing methods. The preparation is supported by the provision of knowledge in related mathematical disciplines such as stochastic processes and statistical methods of systems investigation, systems analysis using functional equations, design of multi-criteria optimization methods, numerical methods for solution of continuous and discrete dynamical systems and others. The aim of the program is to provide a doctoral education to graduates of Master's degree in all these sub-disciplines, to deepen their theoretical knowledge and to develop practical expert skills and to educate them in the methods of scientific work.
Graduates in doctoral study program "Theoretical Electrical Engineering" are able to solve scientific and complex technical innovation tasks in the field of electrical engineering at the theoretical level, as well as its practical use in research, development and production. To solve technical research and development tasks, they are equipped with a complex knowledge of the theory and application of electromagnetic field, electrical circuits, methods of measuring and signal processing and their physical and mathematical description. They are able to use modern computing, measuring and diagnostic techniques in a creative way.
Thanks to the high-quality theoretical education, practical expert skills and specialization in the chosen field, graduates of doctoral study are sought as specialists and executive staff in general electrical engineering. They will apply as researchers in basic or applied research, as specialists and leaders of teams in development, design and operation in research and development institutions and in electrical and electronic manufacturing companies operating in the field of advanced technologies.
Specialists and executive staff in general electrical engineering, researchers in basic or applied research, specialists and leaders of teams in development, design and operation in research and development institutions and in electrical and electronic manufacturing companies operating in the field of advanced technologies
The doctoral study is conducted according to the individual study plan. The individual study plan is prepared by the supervisor in cooperation with the doctoral student at the beginning of the study. The individual study plan specifies all the duties stipulated in accordance with the Study and Examination Rules at the Brno University of Technology, which the doctoral student must fulfill to successfully finish his studies. These responsibilities are scheduled throughout the whole study period; they are scored and they are evaluated at the end of given periods.
The student enrolls and takes examinations of the compulsory courses Numerical Computations with Partial Differential Equations and English for the state doctoral exam; at least two obligatory elective courses relating to the focus of his dissertation and at least two optional courses (English for Post-graduates; Scientific Citing; Solution of Innovational Tasks; Scientific publishing).
The student may enroll for the state doctoral exam only after taking all the exams prescribed by the individual study plan. Before the state doctoral exam, the student prepares a treatise on dissertation thesis, which describes in detail the goals of the thesis, a thorough evaluation of the state of knowledge in the area of the dissertation solved, or the characterization of the methods intended to apply in the solution.
The defense of treatise on dissertation thesis, which is reviewed, is part of the state doctoral exam. In the next part of the exam the student must demonstrate deep theoretical and practical knowledge in the field of electrical engineering, electromagnetic field, circuit theory, methods of measuring electrical and other physical quantities, processing and analysis of signals and mathematical modeling of technical processes. The state doctoral exam has a form of oral presentation and discussion on the treatise on dissertation thesis. In addition, it also includes a discussion on issues of thematic areas related to obligatory and obligatory elective courses.
The doctoral student can apply for the defense of dissertation thesis after passing the state doctoral exam and after fulfilling conditions for termination of the study, such as participation in teaching; scientific and expert activity (creative activity) and at least a monthly study or work internship at a foreign institution or participation in an international creative project.
Study plan creation
The doctoral studies of a student follow the Individual Study Plan (ISP), which is defined by the supervisor and the student at the beginning of the study period. The ISP is obligatory for the student, and specifies all duties being consistent with the Study and Examination Rules of BUT, which the student must successfully fulfill by the end of the study period. The duties are distributed throughout the whole study period, scored by credits/points and checked in defined dates. The current point evaluation of all activities of the student is summarized in the “Total point rating of doctoral student” document and is part of the ISP. At the beginning of the next study year the supervisor highlights eventual changes in ISP. By October, 15 of each study year the student submits the printed and signed ISP to Science Department of the faculty to check and archive.
Within the first four semesters the student passes the exams of compulsory, optional-specialized and/or optional-general courses to fulfill the score limit in Study area, and concurrently the student significantly deals with the study and analysis of the knowledge specific for the field defined by the dissertation thesis theme and also continuously deals with publishing these observations and own results. In the follow-up semesters the student focuses already more to the research and development that is linked to the dissertation thesis topic and to publishing the reached results and compilation of the dissertation thesis.
By the end of the second year of studies the student passes the Doctor State Exam, where the student proves the wide overview and deep knowledge in the field linked to the dissertation thesis topic. The student must apply for this exam by April, 30 in the second year of studies. Before the Doctor State Exam the student must successfully pass the exam from English language course.
In the third and fourth year of studies the student deals with the required research activities, publishes the reached results and compiles the dissertation thesis. As part of the study duties is also completing a study period at an abroad institution or participation on an international research project with results being published or presented in abroad or another form of direct participation of the student on an international cooperation activity, which must be proved by the date of submitting the dissertation thesis.
By the end of the winter term in the fourth year of study students submit the elaborated dissertation thesis to the supervisor, who scores this elaborate. The final dissertation thesis is expected to be submitted by the student by the end of the fourth year of the studies.
In full-time study form, during the study period the student is obliged to pass a pedagogical practice, i.e. participate in the education process. The participation of the student in the pedagogical activities is part of his/her research preparations. By the pedagogical practice the student gains experience in passing the knowledge and improves the presentation skills. The pedagogical practice load (exercises, laboratories, project supervision etc.) of the student is specified by the head of the department based on the agreement with the student’s supervisor. The duty of pedagogical practice does not apply to students-payers and combined study program students. The involvement of the student in the education process within the pedagogical practice is confirmed by the supervisor in the Information System of the university.
Issued topics of Doctoral Study Program
- Advanced methods of low-level measurements
One of the goals of the dissertation will be to optimize the existing apparatus for measuring air ions and to propose new methods for fast determination of their mobility spectrum. The applicability of the new apparatus will be in an environment with high humidity, dustiness and undesirable insects and deep frost. Subsequently, unique measurement applications will be performed with the proposed apparatus, which will lead to a better understanding of the Earth's atmospheric electricity. In addition to studying atmospheric electricity, the research will also focus on enclosed interiors, where it is necessary to achieve maximum sensitivity with a minimum volume flow of air. The influence of cigarette smoke, plants on air ions will be investigated. Research in the experimental forest will be similar. In addition to aerial ions, it will be possible to focus on correlation with other microclimatic elements of closed systems such as caves. It is a long-term measurement of CO2, relative humidity, air flow and subsequent system allowing comprehensive measurement of these quantities in the cave.
Tutor: Roubal Zdeněk, Ing., Ph.D.
- Advanced methods of radiofrequency detection of partial discharges
One of the key problems of high-power high-voltage transformers is the existence of partial discharges PD in their dielectric oil filling. Radiofrequency methods may provide an efficient tool for observing the PD activity. The possibility of PD-radiated UHF electromagnetic (EM) signal detection is crucial for successful methods application. This signal has a relatively low magnitude and its occurrence is accompanied by a strong impulse-like interference from other discharge processes. On the other side, the PD signal dispose with specific time and frequency properties, which can be utilized for its reliable detection and evaluation. The theme of the Ph.D. study is focused on the research of new approach to PD-radiated EM signals detection utilizing signal’s specific time and frequency properties. The goal is to deepen the knowledge in the problematic of reliable detection and identification of PD activity and increasing the reliability of the high-power high-voltage transformers.
- Analysis of image reconstruction methods in EIT
The aim of this work is the analysis of mathematical models for image reconstruction obtained by the electrical impedance tomography from the viewpoint of applicability to individual engineering fields (chemical industry, geology, material engineering and diagnostics, etc.). The output of the work will be a theoretical analysis and optimization of limiting factors of methods in solving selected technical tasks including evaluation of measurement uncertainties (specific conductivity and position of inhomogeneities), computational demands, etc.
- Application of highly birefringent optical fibers for sensing of physical quantities
Novel types of optical fibers allow applications of fiber-optic sensors in areas, where classical sensors are difficult to use. The example is a sensing of electric current or magnetic field, who can achieve extreme magnitudes or sensing under strong disturbing influences. It is possible to use special types of optical fiber with strong latent birefringence for the suppression of the disturbing influences. The potentially allow for design and development of robust sensor with minimized sensitivity to outer influences. The thesis will be focused on the research and development of sensing techniques utilizing highly birefringent fibers.
- Detection and Classification of Moving Objects
The main task is to develop and test convenient algorithms to detect moving objects. Such algorithms should facilitate the detection and recognition of predefined bodies at high safety locations, including airports, nuclear power plants, and ammunition depots. After the character of the intruding object in motion has been specified, relevant disabling options will be outlined.
- Electromagnetic properties of graphene
This thesis is focused on the research, characterization, modeling and experimental verification of the electromagnetic properties of a graphene structures, as monoatomic layers and multilayer structures. The aim is mainly using a numerical model to describe the expected performance of a sample of graphene structures, describe and set up an experiment to verify selected properties of such structures. On tested sample perform a series of experiments that monitored parameters described and it is thus possible to compare with the theoretically obtained.
- Enhancing Inner Perimeter Safety
The tasks are defined as follows: Study various options to improve the safety of an inner perimeter in high risk areas, and design an applicable automated guarding system.
- Fast reconstruction of electrical impedance tomography images
This thesis will be focused on development of the methods for reconstruction of images obtained by electrical impedance tomography. The main emphasis will be placed on the methods of the signals of low SNR measurement as well as on the signal processing and reconstruction of the impedance inside the examined object. Considering the time-consuming calculation with respect to higher number of measuring electrodes or smoother FEM mesh, the work will follow on the current activities of DTEEE in solving the inverse problems and parallelization of computational algorithms and their distribution to the graphics card.
- Image modeling and reconstruction in EIT using IEM-FEM
The aim of the dissertation is to create an IEM-FEM (In / Finite Elements Method) model for image reconstruction in electrical impedance tomography. This modeling method is applicable in the field of geology (monitoring of reservoirs, permafrost, etc.). The outcome of the work should be more accurate results, which based on the reconstructed image will more accurately describe the specific conductivity inside the system compared to FEM. The whole methodology will be verified experimentally in laboratory and real environment.
- Minimizing Susceptibility Artefacts in Medical Images
The research will be centered on methods for the minimization of artifacts that, during medical imaging, result from different magnetic susceptibility values exhibited by various tissues and materials. In the vicinity of dental implants, for example, the MR signal is often lost, causing major procedural problems.
- Modern methods of processing electron microscopy images
The aim of the dissertation thesis is to develop methods of reconstruction of the electron microscopy images. Emphasis will be placed on the detailed highlighting of scanned structures, image noise suppression, optimization of image processing methods based on the microscopy settings. In case of complex, time-consuming algorithms, the part of the work will be focused on parallelizing the calculations. Cooperation is planned with TESCAN Brno, ltd.
- Multispectral Imaging of Plants
The project is aimed to investigate and test diverse techniques to enable evaluation of relevant multispectral camera images. In terms of concrete tasks and stages, the actual work will involve, in particular, extensive data acquisition via drone-based survey and the subsequent designing of suitable image processing methods to associate the data with appropriate plant specimens. The expected outcomes include, among other items, readily applicable plant health maps.
- Numerical solution methods of fractional control systems
The aim of the dissertation thesis is modification of a numerical semi-analytical method based on Adomian decomposition method and integral transformations to solving initial value problems for fractional control systems in the sense of Caputo fractional derivative. Convergence analysis of the proposed method will be investigated as well.
- Optical fiber sensing of electromagnetic transients
The use of a magneto-optical effect in optical fibers is an attractive option for the design of magnetic field and electric current sensors. Their application is particularly interesting in the case of measurements of strong magnetic fields, or currents reaching values in the range of kiloamperes up to tens of megaamperes. In this context, their application in the diagnostics of plasma discharges in future fusion reactors is highly potential. For successful deployment of these sensors it is highly desirable to have the possibility of testing them during development. Many works have already dealt with the measurement of sensor properties. However, the necessary attention has not been paid to the possibility of testing the dynamic properties of the transducers in the nanosecond and sub-nanosecond regions. Moreover, together with the magnetic fields induced by currents of kiloamperes and above. The dissertation thesis will be devoted to the research of properties and testing of sensors in the nano and sub-nanosecond area. The design and development of a unique testing device is expected.
- Polarization optical reflectometry for measurement of plasma current of fusion reactors
In current and future fusion reactors, the plasma current value reaches mega-ampere values. A suitable method for measuring its size as well as stability is polarization optical time domain reflectometry (POTDR). Future large reactors will have a discharge chamber with a non-circular cross-section to facilitate the stability of the fusion reaction. The disadvantage is a more complicated method of analysis of POTDR measurements due to the inhomogeneity of the field around the reactor. The dissertation thesis will deal with the new possibilities of processing POTDR measurements, which will allow to determine the magnitude of plasma current with respect to real measurement conditions.
- Research of properties and applications of noise electromagnetic fields
Measuring and diagnostic methods based on the interaction of radiated electromagnetic (EM) field with test objects are currently mature and widely used technology. However, the vast majority of systems based on such approach use the concept of generating and evaluating EM fields with certain defined or swept frequency. In this case, it is necessary to take into account the possibility of reactive coupling of the measured object and the measuring device in the near field, which can detriorate the measurement. Conversely, if broadband stochastic signals (noise signals) were used for diagnostics, these problematic coupling could be suppressed. The topic of the study is focused on the research of the use of the concept of diagnostic of materials and electromagnetic structures by the noise field, especially in radiofrequency and microwave domain, its development and experimental verification.
- Spatial Analysis of the Force Load on a Deformed Developing Spine, and Corrective Force Modelling Applied to Minimize the Scope of a Scoliosis Surgery
Spinal deformity in children (scoliosis) is a condition whose progression cannot be predicted. The results obtained via conservative therapy are problematic, and a certain degree of curvature requires surgical treatment, including the risk of repeated surgeries and complications. The presently used system of growing rods affects, on the average, 9 spinal segments; these become immobile and influence the excessive stress upon the free segments under fusion, resulting in earlier degenerative changes, back pain at a mature age, restrained bodily activity, and damage to the locomotor system. The project is conceived to propose a novel methodology for minimizing the spurious impacts of the surgical treatment of progressive spinal deformity upon child patients, with 3D modeling to define the mechanical stress distribution within the simulation of the planned intervention. The set of patients to be recruited includes individuals with idiopathic, symptomatologic, and congenital scoliosis progressing despite conservative therapy; all these subjects would otherwise undergo spinal surgery. The project aims to design a surgical solution to correct idiopathic, symptomatologic, and congenital spinal deformities by the osteotomy of 1 vertebra. It will exploit 3D modeling to define the stress on the spine, estimation of the spine development and intervertebral discs regeneration by MRI. The project will be carried out in collaboration with University Hospital in Brno Bohunice.
- The Theory of Nonlinear Acoustics in Relation to Inhomogeneous Locally Periodic Structures
Nonlinear acoustics is a comparatively modern research discipline, whose primary focus lies within the propagation of acoustic waves in a nonlinear environment, modelling of the parametric acoustic field, and applications stemming from these areas. In this branch of science, major problems currently awaiting effective solution include, above all, the analytical description and numerical modelling of a non-linear environment. These two subdomains are complemented with another task element, namely the design of inhomogeneous, locally periodic structures, which enable us to target acoustic waves into a beam and to create nonlinear components, such as acoustic diodes. Further, the discussed research discipline may comprise a number of potential application subregions, for example, contactless material testing. Within the doctoral thesis, the student will characterize and analyze amplitude modulated acoustic waves of final amplitudes, and they will also provide an analysis of parametrically excited acoustic fields. In the wider context, one of the central aims of the thesis is to employ inhomogeneous periodic structures, methods for input signal processing, and carrier wave modulation to deepen the present knowledge of nonlinear acoustic interactions in liquids.
- Transport of heat by turbulent flows in cryogenic helium gas in Rayleigh-Bénard Convection experiments
Turbulent flows are found almost everywhere in Nature (think air travel, flow of air around cars, explosions of supernovae, dynamics of quantum vortices in superfluid helium at temperatures close to absolute zero…). One important feature is the enhancement of heat transport in a layer of fluid. To give an illustration of the magnitude - In an atmospheric boundary layer of 1 km height, the turbulent heat transfer increases by at least 5 orders of magnitude compared to the one by molecular diffusion without turbulent air flow. Detailed understanding of this has an obvious value for understanding Earth’s climate or important technological applications such as processes in cooling blankets in nuclear engineering or the storage of renewable energy in liquid metal batteries. Turbulent heat transport can be modelled and studied in laboratory conditions, however the highest intensity turbulence experiments (approaching the conditions relevant e.g. in our planetary atmosphere), as the Rayleigh Benard convection (RBC) experiments in cryogenic helium gas done in our laboratory at the Institute of Scientific Instruments in Brno involve so-called non-Oberbeck-Boussinesq (NOB) effects occurring due to temperature- and pressure-dependence of the working fluid properties, like density, viscosity, or heat conductivity. These are not sufficiently understood, as even the best current numerical simulations work so far only with constant properties, thus the value for understanding large-scale natural phenomena is limited. In collaboration with the team of prof. J. Schumacher at TU Ilmenau, we are working on novel efficient codes involving NOB effects and plan a systematic and careful comparisons with cryogenic helium experiments at ISI Brno. The PhD student will learn deeply about turbulent heat transport and will be able to analyze, compare and interpret data from two different sources – cryogenic helium RBC experiments performed in Brno and massively parallel direct numerical simulations preformed in Ilmenau. The student can also get involved in designing the electronics and instrumentation for data harvesting in upgrades of the ISI experimental apparatus. The interpretation will be done in collaboration with prof. L. Skrbek from MFF UK Prague and prof. K. Sreenivasan at New York University, USA.
- Using Artificial Intelligence Algorithms to Control a Drone
The actual assignment rests in developing and testing machine learning methods that will enable autonomous control of a drone. To yield appropriate control signals, the image data must be processed in real time, requiring the algorithms to operate in a quick and adaptable manner.
- Vizualization of quantum and classical turbulent flows of superfluid and gaseous helium by a novel optical method via laser-induced fluorescence of long-living molecular excimers He2*
Turbulent flows are found almost everywhere in Nature (think of air travel, flow of air around cars, explosions of supernovae, dynamics of quantum vortices in superfluid helium at temperatures close to absolute zero…). One important feature is the enhancement of heat transport in a layer of fluid. To give an illustration of the magnitude - In an atmospheric boundary layer of 1 km height, the turbulent heat transfer increases by at least 5 orders of magnitude compared to the one by molecular diffusion without turbulent air flow. Detailed understanding of this, has an obvious value for understanding Earth’s climate or important technological applications such as processes in cooling blankets in nuclear engineering or the storage of renewable energy in liquid metal batteries. Turbulent heat transfer can be modelled and studied in laboratory conditions, however the highest intensity turbulence experiments (approaching the conditions relevant e.g. in our planetary atmosphere), as the Rayleigh Benard convection (RBC) experiments in cryogenic helium gas done in our laboratory at the Institute of Scientific Instruments in Brno nowadays measure only temperature fluctuations and lack a suitable visualization technique, allowing to measure the flows velocity field. In collaboration with the group of prof. W. Guo at National High-Magnetic Field Laboratory in Florida, who apply a novel and groundbreaking method using laser-induced fluorescence (LIF) of long-living metastable excimers of helium-4 in the regime of superfluid quantum turbulence, we plan to develop an apparatus for visualization of classical turbulent heat transfer by RBC in gas. The work on the PhD student will involve measurements and large data analysis of the experiments in Florida and/or design of the novel apparatus to be built at ISI Brno. The student can also get involved in designing the electronics and instrumentation for data harvesting in upgrades of the ISI experimental RBC apparatus.
1. round (applications submitted from 01.04.2020 to 15.05.2020)
- Flying and Coordinating Drone Swarms
The researcher will be assigned with the development and testing of artificial intelligence methods to be applied in drones. Considering the entire procedure, a major objective is to facilitate smooth communication between the electronic coordination and timely warning systems. In terms of the hardware, the Ph.D. candidate will be required to choose suitable sensors as well as to design, implement, and test complex machine learning techniques.
- Machine Learning for Image Data Classification
The research will focus on the development and testing of machine learning algorithms to classify image data. The partial tasks will include processing the photometric maps and 3D models; classifying and training the geometry-based algorithms; and assigning semantic information to objects.
- Plasma and its numerical models
The work is focused on theoretical derivation of numerical models based on PDR solution for plasma and discharge activity modeling. The approach will use both stochastic and deterministic methods to find and formulate corresponding numerical models of plasma discharge in chambers with inhomogeneous gas and precursor environments. It follows the research and modification of the model based on the finite element method, finite volume method, boundary elements for static and dynamic models formulated using partial differential equations. The aim of this work is to design a numerical model as a powerful tool for analysis and description of properties of specific chamber arrangement designed for plasma generation and its geometry at atomic and subatomic levels, verification on simple verifiable example. The analyzes will be verified by experiment, the research will be aimed at finding the parameters of the resulting numerical model and compared with the requirements placed on models designed for the dynamics of electric discharge and evaluate the given parameters. The topic is part of the grant.
- Surface treatment by plasma discharge in HV technology
The aim of this work is a summary of research activities in the area of theoretical description and modeling of the effect of plasma discharge on surfaces of selected MV devices that should show specific electrical properties after treatment. The surface properties are determined by the macro, micro and nanoscopic state of the surface of the dielectric material, possibly treated with precursors of inorganic or organic character. The plasma-treated surface will exhibit altered properties from the region of in particular spacing distances at the air-surface interface or in contact with other solid material at a critical electric field strength value. The work will deal with both theoretical description of expected phenomena and numerical models and their analyzes with the part in which the models and analyzes will be verified experimentally.
Course structure diagram with ECTS credits
|DKC-ET1||Electrotechnical materials, material systems and production processes||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-EE1||Mathematical Modelling of Electrical Power Systems||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-ME1||Modern Microelectronic Systems||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-RE1||Modern electronic circuit design||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-TK1||Optimization Methods and Queuing Theory||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-FY1||Junctions and nanostructures||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-TE1||Special Measurement Methods||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-MA1||Statistics, Stochastic Processes, Operations Research||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-AM1||Selected chaps from automatic control||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-VE1||Selected problems from power electronics and electrical drives||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-JA6||English for post-graduates||cs||4||Elective||DrEx||Cj - 26||yes|
|DKC-RIZ||Solving of innovative tasks||cs||2||Elective||DrEx||S - 39||yes|
|DKC-EIZ||Scientific publishing A to Z||cs||2||Elective||DrEx||S - 26||yes|
|DKC-TE2||Numerical Computations with Partial Differential Equations||cs||4||Compulsory||DrEx||S - 39||yes|
|DKC-TK2||Applied cryptography||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-MA2||Discrete Processes in Electrical Engineering||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-ME2||Microelectronic technologies||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-RE2||Modern digital wireless communication||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-EE2||New Trends and Technologies in Power System Generation||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-FY2||Spectroscopic methods for non-destructive diagnostics||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-ET2||Selected diagnostic methods, reliability and quality||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-AM2||Selected chaps from measuring techniques||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-VE2||Topical Issues of Electrical Machines and Apparatus||cs||4||Compulsory-optional||DrEx||S - 39||yes|
|DKC-JA6||English for post-graduates||cs||4||Elective||DrEx||Cj - 26||yes|
|DKC-CVP||Quotations in a research work||cs||2||Elective||DrEx||P - 26||yes|
|DKC-RIZ||Solving of innovative tasks||cs||2||Elective||DrEx||S - 39||yes|
|DKC-QJA||English for the state doctoral exam||cs||4||Compulsory||DrEx||S - 3||yes|