Generation of Clean Hydropower Energy in Multi-Reservoir Systems Based on a New Evolutionary Algorithm

Lingering droughts and shortage of water sources signify the importance of optimal utilization of water reservoirs such as multi-reservoir systems. These systems could be employed not only as a storage system to manage the water utilization but also as a power generation system. To rise the generated power besides the management of water utilization, an optimization algorithm should be used. In this study, the kidney algorithm in three different scenarios, namely the wet, normal, and dry years is employed to fulfill such an engineering operation in a four-reservoir system in China. Simulations show well compatibility of the water level inside the reservoir with real statistical indices in terms of RMSE and MAE. Results also reveal that using the kidney algorithm not only reduces the required calculation but also increases the convergence pace with respect to other algorithms that have been used (bat, shark, abundance of particles, and genetic algorithms). Moreover, it increases the amount of the generated energy by a factor of 2.2–3.2 with respect to the aforementioned algorithms. Results indicate the capability of the kidney algorithm in the management of water sources and engineering operations.

     

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.     

Large Scale Reservoirs System Operation Optimization: the Interior Search Algorithm (ISA) Approach

Reservoirs are built to provide a powerful tool to control and manage surface water resources in order to cover inconsistency between water resources and demands. Due to finite available water and the increasing demands for water especially in arid and semi-arid regions like Iran, reservoirs must be optimally operated in order to use water in the most efficient way. This study applies the Interior Search Algorithm (ISA) to solve large scale reservoirs system operation optimization problems. The ISA is a meta-heuristic algorithm inspired from a systematic methodology of architecture process and mirror work utilized by Persian designers for decoration. Unlike other meta-heuristic algorithms, the ISA just have one parameter to tune which is a great advantage. In this study the parameter of the ISA tuned automatically using a linear equation. A real-world one-reservoir operation problem (i.e. Karun-4) and two large scale benchmark problems (i.e. four-reservoir and ten-reservoir operation problem) were employed to show the effectiveness of the ISA. The results shows the high ability of the ISA to solve reservoirs system operation problems as it achieved solutions 99.97, 99.99 and 99.95 % of global optimum for Karun-4 reservoir, four-reservoir and ten-reservoir system operation problems, respectively. These results are the best results reported so far in the studied problems. Comparing results of the ISA with those of non-linear programming (NLP), linear programming (LP), genetic algorithm (GA) and other meta-heuristic algorithms indicates fast convergence to global optimum. Considering the results, it can be stated that the ISA is a powerful tool to optimize complex large scale reservoir system operation problems.     

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.     

Artificial Life Algorithm for Management of Multi-reservoir River Systems

The design and operation of civil engineering systems, particularly water resources systems, has been pursued from the perspective of minimizing costs and related negative impacts, maximizing benefits, or a combination thereof. Due to the complex, nonlinear nature of the majority of systems, together with an increase in digital computing capabilities, global search algorithms are becoming a common means of meeting these objectives. This paper employs an artificial life algorithm, derived from the artificial life paradigm. The algorithm is evaluated using standard optimization test functions and is subsequently applied to determine optimal dam operations in multi-reservoir river systems. The optimal dam operation scheme is that which indirectly minimizes environmental impacts caused by short-term water level fluctuations. Optimal releases are sought by coupling an artificial life algorithm with FLDWAV, a one-dimensional, steady flow simulation model. The resulting multi-reservoir management model is successfully applied to a portion of the Illinois River Waterway.     

The Enhanced Honey-Bee Mating Optimization Algorithm for Water Resources Optimization

Evolutionary and meta-heuristic algorithms are widely used to solve water resources optimization problems. In this context, the honey bee mating optimization (HBMO) algorithm, inspired by the mating ritual of honey bees, is a reliable and efficient algorithm. The HBMO algorithm is modified in this work leading to the Enhanced HBMO (EHBMO) algorithm. The EHBMO is then applied to solve several unconstrained/constrained mathematical benchmark functions and a multi-reservoir problem. The performance of the EHBMO is compared with those of the elitist genetic algorithm (EGA) and the HBMO algorithm. The results show that the EHBMO achieves a better solution in a smaller number of functional evaluations and with less variance of results about global optima in comparison with the EGA and the HBMO algorithm.     

An Improved Genetic Algorithm-Simulated Annealing Hybrid Algorithm for the Optimization of Multiple Reservoirs

A hybrid evolutionary search algorithm is developed to optimize the classical single-criterion operation of multi-reservoir systems. The proposed improved genetic algorithm-simulated annealing (IGA-SA) which combines genetic algorithms (GAs) and the simulated annealing (SA) is a new global optimization algorithm. The algorithm is capable of overcoming the premature convergence of GAs and escaping from local optimal solutions. In addition, it is faster than a traditional unimproved GA-SA algorithm. A case study of optimization operation on generation electricity of a 3-reservoir system in series over 41-year (from May 1940 to April 1981) time periods in Wujiang River, one branch of Yangtze River in China, was performed. The objective is to maximize generation output from the system over each 12-month operating periods. Trade-off analyses on binary coding representation and real-value coding representation of GAs are performed. Sensitivity to some parameters of the GA, the SA and the IGA-SA is analyzed, respectively, and the appropriate values of parameters are suggested. The performance of the proposed algorithm is compared with that of the existing genetic algorithm, the simulated annealing and the dynamic programming (DP). Results demonstrate that the GA is better than the DP, the SA performs better than the GA and the IGA-SA is more efficient than SA. The IGA-SA produces higher quality solutions and costs less computation time compared with the traditional GA-SA. The results obtained from these applications have proved that the IGA-SA has the ability of addressing large and complex problems and is a new promising search algorithm for multi-reservoir optimization problems.     

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.     

Intelligent Systems in Optimizing Reservoir Operation Policy: A Review

The paper presents a survey of several optimization techniques, mainly artificial intelligences (AIs) which have been applied to the reservoir operation modelling whether its single or multi-reservoir system. The reservoir system modeling is essential for any nations and the optimal use of it is always asked. The main objective of this review article is to discuss the potentiality of the evolutionary algorithms (EAs) and the ability to integrate with other techniques which can provide the best results. Also the formulation of these types of application has described on the ground of a well known benchmark problem regarding this field. The traditional algorithms got some drawbacks. The study provides a complete understanding to the EA users about next generation optimal search procedure and help to overcome the drawbacks. Though the background of application number of swarm intelligences is less comparatively than the genetic algorithm (GA), it provides a great scope for the researcher for further development. Also comparative results with other popular methods (such as, linear programming, stochastic dynamic programming) are discussed on the basis of past research results. Conclusions and suggestive remarks are made for the help of researchers and the reservoir decision makers as well.     

An Improved Continuous Ant Algorithm for Optimization of Water Resources Problems

Ant colony optimization was initially proposed for discrete search spaces while in continuous domains, discretization of the search space has been widely practiced. Attempts for direct extension of ant algorithms to continuous decision spaces are rapidly growing. This paper briefly reviews the central idea and mathematical representation of a recently proposed algorithm for continuous domains followed by further improvements in order to make the algorithm adaptive and more efficient in locating near optimal solutions. Performance of the proposed improved algorithm has been tested on few well-known benchmark problems as well as a real-world water resource optimization problem. The comparison of the results obtained by the present method with those of other ant-based algorithms emphasizes the robustness of the proposed algorithm in searching the continuous space more efficiently as locating the closest, among other ant methods, to the global optimal solution.     

Optimal Operation of Reservoir Systems using Simulated Annealing

A stochastic search technique, simulated annealing (SA), is used to optimize the operation of multiple reservoirs. Seminal application of annealing technique in general to multi-period, multiple-reservoir systems, along with problem representation and selection of different parameter values used in the annealing algorithm for specific cases is discussed. The search technique is improved with the help of heuristic rules, problem-specific information and concepts from the field of evolutionary algorithms. The technique is tested for application to a benchmark problem of four-reservoir system previously solved using a linear programming formulation and its ability to replicate the global optimum solution is examined. The technique is also applied to a system of four hydropower generating reservoirs in Manitoba, Canada, to derive optimal operating rules. A limited version of this problem is solved using a mixed integer nonlinear programming and results are compared with those obtained using SA. A better objective function value is obtained using simulated annealing than the value from a mixed integer non-linear programming model developed for the same problem. Results obtained from these applications suggest that simulated annealing can be used for obtaining near-optimal solutions for multi-period reservoir operation problems that are computationally intractable.     

Coupled Operating Rules for Optimal Operation of Multi-Reservoir Systems

Due to the complexity of multi-reservoir system operation problems, researchers usually prefer to assume lumped demands located downstream of such systems. Consequently, distributed local demands through the system are neglected or supplied completely (e.g. using Standard operating policy, SOP), in order to simplify the problem. In this study, Coupled Operating Rules (COR) as a simple and suitable operating policy is applied for optimal operation of multi-reservoir systems with local demands. The applied policy includes two types of linear rules, which are defined to determine total releases and local water allocations in decision points. This policy is adopted within a simulation-optimization approach to optimally operate a three-reservoir system in the Karkheh river basin. Obtained results indicate that the proposed strategy reduces the intensity of demand deficits and distributes the occurred shortages throughout the system properly. Moreover, the system losses are managed appropriately and big unbalanced local shortages are prevented. Although COR strategy decreases the reliability of local demands compared to SOP, it is a reasonable operating policy for systems with distributed local demand sites. Moreover, in this study an effective Improved Melody Search (IMeS) algorithm is proposed to achieve the optimum values of operating rules’ parameters. The efficiency of the optimization method is compared to the results achieved by other selected well-known heuristic search methods. Based on the experimental results, it is revealed that the proposed algorithm is more effective in finding precise solutions over a long-term period, comparing with the other conventional algorithms.     

Optimization of Multi-Reservoir Operating Rules for a Water Supply System

To obtain the optimal releases of the multi-reservoir system, two sets of joint operating rules (JOR-I and JOR-II) are presented based on the aggregation-disaggregation approach and multi-reservoir approach respectively. In JOR-I, all reservoirs are aggregated to an equivalent reservoir, the operating rules of which, the release rule of the system is optimized following operating rule curves coupled with hedging rules. Then the system release is disaggregated into each reservoir according to water supply priorities and the dynamic demand partition approach. In JOR-II, a two-stage demand partition approach is applied to allocate the different demand priorities to determine the release from each reservoir. To assess the reliability and effectiveness of the joint operating rules, the proposed rules are applied to a multi-reservoir system in Liaoning province of China. Results demonstrate that JOR-I is suitable for high-dimensional multi-reservoir operation problems with large-scale inflow data, while JOR-II is suitable for low-dimensional multi-reservoir operation problems with small-scale inflow data, and JOR-II performs better than JOR-I but requires more computation time. The research provides guidelines for the management of multi-reservoir system.     

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.     

跨流域水库群最优调供水过程耦合研究

为了有效描述和求解跨流域水库群最优调供水过程,本文建立了基于0-1规划方法的水库群最优化调度模型,统一考虑并最终确定了最优调供水过程。为减少模型单次求解的变量数目,同时增加算法全局搜索的能力,本文借用逐步优化算法思想,对传统粒子群进行改进,提出了逐步优化粒子群算法(PRA-PSO)对模型进行求解。最后,通过中国北方某大型跨流域调水工程的实例研究分析了模型的合理性和有效性。最优调供水过程的确定不仅可为采用隐随机优化方法确定跨流域水库群调水规则和供水规则提供最优化样本过程,而且对跨流域调水工程调度运行评价具有重要意义。     

基于聚集度自适应反向学习粒子群算法在水库优化调度中的应用

为高效、快速求解水库优化调度问题,提出基于聚集度自适应反向学习粒子群算法。此算法首先采用聚集度策略分析种群的聚散状态,并在此基础上,提出自适应反向学习策略,生成种群中心的反向解参与进化,引导种群改变聚散状态,进一步平衡算法的勘探与开发能力。将基于聚集度自适应反向学习粒子群算法与经典的和最新的高水平粒子群算法进行比较,在所测的基准函数中,本算法在5个基准函数上都取得最优解,验证了其对连续变量函数的优化能力强于所对比算法。在求解水布垭、隔河岩和高坝洲梯级水库优化调度问题上,本算法求得总发电量为86.335 71×10~8 kW·h,求解所需时间为721 ms,相较所对比算法的调度结果,总发电量最大提高了11.860 2×10~8 kW·h,所需计算时间最大降低了21 380 ms,由此验证了基于聚集度自适应反向学习粒子群算法对水库优化问题的可行性。     

长江上游控制性水库群联合调度及水资源影响分析

针对长江上游控制性水库群联合调度问题,建立了大规模混联水库群联合优化调度模型,并提出离散微分动态规划(DDDP)和逐步优化算法(POA)相结合的混合方法,实现大规模混联梯级水库群联合优化调度问题的高效求解。在此基础上,结合流域长系列历史径流资料,进行了长江上游控制性梯级水库群调度模拟,分析了联合调度的发电效益;并在此基础上,结合相关研究成果,探究并分析了梯级水库群建成投运后,联合调度对流域水资源的影响。成果表明,梯级水库群的建成及联合调蓄对于长江中下游枯水期的流量补偿效益十分明显,供水、航运以及压咸补淡等综合效益十分显著。     

跨流域水库群最优调供水过程耦合研究

为了有效描述和求解跨流域水库群最优调供水过程,本文建立了基于0-1规划方法的水库群最优化调度模型,统一考虑并最终确定了最优调供水过程。为减少模型单次求解的变量数目,同时增加算法全局搜索的能力,本文借用逐步优化算法的思想,对传统粒子群进行改进,提出了逐步优化粒子群算法（PRA-PSO）对模型进行求解。最后,通过中国北方某大型跨流域调水工程的实例研究分析了模型的合理性和有效性。最优调供水过程的确定不仅可为采用隐随机优化方法确定跨流域水库群调水规则和供水规则提供最优化样本过程,而且对跨流域调水工程调度运行评价具有重要意义。     

Improved particle swarm optimization algorithm for multi-reservoir system operation

In this paper, a hybrid improved particle swarm optimization (IPSO) algorithm isproposed for the optimization of hydroelectric power scheduling in multi-reservoir systems. The conventional particle swarm optimization (PSO) algorithm is improved in two ways: (1) The linearly decreasing inertia weight coefficient (LDIWC) is replaced by a self-adaptive exponential inertia weight coefficient (SEIWC), which could make the PSO algorithm more balanceable and more effective in both global and local searches. (2) The crossover and mutation idea inspired by the genetic algorithm (GA) is imported into the particle updating method to enhance the diversity of populations. The potential ability of IPSO in nonlinear numerical function optimization was first tested with three classical benchmark functions. Then, a long-term multi-reservoir system operation model based on IPSO was designed and a case study was carried out in the Minjiang Basin in China,where there is a power system consisting of 26 hydroelectric power plants. The scheduling results of the IPSO algorithm were found to outperform PSO and to be comparable with the results of the dynamic programming successive approximation (DPSA) algorithm.     

Simulation with RBF Neural Network Model for Reservoir Operation Rules

Reservoirs usually have multipurpose, such as flood control, water supply, hydropower and recreation. Deriving reservoirs operation rules are very important because it could help guide operators determine the release. For fulfilling such work, the use of neural network has presented to be a cost-effective technique superior to traditional statistical methods. But their training, usually with back-propagation (BP) algorithm or other gradient algorithms, is often with certain drawbacks. In this paper, a newly developed method, simulation with radial basis function neural network (RBFNN) model is adopted. Exemplars are obtained through a simulation model, and RBF neural network is trained to derive reservoirs operation rules by using particle swarm optimization (PSO) algorithm. The Yellow River upstream multi-reservoir system is demonstrated for this study.