ANALYSIS AND DATA PROCESSING SYSTEMS

Abstract
The article is devoted to optimization problems of hydraulic modes of distribution heat networks which appear at the stage of mode planning before the heating season. The task of scheduling hydraulic modes of heating network distribution is formulated as a problem of two-criterion optimization. A model of a controlled flow distribution in the heat networks and mathematical formulation of optimization problems are given. The statement of one-criterion problems of discrete and continuous optimization and two-criterion problems with continuous and discrete main criterion are also given. We present the proposed methods for solving all tasks. They are based on the method of interior points developed by ESI SB RAS. To account for the discrete nature of the tasks the exhaustion method, the ramification and pruning method and the branch and bound method are used. To solve the problem in the search for a minimum level of pressure in the network with a minimum number of controls a method based on the special properties of the heat distribution network modes and provides a satisfactory speed of response compared to other possible methods. Numerical examples illustrate the performance of the proposed methods to ensure finding a global solution, as well as their comparative computational efficiency.  

References
1. Merenkov A.P., Khasilev V.Ya. Teoriya gidravlicheskikh tsepei [The theory of hydraulic circuits]. Moscow, Nauka Publ., 1985. 278 p. 2. Sennova E.V., Sidler V.G. Matematicheskoe modelirovanie i optimizatsiya razvivayushchikhsya teplosnabzhayushchikh sistem [Mathematical modeling and optimization of developing heat supply systems]. Novosibirsk, Nauka Publ., 1987. 219 p. 3. Yufa A.I., Nosul'ko D.R. Kompleksnaya optimizatsiya teplosnabzheniya [Integrated heat supply optimization]. Kiev, Tekhnika Publ., 1988. 135 p. 4. Haikarainen C., Pettersson F., Saxén H. An MILP model for distributed energy system optimization. Chemical Engineering Transactions, 2013, vol. 35, pp. 295–300. 5. Ortiga J., Bruno J.C., Coronas A., Grossman I.E. Review of optimization models for the design of polygeneration systems in district heating and cooling networks. 17^th European Symposium on Computer Aided Process Engineering (ESCAPE-17). Ed. by V. Pleşu, Ș. Agachi. Amsterdam, Elsevier, 2007. 6. Jiang X.S., Jing Z.X., Li Y.Z., Wu Q.H., Tang W.H. Modelling and operation optimization of an integrated energy based direct district water-heating system. Energy, 2014, vol. 64, pp. 375–388. 7. Mikhailenko I.M. Optimal'noe upravlenie sistemami tsentral'nogo teplosnabzheniya [Optimal control of central heat supply systems]. St. Petersburg, Stroiizdat Publ., 2003. 240 p. 8. Voronovskii G.K. Usovershenstvovanie praktiki operativnogo upravleniya krupnymi teplofikatsionnymi sistemami v novykh ekonomicheskikh usloviyakh. Khar'kov, Khar'kov Publ., 2002. 239 p. 9. Boysen Н., Thorsen J.Е. Нydraulic balance in a district heating system. EuroHeat & Power, 2007, no. 4. 10. Tokarev V.V., Novitskiy N.N., Shalaginova Z.I., Barinova S.Yu. Informatsionno-vychislitel'nyi kompleks dlya rascheta i analiza rezhimov teplosnabzhayushchikh sistem [Information and computer system for the calculation and analysis of heat supply systems modes]. Gidravlicheskie tsepi. Razvitie teorii i prilozheniya [Hydraulic circuit. Development of the theory and application]. Ed. by A.Z. Gamm. Novosibirsk, Nauka Publ., 2000, pp. 138–154. 11. Manyuk V.I., Kaplinskii Ya.I., Khizh E.B., Manyuk A.I., Il'in V.K. Spravochnik po naladke i ekspluatatsii teplovykh setei [Guide to setting up and operation of heat networks]. Moscow, Stroiizdat Publ., 1982. 215 p. 12. Tokarev V.V., Shalaginova Z.I. Razrabotka metodiki mnogourovnevogo naladochnogo teplogidravlicheskogo rascheta sistem teplosnabzheniya i ee realizatsiya v sostave IVK "ANGARA-TS" [Development of the method of calculation of thermal-hydraulic multi-level adjustment of heating systems and its implementation as part of ICS "ANGARA-TS"]. Truboprovodnye sistemy energetiki: metodicheskie i prikladnye problemy matematicheskogo modelirovaniya [Pipeline systems of energetic. Methodological and applied problems of mathematical modeling]. Ed. by N.N. Novitskii, A.D. Tevyashev. Novosibirsk, Nauka Publ., 2015, pp. 110–127. 13. Lutsenko A.V., Novitskiy N.N. Matematicheskie modeli i algoritmy optimizatsii rezhimov teplovykh setei [Mathematical models and algorithms for optimization of modes of heat supply systems]. Metodicheskie voprosy issledovaniya nadezhnosti bol'shikh sistem energetiki [Methodical research questions the reliability of large-scale energetics systems]. Irkutsk, ESI SB RAS Publ., 2014, vol. 64. Nadezhnost' sistem energetiki: dostizheniya, problemy, perspektivy [The reliability of energy systems: achievements, problems and prospects], pp. 396–405. 14. Novitskiy N.N., Dikin I.I. Raschet dopustimykh rezhimov raboty truboprovodnykh setei metodom vnutrennikh tochek [Calculation of feasible pipeline network operating conditions by the interior-point method]. Izvestiya Rossiiskoi akademii nauk. Energetika – Proceedings of the Russian Academy of Sciences. Power Engineering, 2003, no. 5, pp. 104–115. 15. Lutsenko A.V. Issledovanie zadach i algoritmizatsiya metodov rascheta dopustimykh gidravlicheskikh rezhimov teplovykh setei [Research objectives and algorithmization of methods of calculating allowable hydraulic modes of heat supply systems]. Sistemnye issledovaniya v energetike: trudy molodykh uchenykh ISEM SO RAN [System Research in the energy sector: proceedings of young scientists ESI SB RAS]. Irkutsk, 2012, vol. 42, pp. 39–48. 16. Dikin I.I., Zorkal'tsev V.I. Iterativnoe reshenie zadach matematicheskogo programmirovaniya (metody vnutrennikh tochek) [Iterative solutions to mathematical programming problems (interior-point methods)]. Novosibirsk, Nauka Publ., 1980. 144 p. 17. Tsuchiya T. Affine scaling algorithm. Interior point methods of mathematical programming. Ed. by T. Terlaky. Dordrecht, Netherlands, Boston, Kluwer Academic Publ., 1996, pp. 35–82. 18. Dikin I.I. Opredelenie dopustimykh i optimal'nykh reshenii metodom vnutrennikh tochek [Determination of feasible and optimal solutions by the interior-point method]. Novosibirsk, Nauka Publ., 1998. 110 p. 19. Khokhlyuk V.I. Parallel'nye algoritmy tselochislennoi optimizatsii [Parallel algorithms for integer optimization]. Moscow, Radio i svyaz' Publ., 1987. 138 p. 20. Land A.H., Doig A.G. An automatic method of solving discrete programming problems. Econometrica, 1960, vol. 28, pp. 497–520. 21. Korbut A.A., Finkelstein Yu.Yu. Diskretnoe programmirovanie [Discrete programming]. Moscow, Nauka Publ., 1969. 368 p.