Improved tunicate swarm algorithm: Solving the dynamic economic emission dispatch problems
Graphical abstract
Introduction
The demand for electricity is increasing with continuous advancement of industrialization on global scale [1]. Adjusting the power supply mode flexibly according to load changes to improve the economy of the power system has become an urgent problem to be solved in the optimization of power system operation [2], [3]. However, traditional thermal power generation emits a large amount of pollutants into the atmosphere, including sulfur oxides (SO), nitrogen oxides (NO), etc. These pollutants affect not only humans, but also other organisms. Hence, the pollutant emission index must be introduced into the optimization objectives to make the economic dispatch also have the function of environmental protection [4], [5]. Dynamic economic emission dispatch (DEED) is an optimization problem that includes multiple objective functions that usually include reducing pollutant emission and reducing fuel cost. Solving the optimal DEED improves the environmental friendliness and economy of power system [6].
DEED is an urgent problem to be solved in the power system operation optimization, and the task of DEED is to adjust the output power of generator units according to the predicted load demand during the dispatch period [7]. For instance, Kheshiti et al. [8] argued that the DEED improvement helps to develop the power system economy and environmental friendliness. The entire scheduling cycle is usually 24 h, and the output power of generator unit changes with load demand in the dispatching process. The dispatching scheme must satisfy many constraints, such as the slope rate constraint of the generator unit, the output power constraint, etc [9], [10]. In this study, fuel cost and pollutant gas emission are considered simultaneously in the objective function of the DEED problem, which requires higher solving ability of the optimization algorithm.
The output power of the thermal generator unit shows nonlinearity due to the limitation of the valve point effect [11]. Karthik et al. [12] argued that the valve point effect increases the complexity of the objective function and difficulty of solving the DEED problem. In addition, the computational cost of solving the mathematical model of DEED increases with the increase of grid-connected generator units in the power system. When the mathematical method is used to solve the DEED problem, mathematical method is highly sensitive to the initial value, which needs the initial value to be close to the optimal solution [13]. Thus, mathematical method is unsuitable for solving DEED problems. Intelligent optimization method has the advantages of not being affected by the dimension and non-differentiability problem to be solved. Based on the above reason, scholars have developed a variety of intelligent optimization algorithms to solve the DEED problem [14].
In prior studies, classic intelligent algorithms have been applied to solve DEED problem, such as simulated annealing algorithm, particle swarm optimization algorithm (PSO), etc [15], [16]. However, emission and cost are two conflicting goals, so reducing cost leads to increase emission [17]. Therefore, it is difficult for traditional intelligent algorithms to obtain optimal solutions when solving DEED problems. Tunicate swarm algorithm (TSA) is a new type of intelligent algorithm and its optimized performance is better than traditional intelligent algorithms such as PSO [18]. To further enhance the ability of TSA algorithm to solve the DEED problem, this paper improves the TSA algorithm. Specific improvement measures include: initialization based on Tent mapping, global search vector generated by gray wolf optimization algorithm, and Levy flight strategy. This research compares the convergence performance of the proposed ITSA algorithm with the state-of-the-art algorithms, and uses 3 test systems to verify the performance of the ITSA algorithm for solving the DEED problem. The objective of this study is as follows:
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Construct a DEED model considering the valve point effect.
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To propose a new DEED problem solving method.
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To improve the economy and environmental friendliness of the power system.
The contributions of this study are as follows: (1) The weight coefficient is used to transform DEED problem into a single-objective optimization problem for making the DEED problem easier to solve; (2) The valve point effect is considered in the DEED problem to make it closer to the reality; (3) A novel ITSA algorithm is proposed to solve DEED problem; and (4) Compared with the state-of-the-art algorithms, the dispatch scheme given by ITSA algorithm is more competitive with lower operation cost and less pollution gas emission.
Although the ITSA algorithm proposed in this study gives competitive solutions to the DEED problem, there are still several limitations in this study. First, the convergence performance of the ITSA algorithm proposed in this research can be further explored, and the generalization ability of the ITSA algorithm can be improved. Second, the scheduling problem of the integrated energy system considering new energy has become a hot research issue. How to consider the new energy in the modeling process of the integrated energy system requires further research. The above two limitations will be solved in future research work.
This study includes the following sections: Second 2 presents the previous study on DEED. Section 3 constructs the DEED problem mathematical model in detail. Section 4 introduces the TSA and ITSA mathematical models. Section 5 verifies the performance of ITSA through three test systems. Section 6 summarizes the contributions of this study.
Section snippets
Literature review
The goal of DEED problem is to reduce the fuel cost of the power system while reducing its pollutant emission. However, fuel cost and pollutant emission are essentially contradictory. Moreover, the objective function of DEED becomes complicated because the fuel cost and the emission functions are non-smooth and non-convex. The switch of a large steam turbine produces the valve point effect that makes the output curve of the unit not smooth during actual operation. Valve point effect changes the
Objective function
DEED is an optimization problem containing multiple optimization goals. This study uses the coefficient w to change the multi-objective function into a single objective function, as shown below: where FE is the function to be optimized, Fue is the fuel cost function, Emm is the total pollutant emission, and H is the price penalty factor when .
The value of w affects the emphasis of the objective function on fuel cost and pollution emission. The closer the w value is to 1, the
Proposed method
In this section, TSA and ITSA are introduced in detail. The improvement strategies contain: (1) Tent mapping initialization; (2) Global search vector; and (3) Levy flight.
Case analysis
This study verifies the effectiveness and superiority of the ITSA algorithm through the statistical analysis of the test results of single-peak and multi-peak benchmark functions, and compares it with the state-of-the-art algorithms. In addition, three test systems containing five, ten and fifteen generator units are applied to verify the solution performance of the proposed ITSA algorithm. Moreover, each test system considers the transmission loss and slope rate constraint. System parameters
Discussion
Effective optimization of DEED problem considering the valve point effect improves stability of the power system and is of great significance to power system safety. Hence, the valve point effect is considered in the constructed DEED model to make the obtained dispatching scheme closer to reality, but the valve point effect greatly increases difficulty to solve the DEED problem. Therefore, this study proposes ITSA to solve the DEED problem, and ITSA shows better convergence and optimization
Concluding remarks
DEED adjusted each generator unit output, thereby reducing pollutant emission of the power system and improves its economic outcomes. The two conflicting goals of fuel cost and pollutant emission need to be optimized. The unit combination in the optimization result plays a role in reducing fuel costs and emissions. The conclusions are summarized as follows:
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A multi-objective optimal dispatch model considering economy and environmental protection is constructed. In addition, the valve point
CRediT authorship contribution statement
Ling-Ling Li: Conceptualization, Original writing, Final version writing. Zhi-Feng Liu: Conceptualization, Original writing, Final version writing. Ming-Lang Tseng: Original writing, Final version writing. Sheng-Jie Zheng: Original writing, Final version writing. Ming K. Lim: Original writing, Final version writing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study was supported by the key project of Tianjin Natural Science Foundation, China [Project No. 19JCZDJC32100] and the Natural Science Foundation of Hebei Province of China [Project No. E2018202282].
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