Organik Rankine Çevriminin Dinamik Model Lineerleştirilmesi ve Model Öngörülü Kontrolü

Yıl 2025, Cilt: 16 Sayı: 4, 865 - 878, 30.12.2025

Mert Sinan Turgut , Oğuz Emrah Turgut

https://doi.org/10.24012/dumf.1691147

Öz

Bu araştırma, dört ana bileşenden oluşan bir Organik Rankine Çevrimi (ORC) sisteminin kontrolünü incelemektedir: kondenser, türbin, pompa ve buharlaştırıcı. Isı eşanjörleri çift borulu konfigürasyonlar olarak tasarlanmış ve dinamik davranışları hareketli sınır yaklaşımı kullanılarak modellenmiştir. Pompa ve türbin, ısı eşanjörlerine kıyasla çok daha hızlı dinamikleri nedeniyle statik denklemlerle temsil edilmiştir. Çevrimin matematiksel modeli, durum, giriş ve rahatsızlık değişkenlerine göre doğrusal olmayan fonksiyonun Jacobian'ı hesaplanarak lineerleştirilmiştir. Model doğrulama, rastgele giriş dizileri oluşturularak ve bunlar hem geliştirilen ORC modeline hem de aynı özelliklere sahip bir Aspen modeline uygulanarak gerçekleştirilmiştir. Doğrulama sonuçları, iki model arasında yalnızca küçük farklılıklar ile güçlü bir uyum göstermektedir. Ardından, lineerleştirilmiş ORC modelini düzenlemek için birkaç eşitsizlik kısıtlaması içeren bir lineer model öngörülü kontrol çerçevesi kurulmuştur. Dört kontrol stratejisi tanıtılmış olup, her biri termodinamik verimliliği artırma veya entropi üretimini azaltma gibi farklı hedeflere odaklanırken, tümü türbin iş çıktısı yörüngesini takip etme ortak hedefini paylaşmaktadır. Simülasyon sonuçları, dört kontrolörün de belirlenen türbin iş çıktısı yörüngesini etkin bir şekilde takip ettiğini göstermektedir. Birinci yasa ve ikinci yasa kontrolörleri, sırasıyla 0.10250 birinci yasa verimliliği ve 0.31732 ikinci yasa verimliliği ile en yüksek ortalama verimliliklere ulaşmıştır. Türbin iş kontrolörü, 2100.17 W olarak kaydedilen en yüksek toplam ekserji yıkım oranını sergilemiştir.

Anahtar Kelimeler

Organik Rankine Çevrimi , Model Öngörülü Kontrol , Model Lineerizasyonu , Enerji Verimliliği , Termal Sistemler

Dynamic Model Linearization and Model Predictive Control of an Organic Rankine Cycle

Öz

This research investigates the control of an Organic Rankine Cycle (ORC) system, which consists of four main components: a condenser, a turbine, a pump, and an evaporator. The heat exchangers are designed as double-pipe configurations, and their dynamic behavior is modeled using the moving boundary approach. The pump and turbine, due to their significantly faster dynamics compared to the heat exchangers, are represented with static equations. The cycle’s mathematical model is linearized by computing the Jacobian of the nonlinear function with respect to state, input, and disturbance variables. Model validation is performed by generating pseudo-random input sequences and applying them to both the developed ORC model and an Aspen model with identical specifications. The validation results show strong agreement between the two models, with only minor discrepancies. Subsequently, a linear model predictive control framework is established to regulate the linearized ORC model, incorporating several inequality constraints to ensure safe and efficient operation. Four control strategies are introduced, each focusing on distinct objectives such as enhancing thermodynamic efficiency or reducing entropy generation, while all share the common goal of tracking the turbine work output trajectory. Simulation results indicate that all four controllers effectively follow the specified turbine work output trajectory. The first law and second law controllers achieve the highest average efficiencies, with first law efficiency at 0.10250 and second law efficiency at 0.31732, respectively. The turbine work controller exhibits the highest total exergy destruction rate, recorded at 2100.17 W.

Anahtar Kelimeler

Organic Rankine Cycle , Model Predictive Control , Model Lineerization , Energy Efficiency , Thermal Systems

Kaynakça

• [1] M. Imran, R. Pili, M. Usman, and F. Haglind, “Dynamic modeling and control strategies of organic Rankine cycle systems: Methods and challenges,” Appl. Energy, vol. 257, p. 115537, Jan. 2020, DOI: 10.1016/j.apenergy.2020.115537.
• [2] J. G. Andersen, U. Larsen, T. Knudsen, L. Pierobon, and F. Haglind, “Selection and optimization of pure and mixed working fluids for low grade heat utilization using organic Rankine cycles,” Energy, vol. 73, pp. 204–213, Aug. 2014, DOI: 10.1006/j.energy.2014.06.012.
• [3] T. C. Hung, T. Y. Shai, and S. K. Wang, “A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat,” Appl. Energy, vol. 6, pp. 661–667, Jul. 1997, DOI: 10.1016/S0360-5442(96)00165-X.
• [4] B. F. Tchanche, G. Lambrinos, A. Frangoudakis, and G. Papadakis, “Low-grade heat conversion into power using organic Rankine cycles—a review of various applications,” Renew. Sustain. Energy Rev., vol. 15, no. 8, pp. 3963–3979, Oct. 2011, DOI: 10.1016/j.rser.2011.07.024.
• [5] E. Macchi and M. Astolfi, Organic Rankine Cycle (ORC) Power Systems: Technologies and Applications. Cambridge, U.K.: Woodhead Publishing, 2017, DOI: 10.1016/C2014-0-04239-6.
• [6] X. Chen, C. Liu, Q. Li, X. Wang, and X. Xu, “Dynamic analysis and control strategies of organic Rankine cycle system for waste heat recovery using zeotropic mixture as working fluid,” Energy Convers. Manag., vol. 192, pp. 321–334, Jul. 2019, DOI: 10.1016/j.enconman.2019.04.049.
• [7] M. Imran, F. Haglind, M. Asim, and J. Zeb Alvi, “Recent research trends in organic Rankine cycle technology: A bibliometric approach,” Renew. Sustain. Energy Rev., vol. 81, pp. 552–562, Jan. 2018, DOI: 10.1016/j.rser.2017.08.028.
• [8] C. Wieland, C. Schifflechner, K. Braimakis, F. Kaufmann, F. Dawo, S. Kerellas, G. Besagni, and C. N. Markides, “Innovations for organic Rankine cycle power systems: Current trends and future perspectives,” Appl. Therm. Eng., vol. 225, p. 120201, May 2023, DOI: 10.1016/j.applthermaleng.2023.120201.
• [9] B. S. Park, M. Usman, M. Imran, and A. Pesyridis, “Review of organic Rankine cycle experimental data trends,” Energy Convers. Manag., vol. 173, pp. 679–691, Oct. 2018, DOI: 10.1016/j.enconman.2018.07.097.
• [10] A. Landelle, N. Tauveron, P. Haberschill, R. Revellin, and S. Colasson, “Organic Rankine cycle design and performance comparison based on experimental database,” Appl. Energy, vol. 204, pp. 1172–1187, Oct. 2017, DOI: 10.1016/j.apenergy.2017.04.012.
• [11] P. Colonna and H. van Putten, “Dynamic modeling of steam power cycles: Part I—Modeling paradigm and validation,” Appl. Therm. Eng., vol. 27, no. 2–3, pp. 467–480, Feb. 2007, DOI: 10.1016/j.applthermaleng.2006.06.011.
• [12] H. van Putten and P. Colonna, “Dynamic modeling of steam power cycles: Part II—Simulation of a small simple Rankine cycle system,” Appl. Therm. Eng., vol. 27, no. 14–15, pp. 2566–2582, Oct. 2007, DOI: 10.1016/j.applthermaleng.2007.01.035.
• [13] S. Quoilin, R. Aumann, A. Grill, A. Schuster, V. Lemort, and H. Spliethoff, “Dynamic modeling and optimal control strategy of waste heat recovery organic Rankine cycles,” Appl. Energy, vol. 88, no. 6, pp. 2183–2190, Jun. 2011, DOI: 10.1016/j.apenergy.2011.01.015.
• [14] J. Wornski, V. Lemort, S. Quoilin, I. Bell, and A. Desideri, “ThermoCycle: A Modelica library for the simulation of thermodynamic systems,” in Proc. 10th Int. Modelica Conf., Lund, Sweden, 2014, pp. 683–692, DOI: 10.3384/ECP14096683.
• [15] G. Shu, X. Wang, H. Tian, P. Liu, D. Jing, and X. Li, “Scan of working fluids based on dynamic response characters for organic Rankine cycle using for engine waste heat recovery,” Energy, vol. 133, pp. 609–620, Aug. 2017, DOI: 10.1016/j.energy.2017.05.003.
• [16] Z. Gu, K. Feng, L. Ge, and L. Quan, “Dynamic modeling and optimization of organic Rankine cycle in the waste heat recovery of the hydraulic system,” Energy, vol. 263, p. 125673, Jan. 2023, DOI: 10.1016/j.energy.2022.125673.
• [17] T. Wilberforce and I. Muhammad, “Dynamic modeling and analysis of organic Rankine cycle power units for the recovery of waste heat from 110kW proton exchange membrane fuel cell system,” Int. J. Thermofluids, vol. 17, p. 100280, Feb. 2023, DOI: 10.1016/j.ijft.2023.100280.
• [18] M. R. Kaleibar, R. K. Saray, and M. Pourgol, “Comprehensive assumption-free dynamic simulation of an organic Rankine cycle using moving-boundary method,” Energy, vol. 307, p. 132584, Oct. 2024, DOI: 10.1016/j.energy.2024.132584.
• [19] J. Peralez, M. Nadri, P. Dufour, P. Tona, and A. Sciarretta, “Organic Rankine cycle for vehicles: Control design and experimental results,” IEEE Trans. Control Syst. Technol., vol. 25, no. 3, pp. 952–965, May 2017, DOI: 10.1109/TCST.2016.2574760
• [20] A. Hernandez, F. Ruiz, S. Gusev, R. De Keyser, S. Quoilin, and V. Lemort, “Experimental validation of a multiple model predictive control for waste heat recovery organic Rankine cycle systems,” Appl. Therm. Eng., vol. 193, p. 116993, Jul. 2021, DOI: 10.1016/j.applthermaleng.2021.116993.
• [21] P. Pallis, E. Varvagiannis, K. Braimakis, T. Roumpedakis, A.-D. Leontaritis, and S. Karellas, “Development, experimental testing and techno-economic assessment of a fully automated marine organic Rankine cycle prototype for jacket cooling water heat recovery,” Energy, vol. 228, p. 120596, Jul. 2021, DOI: 10.1016/j.energy.2021.120596.
• [22] R. Pili, C. Wieland, H. Spliethoff, and F. Haglind, “Optimal tuning of model predictive controllers for organic Rankine cycle systems recovering waste heat from heavy-duty vehicles,” Appl. Therm. Eng., vol. 220, p. 119803, Feb. 2023, DOI: 10.1016/j.applthermaleng.2022.119803.
• [23] Y.-Q. Feng, Q. Zhang, K.-J. Xu, C.-M. Wang, Z.-X. He, and T.-C. Hung, “Operation characteristics and performance prediction of a 3 kW organic Rankine cycle (ORC) with automatic control system based on machine learning methodology,” Energy, vol. 263, p. 125857, Jan. 2023, DOI: 10.1016/j.energy.2022.125857.
• [24] X. Liu, A. Yebi, P. Anschel, J. Shutty, B. Xu, M. Hoffman, and S. Onori, “Model predictive control of an organic Rankine cycle system,” in Proc. Int. Conf. Appl. Energy (Energy Proc.), Cape Town, South Africa, 2017, pp. 184–191, DOI: 10.1016/j.egypro.2017.09.109.
• [25] H.-X. Wang, B. Lei, and Y.-T. Wu, “Control strategies of pumps in organic Rankine cycle under variable condensing conditions,” Appl. Therm. Eng., vol. 234, p. 121226, Nov. 2023, DOI: 10.1016/j.applthermaleng.2023.121226.
• [26] B. K. Saha, B. Chakraborty, J. Mondal, A. Pesyridis, E. M. B. Messini, and P. Kumar, “Design and implementation of a control strategy for a dynamic organic Rankine cycle-based power system in the context of industrial waste heat recovery,” Energy Technol., vol. 11, no. 11, p. 2300425, Nov. 2023, DOI: 10.1002/ente.202300425.
• [27] H. Enayatollahi, P. Fussey, and B. K. Nguyen, “Control of organic Rankine cycle, a neuro-fuzzy approach,” Control Eng. Pract., vol. 109, p. 104728, Apr. 2021, DOI: 10.1016/j.conengprac.2021.104728.
• [28] X. Wang, R. Wang, M. Jin, G. Shu, H. Tian, and J. Pan, “Control of superheat of organic Rankine cycle under transient heat source based on deep reinforcement learning,” Appl. Energy, vol. 278, p. 115637, Nov. 2020, DOI: 10.1016/j.apenergy.2020.115637.
• [29] F. Galuppo, T. Reiche, V. Lemort, P. Dufour, and M. Nadri, “Organic Rankine cycle based waste heat recovery modeling and control of the low pressure side using direct condensation and dedicated fans,” Energy, vol. 216, p. 119074, Feb. 2021, DOI: 10.1016/j.energy.2020.119074.
• [30] M. Marchionni, M. Usman, L. Chai, and S. A. Tassou, “Inventory control assessment for small scale sCO2 heat to power conversion systems,” Energy, vol. 267, p. 126537, Mar. 2023, DOI: 10.1016/j.energy.2022.126537.
• [31] E. W. Lemmon, I. H. Bell, M. L. Huber, and M. O. McLinden, “NIST standard reference database 23: Reference fluid thermodynamic and transport properties—REFPROP,” Nat. Inst. Stand. Technol., Gaithersburg, MD, USA, Rep. 10.0, 2018, DOI: 10.18434/T4/1502528.
• [32] B. P. Rasmussen and A. G. Alleyne, “Dynamic modeling and advanced control of air conditioning and refrigeration systems,” Univ. Illinois Air Conditioning Refrigeration Center, Urbana, IL, USA, Tech. Rep. ACRC TR-244, 2006. [Online]. Available: https://hdl.handle.net/2142/12355.
• [33] Aspen Plus, Aspen Technol. Inc., Bedford, MA, USA, 2013.
• [34] S. Qin and T. Badgwell, “A survey of industrial model predictive control technology,” Control Eng. Pract., vol. 11, no. 7, pp. 733–761, Jul. 2003, DOI: 10.1016/S0967-0661(02).
• [35] M. L. Darby and M. Nikolaou, “MPC: Current practice and challenges,” Control Eng. Pract., vol. 20, no. 4, pp. 328–342, Apr. 2012, DOI: 10.1016/j.conengprac.2011.12.004.
• [36] D. P. Kingma and L. J. Ba, “Adam: A method for stochastic optimization,” in Proc. Int. Conf. Learning Representations (ICLR), San Diego, CA, USA, 2015.
• [37] K. E. Gungor and R. H. S. Winterton, “A general correlation for flow boiling in tubes and annuli,” Int. J. Heat Mass Transf., vol. 29, no. 3, pp. 351–358, Mar. 1986, DOI: 10.1016/0017-9310(86)90205-X.
• [38] M. M. Shah, “A general correlation for heat transfer during film condensation inside pipes,” Int. J. Heat Mass Transf., vol. 22, no. 4, pp. 547–556, Apr. 1979, DOI: 10.1016/0017-9310(79)90058-9.
• [39] T. L. Bergman, F. P. Incropera, D. P. DeWitt, and A. S. Lavine, Fundamentals of Heat and Mass Transfer. Hoboken, NJ, USA: Wiley, 2011.
• [40] H. K. Fauske, “Some ideas about the mechanism causing two-phase critical flow,” Appl. Sci. Res., vol. 13, no. 1, pp. 149–160, Dec. 1964, DOI: 10.1007/BF00382043.
• [41] J. M. Jensen and H. Tummescheit, “Moving boundary models for dynamic simulations of two-phase flows,” in Proc. 2nd Int. Modelica Conf., Oberpfaffenhofen, Germany, 2002, pp. 235–244. [Online]. Available: http://www.modelica.org/events/Conference2002/papers/p31_Jensen.pdf.
• [42] X. Wang, G. Shu, H. Tian, P. Liu, X. Li, and D. Jing, “Engine working condition effects on the dynamic response of organic Rankine cycle as exhaust waste heat recovery system,” Appl. Therm. Eng., vol. 123, pp. 670–681, Aug. 2017, DOI: 10.1016/j.applthermaleng.2017.05.088.
• [43] M. J. Moran, H. N. Shapiro, D. D. Boettner, and M. B. Bailey, Fundamentals of Engineering Thermodynamics. Hoboken, NJ, USA: Wiley, 2018.
• [44] J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, “Julia: A fresh approach to numerical computing,” SIAM Rev., vol. 59, no. 1, pp. 65–98, Feb. 2017, DOI: 10.1137/141000671.
• [45] J. Baillieul and T. Samad, Encyclopedia of Systems and Control. Cham, Switzerland: Springer Nature, 2021, DOI: 10.1007/978-3-030-44184-5.
• [46] S. V. Rakovic and W. S. Levine, Handbook of Model Predictive Control. Cham, Switzerland: Springer Nature, 2019, DOI: 10.1007/978-3-319-77489-3.
• [47] B. Kovaritakis and M. Cannon, Model Predictive Control: Classical, Robust and Stochastic. Cham, Switzerland: Springer Nature, 2016, DOI: 10.1007/978-3-319-24853-0.
• [48] S. Skogestad, I. Pstlethwaite, Multivariable Feedback Control: Analysis and Design, West Sussex: England, Wiley & Sons, 2006, ISBN: 978-0-470-00168-3.
• [49] S. Y. Dibazar, G. Salehi, and A. Davarpanah, “Comparison of exergy and advanced exergy analysis in three different organic Rankine cycles,” Processes, vol. 8, no. 5, p. 586, May 2020, DOI: 10.3390/pr8050586.
• [50] A. Bejan, “The equivalence of maximum power and minimum entropy generation rate in the optimization of power plants,” J. Energy Resour. Technol., vol. 118, no. 2, pp. 98–101, Jun. 1996, DOI: 10.1115/1.2792711.