Multi-node model of VVER-1200 reactor dynamics for automatic control system synthesis

This paper presents multipoint kinetics of the VVER-1200 nuclear reactor model determined under the Avery coupled reactors formulation. Different numbers, from two to twenty, of axial nodes are modelled in MATLAB. For a more precise description of the transient’s nature, this model was extended by Mann’s thermal hydraulic model. Within the frame of Mann’s approach, one fuel node is adjacent to two coolant nodes. For daily maneuvering modes space-dependent xenon oscillations are considered and the Axial Xenon Oscillation Index is introduced. This paper also introduces the novel nodal mathematical model of the boron acid which is coupled with thermal hydraulic model by coolant mass flow rate. The computational results show that the accuracy of the proposed model is more than satisfactory, and general assumptions about transients align with their physical definitions. This research contributes to the advancement of the point-like nuclear reactor modeling for further improvement of the automatic power controller design.

1. Gritsevskyi A. Outlook for global nuclear power: energy, electricity and nuclear power estimates for the period up to 2050. 11 International Conference of the Croatian Nuclear Society, 5-8 Jun 2016, Zadar (Croatia), р. 20. Available at: https://inis.iaea.org/records/bp7ha-ykh69 (accessed: 01.09.2024).

2. Zhou G., Tan D. Review of nuclear power plant control research: neural network-based methods. Annals of nuclear energy. 2023;181:109513 https://doi.org/10.1016/j.anucene.2022.109513

3. Соловьев Д.А., Хачатрян А.Г., Чернов Е.В., Аль Малкави Р.Т. Исследование алгоритмов подавления ксеноновых колебаний в реакторе ВВЭР-1200. Известия вузов. Ядерная энергетика. 2022;2:37–48. https://doi.org/10.26583/npe.2022.2.04

4. Dong Z., Cheng Z., Zhu Y., Huang X., Dong Y., Zhang Z. Review on the recent progress in nuclear plant dynamical modeling and control. Energies. 2023;16(3):1443. https://doi.org/10.3390/en16031443

5. Пикина Г.А., Ле В.Д., Пащенко Ф.Ф. Модели динамики реактора ВВЭР с мощностным коэффициентом реактивности. Вестник МЭИ. 2016;2:75–83. EDN: TRYICK. Режим доступа: https://vestnik.mpei.ru/index.php/vestnik/article/view/65 (дата обращения 15.07.2024).

6. Curtain R., Morris K. Transfer functions of distributed parameter systems: а tutorial. Automatica. 2009;45(5):1101–1116. https://doi.org/10.1016/j.automatica.2009.01.008

7. Bridges D.N., Clement J.D. An investigation of space-dependent reactor transfer functions with temperature feedback. Nuclear science and engineering. 1972;47(4):421–434. https://doi.org/10.13182/NSE72-A22434

8. Shimjith S.R., Tiwari A.P., Naskar M., Bandyopadhyay B. Space–time kinetics modeling of Advanced Heavy Water Reactor for control studies. Annals of nuclear energy. 2010;37:310–324 https://doi.org/10.1016/j.anucene.2009.12.011

9. Wang P.F., Liu Y., Jiang B.T., Wan J.S., Zhao F.Y. Nodal dynamics modeling of AP1000 reactor for control system design and simulation. Annals of nuclear energy. 2013;62:208–223. http://dx.doi.org/10.1016/j.anucene.2013.05.036

10. Dong Z., Huang X., Zhang L. A nodal dynamic model for control system design and simulation of an MHTGR core. Nuclear engineering and design. 2010;240(5):1251–261. https://doi.org/10.1016/j.nucengdes.2009.12.032

11. Puchalski B., Rutkowski T.A., Duzinkiewicz K. Multi-nodal PWR reactor model – methodology proposition for power distribution coefficients calculation. 21st International Conference on Methods and Models in Automation and Robotics (MMAR) 29.08.2016–01.09.2016. Miedzyzdroje, Poland. 2016:385–390. https://doi.org/10.1109/MMAR.2016.7575166

12. Puchalski B., Rutkowski T.A., Duzinkiewicz K. Nodal models of pressurized water reactor core for control purposes – a comparison study. Nuclear engineering and design. 2017;322:444–463. http://dx.doi.org/10.1016/j.nucengdes.2017.07.005

13. Ball S J. Aproximate model for distributed-parameter heat-transfer systems. Jan. 1963. Available at: https://www.osti.gov/biblio/4651013 (accessed: 01.11.2024).

14. Правосуд С.С., Маслаков Д. С., Якубов Я.О., Овчеренко А.А. Верификация модели динамики ядерного реактора ВВЭР-1200, состоящей из одного топливного узла, примыкающего к двум узлам теплоносителя. Глобальная ядерная безопасность. 2023;48(3):82–95. EDN: YBZMTK. https://doi.org/10.26583/gns-2023-03-08

15. Juslin K., Paljakka M. Apros – a multifunctional modelling environment. 1999. Available at: https://www.osti.gov/etdeweb/biblio/20122527 (accessed: 17.09.2024).

16. Правосуд С.С., Якубов Я.О., Сусакин В.А. Многоточечная модель кинетики с мощностным эффектом реактивности для контроля аксиального офсета реактора ВВЭР-1200 в режиме следования за нагрузкой. Глобальная ядерная безопасность. 2024;14(2):73–90. EDN: LQRKEU https://doi.org/10.26583/gns-2024-02-07

17. Mousakazemi S.M.H. Control of a pressurized light-water nuclear reactor two-point kinetics model with the performance index-oriented PSO. Nuclear engineering and technology. 2021;53(8):2556–2563. https://doi.org/10.1016/j.net.2021.02.018

18. Aftab A., Luan X. A Takagi Sugeno based reactor power control of VVER-1000 using linear parameter varying identification of two-point kinetic model. Progress in nuclear energy. 2021;140:103905. https://doi.org/10.1016/j.pnucene.2021.103905

19. Eliasi H., Menhaj M.B., Davilu H. Robust nonlinear model predictive control for nuclear power plants in load following operations with bounded xenon oscillations. Nuclear engineering and design. 2011;241(2):533–543. https://doi.org/10.1016/j.nucengdes.2010.12.004

20. Rafiei M., Ansarifar G.R., Hadad K., Mohammadi M. Load-following control of a nuclear reactor using optimized FOPID controller based on the two-point fractional neutron kinetics model considering reactivity feedback effects. Progress in nuclear energy. 2021;141:103936. https://doi.org/10.1016/j.pnucene.2021.103936

21. Abdulraheem K. et al. Adaptive second order sliding mode control for a pressurized water nuclear reactor in load following operation with Xenon oscillation suppression. Nuclear engineering and design. 2022;391:111742. https://doi.org/10.1016/j.nucengdes.2022.111742

22. Zaidabadi nejad M., Ansarifar G.R. Adaptive robust control for axial offset in the P.W.R nuclear reactors based on the multipoint reactor model during load-following operation. Annals of nuclear energy. 2017;103:251–264. http://dx.doi.org/10.1016/j.anucene.2017.01.025

23. Zaidabadi nejad M., Ansarifar G.R. Estimation of axial xenon oscillations with online parameter adaptation in the P.W.R nuclear reactors using Lyapunov approach based on the multipoint kinetics reactor model. Annals of nuclear energy. 2017;108:277–300. http://dx.doi.org/10.1016/j.anucene.2017.04.028

24. Aftab A., Luan X., Anjum M.S. Design of multi-module adaptive fuzzy power tracking control for nonlinear four-point reactor core model under multiple transient conditions. Progress in nuclear energy. 2022;149:104248. https://doi.org/10.1016/j.pnucene.2022.104248

25. Zarei M. A multi-point kinetics-based MIMO-PI control of power in PWR reactors. Nuclear Engineering and Design. 2018;328:283–291. https://doi.org/10.1016/j.nucengdes.2018.01.011

26. Zarei M. Closed loop configuration in the axial flux tilt control of a PWR. Annals of nuclear energy. 2019;134:47–53. https://doi.org/10.1016/j.anucene.2019.05.059

27. Avery R. Theory of coupled reactors. In: Proc. 2nd UN Int. Conf. Peaceful Uses of Atomic Energy, United Nations, 1958;. Vol. 2. P. 182. https://doi.org/10.2172/4315469

28. Belleni-Morante A. The kinetic behaviour of a reactor composed of G loosely coupled cores: Integral formulation. Journal of nuclear energy. Parts A/B. Reactor science and technology. 1964;18(10):547–559, https://doi.org/10.1016/0368-3230(64)90139-9

29. Komata M. On the derivation of Avery’s coupled reactor kinetics equations. Nuclear science and engineering. 1969;38(3):193–204. https://doi.org/10.13182/nse69-a21154

30. Kobayashi K. Rigorous derivation of multi-point reactor kinetics equations with explicit dependence on perturbation. Journal of nuclear science and technology. 1992;29(2):110–120. https://doi.org/10.1080/18811248.1992.9731503

31. Valocchi G., Tommasi J., Ravetto P. Reduced order models in reactor kinetics: A comparison between point kinetics and multipoint kinetics. Annals of nuclear energy. 2020;147:107702. https://doi.org/10.1016/j.anucene.2020.107702

32. Гулевич А.В., Кухарчук О.Ф. Методы расчета связанных реакторных систем. Атомная энергия. 2004;97(6):403–414. EDN PEUJFB. Available at: https://j-atomicenergy.ru/index.php/ae/article/view/3399 (дата обращения: 22.09.2024).

33. Skinner R.E., Cohen E.R. Reduced delayed neutron group representations. Nuclear science and engineering, 1959(2017);5(5):291–298. https://doi.org/10.13182/NSE59-A25601

34. Джарум Б., Соловьёв Д.А., Семенов А.А., Щукин Н.В., Выговский С.Б., Аль-Шамайлех А.И., Танаш Х.А. Влияние температурного регулирования при работе ВВЭР-1000 и ВВЭР-1200 в режиме следования за нагрузкой. Вестник НИЯУ МИФИ. 2020;9(3):201–209. Режим доступа: https://vestnikmephi.elpub.ru/jour/article/view/84 (дата обращения: 01.11.2024).

35. Yu H., Wang M., Cai R., Zhang D., Tian W., Qiu S., Su G.H. Development and validation of boron diffusion model in nuclear reactor core subchannel analysis. Annals of nuclear energy. 2019;130:208–217. https://doi.org/10.1016/j.anucene.2019.02.046

36. Hafez N., Shahbunder H., Amin E., Elfiki S.A., Abdel-Latif A. Study on criticality and reactivity coefficients of VVER-1200 reactor. Progress in nuclear energy. 2021;131:103594 https://doi.org/10.1016/j.pnucene.2020.103594

37. Правосуд С.С., Маслаков Д.С., Якубов Я.О. Применение нечетких регуляторов для управления мощностью ядерного реактора ВВЭР-1200. Вестник НИЯУ МИФИ. 2024;13(2):97–109. EDN: QBFVFE. https://doi.org/10.26583/vestnik.2024.320

38. Ramaswamy P., Edwards R.M., Lee K.Y. An automatic tuning method of a fuzzy logic controller for nuclear reactors. IEEE Transactions on nuclear science. 1993;40(4):1253–1262. https://doi.org/10.1109/TNS.1993.8526778