Extracting Optimal Policies of Hydropower Multi-Reservoir Systems Utilizing Enhanced Differential Evolution Algorithm

Deriving the optimal policies of hydropower multi-reservoir systems is a nonlinear and high-dimensional problem which makes it difficult to achieve the global or near global optimal solution. In order to optimally solve the problem effectively, development of optimization methods with the purpose of optimizing reservoir operation is indispensable as well as inevitable. This paper introduces an enhanced differential evolution (EDE) algorithm to enhance the exploration and exploitation abilities of the original differential evolution (DE) algorithm. The EDE algorithm is first applied to minimize two benchmark functions (Ackley and Shifted Schwefel). In addition, a real world two-reservoir hydropower optimization problem and a large scale benchmark problem, namely ten-reservoir problem, were considered to indicate the effectiveness of the EDE. The performance of the EDE was compared with the original DE to solve the three optimization problems. The results demonstrate that the EDE would have a powerful global ability and faster convergence than the original DE to solve the two benchmark functions. In the 10-reservoir optimization problem, the EDE proved to be much more functional to reach optimal or near optimal solution and to be effective in terms of convergence rate, standard deviation, the best, average and worst values of objective function than the original DE. Also, In the case of two-reservoir system, the best values of the objective function obtained 93.86 and 101.09 for EDE and DE respectively. Based on the results, it can be stated that the most important reason to improve the performance of the EDE algorithm is the promotion of local and global search abilities of the DE algorithm using the number of novel operators. Also, the results of these three problems corroborated the superior performance, the high efficiency and robustness of the EDE to optimize complex and large scale multi-reservoir operation problems.     

Identifying Explicit Formulation of Operating Rules for Multi-Reservoir Systems Using Genetic Programming

Operating rules have been widely used to handle the inflows uncertainty for reservoir long-term operations. Such rules are often expressed in implicit formulations not easily used by other operators and/or reservoirs directly. This study presented genetic programming (GP) to derive the explicit nonlinear formulation of operating rules for multi-reservoir systems. Steps in the proposed method include: (1) determining the optimal operation trajectory of the multi-reservoir system using the dynamic programming to solve a deterministic long-term operation model, (2) selecting the input variables of operating rules using GP based on the optimal operation trajectory, (3) identifying the formulation of operating rules using GP again to fit the optimal operation trajectory, (4) refining the key parameters of operating rules using the parameterization-simulation-optimization method. The method was applied to multi-reservoir system in China that includes the Three Gorges cascade hydropower reservoirs (Three Gorges and Gezhouba reservoirs) and the Qing River cascade hydropower reservoirs (Shuibuya, Geheyan and Gaobazhou reservoirs). The inflow and storage energy terms were selected as input variables for total output of the aggregated reservoir and for decomposition. It was shown that power energy term could more effectively reflect the operating rules than water quantity for the hydropower systems; the derived operating rules were easier to implement for practical use and more efficient and reliable than the conventional operating rule curves and artificial neural network (ANN) rules, increasing both average annual hydropower generation and generation assurance rate, indicating that the proposed GP formulation had potential for improving the operating rules of multi-reservoir system.     

A Multi-Objective Optimization Model for Coordinated Regulation of Flow and Sediment in Cascade Reservoirs

This paper presents a multi-objective optimization model for the coordinated regulation of flow and sediment in cascade reservoirs. The model was developed to address two contradicting issues: sediment trapping and flow regulation. The benefits of flood control, hydropower generation and navigation, and sedimentation in cascade reservoirs were considered as the target functions; then the corresponding submodels for reservoir operation and sediment computation were established. The model was implemented by reducing it to a single objective nonlinear model using the constraint method. Non-inferior solutions were obtained by solving the model with catfish effect particle swarm optimization algorithm. The model was applied to the cascade system of Xiluodu and Xiangjiaba reservoirs in the lower Jinsha River in the flood recession period. Under the safety of flood control and navigation, a non-inferior set for impounding time, power generation, and siltation-loss rate of capacity was obtained and optimal solutions with different weights were derived. The results demonstrate that the model is a useful tool in coordinated operations of cascade reservoirs.     

Multi-Objective Differential Evolution for Design of Cascade Hydropower Reservoir Systems

After Paris Agreement and obligation made by various countries to decrease greenhouse gases, generation of clean energy with low carbon was taken into consideration. Hydropower plant is considered as a clean, cheap and renewable energy source for generating electrical energy. Through the construction of the multipurpose dams and their optimal planning and management, we may decrease the potential losses sustained by aquatic ecosystem in addition to supplying the energy and fulfilling the industrial, agricultural and drinking water demands. In the present study, a multi-objective optimization model was proposed for determination of design parameters in cascade hydropower multi-purpose reservoir systems. Considering the significant number of constraints and decision variables and non-convex form of the objective functions and constraints, particularly in multi-reservoir systems, a multi-objective evolutionary algorithm (MOEA) known as non-dominated sorting differential evolution (NSDE) was developed to solve the problem and reduce the computational costs. Karkheh River basin was selected as a case study in order to make an assessment on the capabilities and strength of the model. This basin is capable of generating hydropower energy and agricultural development with high environmental considerations due to Hurolazim International Wetland. Based on the results, we may supply various demands such as environmental demands of the aquatic ecosystem with high reliability as well as generating firm hydropower energy through optimal design of cascade hydropower reservoirs.     

Application of an Interior-Point Algorithm For Optimization of a Large-Scale Reservoir System

Optimization of a multi-reservoir system operation is challenging due to the non-linearity, stochasticity, and dimensionality involved in such a problem. In this research, a long-term planning model is presented for optimizing the operation of Iranian Karoon-Dez reservoir system using an interior-point algorithm. The system is the largest multi-purpose reservoir system in Iran with hydropower generation, water supply, and environmental objectives. The focus is on resolving the dimensionality of this problem while considering hydropower generation and water supply objectives. The weighting and constraints methods of multi-objective programming are used to assess the trade-off between water supply and hydropower objectives so as to find noninferior solutions. The computational efficiency of the proposed approach is demonstrated using historical data taken from Karoon-Dez reservoir system.     

Multi-Objective Optimization of the Proposed Multi-Reservoir Operating Policy Using Improved NSPSO

Severe water shortage is unacceptable for water-supply reservoir operation. For avoiding single periods of catastrophic water shortage, this paper proposes a multi-reservoir operating policy for water supply by combining parametric rule with hedging rule. In this method, the roles of parametric rule and hedging rule can be played at the same time, which are reducing the number of decision variables and adopting an active reduction of water supply during droughts in advance. In order to maintain the diversity of the non-dominated solutions for multi-objective optimization problem and make them get closer to the optimal trade-off surfaces, the multi-population mechanism is incorporated into the non-dominated sorting particle swarm optimization (NSPSO) algorithm in this study to develop an improved NSPSO algorithm (I-NSPSO). The performance of the I-NSPSO on two benchmark test functions shows that it has a good ability in finding the Pareto optimal set. The water-supply multi-reservoir system located at Taize River basin in China is employed as a case study to verify the effect of the proposed operating policy and the efficiency of the I-NSPSO. The operation results indicate that the proposed operating policy is suitable to handle the multi-reservoir operation problem, especially for the periods of droughts. And the I-NSPSO also shows a good performance in multi-objective optimization of the proposed operating policy.     

Chaotic Evolutionary Algorithms for Multi-Reservoir Optimization

The water sharing dispute in a multi-reservoir river basin forces the water resources planners to have an integrated operation of multi-reservoir system rather than considering them as a single reservoir system. Thus, optimizing the operations of a multi-reservoir system for an integrated operation is gaining importance, especially in India. Recently, evolutionary algorithms have been successfully applied for optimizing the multi-reservoir system operations. The evolutionary optimization algorithms start its search from a randomly generated initial population to attain the global optimal solution. However, simple evolutionary algorithms are slower in convergence and also results in sub-optimal solutions for complex problems with hardbound variables. Hence, in the present study, chaotic technique is introduced to generate the initial population and also in other search steps to enhance the performance of the evolutionary algorithms and applied for the optimization of a multi-reservoir system. The results are compared with that of a simple GA and DE algorithm. From the study, it is found that the chaotic algorithm with the general optimizer has produced the global optimal solution (optimal hydropower production in the present case) within lesser generations. This shows that coupling the chaotic algorithm with evolutionary algorithm will enrich the search technique by having better initial population and also converges quickly. Further, the performances of the developed policies are evaluated for longer run using a simulation model to assess the irrigation deficits. The simulation results show that the model satisfactorily meets the irrigation demand in most of the time periods and the deficit is very less.     

Multi-objective reservoir operation using particle swarm optimization with adaptive random inertia weights

Based on conventional particle swarm optimization(PSO), this paper presents an efficient and reliable heuristic approach using PSO with an adaptive random inertia weight(ARIW) strategy, referred to as the ARIW-PSO algorithm, to build a multi-objective optimization model for reservoir operation. Using the triangular probability density function, the inertia weight is randomly generated, and the probability density function is automatically adjusted to make the inertia weight generally greater in the initial stage of evolution, which is suitable for global searches. In the evolution process, the inertia weight gradually decreases, which is beneficial to local searches. The performance of the ARIWPSO algorithm was investigated with some classical test functions, and the results were compared with those of the genetic algorithm(GA), the conventional PSO, and other improved PSO methods. Then, the ARIW-PSO algorithm was applied to multi-objective optimal dispatch of the Panjiakou Reservoir and multi-objective flood control operation of a reservoir group on the Luanhe River in China, including the Panjiakou Reservoir, Daheiting Reservoir, and Taolinkou Reservoir. The validity of the multi-objective optimization model for multi-reservoir systems based on the ARIW-PSO algorithm was verified.     

Optimal Operation of Multi-reservoir Systems Considering Time-lags of Flood Routing

Operations of multi-reservoir systems are nonlinear and high-dimensional problems, which are difficult to find the optimal or near-optimal solution owing to the heavy computation burden. This study focuses on flood control operation of multi-reservoir systems considering time-lags caused by Muskingum flood routing of river channels. An optimal model is established to jointly minimize the flood peak on the downstream flood control station for the multi-reservoir systems. A hybrid algorithm, Progressive Optimality Algorithm and Successive Approximation (POA-SA), is improved to solve the multi-reservoir operation model by modifying the POA. The POA-SA uses the DPSA to reduce the spatial dimensionality due to the multiple reservoirs, and adopts an improved POA to alleviate the temporal dimensionality caused by the time-lags of the Muskingum flood routing. Linear programming is then implemented to verify the solution of the POA-SA method with a linear approximation of the discharge capacity curve. The multi-reservoir systems of China’s Xijiang River is selected for a case study. Results show that the flood peak of Wuzhou station can be averagely decreased by 6730 m³/s (12.8 %) for the 100-year return period floods, indicating that the proposed method is efficient to operate the multi-reservoir systems and resolve the time-lags issues.     

Design-Operation of Multi-Hydropower Reservoirs: HBMO Approach

To illustrate and test the applicability and performance of the innovative honey-bee mating optimization (HBMO) algorithm in highly non-convex hydropower system design and operation, two problems are considered: single reservoir and multi-reservoir. Both hydropower problems are formulated to minimize the total present net cost of the system, while achieving the maximum possible ratio for generated power to installed capacity. The single hydropower reservoir problem is approached by the developed algorithm in 10 different runs. The first feasible solution was generated initially and later improved significantly and solutions converged to a near optimal solution very rapidly. In the application of the proposed algorithm to a five-reservoir hydropower system with 48 periods and a total of 230 decision variables, in early mating flights, the first feasible solution was identified and the results converged to a near optimal solution in later mating flights. In the case of the multi-reservoir problem, an efficient gradient-based nonlinear-programming solver (LINGO 8.0) failed to find a feasible solution and for the single hydropower reservoir design problem it performed much worse than the proposed algorithm.     

Robust Diversity-based Sine-Cosine Algorithm for Optimizing Hydropower Multi-reservoir Systems

Hydropower energy generation depends on the available water resources. Therefore, planning and operation of the water resource systems are paramount tasks for energy management. Since reservoirs are one of the important components of water resources systems, extracting optimal operating policies for proper management of energy generated from these systems is an imperative step. Optimizing reservoir system operation (ORSO) is a non-linear, large-scale, and non-convex problem with a large number of constraints and decision variables. To solve ORSO problem effectively, a robust diversity-based, sine-cosine algorithm (RDB-SCA) is developed in the present study by introducing several strategies to balance the global exploration and local exploitation ability and to achieve accurate and reliable solutions. An efficient linear operation rule is coupled with the RDB-SCA to maximize the energy generation. The proposed method is then applied to a real-world, multi-reservoir system to extract optimal operational policies and, consequently, maximize the energy production. It is shown that the RDB-SCA is able to generate 24, 14, and 6% more energy than the original SCA, respectively for 2-, 3-, and 4-reservoir systems. The present findings are useful to suggest guidelines for efficient operation of hydropower multi-reservoir systems. This paper is supported by https://imanahmadianfar.com/codes.

     

Optimal Short-term Reservoir Operation with Integrated Long-term Goals

A methodology to incorporate long-term goals within the short-term reservoir operation optimization model is proposed. Two conflicting objectives for the management of hydropower generation in two different power plants are incorporated. A chance-constrained optimization model is used to derive long-term (annual) operation strategies. With the time horizon of operation for the short-term optimization model kept equal to a single time-step of the long-term optimization model, the optimum end storages derived from the long-term model are incorporated as constraints (storage lower bounds) within the short-term model. The long-term benefits accrued from such an operation model are illustrated for a small reservoir, in South India. The solutions are compared with the historic operation. These are also compared with the solutions of a short-term optimal operation model ignoring long-term goals. The optimization model is solved using a multi-objective genetic algorithm.     

群库优化调度研究综述

我国是一个水资源紧缺的国家,主要江河都形成了由水库、堤防、分蓄洪区组成的防洪工程系统,水库群的优化调度已经成为我国各大流域防洪研究的重点.目前,这一研究领域主要采用系统分析理论与方法,如:线性规划、非线性规划、动态规划、多目标优化分析、大系统分解协调等方法.同时,大量的新理论新算法极大地丰富了水库群优化调度的理论研究.文中在介绍了水库群优化调度研究意义的基础上,分别从常规方法和系统分析方法两个方面概述了国内外的研究进展,并对水库群优化调度今后的研究进行了展望.     

Deriving Optimal Operating Rules of a Multi-Reservoir System Considering Incremental Multi-Agent Benefit Allocation

Joint multi-reservoir operation is one of the most efficient measures to meet the demand for increasing economic benefits. Operating rules have been widely used in long-term reservoir operations. However, reservoirs belong to multiple agents in most cases, which imposes difficulties on benefit allocation. This motivated us to derive optimal operating rules for a multi-reservoir system, considering incremental benefit allocation among multiple agents. Fairness of incremental benefits for multiple agents is proposed as one of the objective functions, and then optimal joint operating rules with fairness are derived. The optimal joint operating rules with fairness are compared with conventional, optimal individual, and joint operating rules. The Three Gorges (Three Gorges and Gezhouba) and Qing River (Shuibuya, Geheyan and Gaobazhou) cascade reservoirs are selected for case study. The optimal joint operating rules with fairness not only encourage agents to participate in joint operation, but also increase average annual hydropower generation and the assurance rate of hydropower generation relative to those of the conventional operating rules. Furthermore, the proposed optimal operating rules with fairness are easier to implement in practice than the optimal joint rules. This indicates that the proposed method has potential for improving operating rules of a multi-reservoir system.     

“以电定水”模式下蓄能最大与耗能最小一致性研究

梯级蓄能最大与耗能最小是"以电定水"模式下常用的2个优化准则,它们追求目标的角度不同,但本质上是一致的。传统梯级蓄能最大、耗能最小准则未考虑水电站发电效率的影响,无法真实反映梯级水库的调度目标;并且两者采用时段平均值近似计算能量,导致蓄能最大与耗能最小出现了差异。鉴于此,首先引入能效系数来表征水电站对水能资源的利用能力,对传统准则进行了改进;其次在验证了改进梯级蓄能最大、耗能最小准则一致性的基础上,建立了梯级负荷分配蓄、耗能一致性模型;最后对堵河流域潘口、小漩梯级水库进行了实例计算。结果表明:改进的梯级蓄能最大、耗能最小准则完全一致,并且较传统准则能够更加真实地反映梯级水库的调度目标。所建模型较传统模型更优,能够为"以电定水"模式下的梯级水库优化调度提供更加有效的指导。     

水库群系统发电调度的合作博弈研究

水资源的竞争性和非排他性导致水库管理者基于个体利益进行发电调度,使得水库在满足个体利益的同时往往忽略了系统的整体效益。为了在保证个体利益的基础上实现系统总效益的最大化,建立了梯级水库群发电调度合作博弈模型;采用改进后的水循环算法对模型进行分层求解。以金沙江两库与三峡梯级构成的梯级水库群为研究对象,选取典型年进行实例计算。计算结果表明：梯级水库群发电调度的合作博弈模型在获得系统最大效益的同时使得个体利益达到Pareto最优状态,实现水库群总效益和单库个体效益的双赢,既优于联合优化调度模型又优于单库优化调度模型。该合作博弈模型及其新解法可为水库群调度决策分析开创一种新思路。     

Implementation and Comparison of Reservoir Operation Strategies for the Hoa Binh Reservoir, Vietnam using the Mike 11 Model

Hoa Binh is the largest reservoir in Vietnam. It has been operated since 1990 with the main purposes of flood control in the Red River basin and hydropower generation. Because these different purposes always cause conflicts and disputes during the flood season, it is desirable to improve the current operational regulations of the reservoir. In this paper, the operation rules of the reservoir are analysed by applying the Mike 11 river modelling tool. The model set up includes the main rivers and tributaries of the Red River basin and a logical decision tree defining the reservoir regulation. These strategies define the reservoir release as function of the time of the year, the actual reservoir stage, and the water level forecast at Hanoi. A data set consisting of twenty years of flood season data was used to evaluate the control strategies with respect to flood control and hydropower generation. The reservoir operation using the complete control system and the current as well as alternative regulation strategies has been evaluated and compared to the actual operation practice. Results showed that the implemented control system performs better than the actual operation. In addition, lowering the target downstream water level for flood control improves the operation with respect to both flood protection and hydropower generation. An alternative strategy where the target water level in the reservoir is increased can improve hydropower generation but at the expense of a reduced flood protection.     

A Study on the Large-scale System Decomposition—Coordination Method Used in Optimal Operation of a Hydroelectric System

Abstract

The optimal operation problem of multiple hydroelectric reservoir systems is very complex because of the large dimensions. Large-scale system decomposition-coordination methods, which can simplify complex problems into several interrelated sub-problems to avoid the “curse of dimensionality” and to obtain the global optimum on the global through coordination among sub-systems, is particularly well suited for optimizing large-scale, multi-reservoir systems. Applying this kind of theory and method, this paper studies and analyzes the problems of optimal operation of multiple hydroelectric reservoir systems in series, and sets up the optimal operation model of hydroelectric reservoir systems in series. On this basis, a practical example of two hydroelectric reservoirs in series on the upper reaches of the Yellow River in China is calculated and analyzed and the results are satisfactory. It is believed that applying this model can cut down the dimensions of the problem notably and that the theory and method are effective for real time operation.     

A Derivative-Free Hybrid Optimization Model for Short-Term Operation of a Multi-Objective Reservoir System Under Uncertainty

Short-term operation of a multi-objective reservoir system under inflow uncertainty has been receiving increasing attention, however, major challenges for the optimization of this system still remain due to the multiple and often conflicting objectives, highly nonlinear constraints and uncertain parameters in which derivative information may not be directly available. Population-based optimization methods do not rely on derivatives while generally have a slow convergence. This study presents a hybrid optimization model for short-term operation of multi-objective reservoirs under uncertainty that is derivative free and has a relatively fast convergence. The model incorporates a local improvement method called Mesh Adaptive Direct Search (MADS) into a population-based method NSGA-II and has no requirement for differentiability, convexity and continuity of the optimization problem. The operation of a multi-objective and multi-reservoir system on the Columbia River under inflow uncertainty is used as a case study. Overall, the hybrid model outperforms optimization models based on either the NSGA-II only or the MADS only. The model is intended for conditions where derivative information of the optimization problem is unavailable, which could have a wide array of applications in water resources systems.     

Deriving Optimal Refill Rules for Multi-Purpose Reservoir Operation

This paper focuses on deriving optimal refill rules for a multi-purpose reservoir, and aims to maximize utilization benefits under the condition of flood control safety. The entire flood season is divided into multiple sub-seasons (i.e. pre-flood season, main-flood season and post-flood season). By advancing the start of the refill period to the beginning of the post-flood season, seasonal design flows during the new refill period are estimated. A multi-objective refill operation model is proposed by combining flood control and conservation together. The simulation–optimization-test framework and hybrid multi-objective genetic algorithms are developed and used to optimize the rule curves. China’s Three Gorges Reservoir is selected as a case study and the application results show that the proposed model can increase the hydropower generation by 17.4%, decrease spilled water by 43.9%, and improve the refill probability greatly without decreasing the flood control standard and navigation probability during the refill period.