Course detail

1D Modelling in Power Engineering

FSI-L1D Acad. year: 2025/2026 Summer semester

In this course, students will acquire the skill to create one-dimensional mathematical models representing physical processes. The theory covers the basic mathematical principles relevant to these models and presents the fundamental numerical methods and algorithms commonly used in 1D modeling across various software tools. Using the OpenModelica programming environment along with standard MSL libraries and third-party resources, students will apply theoretical concepts during practical lessons. The graphical environment allows easy assembly of models with many components, simplifying the effort during modeling. Emphasis on 1D modeling enables fast simulation of individual processes but also complex systems, resulting in significant computational efficiency, but at the cost of reducing the quality of prediction. Through assigned tasks, students will gain competence in using OpenModelica to simulate processes and strengthen their understanding.

Language of instruction

Czech

Number of ECTS credits

4

Supervisor

prof. Ing. Jiří Pospíšil, Ph.D.

Department

Energy Institute

Entry knowledge

A foundational understanding of mathematics and physics at the undergraduate level, coupled with analytical thinking skills.

Rules for evaluation and completion of the course

Regular and active participation in exercises, delivery of all assigned tasks is required for credit to be granted.

Aims

To acquaint students with the mathematical, theoretical and practical aspects of 1D modeling of processes in energy related subjects using the freely available Modelica programming syntax, the OpenModelica-Compiler compiler, MSL standard libraries, and freely available third-party libraries. The subject is focused on the general theory related to the numerical solution of large systems of equations, but also on the description of individual physical mechanisms in mathematical form. When using 1D models, machine time is reduced. When using component-oriented modeling, engineering work is reduced, because already existing code is used effectively. Students will learn to use this abstraction effectively

Study aids

The course is complemented by a body of online resources, primarily in the form of instructional videos, providing comprehensive explanations of the theoretical and practical aspects of the topics covered. Students are strongly encouraged to make use of these resources while tackling their assignments during the semester.

The study programmes with the given course

Programme N-SUE-P: Computational Simulations for Sustainable Energy, Master's, compulsory

Type of course unit

 

Lecture

13 hours, optionally

Syllabus


  1. Introduction – what is 1D modeling, advantages, disadvantages, quasi-static models, dynamic models, tools -> OpenModelica,

  2. Algebraic, ordinary differential equations and initial conditions, partial differential equations and boundary conditions, linear vs. nonlinear equation,

  3. Systems of differential and algebraic equations, numerical errors and tolerances, time step, types of solvers – how to choose, numerical stability,

  4. What to watch out for – overdetermined, underdetermined, and singular systems, expressions with conditional existence (division by zero, negative log, etc.), numerical diffusion, numerical oscillations,

  5. Accuracy of the model – finding/adding more detailed mechanisms/effects (shaving the errors), correctness of assumptions, validation with experiment,

  6. Limits of 1D modeling, when to switch to 2D/3D, characteristics of real components vs. ideal components.

  7. PID and controlled system simulation, response, delay, predictive control,

  8. Pipeline flow, pressure drops, branched system, pump, Heat conduction and transfer, heat accumulation, exchanger, phase change,

  9. Identification of model parameters according to experimental data.

Computer-assisted exercise

26 hours, compulsory

Syllabus


  1. OM installation, UI overview, basic concepts, syntax basics, units, data types,

  2. Algebraic system/quasi-static model, ODE system/dynamic model,

  3. Kirchhoff's laws or conservation laws, connectors,

  4. Domain discretization and partial differential equation methods, FEM, FVM, FDM in 1D modeling, what to use when.

  5. Overview of MSL, component-oriented modeling, and third-party libraries.

  6. Fluid systems, properties of the medium, throttling, characteristics of pumps and other elements of pipeline routes,

  7. Chemical reactions, pyrolysis of wood particles,

  8. Heat transfer by convection, conduction, and radiation, dynamic countercurrent heat exchanger.

  9. Control of the CZT system using PID controllers,

  10. Compressor and absorption heat pump,

  11. RC circulation, design balance calculation,

  12. Electronics, batteries, motors,

  13. Grading the assignments, awarding credits.