Complexity

Volume 2018, Article ID 6468517, 18 pages

https://doi.org/10.1155/2018/6468517

## A Novel Fuzzy Model Predictive Control of a Gas Turbine in the Combined Cycle Unit

^{1}School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China^{2}Colleges and Universities Key Laboratory of Intelligent Integrated Automation, Guilin University of Electronic Technology, Guangxi 541004, China

Correspondence should be addressed to Guolian Hou; nc.ude.upecn@lgh

Received 11 July 2018; Accepted 8 September 2018; Published 5 November 2018

Guest Editor: Zhile Yang

Copyright © 2018 Guolian Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The complex characteristics of the gas turbine in a combined cycle unit have brought great difficulties in its control process. Meanwhile, the increasing emphasis on the efficiency, safety, and cleanliness of the power generation process also makes it significantly important to put forward advanced control strategies to satisfy the desired control demands of the gas turbine system. Therefore, aiming at higher control performance of the gas turbine in the gas-steam combined cycle process, a novel fuzzy model predictive control (FMPC) strategy based on the fuzzy selection mechanism and simultaneous heat transfer search (SHTS) algorithm is presented in this paper. The objective function of rolling optimization in this novel FMPC consists of two parts which represent the state optimization and output optimization. In the weight coefficient selection of those two parts, the fuzzy selection mechanism is introduced to overcome the uncertainties existing in the system. Furthermore, on account of the rapidity of the control process, the SHTS algorithm is used to solve the optimization problem rather than the traditional quadratic programming method. The validity of the proposed method is confirmed through simulation experiments of the gas turbine in a combined power plant. The simulation results demonstrate the remarkable superiorities of the adopted algorithm with higher control precision and stronger disturbance rejection ability as well as less optimization time.

#### 1. Introduction

At present, thermal power generation still occupies the leading position in the power generation industry in China [1, 2]. Meanwhile, the increasing attention paid to energy conservation and emission reduction [3] has promoted the emergence and development of clean energy-based power generation. As a readily available clean energy, natural gas shows outstanding superiorities in environmental sustainability, energy efficiency, and security [4]. Therefore, there are certain development prospects using natural gas as fuel in power generation.

The combined cycle unit which consists of the gas turbine, heat recovery boiler, and steam turbine [5] is one of the maturely developed power generation devices using natural gas. In the generation process, the generator is driven by the gas turbine; meanwhile, turbine exhaust enters the heat recovery boiler and the residual heat of the gas is made full use of through the steam circulation system [6]. In this way, the characteristics of the gas turbine cycle with high average endothermic temperature and the steam turbine cycle with low average exothermic temperature are combined based on the principle of thermal cascade utilization. Considering the aforementioned process, the gas turbine is regarded as one of the most critical components in the combined cycle unit. Accordingly, it needs to be precisely controlled. However, because of the complex characteristics of the gas turbine with nonlinearity, variable coupling, and uncertainty, conventional control methods have difficulty in achieving the desired performance [7, 8]. Thus, it is remarkably significant to select one of the advanced control strategies for the control of the gas turbine.

With the flourishing development of control methods in recent years, some advanced control algorithms have emerged continuously and obtained great achievements, such as fuzzy control [9–11], predictive control [12–15], and neural network control [16–19]. In all of those methods, predictive control is developed in the industrial process directly [20]. The predictive control consists of these three main components: predictive model, rolling optimization, and feedback correction [21]. Compared with the other aforementioned control strategies, predictive control has stronger ability to handle the time-varying processes with variable constraints and disturbances. Furthermore, this high-performance strategy also can combine the practical requirements of the control process with theoretical derivation maximally. Consequently, the predictive control will be the selected control method in this paper. Since its appearance, predictive control has attracted the great attention of experts and scholars of the world. Among all of the existing predictive control algorithms, the generalized predictive control (GPC) method [22, 23] and the model predictive control (MPC) method [24, 25] are commonly used. The most difference between these two predictive control strategies is that the GPC algorithm is based on the controlled autoregressive integrated moving average (CARIMA) model while the MPC method is based on the state space model [26]. In view of the state space model, it can not only reflect the internal state of the system but also reveal the relationship between the internal state and external input/output variables [27]. Therefore, the MPC algorithm will be used as the starting point of the novel algorithm adopted in this paper. In El-Ferik et al. [28], a distributed nonlinear model predictive control (NMPC) method was put forward for formation control of constrained autonomous vehicles in consideration of the communication bandwidth limitation and transmission delays. The collision was avoided effectively through the spatially filtered potential field, and the satisfactory performance of the presented scheme was also demonstrated through simulation experiments in either strongly connected or weakly connected networks. However, the model uncertainty and disturbances were not taken into consideration which would cause the reduction of control performance and universality of the proposed algorithm. In addition to that, the model predictive control (MPC) algorithm was applied to the coal-conveying process of a coal-fired power plant [29]. In that control scheme, the energy models of the belt conveyor and crusher were constructed and employed to formulate an open-loop energy efficiency optimization problem. Then, based on the open-loop optimization problem, a close-loop MPC strategy was adopted and applied to handle the nonlinearity of the controlled system. This control strategy showed strong robustness, adaptability, and energy-saving ability. Unfortunately, the performance reduction caused by the uncertainties of the system was inevitable. Considering the control of the complex nonlinear process with strong coupling and model mismatch, an extended nonminimal state space predictive control (ENMSSPC) strategy combined with a modified linear quadratic regulator (LQR) was put forward for the improvement of the control performance [30]. Although this method showed better properties with ideal tracking performance and strong disturbance rejection ability, the accompanying increased calculation burden was ignored at the same time. Furthermore, the distributed stochastic MPC [31, 32] was adopted for these control systems with uncertainty and probabilistic constraints as well as disturbances. According to the distribution manner, only one subsystem was selected at each time interval. Meanwhile, the probabilistic constraints were transformed into a set of deterministic constraints through the probabilistic distribution. The outstanding advantages of this strategy with assurances of recursive feasibility and close-loop stability for any updated sequence had been verified through numerical experiments. Nevertheless, the rapidity of the control process should also be taken into account in the design of the controller.

Considering that there are many values that cannot be expressed accurately in most control processes, the concept of “fuzzy” was introduced and applied in the construction of the control strategy to handle uncertainties existing in the controlled system [33, 34]. Aiming at a better dynamic response and reduction in the low-frequency ripple of integrated LED drivers, a fast fuzzy logic control algorithm based on a Takagi-Sugeno-Kang fuzzy controller was put forward [35]. The high-speed mathematical engine of a digital signal controller was used to increase the calculation speed which contributed to a less settling time of the control process. Unfortunately, this method had a less positive effect on the improvement of control precision. The accurate mobile positioning in the cellular network is a matter of great challenge when it comes to the uncertainty in the signal intensity measurement process. Therefore, the fuzzy reasoning was added to a Kalman filter for improving the accuracy of localization [36], and the formed fuzzy extended filter showed remarkable feasibility and superiority compared with single Kalman filter method or fuzzy control strategy [37]. What is more, the fuzzy logic also can be satisfactorily combined with the MPC algorithm. In Boulkaibet et al. [38], the T-S fuzzy model of each typical operating condition was identified by particle swarm optimization (PSO) clustering method and Kernel ridge regression algorithm initially. Then, the predictive control was introduced based on the fuzzy model, and the resulting adaptive fuzzy predictive control strategy could deal with the disturbances and parameter variations effectively. Nevertheless, the output variations and operating time of the control process were not taken into account. In view of the nonlinearities and various disturbances inevitably existing in a complex multivariable system, the fuzzy model predictive control (FMPC) method has become a desired candidate for the promotion of the control performance [39]. The application of extended state observer-based FMPC algorithms on the boiler-turbine system in the ultra-supercritical unit of the power plant had handled these problems and obtained better tracking ability [40], whereas the rapidity of this method needed to be verified. Thus, considering the complex characteristics of the controlled system and the significant superiorities of the FMPC mentioned above, a new FMPC strategy will be constructed for the control of the gas turbine system in a combined cycle unit.

As one of the emerging intelligent algorithms in recent years, the bionic algorithm has developed rapidly with many branches, in which the swarm-based optimization technique [41, 42] stands out and has been extensively applied in modeling and control processes. Model identification of an unknown plant is important for the subsequent controller design to meet desired control specifications. Therefore, in the modeling process of an unknown digital system, a multiple subpopulation-based modified particle swarm optimization (PSO) algorithm was introduced to solve the coefficients of the infinite impulse response (IIR) digital filter [43]. Although this method was able to overcome the multimodal error surface problem effectively, its precise identification would decrease when the order of the controlled system has increased. In addition, an artificial bee colony (ABC) algorithm and a grey wolf optimization (GWO) algorithm were used for solving portfolio optimization problems with cardinality constrains [44] and smart wind speed forecasting [45], respectively. The solution approach combined with the ABC algorithm had reduced the computational difficulties from large-scale optimization problems to a certain extent. Meanwhile, the proposed new hybrid strategy with the addition of GWO algorithm had ensured high accuracy and stability in the prediction process of wind speed. However, similar to most other swarm intelligence algorithms, it is difficult to achieve a win-win situation considering both the accuracy and the rapidity of the control process. Heat transfer search (HTS) algorithm is a novel method for solving the optimization problem which was presented in 2015 [46]. On the basis of the law of thermodynamics in the heat transfer process, the molecule which consisted of the decision variables of the optimization problem made every effort to maintain the thermal equilibrium between itself and the surrounding environment through the three manners of heat transfer: conduction, convection, and radiation. This algorithm had won the first place in the Friedman rank test compared with some other optimization methods, such as PSO algorithm, ABC algorithm, and Yin-Yang pair optimization. Furthermore, in view of the expensive calculating burden in the iterative optimization process, a simultaneous heat transfer search (SHTS) was adopted and its lower computational complexity had been verified through simulation experiments [47]. Consequently, a SHTS algorithm considering the variable constraints will be utilized in this paper to decrease the computational complexity and optimization time of the control process.

On account of the content mentioned above, a novel fuzzy model predictive control (FMPC) which combined fuzzy selection mechanism with the SHTS algorithm is proposed for the promotion of control performance. Firstly, the objective function of the presented algorithm is made up of two parts which represent the state optimization and output optimization. These two parts occupy different weights according to the variations of state variables and output error of the system. Then, considering the uncertainties of the control system, the fuzzy selection mechanism is introduced for the adaptive selections of the above two weighting coefficients in each time interval. What is more, aiming at the reductions of computational burden and optimization time of the control process, the quadratic programming solving process in rolling optimization of conventional MPC is replaced by a SHTS algorithm while taking the variable constraints into account. This SHTS method is a less subjective strategy with two artificially defined parameters. Unlike the original HTS method, the whole population of SHTS is divided into three groups randomly, and each group is assigned to one of three modes of heat transfer. In this way, a great decline of the optimization time of the control process is obtained easily. Finally, the proposed algorithm will be utilized in the control of the gas turbine system in the combined cycle unit and compared with some other similar algorithms. The main contributions of this paper are summarized as follows briefly: (i)A novel FMPC algorithm is put forward based on the fuzzy selection of parameters while taking the state optimization problem and output optimization problem into consideration simultaneously. The addition of the fuzzy selection mechanism can overcome the uncertainties of the complex control system effectively. Furthermore, the precision of the control process also has great promotion(ii)Based on the FMPC algorithm described in (i), a HSTS method which takes variable constraints into account is adopted to replace the quadratic programming solving process in rolling optimization of the traditional MPC algorithm. This replacement can decrease the optimization time of the control system to a certain extent(iii)The presented algorithm is firstly applied in the control of the gas turbine in a combined cycle unit. The simulation results demonstrate that this control strategy can overcome the complex characteristics of a multivariable system effectively. Meanwhile, it is proved to be valuable in the promotions of control precision, disturbance rejection ability, and optimization speed.

The rest of paper is organized as follows. The gas turbine system in the combined cycle unit is described briefly in Section 2. The construction process of the proposed novel FMPC algorithm is introduced in Section 3. Next, the simulation results are shown to verify the superiorities of this algorithm in Section 4. Finally, some general conclusions are presented in Section 5.

#### 2. Problem Description

##### 2.1. The Combined Cycle Unit in a Power Plant

In order to increase the overall efficiency of electric power plants, multiple thermodynamic cycles can be combined to fully utilize energy. The term “combined cycle” refers to the combination of different thermodynamic processes. Compared with the simple cycle, the combined cycle can achieve the utmost utilization of energy and produce more electricity from the same fuel.

The combined cycle is always assembled by a topping cycle and a bottoming cycle, and its most common type is combined with the Brayton cycle operated by a gas turbine and the Rankine cycle operated by a steam turbine separately, which is usually called the combined cycle gas turbine (CCGT). The principle of the combined cycle is that the temperature of the working fluid is still high enough to supply power for the subsequent engine after completing the cycle in the first engine. The operating process of the combined cycle can be described briefly as follows. The gas is burned in a gas turbine and becomes exhaust gases with temperature range from 550°C to 610°C. Meanwhile, the heat obtained in the burning process is converted to electric power through a coupled generator. Then a heat recovery steam generator is employed to produce steam and hot water by capturing exhaust heat. Next, a steam turbine is driven by the steam to deliver additional electricity by driving the corresponding generator. Finally, these two electric powers are transported to the grid synchronously. The diagram of the combined cycle unit described above is structured in Figure 1.