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Mathematical Problems of Electric Power Engineering
Major: Electrical Energetics, Electrical Engineering and Electromechanics
Code of subject: 6.141.01.E.043
Credits: 4.00
Department: Electric Power Engineering and Control Systems
Lecturer: Professor, D.Sc. Seheda Mykhaylo
Semester: 4 семестр
Mode of study: денна
Завдання: The study of an educational discipline involves the formation of competencies in students of education:
general competences:
• knowledge of special sections of mathematics, to the extent necessary for mastering professionally oriented disciplines;
• ability to analyze and synthesize;
• the ability to search, analyze and critically evaluate information from various sources;
• the ability to work both individually and in a team;
• the ability to communicate effectively at the professional and social levels;
• understanding the need for lifelong learning and the transfer of acquired knowledge;
• responsibility for the quality of work performed;
professional competences:
• knowledge of development trends and the most important new developments in the field of electrical engineering and electromechanics, as well as related fields;
• knowledge and understanding of scientific concepts, theories and methods necessary for solving problems in electric power, electrotechnical and electromechanical systems and their equipment;
• the ability to apply information and communication technologies and programming skills to solve typical engineering tasks;
• the ability to use the acquired knowledge and skills to work in industry and to understand the need to comply with the rules of safety technology when performing job duties;
• the ability to apply analytical methods of analysis, mathematical modeling and perform physical and mathematical experiments to solve engineering problems and when conducting scientific research;
• the ability to integrate knowledge from other disciplines, apply a systematic approach and take into account non-technical aspects when solving engineering problems and conducting research;
• the ability to evaluate the expediency and possibility of applying new methods and technologies in the problems of synthesis of electric power, electrotechnical and electromechanical systems.
Learning outcomes: As a result of studying the academic discipline, the student must be able to demonstrate the following learning outcomes:
1. The ability to demonstrate knowledge and understanding of scientific physical and mathematical principles necessary for solving engineering problems and conducting research in the field of electric power, electrical engineering and electromechanics.
2. Reasonably choose methods for modeling modes and processes in dynamic systems, as well as analyze the obtained results.
3. Apply information technologies and programming skills to solve typical engineering problems in the field of electric power.
4. Apply knowledge and understanding to solve problems of synthesis and analysis of system elements characteristic of the chosen specialization.
5. Independently perform experimental research and apply research skills on professional topics.
6. Apply a systematic approach, integrating knowledge from other disciplines when solving engineering problems of the chosen specialization and conducting research.
7. Assess the expediency and possibility of applying new methods and technologies in the problems of synthesis of electric power, electrotechnical and electromechanical systems.
8. Argue the choice of methods for solving a specialized problem, critically evaluate the obtained results and defend the adopted engineering solutions.
Required prior and related subjects: Prerequisites:
• Higher mathematics,
• Theoretical bases of electrical engineering;
• Electric networks and systems..
Summary of the subject: Studying of mathematical apparatus that allows students to make a research into the electromagnetic processes in electric power systems; solving of systems of linear and nonlinear equations both algebraic and differential, analysis of processes in such type systems, usage of principles and methods of digital simulation.
Опис: 1. Basics of the theory of similarity in problems of electric power engineering. Elements of set theory and graph theory and their scope of application in electrical, electric power and power supply
systems
2. Methods of forming equations of regimes and processes of electric power and power supply systems. Structural elements and their physical quantities.
3. Equations of regimes and processes according to Ohm's and Kirchhoff's laws, contour and nodal coordinates.
4. Equations of modes and processes in the methods of independent and loop currents.
5. Equations of modes and processes in methods of independent, nodal and internodal voltages.
6. Equations of modes and processes in the methods of branch coordinates and defining coordinates.
7. Matrices of input and mutual impedances, distribution coefficients, matrices of nodal and conditionally nodal impedances.
8. Special computing methods. Interpolation and extrapolation of functions. Approximation of functions. Approximate differentiation and integration of functions.
9. Methods of solving a system of finite linear equations. Eigenvalues and eigenvectors of a matrix. Matrix and vector norms.
10. Numerical methods of solving systems of linear and nonlinear finite equations.
11. Mathematical models of steady-state analysis of power and power supply systems. Methods of nodal voltages, loop currents and power balance.
12. Analysis and synthesis of electric power and power supply systems by the method of state coordinates (variables).
13. Numerical methods of solving ordinary differential equations. Accuracy and stability of numerical methods. Algorithms for choosing the integration step of ordinary differential equations.
14. One-step and multi-step explicit methods.
15. One-step and multi-step implicit methods.
Assessment methods and criteria: • written reports on laboratory course, oral questioning (30%);
• final control (control event – exam): written and oral form (70%).
Критерії оцінювання результатів навчання: Distribution of points on a 100-point scale
Performance and defense of laboratory work - 30 points
Credit work written component – 65 points
Oral component – 5 points
Порядок та критерії виставляння балів та оцінок: 100–88 points – (“excellent”) is awarded for a high level of knowledge (some inaccuracies are allowed) of the educational material of the component contained in the main and additional recommended literary sources, the ability to analyze the phenomena being studied in their interrelationship and development, clearly, succinctly, logically, consistently answer the questions, the ability to apply theoretical provisions when solving practical problems; 87–71 points – (“good”) is awarded for a generally correct understanding of the educational material of the component, including calculations, reasoned answers to the questions posed, which, however, contain certain (insignificant) shortcomings, for the ability to apply theoretical provisions when solving practical tasks; 70 – 50 points – (“satisfactory”) awarded for weak knowledge of the component’s educational material, inaccurate or poorly reasoned answers, with a violation of the sequence of presentation, for weak application of theoretical provisions when solving practical problems; 49-26 points - ("not certified" with the possibility of retaking the semester control) is awarded for ignorance of a significant part of the educational material of the component, significant errors in answering questions, inability to apply theoretical provisions when solving practical problems; 25-00 points - ("unsatisfactory" with mandatory re-study) is awarded for ignorance of a significant part of the educational material of the component, significant errors in answering questions, inability to navigate when solving practical problems, ignorance of the main fundamental provisions.
Recommended books: 1. Кириленко О.В., Сегеда М.С., Буткевич О.Ф., Мазур Т.А. Математичне моделювання в електроенергетиці: Підручник / – Львів: 2-е видання. Вид-во нац. ун-ту «Львівська політехніка», 2013. – 608 с.
2. Перхач В.С. Математичні задачі електроенергетики – 3-е вид., перероб. і доп. – Львів: Вища шк., 1989. – 464 с.
3. Сегеда М.С. Математичне моделювання в електроенергетиці: Навч. посібник / Мін. освіти і науки України; Національний університет “Львівська політехніка” – Львів: Видавництво Національного університету “Львівська політехніка”, 2002. – 300 с.
4. Чуа Л.О., Пен-Мин Лин. Машинный анализ электрических схем (алгоритмы и вычислительные методы). – М.: "Энергия", 1980. – 640 с.
5. Данилина Н.И., Дубровская Н.С. и др. Численные методы. – М.: "Высшая школа", 1976 – 368 с.
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