Reliable generator power control is vital for the stability of coal-fired power plants. This study proposes a strategy that integrates model predictive control (MPC) with a neural network PID controller to address the nonlinear and complex dynamics of generator systems. The boiler–turbine–generator (BTG) unit is modeled as a representative three-input, three-output nonlinear system. To mitigate excessive overshoot in traditional PID controllers, a BP neural network adaptively adjusts PID parameters, enabling real-time learning of system dynamics and improving transient response. Furthermore, MPC is combined with the BP neural network PID controller, where rolling horizon prediction and feedback correction ensure precise power regulation, reduced steady-state error, and enhanced dynamic performance. A 660 MW generator model is established in MATLAB/Simulink, and the proposed approach is compared with traditional PID and BP neural network PID control. Simulation results confirm the superiority of the proposed approach. It nearly eliminates overshoot, reducing it to 3.0% from 43.9% (traditional PID) and 24.2% (BP NN-PID control). Unlike the slower BP-NN PID, our method maintains a rapid 450-second settling time, comparable to the traditional PID. This combined improvement in stability and speed results in the integral absolute error (IAE) being reduced by 85% and approximately 77% compared to the traditional PID and BP neural network PID controllers, respectively.
Citation: Minan Tang, Shengqi Zhang, Zhongcheng Bai, Chuntao Rao. Power control of generator sets in coal-fired power plants based on the combination of MPC and neural network PID[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 450-485. doi: 10.3934/jimo.2026017
Reliable generator power control is vital for the stability of coal-fired power plants. This study proposes a strategy that integrates model predictive control (MPC) with a neural network PID controller to address the nonlinear and complex dynamics of generator systems. The boiler–turbine–generator (BTG) unit is modeled as a representative three-input, three-output nonlinear system. To mitigate excessive overshoot in traditional PID controllers, a BP neural network adaptively adjusts PID parameters, enabling real-time learning of system dynamics and improving transient response. Furthermore, MPC is combined with the BP neural network PID controller, where rolling horizon prediction and feedback correction ensure precise power regulation, reduced steady-state error, and enhanced dynamic performance. A 660 MW generator model is established in MATLAB/Simulink, and the proposed approach is compared with traditional PID and BP neural network PID control. Simulation results confirm the superiority of the proposed approach. It nearly eliminates overshoot, reducing it to 3.0% from 43.9% (traditional PID) and 24.2% (BP NN-PID control). Unlike the slower BP-NN PID, our method maintains a rapid 450-second settling time, comparable to the traditional PID. This combined improvement in stability and speed results in the integral absolute error (IAE) being reduced by 85% and approximately 77% compared to the traditional PID and BP neural network PID controllers, respectively.
| [1] |
Y. B. Shu, G. P. Chen, J. B. He, F. Zhang, Building a new electric power system based on new energy sources, Eng. Sci., 23 (2021), 61–69. https://doi.org/10.15302/J-SSCAE-2021.06.003 doi: 10.15302/J-SSCAE-2021.06.003
|
| [2] |
L. B. Liu, Y. Wang, Z. Wang, S. C. Li, J. T. Li, G. He, et al., Potential contributions of wind and solar power to China's carbon neutrality, Resour. conserv. recycl., 180 (2022), 106155. https://doi.org/10.1016/j.resconrec.2022.106155 doi: 10.1016/j.resconrec.2022.106155
|
| [3] |
M. Dreidy, H. Mokhlis, S. Mekhilef, Inertia response and frequency control techniques for renewable energy sources: A review, Renew. Sust. Energ. Rev., 69 (2017), 144–155. https://doi.org/10.1016/j.rser.2016.11.170 doi: 10.1016/j.rser.2016.11.170
|
| [4] | G. Q. Yu, K. T. Liu, Z. M. Hu, N. N. Liu, X. Y. Xiao, Optimal scheduling of deep peak regulation for thermal power units in power grid with large-scale new energy, Electr. Power Eng. Technol., 42 (2023). https://doi.org/10.12158/j.2096-3203.2023.01.029 |
| [5] |
L. M. Abadie, J. M. Chamorro, Valuing flexibility: the case of an integrated gasification combined cycle power plant, Energy Econ., 30 (2008), 1850–1881. https://doi.org/10.1016/j.eneco.2006.10.004 doi: 10.1016/j.eneco.2006.10.004
|
| [6] |
R. A. Mikulandric, D. M. Loncar, D. Cvetinović, Improvement of environmental aspects of thermal power plant operation by advanced control concepts, Therm. Sci., 16 (2012), 759–772. https://doi.org/10.2298/TSCI120510134M doi: 10.2298/TSCI120510134M
|
| [7] |
X. Hao, C. Yang, H. Chen, J. N. Dong, J. D. Bao, H. Wang, et al., Optimization of the load command for a coal-fired power unit via particle swarm optimization-long short-term memory model, Energies, 17 (2024), 2668. https://doi.org/10.3390/en17112668 doi: 10.3390/en17112668
|
| [8] |
H. Rao, F. Han, Z. Chen, G. Huang, D. Wang, Y. Zhang, et al., Strategy for guaranteeing power supply security of China, Strateg. Stud. Chin. Acad. Eng., 25 (2023), 100–110. https://doi.org/10.15302/j-sscae-2023.02.009 doi: 10.15302/j-sscae-2023.02.009
|
| [9] |
D. Wang, H. Li, N. C. Wang, Y. L. Zhou, X. L. Li, M. Yang, Thermodynamic analysis of coal-fired power plant based on the feedwater heater drainage-air preheating system, Appl. Therm. Eng., 185 (2021), 116420. https://doi.org/10.1016/j.applthermaleng.2020.116420 doi: 10.1016/j.applthermaleng.2020.116420
|
| [10] |
W. Wang, Y. Sun, S. Jing, W. Q. Zhang, C. Cui, Improved boiler-turbine coordinated control of CHP units with heat accumulators by introducing heat source regulation, Energies, 11 (2018), 2815. https://doi.org/10.3390/en11102815 doi: 10.3390/en11102815
|
| [11] |
K. J. Åström, T. Hägglund, The future of PID control, Control Eng. Pract., 9 (2001), 1163–1175. https://doi.org/10.1016/S0967-0661(01)00062-4 doi: 10.1016/S0967-0661(01)00062-4
|
| [12] |
R. Munje, S. Lin, G. Q. Zhang, W. D. Zhang, Observer-based output feedback integral control for coal-fired power plant: A three-time-scale perspective, IEEE Trans. Control Syst. Technol., 28 (2018), 601-608. https://doi.org/10.1109/TCST.2018.2879045 doi: 10.1109/TCST.2018.2879045
|
| [13] |
A. Boulkroune, M. M'Saad, M. Farza, Adaptive fuzzy controller for multivariable nonlinear state time-varying delay systems subject to input nonlinearities, Fuzzy Sets Syst., 164 (2011), 45–65. https://doi.org/10.1016/j.fss.2010.09.001 doi: 10.1016/j.fss.2010.09.001
|
| [14] |
R. Nasiri, A. Radan, Adaptive decoupled control of 4-leg voltage-source inverters for standalone photovoltaic systems: Adjusting transient state response, Renewable Energy, 36 (2011), 2733–2741. https://doi.org/10.1016/j.renene.2011.03.007 doi: 10.1016/j.renene.2011.03.007
|
| [15] |
S. C. Tong, C. Y. Li, Y. M. Li, Fuzzy adaptive observer backstepping control for MIMO nonlinear systems, Fuzzy Sets Syst., 160 (2009), 2755–2775. https://doi.org/10.1016/j.fss.2009.03.008 doi: 10.1016/j.fss.2009.03.008
|
| [16] |
Y. Wang, L. Nie, Application of fuzzy control on smart car servo steering system, Adv. Sci. Lett., 4 (2011), 2099–2103. https://doi.org/10.1166/asl.2011.1471 doi: 10.1166/asl.2011.1471
|
| [17] |
D. Rastovic, Tokamak design as one sustainable system, Neural Netw. World, 21 (2011), 493. https://doi.org/10.14311/NNW.2011.21.029 doi: 10.14311/NNW.2011.21.029
|
| [18] |
M. Chen, C. S. Jiang, Q. X. Wu, Disturbance-observer-based robust flight control for hypersonic vehicles using neural networks, Adv. Sci. Lett., 4 (2011), 1771–1775. https://doi.org/10.1166/asl.2011.1491 doi: 10.1166/asl.2011.1491
|
| [19] |
V. A. Akpan, G. D. Hassapis, Nonlinear model identification and adaptive model predictive control using neural networks, ISA Trans., 50 (2011), 177–194. https://doi.org/10.1016/j.isatra.2010.12.007 doi: 10.1016/j.isatra.2010.12.007
|
| [20] | E. Irigoyen, M. Larrea, J. Valera, V. Gómez, F. Artaza, A hybridized neuro-genetic solution for controlling industrial R3 workspace, Neural Netw. World, 20 (2010), 811. |
| [21] |
J. Garrido, F. Vázquez, F. Morilla, Centralized multivariable control by simplified decoupling, J. Process Control, 22 (2012), 1044–1062. https://doi.org/10.1016/j.jprocont.2012.04.008 doi: 10.1016/j.jprocont.2012.04.008
|
| [22] |
C. Cha, S. Y. Kim, L. Cao, H. Kong, Decoupled control of stiffness and permeability with a cell-encapsulating poly (ethylene glycol) dimethacrylate hydrogel, Biomaterials, 31 (2010), 4864–4871. https://doi.org/10.1016/j.biomaterials.2010.02.059 doi: 10.1016/j.biomaterials.2010.02.059
|
| [23] |
I. García-Herreros, X. Kestelyn, J. Gomand, R. Coleman, P. J. Barre, Model-based decoupling control method for dual-drive gantry stages: A case study with experimental validations, Control Eng. Pract., 21 (2013), 298–307. https://doi.org/10.1016/j.conengprac.2012.10.010 doi: 10.1016/j.conengprac.2012.10.010
|
| [24] |
S. Dettori, V. Iannino, V. Colla, A. Signorini, An adaptive fuzzy logic-based approach to PID control of steam turbines in solar applications, Appl. Energy, 227 (2018), 655–664. https://doi.org/10.1016/j.apenergy.2017.08.145 doi: 10.1016/j.apenergy.2017.08.145
|
| [25] |
Z. Zeng, T. Huang, New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays, J. Ind. Manag. Optim., 7 (2011), 283. https://doi.org/10.3934/jimo.2011.7.283 doi: 10.3934/jimo.2011.7.283
|
| [26] |
F. Liu, X. Xue, Subgradient-based neural network for nonconvex optimization problems in support vector machines with indefinite kernels, J. Ind. Manag. Optim., 12 (2016), 285–301. https://doi.org/10.3934/jimo.2016.12.285 doi: 10.3934/jimo.2016.12.285
|
| [27] | S. A. Elfandi, M. A. Osman, N. Ali, Application of neural networks and PID in on line of real-time temperature control system, in Appl. Mech. Mater., Trans Tech Publications Ltd, 110 (2012), 5009-5014. https://doi.org/10.4028/www.scientific.net/AMM.110–116.5009 |
| [28] |
K. S. Narendra, Identification and control of dynamical systems using neural networks, IEEE Trans. Neural Netw., 1 (1989), 183–192. https://doi.org/10.1109/72.80231 doi: 10.1109/72.80231
|
| [29] |
X. J. Liu, C. W. Chan, Neuro-fuzzy generalized predictive control of boiler steam temperature, IEEE Trans. Energy Convers., 21 (2006), 900–908. https://doi.org/10.1109/TEC.2005.853758 doi: 10.1109/TEC.2005.853758
|
| [30] |
F. Dai, Y. Yan, B. Wei, Y. X. Ouyang, L. R. An, Simulation of main steam temperature control system based on neural network, J. Robotics Netw. Artif. Life, 5 (2018), 63–66. https://doi.org/10.2991/jrnal.2018.5.1.14 doi: 10.2991/jrnal.2018.5.1.14
|
| [31] |
K. Y. Han, G. Y. Park, M. K. Lee, D. H. Yoo, H. H. Lee, Self-adjusting PID control system using a neural network for a binary power plant, Artif. Life Robot., 29 (2024), 274–285. https://doi.org/10.1007/s10015-024-00940-z doi: 10.1007/s10015-024-00940-z
|
| [32] |
D. T. Mugweni, H. Harb, Neural networks-based process model and its integration with conventional drum level pid control in a steam boiler plant, Int. J. Eng. Manuf., 11 (2021), 1. https://doi.org/10.12968/S2514-9768(22)90056-0 doi: 10.12968/S2514-9768(22)90056-0
|
| [33] | G. Moustafa, F. Noureddinece, A. M. El-Rifaie, A. R. Ginidi, Fractional order PID controller tuned–artificial protozoa optimiser for LFR in multi-area interconnected power systems, Sci. Afr., 2025, e02880. https://doi.org/10.1016/j.sciaf.2025.e02880 |
| [34] |
A. M. El-Rifaie, S. Abid, A. R. Ginidi, A. M. Shaheen, Fractional order PID controller based-neural network algorithm for LFC in multi-area power systems, Eng. Rep., 7 (2025), e70028. https://doi.org/10.1002/eng2.70028 doi: 10.1002/eng2.70028
|
| [35] |
S. Abid, A. M. El-Rifaie, M. Elshahed, A. R. Ginidi, A. M. Shaheen, G. Moustafa, et al., Development of slime mold optimizer with application for tuning cascaded PD-PI controller to enhance frequency stability in power systems, Mathematics, 11 (2023), 1796. https://doi.org/10.3390/math11081796 doi: 10.3390/math11081796
|
| [36] |
S. Chandrasekharan, R. C. Panda, B. N. Swaminathan, Modeling, identification, and control of coal-fired thermal power plants, Rev. Chem. Eng., 30 (2014), 217–232. https://doi.org/10.1515/revce-2013-0022 doi: 10.1515/revce-2013-0022
|
| [37] |
D. Wang, X. Wu, J. Shen, An efficient robust predictive control of main steam temperature of coal-fired power plant, Energies, 13 (2020), 3775. https://doi.org/10.3390/en13153775 doi: 10.3390/en13153775
|
| [38] |
X. Liang, Y. Li, X. Wu, Nonlinear modeling and inferential multi-model predictive control of a pulverizing system in a coal-fired power plant based on moving horizon estimation, Energies, 11 (2018), 589. https://doi.org/10.3390/en11030589 doi: 10.3390/en11030589
|
| [39] |
B. Ping, D. Zeng, Y. Hu, Y. Xie, Neural network predictive controller based on the improved TPA–LSTM model for ultra-supercritical units, Heliyon, 10 (2024), 12. https://doi.org/10.1016/j.heliyon.2024.e31997 doi: 10.1016/j.heliyon.2024.e31997
|
| [40] |
G. Shi, M. Ma, D. Li, Y. J. Ding, K. Y. Lee, A process-model-free method for model predictive control via a reference model-based proportional–integral–derivative controller with application to a thermal power plant, Front. Control Eng., 4 (2023), 1185502. https://doi.org/10.3389/fcteg.2023.1185502 doi: 10.3389/fcteg.2023.1185502
|
| [41] |
T. Zhang, S. Gao, Y. Yang, S. X. Wang, Z. Ding, Economic model predictive control of thermal-power boiler–turbine units with extreme learning machine–deep belief network, Eng. Appl. Artif. Intell., 162 (2025), 112505. https://doi.org/10.1016/j.engappai.2025.112505 doi: 10.1016/j.engappai.2025.112505
|
| [42] |
D. Q. Mayne, J. B. Rawlings, C. V. Rao, P. O. M. Scokaert, Constrained model predictive control: Stability and optimality, Automatica, 36 (2000), 789–814. https://doi.org/10.1016/S0005-1098(99)00214-9 doi: 10.1016/S0005-1098(99)00214-9
|
| [43] |
X. Liu, J. Cui, Economic model predictive control of boiler-turbine system, J. Process Control, 66 (2018), 59–67. https://doi.org/10.1016/j.jprocont.2018.02.010 doi: 10.1016/j.jprocont.2018.02.010
|
| [44] | L. Gao, Y. Yang, X. Ren, Temperature MPC strategy for air source heat pump based on BP neural network, Control Eng., 28 (2021), 1765–1772. |
| [45] |
X. Kong, X. Liu, K. Y. Lee, Nonlinear multivariable hierarchical model predictive control for boiler-turbine system, Energy, 93 (2015), 309–322. https://doi.org/10.1016/j.energy.2015.09.030 doi: 10.1016/j.energy.2015.09.030
|
| [46] |
S. Liu, B. Zhao, S. Zhao, L. Y. Zhang, L. Wu, An intelligent bio-inspired cooperative decoupling control strategy for the marine boiler-turbine system with a novel energy dynamic model, Energies, 12 (2019), 4659. https://doi.org/10.3390/en12244659 doi: 10.3390/en12244659
|
| [47] |
P. Appeltans, S. I. Niculescu, W. Michiels, Analysis and design of strongly stabilizing PID controllers for time-delay systems, SIAM J. Control Optim., 60 (2022), 124–146. https://doi.org/10.1137/20M136726X doi: 10.1137/20M136726X
|
| [48] |
J. Kang, W. Meng, A. Abraham, H. B. Liu, An adaptive PID neural network for complex nonlinear system control, Neurocomputing, 135 (2014), 79–85. https://doi.org/10.1016/j.neucom.2013.03.065 doi: 10.1016/j.neucom.2013.03.065
|
| [49] |
E. Hernandez, Y. Arkun, Study of the control-relevant properties of backpropagation neural network models of nonlinear dynamical systems, Comput. Chem. Eng., 16 (1992), 227–240. https://doi.org/10.1016/0098-1354(92)80044-A doi: 10.1016/0098-1354(92)80044-A
|
| [50] |
S. J. Qin, T. A. Badgwell, A survey of industrial model predictive control technology, Control Eng. Pract., 11 (2003), 733–764. https://doi.org/10.1016/S0967-0661(02)00186-7 doi: 10.1016/S0967-0661(02)00186-7
|
| [51] | E. Fernandez-Camacho, C. Bordons-Alba, Model predictive control in the process industry, Springer London, 1995. |
| [52] |
X. Y. Huang, J. C. Wang, L. W. Zhang, B. H. Wang, Data-driven modelling and fuzzy multiple-model predictive control of oxygen content in coal-fired power plant, Trans. Inst. Meas. Control, 39 (2017), 1631–1642. https://doi.org/10.1177/0142331216644498 doi: 10.1177/0142331216644498
|
| [53] |
A. S. Kumar, Z. Ahmad, Model predictive control (MPC) and its current issues in chemical engineering, Chem. Eng. Commun., 199 (2012), 472–511. https://doi.org/10.1080/00986445.2011.592446 doi: 10.1080/00986445.2011.592446
|
| [54] |
S. Agbleze, L. J. Shadle, F. V. Lima, Dynamic modeling and simulation of a subcritical coal-fired power plant under load-following conditions, Ind. Eng. Chem. Res., 63 (2024), 11044–11056. https://doi.org/10.1021/acs.iecr.4c00494 doi: 10.1021/acs.iecr.4c00494
|
| [55] |
C. Maffezzoni, Issues in modelling and simulation of power plants, IFAC Proc. Vol., 25 (1992), 15–23. https://doi.org/10.1016/S1474-6670(17)50423-1 doi: 10.1016/S1474-6670(17)50423-1
|
| [56] |
J. W. Jang, J. J. L. Velázquez, On the temperature distribution of a body heated by radiation, SIAM J. Math. Anal., 56 (2024), 3478–3508. https://doi.org/10.1137/23M1580917 doi: 10.1137/23M1580917
|
| [57] |
A. Lawal, M. Wang, P. Stephenson, O. Obi, Demonstrating full-scale post-combustion CO2 capture for coal-fired power plants through dynamic modelling and simulation, Fuel, 101 (2012), 115–128. https://doi.org/10.1016/j.fuel.2010.10.056 doi: 10.1016/j.fuel.2010.10.056
|
| [58] |
J. A. Carrillo, J. Mateu, M. G. Mora, L. Rondi, L. Scardia, J. Verdera, The ellipse law: Kirchhoff meets dislocations, Commun. Math. Phys., 373 (2020), 507–524. https://doi.org/10.1007/s00220-019-03368-w doi: 10.1007/s00220-019-03368-w
|
| [59] |
M. Z. Yousaf, A. R. Singh, S. Khalid, M. Bajaj, B. H. Kumar, I. Zaitsev, Bayesian-optimized LSTM–DWT approach for reliable fault detection in MMC-based HVDC systems, Sci. Rep., 14 (2024), 17968. https://doi.org/10.1038/s41598-024-68985-5 doi: 10.1038/s41598-024-68985-5
|
| [60] |
M. Z. Yousaf, A. R. Singh, S. Khalid, M. Bajaj, B. H. Kumaret, I. Zaitsev, Enhancing HVDC transmission line fault detection using disjoint bagging and Bayesian optimization with artificial neural networks and scientometric insights, Sci. Rep., 14 (2024), 23610. https://doi.org/10.1038/s41598-024-74300-z doi: 10.1038/s41598-024-74300-z
|
Figures(21) / Tables(4)
Minan Tang, Shengqi Zhang, Zhongcheng Bai, Chuntao Rao. Power control of generator sets in coal-fired power plants based on the combination of MPC and neural network PID[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 450-485. doi: 10.3934/jimo.2026017
DownLoad: