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.     

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.     

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.     

Sustainable Basin-Scale Water Allocation with Hydrologic State-Dependent Multi-Reservoir Operation Rules

This study extends the PSO-MODSIM model, integrating particle swarm optimization (PSO) algorithm and MODISM river basin decision support system (DSS) to determine optimal basin-scale water allocation, in two aspects. The first is deriving hydrologic state-dependent (conditional) operating rules to better account for drought and high-flow periods, and the second is direct, explicit consideration of sustainability criteria in the model’s formulation to have a better efficiency in basin-scale water allocation. Under conditional operating rules, the operational parameters of reservoir target storage levels and their priority rankings were conditioned on the hydrologic state of the system in a priority-based water allocation scheme. The role of conditional operating rules and policies were evaluated by comparing water shortages associated with objective function values under unconditional and conditional operating rules. Optimal basin-scale water allocation was then evaluated by incorporating reliability, vulnerability, reversibility and equity sustainability indices into the PSO objective function. The extended model was applied for water allocation in the Atrak River Basin, Iran. Results indicated improved distribution of water shortages by about 7.5% using conditional operating rules distinguishing dry, normal and wet hydrologic states. Alternative solutions with nearly identical objective function values were found with sustainability indices included in the model.     

Investigation of a New Hybrid Optimization Algorithm Performance in the Optimal Operation of Multi-Reservoir Benchmark Systems

Water Resources Management - Reservoirs’ optimal operation is a critical issue in the management of surface water resources. In the present study, after combining the whale optimization...     

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.     

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.     

Optimizing Multiple Linear Rules for Multi-Reservoir Hydropower Systems Using an Optimization Method with an Adaptation Strategy

Water Resources Management - Water resources crisis has a significant impact on hydropower energy production, which highlights the importance of water resources management. Reservoirs are effective...     

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.     

Evaluation of Real-Time Operation Rules in Reservoir Systems Operation

Reservoir operation rules are logical or mathematical equations that take into account system variables to calculate water release from a reservoir based on inflow and storage volume values. In fact, previous experiences of the system are used to balance reservoir system parameters in each operational period. Commonly, reservoir operation rules have been considered to be linear decision rules (LDRs) and constant coefficients developed by using various optimization procedures. This paper addresses the application of real-time operation rules on a reservoir system whose purpose is to supply total downstream demand. Those rules include standard operation policy (SOP), stochastic dynamic programming (SDP), LDR, and nonlinear decision rule (NLDR) with various orders of inflow and reservoir storage volume. Also, a multi-attribute decision method, elimination and choice expressing reality (ELECTRE)-I, with a combination of indices, objective functions, and reservoir performance criteria (reliability, resiliency, and vulnerability) are used to rank the aforementioned rules. The ranking method employs two combinations of indices: (1) performance criteria and (2) objective function and performance criteria by using the same weights for all criteria. Results show that the NLDR gives an appropriate rule for real-time operation. Moreover, NLDR validation is presented by testing predefined curves for dry, normal, and wet years.     

Rules for Optimal Operation of Reservoir-River-Groundwater Systems Considering Water Quality Targets: Application of M5P Model

The aim of this paper is to develop rules for optimal reservoir operation and water withdrawal from river and aquifer considering water supply and pollution control targets. The general approach is making use of an integrated water quantity-quality management (IWQM) modeling in conjunction with accurate data mining techniques. The IWQM model generates data, including; optimal releases and water withdrawal from river and aquifer for different conditions, and M5P and Support Vector Regression (SVR) data mining models utilize the results of the IWQM model for the derivation of rules. The IWQM model minimizes the deviation from water supply and water quality targets during the planning horizon. This method for derivation of operating rules is applied to a real world case study, Zayandehrood system, in Iran, with serious water supply and water pollution problems. The IWQM model is analyzed for different hydrologic and water demands scenarios with total dissolved solids (TDS) as the water quality indicator. Results show that an integrated approach to reservoir-river-aquifer operation in the study area can reduce the TDS by 43 % in the downstream river.     

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.     

Genetic Algorithms for Optimal Operation of Soil Aquifer Treatment Systems

The genetic algorithm (GA) is a nonconventional search technique which is patterned after the biological processes of natural selection and evolution. It has the ability to search large and complex decision spaces and handle nonconvexities. In this paper, the genetic algorithm is investigated and applied to solve the optimal operation problem of soil aquifer treatment (SAT) systems. This problem involves finding optimal water application time and drying time which maximize infiltration for a predetermined starting influent rate of waste water and subject to various physical and operational constraints. A new scaling method is developed and some improvements on the evolution procedure are presented. A comprehensive GA–SAT computer model was developed and applied to an example SAT problem. The results are encouraging, when compared with using the successive approximation linear quadratic regulator algorithm. It was found that genetic algorithms are easy to program and interface with large complicated simulators.     

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.     

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.     

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.     

Deriving Hedging Rules of Multi-Reservoir System by Online Evolving Neural Networks

This paper presents an online optimization scheme for combined use of Artificial Neural Networks (ANN), hedging policies and harmony search algorithm (HS) in developing optimum operating policies for Tehran water resources system. Past efforts in this area are concentrated on using an offline approach. In that approach, an optimization method is first used to derive a long-term set of optimum reservoir releases. These releases are then used as the target vector for training the ANN model. The online method simultaneously uses the optimization and ANN methods and can adopt objective functions other than minimizing the error indices. Therefore, it requires methods other than the backpropagation for training the ANN model. Hence, under the proposed online approach the application of a heuristic method, such as HS, is inevitable for training the network. This is accomplished by using an optimization-simulation procedure where different objective functions and system constraints could be easily handled. The proposed approach is a novel and efficient method for finding the parameters of hedging policies where earlier methods suffered from high computational costs and the curse of dimensionality. The results show the superiority of the proposed online scheme. Moreover, a surrogate model for the hedging policy is presented, which by adhering to the principle of parsimony is more efficient in large scale systems involving many decision variables.     

Decision Tree-Based Conditional Operation Rules for Optimal Conjunctive Use of Surface and Groundwater

Water Resources Management - Conjunctive use (CU) of surface water (SW) and groundwater (GW) implies the optimal operation of water resources to reduce the negative effects compared to when each of...     

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.     

Reducing Irrigation Deficiencies Based Optimizing Model for Multi-Reservoir Systems Utilizing Spider Monkey Algorithm

Continuous droughts and water scarcity have led to the need for optimal exploitation of dams’ reservoirs. Thus, the new meta-heuristic algorithm, spider monkey, is suggested for complex modeling of the multi-reservoir system in Iran with the aim of decreasing irrigation deficiencies. Golestan and Voshmgir dams’ operations are optimized with the spider monkey algorithm. The algorithm based on the exchange of information between local and global leaders with the other monkeys which improves the convergence speed. Average deficiencies for Golestan dam is computed as 2.1 and 1.9 MCM by spider monkey algorithm while it is respectively computed as 6.7, 16.4, 11.1, 4.1, 14.6, 19 MCM by particle swarm algorithm, harmony search algorithm, imperialist competitive algorithm, water cycle algorithm, genetic algorithm, and standards operation policy method. Also, the computation time of the spider monkey algorithm is 50 and 47 s for the Golestan and Voshmgir dams while the genetic algorithm optimizes the problem in 172.6 s and 112 s and the particle swarm algorithm needs 117.4 s and 100 s for the Golestan and Voshmgir, respectively. Also, root means square error (RMSE) and mean absolute error between demand and released water for the spider monkey algorithm have the least values among the applied evolutionary algorithms. Thus, the spider monkey algorithm is suggested as an appropriate method for optimizing the operation policy for the dam and reservoir systems.