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.     

Multi-Colony Ant Algorithm for Continuous Multi-Reservoir Operation Optimization Problem

Ant Colony Optimization (ACO) algorithms are basically developed for discrete optimization and hence their application to continuous optimization problems require the transformation of a continuous search space to a discrete one by discretization of the continuous decision variables. Thus, the allowable continuous range of decision variables is usually discretized into a discrete set of allowable values and a search is then conducted over the resulting discrete search space for the optimum solution. Due to the discretization of the search space on the decision variable, the performance of the ACO algorithms in continuous problems is poor. In this paper a special version of multi-colony algorithm is proposed which helps to generate a non-homogeneous and more or less random mesh in entire search space to minimize the possibility of loosing global optimum domain. The proposed multi-colony algorithm presents a new scheme which is quite different from those used in multi criteria and multi objective problems and parallelization schemes. The proposed algorithm can efficiently handle the combination of discrete and continuous decision variables. To investigate the performance of the proposed algorithm, the well-known multimodal, continuous, nonseparable, nonlinear, and illegal (CNNI) Fletcher–Powell function and complex 10-reservoir problem operation optimization have been considered. It is concluded that the proposed algorithm provides promising and comparable solutions with known global optimum results.     

Optimal Operation of Hydropower Reservoir Systems Using Weed Optimization Algorithm

The optimal hydropower operation of reservoir systems is known as a complex nonlinear nonconvex optimization problem. This paper presents the application of invasive weed optimization (IWO) algorithm, which is a novel evolutionary algorithm inspired from colonizing weeds, for optimal operation of hydropower reservoir systems. The IWO algorithm is used to optimally solve the hydropower operation problems for both cases of single reservoir and multi reservoir systems, over short, medium and long term operation periods, and the results are compared with the existing results obtained by the two most commonly used evolutionary algorithms, namely, particle swam optimization (PSO) and genetic algorithm (GA). The results show that the IWO is more efficient and effective than PSO and GA for both single reservoir and multi reservoir hydropower operation problems.     

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.     

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.

     

Multi-Reservoir System Optimization Based on Hybrid Gravitational Algorithm to Minimize Water-Supply Deficiencies

The growing prevalence of droughts and water scarcity have increased the importance of operating dam and reservoir systems efficiently. Several methods based on algorithms have been developed in recent years in a bid to optimize water release operation policy, in order to overcome or minimize the impact of droughts. However, all of these algorithms suffer from some weaknesses or drawbacks – notably early convergence, a low rate of convergence, or trapping in local optimizations – that limit their effectiveness and efficiency in seeking to determine the global optima for the operation of water systems. Against this background, the present study seeks to introduce and test a Hybrid Algorithm (HA) which integrates the Gravitational Search Algorithm (GSA) with the Particle Swarm Optimization Algorithm (PSOA) with the goal of minimizing irrigation deficiencies in a multi-reservoir system. The proposed algorithm was tested for a specific important multi-reservoir system in Iran: namely the Golestan Dam and Voshmgir Dam system. The results showed that applying the HA could reduce average irrigation deficiencies for the Golestan Dam substantially, to only 2 million cubic meters (MCM), compared to deficiency values for the Genetic Algorithm (GA), PSOA and GSA of 15.1, 6.7 and 5.8 MCM respectively. In addition, the HA performed very efficiently, reducing substantially the computational time needed to achieve the global optimal when compared with the other algorithms tested. Furthermore, the HA showed itself capable of assuring a high volumetric reliability index (VRI) to meet the pattern of water demand downstream from the dams, as well as clearly outperforming the other algorithms on other important indices. In conclusion, the proposed HA seems to offer considerable potential as an optimizer for dam and reservoir operations world-wide.

     

Optimal Allocation of Flood Control Capacity for Multi-Reservoir Systems Using Multi-Objective Optimization Approach

Operation of multi-reservoir systems during flood periods is of great importance in the field of water resources management. This paper proposes a multi-objective optimization model with new formulation for optimal operation of multi-reservoir systems. In this model, the release rate and the flood control capacity of each reservoir is considered as decision variable and the resulting nonlinear non-convex multi-objective optimization problem is solved with ε-constraint method through the mixed integer linear programming (MILP). Objective functions of the model are minimizing the flood damage at downstream sites and the loss of hydropower generation. The developed model is used to determine optimal operating strategies for Karkheh multi-reservoir system in southwestern Iran. For this purpose, the model is executed in two scenarios based on “two-reservoir” and “six-reservoir” systems and for floods with return periods of 25 and 50 years. The results show that in two-reservoir system, flood damage is at least about 114 million dollars and cannot be mitigated any further no matter how hydropower generation is managed. But, in the case of developing all six reservoirs, optimal strategies of coordinated operation can mitigate and even fully prevent flood damage.     

Simulation and Optimization of Multi-Reservoir Operation in Inter-Basin Water Transfer System

Inter-basin water transfer projects are usually considered as one of the most effective facilities to balance the non-uniform temporal and spatial distribution of water resources and water demands by diverting water from surplus to deficient area. However, the operation of these projects are always daunting, especially for projects with multi-donor reservoirs but only one recipient reservoir. In this study, a set of water transfer rule curves are firstly proposed to determine when, where and how much water should be diverted from each donor reservoir. In addition, a simulation-optimization model with the objective to minimize both water shortage risk and vulnerability is established to derive the optimal operation rule curves. Following that, the new transfer rules are applied to provide guidelines for the operation of a water transfer-supply project with two donor reservoirs in central China. The effects of water diversion on each reservoir are evaluated under different scenarios including no diversion, diversion from the donor reservoir with relatively sufficient water, diversion from the donor reservoir with relatively limited water, and diversion from both donor reservoirs. The results show the advantages of improving the performance of whole water diversion system and demonstrate the feasibility of the proposed approach.     

Performance of the Equivalent Reservoir Modelling Technique for Multi-Reservoir Hydropower Systems

This paper investigates the validity of a simplified equivalent reservoir representation of a multi-reservoir hydroelectric system for modelling its optimal operation for power maximization. This simplification, proposed by Arvanitidis and Rosing (IEEE Trans Power Appar Syst 89(2):319–325, 1970), imputes a potential energy equivalent reservoir with energy inflows and outflows. The hydroelectric system is also modelled for power maximization considering individual reservoir characteristics without simplifications. Both optimization models employed MINOS package for solution of the non-linear programming problems. A comparison between total optimized power generation over the planning horizon by the two methods shows that the equivalent reservoir is capable of producing satisfactory power estimates with less than 6% underestimation. The generation and total reservoir storage trajectories along the planning horizon obtained by equivalent reservoir method, however, presented significant discrepancies as compared to those found in the detailed modelling. This study is motivated by the fact that Brazilian generation system operations are based on the equivalent reservoir method as part of the power dispatch procedures. The potential energy equivalent reservoir is an alternative which eliminates problems with the dimensionality of state variables in a dynamic programming model.     

Multi-Reservoir Operation Planning Using Hybrid Genetic Algorithm and Linear Programming (GA-LP): An Alternative Stochastic Approach

Many models have been suggested to deal with the multi-reservoir operation planning stochastic optimization problem involving decisions on water releases from various reservoirs in different time periods of the year. A new approach using genetic algorithm (GA) and linear programming (LP) is proposed here to determine operational decisions for reservoirs of a hydro system throughout a planning period, with the possibility of considering a variety of equally likely hydrologic sequences representing inflows. This approach permits the evaluation of a reduced number of parameters by GA and operational variables by LP. The proposed algorithm is a stochastic approximation to the hydro system operation problem, with advantages such as simple implementation and the possibility of extracting useful parameters for future operational decisions. Implementation of the method is demonstrated through a small hypothetical hydrothermal system used in literature as an example for stochastic dual dynamic programming (SDDP) method of Pereira and Pinto (Pereira, M. V. F. and Pinto, L. M. V. G.: 1985, Water Res. Res. 21(6), 779–792). The proposed GA-LP approach performed equally well as compared to the SDDP method.     

Application of the Grasshopper Optimization Algorithm (GOA) to the Optimal Operation of Hydropower Reservoir Systems Under Climate Change

Hydropower is a low-carbon energy source, which may be adversely impacted by climate change. This work applies the Grasshopper Optimization Algorithm (GOA) to optimize hydropower multi-reservoir systems. Performance of GOA is compared with that of particle swarm optimization (PSO). GOA is applied to hydropower, three-reservoir system (Seymareh, Sazbon, and Karkheh), located in the Karkheh basin (Iran) for baseline period 1976–2005 and two future periods (2040–2069) and (2070–2099) under greenhouse gases pathway scenarios RCP2.6, RCP4.5, and RCP8.5. GOA minimizes the shortage of hydropower energy generation. Results from GOA optimization of Seymareh reservoir show that average objective function in baseline is 85 and minimum value of average objective function in 2040–2069 would be under RCP2.6 (equal to 0.278). Optimization of Seymareh-reservoir based on PSO shows that average value of objective function in baseline is less (that is, better) than value obtained with GOA (10.953). Optimization results for two-reservoir system (Sazbon and Karkheh) based on GOA optimization show that objective function in baseline is 5.44 times corresponding value obtained with PSO, standard deviation is 2.3 times that calculated with PSO, and run-time is 1.5 times PSO’s. Concerning three-reservoir systems it was determined that objective function based on PSO had the best value (the lowest energy deficit), especially in future. GOA converges close to the best objective function, especially in future-periods optimization, and convergence to solutions is more stable than PSO’s. A comparison of performance of GOA and PSO indicates PSO converges faster to optimal solution, and produces better objective function than GOA.

     

混沌蚁群算法在水库优化调度中的应用

提出一种基于混沌优化算法和蚁群算法相结合的混合算法,在求解水库优化调度问题的方法。根据混沌变量的随机性和遍历性,利用混沌变量进行优化搜索,从而有效地克服了蚁群算法存在的效率低、易于演化停滞及陷入局部最优等问题。又利用蚁群算法信息素正反馈的优点,改善了混沌搜索的盲目性,提高了搜索的效率。通过实例计算,结果表明该算法具有效率高及较强的全局寻优能力。     

New Methodology for Optimal Operation of Soil Aquifer Treatment Systems

A new methodology is presented in thisarticle for computing the optimal operation of soilaquifer treatment systems. The mathematical problemis stated as a discrete-time optimal control problemto maximize infiltration subject to various physicaland operation constraints. The methodology is basedupon solving the discrete-time optimal control problemusing a successive approximation linear quadraticregulator interfaced with a simulator. Theunsaturated flow model HYDRUS is modified to simulatethe water content distribution, the infiltrationprocess, and the draining process. A penalty functionmethod is used to treat the bound constraints on thewater content and the cycle time. Sample problems aregiven to illustrate the capability of the model tosolve the optimal operation of soil aquifer treatment systems.     

Investigation of Rainfall Forecast System Characteristics in Real-Time Optimal Operation of Urban Drainage Systems

This study investigates the role of rainfall forecast system characteristics in predictive real-time optimal operation (PRTOP) of urban drainage systems (UDSs). A simulation-optimization model is proposed integrating the stormwater management rainfall-runoff simulator, the harmony search optimization algorithm, and a rainfall forecasting module. This module generates different rainfall forecast scenarios depending on the forecast (time) horizon (FH) and the forecast type (perfect or imperfect). Five adaptive PRTOP models are compared to evaluate the relationships between the FH, forecast type, and the system’s relative regulating capacity (SRRC). The models are tested in a part of UDS of Tehran, capital of Iran. Results indicate that for the studied system, perfect knowledge of future rainfall is more beneficial for a specific range of the SRRC, equal to 80–90% of its upper bound. Besides, the performance of the PRTOP model improves with increasing the FH up to a certain point, and then having no further positive effect. Finally, the PRTOP model equipped with a hypothetical forecasting model where the forecast error is a nonlinear function of the forecast lead time still performs better than both a zero-FH reactive RTOP model and short forecast horizon PRTOP models.

     

A Novel Optimization Method for Multi-Reservoir Operation Policy Derivation in Complex Inter-Basin Water Transfer System

Joint operation of multiple reservoir system in inter-basin water transfer-supply project is a complex problem because of the complicated structure and cooperated operation policy. The combination of high-dimensional, multi-peak and multiple constraints makes it incredibly difficult to obtain the optimal rule curves for multi-reservoir operation. In view of this, we constructed a joint optimization operation model, considering both water supply and transfer, and proposed the concept of “shape constraints”. To obtain the solution of this high-dimensional optimization model, a novel progressive optimum seeking method, namely Progressive Reservoir Algorithm-Particle Swarm Optimization (PRA-PSO), is presented based on the nature of progressive optimization algorithm (POA) and standard particle swarm optimization (PSO). The water transfer project in northeast China, consisting of three routes eight reservoirs, is selected as a case study. The results show that (1) PRA-PSO is yielding much more promising results when compared with other optimization techniques; (2) shape constraints would narrow the scope of feasible solution area but increase the convergence of algorithm; (3) because of the strong interaction between water transfer and water supply action, the progressive setting of PRA-PSO should be in accordance with the order of reservoir water transfer. The case study indicates the novel optimization method could effectively increase the chance of jumping out of local optimal points, thereby searching for better solutions.     

Optimization of Reservoir Operation with a New Approach in Evolutionary Computation Using TLBO Algorithm and Jaya Algorithm

Reservoir operation and management are complex engineering problems, due to the stochastic nature of inflow, various demands and as well as tailwater in the downstream. The complexity increases when the number of reservoirs gets increased such as multi-reservoir system or chain system. To obtain optimal operation in such condition become more difficult. It requires powerful optimization algorithm to solve aforesaid problems. Teaching Learning Based Optimization (TLBO) algorithm and Jaya Algorithm (JA) are recently developed advanced optimization techniques a novel approach comparatively simple, easy, and robust. The main advantages of these algorithms are it only requires the common control parameters such as number of iterations and population size. In the present study, three different benchmark problems were evaluated to check the applicability and performance of TLBO and JA in multi-reservoir operation problems. The benchmark problems are the discrete time four-reservoir operation (DFRO), the continuous time four-reservoir operation (CFRO), and the ten-reservoir operation (TRO). The results from the TLBO and JA are compared with different approaches from the literature. The optimal net benefits obtained from JA for DFRO, CFRO and TRO problems are 401.44, 308.40 and 1194.59, respectively, and that of TLBO algorithm are 401.33, 308.30 and 1194.44, respectively. It is found that both JA and TLBO algorithms provided a satisfactory solution as other optimization techniques, from literature. In conclusion, JA outperformed over TLBO.     

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.     

改进粒子群优化算法在水电站群优化调度中的应用研究

针对常规粒子群优化算法易早熟，后期收敛慢且易陷入局部最优解的不足，提出一种新的惯性权重系数更新策略—自适应指数惯性权重系数（SEIWC）代替线性递减惯性权重系数（LDIWC），同时，将遗传算法中的染色体交叉、变异思想引入粒子的更新策略，提高粒子的多样性，增强算法的全局搜索能力。使用Rosenbrock函数和Schaffer函数验证了改进粒子群优化算法的有效性。以福建电网闽江流域水电站群优化调度为例，建立基于改进粒子群优化算法的库群长期优化调度模型，计算结果表明，该模型的调度结果显著优于常规粒子群优化算法，与逐步优化算法获得的结果达到相当水平。     

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.     

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.