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This paper proposes a nonlinear model predictive control (NMPC) strategy based on a local model network (LMN) and a heuristic optimization method to solve the control problem for a nonlinear boiler–turbine unit. First, the LMN model of the boiler–turbine unit is identified by using a data-driven modeling method and converted into a time-varying glo...
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... schematic of a typical coal-fired subcritical drum-type boiler-turbine unit is shown in Figure 1. The boiler transfers the chemical energy of fuel into the thermal energy of steam, which is directly fed to the turbine where the thermal energy is converted into mechanical energy and the generator is driven to generate electricity. ...
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... schematic of a typical coal-fired subcritical drum-type boiler-turbine unit is shown in Figure 1. The boiler transfers the chemical energy of fuel into the thermal energy of steam, which is directly fed to the turbine where the thermal energy is converted into mechanical energy and the generator is driven to generate electricity. ...
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... model accuracy was verified by the field data. The model is in the form of Figure 1. Simplified schematic view of a coal-fired subcritical boiler-turbine (B-T) unit. ...
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... LMN model of the 500 MW coal-fired B-T unit shown in Figure 1 is identified to provide the prediction mode for the proposed nonlinear predictive control method. In order to fully stimulate the nonlinearity of the B-T unit under different load conditions, two uncorrelated modified pseudo-random sequences are respectively applied to the two manipulated variables u B and u T to generate identification data, as shown in Figure 7. ...
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... time t = 400 s, the setpoint of output power N E is increased by 20 MW, and at time t = 1200 s, the setpoint of N E is decreased by 20 MW and returned to 450 MW, while the main steam pressure P T is kept unchanged. The responses of outputs N E and P T as well as the control inputs u B and u T are shown in Figure 10. The similar test is also carried out under 60% load condition (N E = 300 MW,P T = 11.69 ...
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... similar test is also carried out under 60% load condition (N E = 300 MW,P T = 11.69 MPa), and the results are shown in Figure 11. ...
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... can be seen from Figures 10 and 11 that, for the NMPC, no matter whether under high-load or low-load condition, under the premise of satisfying the constraints on the control action, the output power can be quickly tracked to its setpoint without overshoot, and the fluctuation of main steam pressure is small. The setting time is no more than 250 s and the maximum deviation of main steam pressure is less than 0.3 MPa. ...
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... 2: The second case is designed to test the tracking capability of the proposed control strategy under wide-range operation, which simulates the automatic generation control (AGC) operation. As shown in Figure 12, the unit is operating in variable-steam-pressure mode; the setpoint of the output power is first increased linearly from 400 (80% load condition) to 500 MW (100% load condition) at a rate of 2% maximum continuous rating/min, then the setpoint is decreased to 250 MW (50% load condition) at the same rate, and finally ramped back to 400 MW. Meanwhile, the setpoint of the main steam pressure is changed in proportion to the load. ...
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... can be observed from Figure 12 that good tracking behavior of the power and main steam pressure is obtained by using the proposed NMPC. The performance of LMPC is worse than the NMPC, especially in the main steam pressure, where a huge control offset occurred under low-load conditions, which is due to the significant modeling mismatch caused by the nonlinearity of the B-T unit. ...
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... indicates the dynamic behavior of the unit has changed significantly; and the setpoints of output power and main steam pressure are changed the same as in Case 2. The responses of the NMPC system under wide-range operation are shown in Figure 13. It can be seen that both the output power and main steam pressure can track the change of their setpoints rapidly and steadily even if the dynamic behavior of the B-T unit has changed significantly, which indicates that the nonlinear predictive control based on an LMN and IGA has strong robustness. ...
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... can be seen that both the output power and main steam pressure can track the change of their setpoints rapidly and steadily even if the dynamic behavior of the B-T unit has changed significantly, which indicates that the nonlinear predictive control based on an LMN and IGA has strong robustness. Since the control performances of LMPC and PI are very poor in this severe situation, they are not shown in Figure 13. operation. As shown in Figure 12, the unit is operating in variable-steam-pressure mode; the setpoint of the output power is first increased linearly from 400 (80% load condition) to 500 MW (100% load condition) at a rate of 2% maximum continuous rating/min, then the setpoint is decreased to 250 MW (50% load condition) at the same rate, and finally ramped back to 400 MW. ...
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... As shown in Figure 12, the unit is operating in variable-steam-pressure mode; the setpoint of the output power is first increased linearly from 400 (80% load condition) to 500 MW (100% load condition) at a rate of 2% maximum continuous rating/min, then the setpoint is decreased to 250 MW (50% load condition) at the same rate, and finally ramped back to 400 MW. Meanwhile, the setpoint of the main steam pressure is changed in proportion to the load. ...
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... can be observed from Figure 12 that good tracking behavior of the power and main steam pressure is obtained by using the proposed NMPC. The performance of LMPC is worse than the NMPC, especially in the main steam pressure, where a huge control offset occurred under low-load conditions, which is due to the significant modeling mismatch caused by the nonlinearity of the B-T unit. ...
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... PI control shows the worst performance and is completely unable to deal with the rapidly changing operating conditions. which indicates the dynamic behavior of the unit has changed significantly; and the setpoints of output power and main steam pressure are changed the same as in Case 2. The responses of the NMPC system under wide-range operation are shown in Figure 13. It can be seen that both the output power and main steam pressure can track the change of their setpoints rapidly and steadily even if the dynamic behavior of the B-T unit has changed significantly, which indicates that the nonlinear predictive control based on an LMN and IGA has strong robustness. ...
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... can be seen that both the output power and main steam pressure can track the change of their setpoints rapidly and steadily even if the dynamic behavior of the B-T unit has changed significantly, which indicates that the nonlinear predictive control based on an LMN and IGA has strong robustness. Since the control performances of LMPC and PI are very poor in this severe situation, they are not shown in Figure 13. ...
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... taking the identified local model network of the nonlinear system as the prediction model, a nonlinear predictive control strategy based on an immune genetic algorithm (IGA) optimization is proposed in this paper to improve the control performance of the boiler-turbine (B-T) unit, because of its ability in dealing with the control constraints and nonlinearity. An accurate local model Figure 13. Case 3: Output responses and control inputs of the system under wide-range operation in the presence of model mismatch. ...
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Citations
... The boiler combustion efficiency can be efficiently controlled by the model predictive control algorithm, and the average simulation error is about 5%. Zhu et al. (2019) developed a nonlinear model predictive control technique based on a local model network and a heuristic optimization method to address the control issue of a nonlinear boiler-turbine unit, and the results show limited tracking capacity. To control the steam temperature of a power plant boiler, Tavoosi and Mohammadzadeh (2021) introduced RBF network-based model predictive control. ...
... To address this, Hyatt et al. [11] propose a parallelized GA implementation that can solve NMPC problems in real-time by evaluating multiple candidate control inputs simultaneously on a GPU. Additionally, in [12], [13], a specially designed GA is used to solve the nonlinearly constrained optimization problem for predictive control in an online setting. ...
Nonlinear model predictive control (NMPC) solves a multivariate optimization problem to estimate the system's optimal control inputs in each control cycle. Such optimization is made more difficult by several factors, such as nonlinearities inherited in the system, highly coupled inputs, and various constraints related to the system's physical limitations. These factors make the optimization to be non-convex and hard to solve traditionally. Genetic algorithm (GA) is typically used extensively to tackle such optimization in several application domains because it does not involve differential calculation or gradient evaluation in its solution estimation. However, the size of the search space in which the GA searches for the optimal control inputs is crucial for the applicability of the GA with systems that require fast response. This paper proposes an approach to accelerate the genetic optimization of NMPC by learning optimal search space size. The proposed approach trains a multivariate regression model to adaptively predict the best smallest search space in every control cycle. The estimated best smallest size of search space is fed to the GA to allow for searching the optimal control inputs within this search space. The proposed approach not only reduces the GA's computational time but also improves the chance of obtaining the optimal control inputs in each cycle. The proposed approach was evaluated on two nonlinear systems and compared with two other genetic-based NMPC approaches implemented on the GPU of a Nvidia Jetson TX2 embedded platform in a processor-in-the-loop (PIL) fashion. The results show that the proposed approach provides a 39-53\% reduction in computational time. Additionally, it increases the convergence percentage to the optimal control inputs within the cycle's time by 48-56\%, resulting in a significant performance enhancement. The source code is available on GitHub.
... Moreover, a nonlinear model predictive control strategy based on a local model network is used to deal with the control problem of a 500 MW boiler-turbine unit. As a result, a good tracking behavior of the power and the main steam pressure was obtained [9]. However, the above scheme is restricted by the safety of coal-fired units, where an intelligent control algorithm increases the complexity of the control system. ...
In this study, a coal-fired power plant with an integrated S-CO2 cycle is proposed to improve the system operational flexibility. To optimize the performance, a control strategy of variable load regulation is proposed. First, a dynamic mathematical model of the system is established based on the conservation of mass and energy principles, and then, dynamic verification of the model is carried out. In order to evaluate the performance of the proposed system, an exergy analysis is performed on the S-CO2 cycle, indicating that the exergy loss rate of the heater in the cycle is the highest. Finally, the dynamic performance of the system is simulated, and the dynamic response of the power generation load is analyzed. In addition, the system is evaluated based on the performance indicator of the flexibility of the power generation. It was found that the proposed system in this paper has a large load ramp rate which can quickly follow the load response. Meanwhile, compared with load downregulation, the system has greater potential for load upregulation.
... The data used for model development was collected from a 210 MW power plant over a 2-3 hour period. In Zhu et al. [3], a local model network (LMN) was used to model the boiler-turbine unit of a sub-critical coal-fired power plant and applied as the prediction model in a non-linear model predictive controller. The model was validated with data from a 500 MW unit in China. ...
Due to increasing shares of renewable electricity sources in the grid, thermal power plants need to operate in a more flexible manner in the future. This will involve more frequent startups, shutdowns, and load changes. A central part of a thermal power plant analysed in this study is the coal-fired boiler. In a previous study, a first-principle model of a sub-critical coalfired boiler has been developed and validated with operational data from a Polish power plant. Based on this model, this work aims to develop a computationally efficient and sufficiently accurate data-driven model that is easy to implement in new software. A selection of multi-output algorithms was first compared using nonoptimised parameters, with very few adaptations to the data set. Then, each algorithm had undergone three different optimisation routines to tune the hyper-parameters. The results of the nonoptimised models were compared with the optimised ones, and then compared to the reference first-principle model using the average Mean Absolute Percentage Error as a score. The methods used comprise six base learners and three algorithms using ensemble methods. The optimisation routines were based on the Powell conjugate direction method, Bayesian optimisation and evolutionary algorithm. All the data-driven models had shown a lower percentage error than the first principle model, and optimisation had resulted in improved prediction capacity for every base learner, but not for ensemble method-based algorithms.
... Unfortunately, the linearized model approach usually assumes that the non-linear part can be ignored, which may cause model mismatch, and results in inaccurate control and performance deterioration. More recently, considering the complexity on the modeling for boiler-turbine system, since artificial intelligence techniques show potential solutions for several complex problems, the academic circle attempt to introduce these techniques, especially in non-linear system modeling [10,26,27] and controller design [28][29][30][31]. ...
This paper aims to address a finite-horizon model predictive control (MPC) for non-linear drum-type boiler-turbine system using a system-identification method. Considering that the strong state coupling of a non-linear mechanism model, the subspace identification method is first utilized to obtain a linear state-space model, and transformed into an input–output model. By taking the inputs and outputs of the input–output model as system states, an augmented non-minimal state-space (NMSS) model of state measurable is constructed. In order to reduce the computation burden, the augmented NMSS model is further transformed into a canonical formulation by adopting a Kalman decomposition. Based on the minimal realization state-space model, the MPC controller is parameterized as a finite-horizon optimization problem. Finally, simulations are performed and evaluated the performance of the proposed method, and the simulation results show that: the linear model approximate the non-linear system accurately; the proposed MPC method can achieve a satisfactory stable control performance; and the computation time 18.388 s for the overall optimization problem also illustrates the real-time performance effectively.
... For the boiler-turbine system, there are also some applications of MPC. A nonlinear model predictive control method was designed for boiler-turbine system with a data driven model [23], and the optimal problem was solved by immune genetic algorithm. Ref. [24] presented a zone economic model predictive cotroller to fulfill the economic target of the boiler-turbine system. ...
The marine boiler-turbine system is the core part for the steam-powered ships with complicated dynamics. To improve the power tracking performance and fulfill the requirement of high utilization rate of fossil energy, the control performance of the system should be improved. In this paper, a nonlinear model predictive control method is proposed for the boiler-turbine system with fractional order cost functions. Firstly, a nonlinear model of the boiler-turbine system is introduced. Secondly, a nonlinear extended predictive self adaptive control(EPSAC) method is designed to the system. Then, integer order cost function is replaced with a fractional order cost function to improve the control performance, and also the configuration of the cost function is simplified. Finally, the superiority of the proposed method is proved accordring to the comparison experiments between the fractional order model predictive control and the traditional model predictive control.
... In general, the NMPC scheme is designed based on the discrete-time model of the system. Therefore, referring to Zhu et al. [26] and Veerasamy et al. [27], the ship model (5) can be discretized utilizing a sampling time of T s as: ...
This paper presents a weight optimization method for a nonlinear model predictive controller (NMPC) based on the genetic algorithm (GA) for ship trajectory tracking. The weight coefficients Q and R of the objective function in NMPC are obtained via the real-time optimization of the genetic algorithm instead of the trial and error method, which improves the efficiency and accuracy of the controller. In addition, targeted improvements are made to the internal crossover operator, mutation operator, crossover rate, and mutation rate of the genetic algorithm. The simulation comparison of trajectory tracking between NMPC with real-time-optimized weight coefficients and the one with constant coefficients is performed. Finally, the simulation result shows that the controller with real-time-optimized weight coefficients has a better trajectory tracking effect than that with constant weight coefficients.
... All of these methods applied to linear time-invariant system have achieved good tracking performance. In order to improve the control performance of nonlinear system, Zhu et al. in [29] investigated nonlinear predictive control strategy based on local model network for a 500 MW coalfired boiler-turbine system, in which the nonlinear optimization problem was solved by the immune genetic algorithm. However, due to the model uncertainty, the future state predictions of robust MPC are uncertain. ...
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