System approach to mathematical modeling of thermal processes in buildings

Authors

  • Александр Сергеевич Куценко National Technical University "Kharkov Polytechnic Institute" Str. Frunze, 21, Kharkov, Ukraine, 61002, Ukraine https://orcid.org/0000-0001-8017-3427
  • Сергей Владимирович Коваленко National Technical University "Kharkov Polytechnic Institute" Str. Frunze, 21, Kharkov, Ukraine, 61002, Ukraine https://orcid.org/0000-0001-8763-0862
  • Владимир Игоревич Товажнянский National Technical University "Kharkov Polytechnic Institute" Str. Frunze, 21, Kharkov, Ukraine, 61002, Ukraine https://orcid.org/0000-0002-8293-4047

DOI:

https://doi.org/10.15587/1729-4061.2014.26200

Keywords:

thermal processes, heat supply of buildings, mathematical model, heat-conduction equation, differential equations

Abstract

An approach to constructing a mathematical model of the heat supply process of building, consisting of interconnected premises is proposed in the paper.

The approach is based on replacing heat-conduction equations, describing heat transfer processes between the elements of buildings and the environment, by a finite-dimensional system of ordinary differential equations. Substantiation of the dimension of the approximating system, based on comparing the analytical solution of the heat-conduction equation and the results of the numerical integration of the approximate differential equation system is carried out. Numerical experiments have shown that for different values of the criteria with sufficient accuracy for practical purposes one can content himself with the system of the 2nd order.

It is shown that the time constants of thermal processes of air of premises, partitions and filling of premises are by 2-3 orders lower than the time constants of the processes in the outer perimeter. This allows to replace the system of differential equations of heat balance for air, partitions and filling by static equations.

The obtained structure of the mathematical model of the thermal process in a complex system is a linear model of controlled processes. This allows to effectively adapt all the basic methods of analysis and synthesis of automatic control systems to the problems of heat supply management.

Author Biographies

Александр Сергеевич Куценко, National Technical University "Kharkov Polytechnic Institute" Str. Frunze, 21, Kharkov, Ukraine, 61002

Doctor of Technical Sciences, Professor

Head. Department of Systems Analysis and Management

Сергей Владимирович Коваленко, National Technical University "Kharkov Polytechnic Institute" Str. Frunze, 21, Kharkov, Ukraine, 61002

Senior lecturer

Department of Systems Analysis and Management

Владимир Игоревич Товажнянский, National Technical University "Kharkov Polytechnic Institute" Str. Frunze, 21, Kharkov, Ukraine, 61002

Master

Department of Systems Analysis and Management

References

  1. Malyarenko, V. A., Orlova, N. A. (2004). Analysis criterion of energy efficiency of buildings and structures. Integrated technologies and energy efficiency, 2, 43–48.
  2. Panferov, S. V. (2010). Some problems of energy saving and automation in heating buildings. Herald SUSU. Series Computer technology, management, electronics, 22, 79–86.
  3. Tabunshchikov, Yu. A., Borodach, M. M. (2002). Mathematical modeling and optimization of the thermal performance of buildings. Moscow, Russia: AVOK-PRESS, 194.
  4. Sokolov, E. Ya. (1999). District heating and heat networks. Moscow, Russia: “Publishing MPEI”, 472.
  5. Medina, M. A. (1999). Validation and simulations of a quasi-steady state heat balance model of residential walls. Mathematical and Computer Modelling, 30 (7-8), 93–102. doi:10.1016/s0895-7177(99)00166-1
  6. Malyarenko, V. A. (2006). Basics thermal physics and energy efficiency of buildings. Kharkiv, Ukraine: “Publishing SAGA”, 484.
  7. Vasilyev, G. P., Lichman, V. A., Peskov, N. V. (2010). A numerical optimization method for intermittent heating. Mathematical modeling, 11, 123–130.
  8. Gabriel, T. (2013). Hybrid Predictive Control for Building Climate Control and Energy Optimization. 7th IFAC Conference on Manufacturing Modelling, Management, and Control, 2013. doi:10.3182/20130619-3-ru-3018.00480
  9. Kutsenko, A. S., Kovalenko, S. V. (2012). Mathematical model of the thermal regime of the building as a management object. Mathematical methods in engineering and technologies, 4, 190–191.
  10. Jury, E. (1967). A note on multirate sampled-data systems. IEEE Trans. Automat. Contr., 12 (3), 319–320. doi:10.1109/tac.1967.1098564

Published

2014-07-24

How to Cite

Куценко, А. С., Коваленко, С. В., & Товажнянский, В. И. (2014). System approach to mathematical modeling of thermal processes in buildings. Eastern-European Journal of Enterprise Technologies, 4(4(70), 9–12. https://doi.org/10.15587/1729-4061.2014.26200

Issue

Section

Mathematics and Cybernetics - applied aspects