Elsevier

Journal of Hydrology

Volume 590, November 2020, 125223
Journal of Hydrology

Research papers
Multiple hydropower reservoirs operation optimization by adaptive mutation sine cosine algorithm based on neighborhood search and simplex search strategies

https://doi.org/10.1016/j.jhydrol.2020.125223Get rights and content

Highlights

  • Adaptive sine cosine algorithm is proposed for hydropower operation.

  • Elite mutation strategy is introduced to increase individual diversity.

  • Simplex dynamic search strategy is used to improve solution accuracy.

  • Neighborhood search strategy is used to improve the convergence rate.

  • Simulations demonstrate the superiority of the presented method.

Abstract

Recently, the multiple hydropower reservoirs operation optimization is attracting rising concerns from researchers and engineers since it can not only improve the utilization efficiency of water resource but also increase the generation benefit of hydropower enterprises. Mathematically, the reservoir operation problem is a typical multistage constrained optimization problem coupled with numerous decision variables and physical constraints. Sine cosine algorithm (SCA), a new swarm-based method, has the merits of clear principle and easy implementation but suffers from the premature convergence and falling into local optima. To improve the SCA performance, this paper proposes an adaptive sine cosine algorithm (ASCA) where the elite mutation strategy is used to increase the population diversity, the simplex dynamic search strategy is used to enhance the solution quality, while the neighborhood search strategy is used to improve the convergence rate. The simulations of 25 test functions show that ASCA outperforms several existing methods in both convergence rate and solution quality. The results of a real-world hydropower system in China demonstrate that ASCA betters the SCA method with obvious increase in power generation. Thus, the main contribution of this study is to provide an effective optimizer for multiple hydropower reservoirs operation.

Introduction

Over the past decades, the booming economic development has promoted the rapid increase of water and energy demands all over the world (Feng et al., 2019a, Wang et al., 2009, Yan et al., 2017). Reservoir is recognized as one of the most effective engineering measures to improve the utilization efficiency of water-energy resources (Yang et al., 2016, Feng et al., 2020a, Niu et al., 2018, Niu et al., 2020, Zhang et al., 2017, Yin et al., 2014). Thus far, a large number of hydropower projects have been put into operation (Hui et al., 2016, Pang et al., 2018a, Pang et al., 2018b, Xu et al., 2019). In China, the representatives are the world's biggest inter-basin water transfer project (South-North Water Transfer Project) and hydropower project (Three Gorges) (Liu et al., 2015, Wang et al., 2018, Xu et al., 2018, Zhao et al., 2015), and about a quarter of the total installed electricity capacity is provided by reservoirs equipped with huge hydropower turbines (Chen et al., 2013, Feng et al., 2020b, Ming et al., 2017). At the present stage, reservoirs are playing an increasingly important role in raising the people’s living standards by providing comprehensive benefits, like power generation, flood control, navigation, ecological protection and water supply. Thus, researchers and engineers are paying more and more attention to the reservoir operation problem (Bai et al., 2017, Li and Huang, 2008, Li et al., 2009a).

Mathematically, the reservoir operation problem is a complex constrained optimization problem involved numerous decision variables and physical constraints, like water balance equations and turbine discharge limits (Chen et al., 2014, Madani, 2010, Madani, 2011, Yang et al., 2017a). In order to effectively resolve this problem, various optimization methods have been successfully developed by scholars all over the world (He et al., 2004, Feng et al., 2019b, Ji et al., 2014, Li et al., 2010, Yang et al., 2017b), including linear programming, nonlinear programming, dynamic programming, network-based methods, swarm intelligence methods. However, some defects have greatly limited the widespread application of the above methods in practical engineering problems (Li et al., 2009b, Liu et al., 2019a, Zeng et al., 2013, Feng et al., 2018). For instance, linear programming cannot address the nonlinearity in both objective function and physical constraints (Cai et al., 2001, Xie et al., 2018); due to the expensive computational overhead, nonlinear programming may fail to produce the global optimal solution for non-differentiable or discontinuous optimization problems (Catalao et al., 2009, Catalão et al., 2012, Xu et al., 2014); the dynamic programming family methods often suffer from the severe curse of dimensionality in the multidimensional hydropower operation problem (Feng et al., 2020c, Li et al., 2014, Zeng et al., 2019, Jiang et al., 2018); for network-based methods, it is still difficult to determine the rational parameters and stopping criterion (Wen et al., 2019, Cao et al., 2019, Cao et al., 2020, Wang et al., 2020, Xiao et al., 2020); the swarm intelligence methods are usually limited by the premature convergence and unstable solution (Samadi-koucheksaraee et al., 2019, Wu and Chau, 2010, Zheng et al., 2017). Thus, scholars try to develop more effective optimization tools suitable for multiple hydropower reservoirs operation problem (Ahmadianfar et al., 2017, Ahmadianfar et al., 2019a, Ahmadianfar et al., 2019b, Azizi et al., 2019a, Taghian and Ahmadianfar, 2018, Duan, 2019).

Sine cosine algorithm (SCA) is a brand-new swarm intelligence method inspired by both sine and cosine functions (Mirjalili, 2016). In SCA, a set of solutions are randomly produced in the problem space, and then iteratively update their positions from generation to generation. During the evolutionary process, the sine and cosine functions are adopted to achieve a balance between global exploration and local exploitation, and thereby the probability of capturing the global optima will be increased when the amount of iterations becomes sufficient (Gupta and Deep, 2019, Nenavath et al., 2018, Fu et al., 2019). With the merits of simple evolutionary mode and easy implementation, SCA has been widely used to solve various real-world application cases (like wind speeding forecasting and optimal power flow) (Long et al., 2018). However, for all we know, there are still a few reports about using SCA to address the power generation operation of multiple hydropower reservoirs. In order to fill this research gap, this paper tries to verify the feasibility of SCA in the reservoir operation field. From the experimental analysis, it is unfortunately observed that like other swarm-based methods, SCA usually falls into local optima with a high probability due to the loss of swarm diversity. Therefore, this paper aims at developing a SCA variant named as adaptive sine cosine algorithm (ASCA) to resolve the reservoir operation problem. In ASCA, three modified strategies are incorporated into the standard SCA approach, including the elite mutation strategy for increasing the individual diversity, the simplex dynamic search strategy for enhancing the solution quality and the neighborhood search strategy for improving the search rate. The results from numerical experiments and real-world simulations demonstrate the effectiveness and robustness of the proposed method.

To sum up, the main contributions of this research lie in: (1) a practical optimization model is developed for power generation of multiple hydropower reservoirs; (2) the ASCA algorithm based on mutation operator, neighborhood and simplex search strategies are presented to effectively improve the SCA performance; (3) the developed method can produce better results as compared with several existing methods in numerical experiments and real-world simulations, providing a practical method for the complicated engineering optimization problems.

The rest of this paper is organized as below. Section 2 gives the optimization model for multiple hydropower reservoirs operation. Section 3 presents the ASCA method. Section 4 tests the ASCA feasibility in 25 numerical functions. Section 5 gives the technical details of ASCA for reservoir operation problem. Section 6 testifies the ASCA performances in a real-world hydropower system. The conclusions are summarized in the end.

Section snippets

Objective function

Here, the maximization of the total power generation is chosen as the objective function and the mathematical formula can be established as below:E=maxn=1Nt=1TPn,tΔtwhere E is the total generation of hydropower system. N is the number of reservoirs. T is the number of periods. Δt is the number of hours at the tth period. Pn,t is the power output of the nth hydropower reservoir at the tth period.

Operation constraints

(1) Water balance equation:Vn,t+1=Vn,t+3600×Δt×(qn,t-Qn,t-Sn,t)qn,t=In,t+uΩnQu,t+Su,twhere Vn,t, q

Overview of sine cosine algorithm (SCA)

With the rapid development of computer technology, the swarm-based approaches simulating the biological evolution in nature have been successfully proposed by scholars in recent years. As a brand-new swarm evolutionary algorithm, SCA can dynamically adjust the search range of the population to achieve the desired optimization effect (Rizk-Allah, 2018, Liu et al., 2019b, Fu et al., 2018). Generally, SCA starts from a set of solutions randomly placed in the decision space, and then uses the

Benchmark functions

Generally, 25 test functions listed in Table 1, Table 2 can be roughly divided into two different kinds of groups: unimodal functions (F1-F11) with one global optimal solution and multimodal functions (F12-F25) with multiple local optimal solution. The unimodal function can test the search speed of the evolutionary algorithm, while the multimodal function can prove the robust ability of avoiding local minimum. In the following sections, the ASCA performance in two kinds of test functions will

ASCA for solving multiple hydropower reservoirs operation optimization problem

Due to the complexity of practical engineering problems, it is often difficult to directly use the ASCA approach to solve the optimal operation of multiple hydropower reservoirs problem. Hence, the information of the ASCA method for hydropower operation is given in detail.

Study area

The Wu River cascade hydropower system in southwest China is chosen to test the performance of the ASCA method. As the largest tributary on the right bank of the Upper Yangtze River, this river is originated from the eastern part of the Censer mountain and flows through four provinces before injecting into the Yangtze River. With enormous hydropower potential and huge head drop, the Wu River has become one of the largest hydropower bases in China. Here, five reservoirs on the Wu River’s

Conclusion

In this study, a practical population-based method called adaptive sine cosine algorithm (ASCA) is developed to address the numerical optimization and multiple hydropower reservoirs operation optimization problem. In ASCA, three modified strategies are used to improve the performances of the standard sine cosine algorithm (SCA), including elite mutation strategy, simplex dynamic search strategy and neighborhood search strategy. The results of 25 famous test functions show that the presented

Author contribution

All authors contributed extensively to the work presented in this paper. Zhong-kai Feng and Wen-jing Niu contributed to model development and finalized the manuscripts. Shuai Liu contributed to programming implementation and data analysis. Bin Luo and Shu-min Miao; contributed to manuscripts revision and supervision. Kang Liu contributed to the literature review.

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 paper is supported by the National Natural Science Foundation of China (51709119), Natural Science Foundation of Hubei Province (2018CFB573), National Natural Science Foundation of China (U1865202 and 51909133) and the Fundamental Research Funds for the Central Universities (HUST: 2017KFYXJJ193). The writers would like to thank editors and reviewers for their valuable comments and suggestions.

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