Neural Network Supervisory Proportional-Integral-Derivative Control of the Pressurized Water Reactor Core Power Load Following Operation

This work presents the particle swarm optimization trained neural network (PSO-NN) supervisory proportional integral derivative (PID) control method to monitor the pressurized water reactor (PWR) core power for safe operation. The proposed control approach is implemented on the transfer function of the PWR core, which is computed from the state-space model. The PWR core state-space model is designed from the neutronics, thermal-hydraulics, and reactivity models using perturbation around the equilibrium value. The proposed control approach computes the control rod speed to maneuver the core power to track the reference in a closed-loop scheme. The particle swarm optimization (PSO) algorithm is used to train the neural network (NN) and to tune the PID simultaneously. The controller performance is examined using integral absolute error, integral time absolute error, integral square error, and integral time square error functions, and the stability of the system is analyzed by using the Bode diagram. The simulation results indicated that the controller shows satisfactory performance to control and track the load power effectively and smoothly as compared to the PSO-PID control technique. This study will give benefit to design a supervisory controller for nuclear engineering research fields for control application.

• Derjew Ayele Ejigu
• Houde Song
• Xiaojing Liu

• machine learning
• neural network
• pressurized water reactor
• supervisory controller

[1] R. P. Borase, D. K. Maghade, S. Y. Sondkar, and S. N. Pawar, “A review of PID control, tuning methods and applications,” Int. J. Dyn. Control, Jul. 2020, doi: 10.1007/s40435-020-00665-4.
[2] M. Zarei, R. Ghaderi, N. Kojuri, and A. Minuchehr, “Robust PID control of power in lead cooled fast reactors: A direct synthesis framework,” Ann. Nucl. Energy, vol. 102, pp. 200–209, Apr. 2017, doi: 10.1016/j.anucene.2016.12.017.
[3] S. M. H. Mousakazemi, N. Ayoobian, and G. R. Ansarifar, “Control of the reactor core power in PWR using optimized PID controller with the real-coded GA,” Ann. Nucl. Energy, vol. 118, pp. 107–121, Aug. 2018, doi: 10.1016/j.anucene.2018.03.038.
[4] M. Zarei, “A physically-based PID controller for the power maneuvering of nuclear reactors,” Prog. Nucl. Energy, vol. 127, p. 103431, Sep. 2020, doi: 10.1016/j.pnucene.2020.103431.
[5] A. Salehi, O. Safarzadeh, and M. H. Kazemi, “Fractional-order PID control of steam generator water level for nuclear steam supply systems,” Nucl. Eng. Des., vol. 342, pp. 45–59, Feb. 2019, doi: 10.1016/j.nucengdes.2018.11.040.
[6] K. Nabeshima, T. Suzudo, T. Ohno, and K. Kudo, “Nuclear reactor monitoring with the combination of neural network and expert system,” Math. Comput. Simul., vol. 60, no. 3–5, pp. 233–244, Sep. 2002, doi: 10.1016/S0378-4754(02)00018-6.
[7] M. N. Khajavi, M. B. Menhaj, and A. A. Suratgar, “A neural network controller for load following operation of nuclear reactors,” Ann. Nucl. Energy, p. 10, 2002, doi:10.1016/S0306-4549(01)00075-5
[8] J. H. Pérez-Cruz and A. Poznyak, “Automatic startup of nuclear reactors using differential neural networks,” IFAC Proc. Vol., vol. 40, no. 20, pp. 112–117, 2007, doi: 10.3182/20071017-3-BR-2923.00019.
[9] H. Shen and J. M. Doster, “Application of a neural network-based feedwater controller to helical steam generators,” Nucl. Eng. Des., vol. 239, no. 6, pp. 1056–1065, Jun. 2009, doi: 10.1016/j.nucengdes.2009.02.011.
[10] H. G. Kim, S. H. Chang, and B. H. Lee, “Pressurized Water Reactor Core Parameter Prediction Using an Artificial Neural Network,” Nucl. Sci. Eng., vol. 113, no. 1, pp. 70–76, Jan. 1993, doi: 10.13182/NSE93-A23994.
[11] S. O. Starkov and Y. N. Lavrenkov, “Prediction of the moderator temperature field in a heavy water reactor based on a cellular neural network,” Nucl. Energy Technol., vol. 3, no. 2, pp. 133–140, Jun. 2017, doi: 10.1016/j.nucet.2017.05.008.
[12] T. V. Santosh, G. Vinod, R. K. Saraf, A. K. Ghosh, and H. S. Kushwaha, “Application of artificial neural networks to nuclear power plant transient diagnosis,” Reliab. Eng. Syst. Saf., vol. 92, no. 10, pp. 1468–1472, Oct. 2007, doi: 10.1016/j.ress.2006.10.009.
[13] M. Gomez Fernandez, A. Tokuhiro, K. Welter, and Q. Wu, “Nuclear energy system’s behavior and decision-making using machine learning,” Nucl. Eng. Des., vol. 324, pp. 27–34, Dec. 2017, doi: 10.1016/j.nucengdes.2017.08.020.
[14] A. Mathew, P. Amudha, and S. Sivakumari, “Deep Learning Techniques: An Overview, in Advanced Machine Learning Technologies and Applications,” vol. 1141, A. E. Hassanien, R. Bhatnagar, and A. Darwish, Eds. Singapore: Springer Singapore, 2021, pp. 599–608. doi: 10.1007/978-981-15-3383-9_54.
[15] B. Vasumathi and S. Moorthi, “Implementation of hybrid ANN–PSO algorithm on FPGA for harmonic estimation,” Eng. Appl. Artif. Intell., vol. 25, no. 3, pp. 476–483, Apr. 2012, doi: 10.1016/j.engappai.2011.12.005.
[16] P. Pant, Prediction of clad characteristics using ANN and combined PSO-ANN algorithms in laser metal deposition process, Surf. Interfaces, p. 10, 2020.
[17] C. M. Pareek, V. K. Tewari, R. Machavaram, and B. Nare, “Optimizing the seed-cell filling performance of an inclined plate seed metering device using integrated ANN-PSO approach,” Artif. Intell. Agric., vol. 5, pp. 1–12, 2021, doi: 10.1016/j.aiia.2020.11.002.
[18] S. Ahmadi, Sh. Abdi, and M. Kakavand, “Maximum power point tracking of a proton exchange membrane fuel cell system using PSO-PID controller,” Int. J. Hydrog. Energy, vol. 42, no. 32, pp. 20430–20443, Aug. 2017, doi: 10.1016/j.ijhydene.2017.06.208.
[19] S. M. H. Mousakazemi and N. Ayoobian, “Robust tuned PID controller with PSO based on two-point kinetic model and adaptive disturbance rejection for a PWR-type reactor,” Prog. Nucl. Energy, vol. 111, pp. 183–194, Mar. 2019, doi: 10.1016/j.pnucene.2018.11.003.
[20] L. K. Carvalho, Y.-C. Wu, R. Kwong, and S. Lafortune, “Detection and mitigation of classes of attacks in supervisory control systems,” Automatica, vol. 97, pp. 121–133, Nov. 2018, doi: 10.1016/j.automatica.2018.07.017.
[21] M. Baranwal and S. Salapaka, “Clustering and supervisory voltage control in power systems,” Int. J. Electr. Power Energy Syst., vol. 109, pp. 641–651, Jul. 2019, doi: 10.1016/j.ijepes.2019.02.025.
[22] M. Lotfi, M. B. Menhaj, S. A. Hosseini, and A. S. Shirani, “A design of switching supervisory control based on fuzzy-PID controllers for VVER-1000 pressurizer system with RELAP5 and MATLAB coupling,” Ann. Nucl. Energy, vol. 147, p. 107625, Nov. 2020, doi: 10.1016/j.anucene.2020.107625.
[23] Z. Dong, X. Huang, Y. Dong, and Z. Zhang, “Multilayer perception-based reinforcement learning supervisory control of energy systems with application to a nuclear steam supply system,” Appl. Energy, vol. 259, p. 114193, Feb. 2020, doi: 10.1016/j.apenergy.2019.114193.
[24] A. Ouaret, H. Lehouche, B. Mendil, and H. Guéguen, “Supervisory control of building heating system with insulation changes using three architectures of neural networks,” J. Frankl. Inst., vol. 357, no. 18, pp. 13362–13385, Dec. 2020, doi: 10.1016/j.jfranklin.2020.09.027.
[25] T. Zhang and K. E. Holbert, “Frequency Domain Comparison of Multi-lump and Distributed Parameter Models for Pressurized Water Reactor Cores,” Am. J. Energy Res., vol. 1, no. 1, pp. 17–24, Feb. 2013, doi: 10.12691/ajer-1-1-3.
[26] G. Wang, J. Wu, B. Zeng, Z. Xu, W. Wu, and X. Ma, “State-Space Model Predictive Control Method for Core Power Control in Pressurized Water Reactor Nuclear Power Stations,” Nucl. Eng. Technol., vol. 49, no. 1, pp. 134–140, Feb. 2017, doi: 10.1016/j.net.2016.07.008.
[27] S. M. H. Mousakazemi, “Control of a PWR nuclear reactor core power using scheduled PID controller with GA, based on two-point kinetics model and adaptive disturbance rejection system,” Ann. Nucl. Energy, vol. 129, pp. 487–502, Jul. 2019, doi: 10.1016/j.anucene.2019.02.019.
[28] O. Ahmed, L. Hocine, M. Boubekeur, F. Siham, and G. Herve, “Supervisory control of a building heating system based on radial basis function neural networks,” in 2017 5th International Conference on Electrical Engineering - Boumerdes (ICEE-B), Boumerdes, Oct. 2017, pp. 1–6. doi: 10.1109/ICEE-B.2017.8192182.
[29] S. Khatir, S. Tiachacht, C.-L. Thanh, T. Q. Bui, and M. Abdel Wahab, “Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator,” Compos. Struct., vol. 230, p. 111509, Dec. 2019, doi: 10.1016/j.compstruct.2019.111509.
[30] W. J. Blackwell, “Neural network Jacobian analysis for high-resolution profiling of the atmosphere,” EURASIP J. Adv. Signal Process., vol. 2012, no. 1, p. 71, Dec. 2012, doi: 10.1186/1687-6180-2012-71.