A STOCHASTIC DYNAMIC PROGRAMMING MODEL FOR THE OPTIMUM OPERATION OF A MULTI-PURPOSE RESERVOIR1

ABSTRACT: The main objective of this paper is to present a stockastic dynamic programming model useful in determining the optimal operating policy of a single multipurpose surface reservoir. It is the unreliability of forecasting the amount of future streamflow which makes the problem of a reservoir operation a stochastic process. In this paper the stochastic nature of the streamflow is taken into account by considering the correlation between the streamflows of each pair of consecutive time intervals. This interdependence is used to calculate the probability of transition from a given state and stage to its succeeding ones. A dynamic programming model with a physical equation and a stochastic recursive equation is developed to find the optimum operational policy. For illustrative purposes, the model is applied to a real surface water reservoir system.     

A COMPARISON OF TWO METHODS FOR MULTIOBJECTIVE OPTIMIZATION FOR RESERVOIR OPERATION1

ABSTRACT: Two major objectives in operating the multireservoir system of the Upper Colorado River basin are maximization of hydroelectric power production and maximization of the reliability of annual water supply. These two objectives conflict. Optimal operation of the reservoir system to achieve both is unattainable. This paper seeks the best compromise solution for an aggregated reservoir as a surrogate of the multireservoir system by using two methods: the constraint method and the method of combined stochastic and deterministic modeling. Both methods are used to derive the stationary optimal operating policy for the aggregated reservoir by using stochastic dynamic programming but with different objective functions and minimum monthly release constraints. The resulting operating policies are then used in simulated operation of the reservoir with historical inflow records to evaluate their relative effectiveness. The results show that the policy obtained from the combination method would yield more hydropower production and higher reliability of annual water supply than that from the constraint-method policy.     

A COMPARISON OF SOME DYNAMIC,LINEAR AND POLICY ITERATION METHODS FOR RESERVOIR OPERATION1

Within the past few years, a number of papers have been published in which stochastic mathematical programming models, incorporating first order Markov chains, have been used to derive alternative sequential operating policies for a multiple purpose reservoir. This paper attempts to review and compare three such mathematical modeling and solution techniques, namely dynamic programming, policy iteration, and linear programming. It is assumed that the flows into the reservoir are serially correlated stochastic quantities. The design parameters are assumed fixed, i.e., the reservoir capacity and the storage and release targets, if any, are predetermined. The models are discrete since the continuous variables of time, volume, and flow are approximated by discrete units. The problem is to derive an optimal operating policy. Such a policy defines the reservoir release as a function of the current storage volume and inflow. The form of the solution and some of the advantages, limitations and computational efficiencies of each of the models and their algorithms are compared using a simplified numerical example.     

COMPARISON OF STOCHASTIC AND DETERMINISTIC DYNAMIC PROGRAMMING FOR RESERVOIR OPERATING RULE GENERATION1

ABSTRACT: Two dynamic programming models — one deterministic and one stochastic — that may be used to generate reservoir operating rules are compared. The deterministic model (DPR) consists of an algorithm that cycles through three components: a dynamic program, a regression analysis, and a simulation. In this model, the correlation between the general operating rules, defined by the regression analysis and evaluated in the simulation, and the optimal deterministic operation defined by the dynamic program is increased through an iterative process. The stochastic dynamic program (SDP) describes streamflows with a discrete lag-one Markov process. To test the usefulness of both models in generating reservoir operating rules, real-time reservoir operation simulation models are constructed for three hydrologically different sites. The rules generated by DPR and SDP are then applied in the operation simulation model and their performance is evaluated. For the test cases, the DPR generated rules are more effective in the operation of medium to very large reservoirs and the SDP generated rules are more effective for the operation of small reservoirs.     

A STOCHASTIC DYNAMIC PROGRAMMING BASED APPROACH TO THE OPERATION OF A MULTI-RESERVOIR SYSTEM1

ABSTRACT: An heuristic iterative technique based upon stochastic dynamic programming is presented for the analysis of the operation of a three reservoir ‘Y’ shaped hydroelectric system. The technique is initiated using historical inflow data for the downstream reservoir. At each iteration the optimal policies for the downstream hydroelectric generating unit are used to provide relative weightings or targets for operation of upstream reservoirs. New input inflows to the downstream reservoir are then obtained by running the historical streamflow record through the optimal policies for the upstream reservoirs. These flows are then used to develop a new operating policy for the downstream reservoir and hence new targets for the upstream reservoirs. The process is continued until the operating policies for each reservoir provide the same overall system benefit for two successive iterations. Results obtained from the procedure are compared to the results obtained by historical operation of the system. The procedure is shown to develop operating policies which give benefits which are as close to the historical benefits as can be expected given the choice of the number of storage state variables.     

COMPARISON OF RESERVOIR LINEAR OPERATION RULES USING LINEAR AND DYNAMIC PROGRAMMING1

ABSTRACT: Mathematical optimization techniques are used to study the operation and design of a single, multi-purpose reservoir system. Optimal monthly release policies are derived for Hoover Reservoir, located in Central Ohio, using chance-constrained linear programming and dynamic programming-regression methodologies. Important characteristics of the former approach are derived, discussed, and graphically illustrated using Hoover Reservoir as a case example. Simulation procedures are used to examine and compare the overall performance of the optimal monthly reservoir release policies derived under the two approaches. Results indicate that, for the mean detention time and the corresponding safe yield target water supply release under existing design of Hoover Reservoir, the dynamic programming policies produce lower average annual losses (as defined by a two-sided quadratic loss function) while achieving at least as high reliability levels when compared to policies derived under the chance-constrained linear programming method. In making this comparison, the reservoir release policies, although not identical, are assumed to be linear. This restricted form of the release policy is necessary to make the chance-constrained programming method mathematically tractable.     

RESERVOIR OPERATION ANI EVALUATION OF DOWNSTREAM FLOW AUGMENTATION1

ABSTRACT: Operation of a storage‐based reservoir modifies the downstream flow usually to a value higher than that of natural flow in dry season. This could be important for irrigation, water supply, or power production as it is like an additional downstream benefit without any additional investment. This study addresses the operation of two proposed reservoirs and the downstream flow augmentation at an irrigation project located at the outlet of the Gandaki River basin in Nepal. The optimal operating policies of the reservoirs were determined using a Stochastic Dynamic Programming (SDP) model considering the maximization of power production. The modified flows downstream of the reservoirs were simulated by a simulation model using the optimal operating policy (for power maximization) and a synthetic long‐term inflow series. Comparing the existing flow (flow in river without reservoir operation) and the modified flow (flow after reservoir operation) at the irrigation project, the additional amount of flow was calculated. The reliability analysis indicated that the supply of irrigation could be increased by 25 to 100 percent of the existing supply over the dry season (January to April) with a reliability of more than 80 percent.     

DERIVING THE NONLINEAR RISK-BENEFIT ALGORITHM FOR RESERVOIRS1

ABSTRACT: The Nonlinear Risk-Benefit (NRB) Algorithm includes risk as one of the objectives in a multiple-objective optimization problem. The NRB Algorithm is derived by extending the Surrogate Worth Trade-Off method to quadratic programming. This category of problem is common in water resources planning and design, especially multipurpose reservoir systems. Consequently, an example is given using the algorithm for optimally operating a multipurpose reservoir.     

OPTIMIZATION OF MULTIPURPOSE RESERVOIR SYSTEM OPERATION1

ABSTRACT: The goal programming approach for multipurpose reservoir operation has been proposed and applied to the Bhadra reservoir system, having irrigation and hydropower production as dual purposes, in India. The objective of the model is to satisfy sequentially a series of operating criteria. Two goal programming models, one with the objective function as minimizing the deviations from storage targets and the other with the objective function as minimizing the deviations from release targets, have been formulated and applied to the reservoir system under study. The results proved that the model with release targets is preferred over the model with storage targets for determining operational policies for multipurpose reservoir system.     

A DECISION SUPPORT SYSTEM TO MANAGE SUMMER STREAM TEMPERATURES1

ABSTRACT: Warm summer stream temperatures due to low flows and high air temperatures are a critical water quality problem in many western United States river basins because they impact threatened fish species’habitat. One way to alleviate this problem is for local and federal organizations to purchase water rights to be used to increase flows, hence decrease temperatures. Presented is a Decision Support System (DSS) that can be used in an operations mode to effectively use water acquired to mitigate warm stream temperatures. The DSS uses a statistical model for predicting daily stream temperatures and a rule‐based module to compute reservoir releases. Water releases are calculated to meet fish habitat temperature targets based on the predicted stream temperature and a user specified confidence of the temperature predictions. Strategies that enable effective use of a limited amount of water throughout the season have also been incorporated in the DSS. The utility of the DSS is demonstrated by an example application to the Truckee River near Reno, Nevada, using hypothetical operating policy and 1988 through 1994 inflows. Results indicate that the DSS could substantially reduce the number of target temperature violations (i.e., stream temperatures exceeding the target temperature levels detrimental to fish habitat).     

APPLICATION OF A SINGLE RESERVOIR OPERATION POLICY TO A RAIN WATER CISTERN SYSTEM1

The operation policy for a single reservoir is applied to a rain water cistern system because the functions of a cistern are similar to a simple single reservoir. Since the cistern is a closed system, water loss is negligible. In this study, a dynamic programming analysis has been made to study the effects of the probable weekly rainfall and the water storage in the cistern towards the water consumption policy. The result of this study indicates that the water consumption rate should be adjusted into a lower rate when the water storage in the cistern is low and/or when the expected probable weekly rainfall is low if the owner of the cistern does not want to risk the chance of an empty cistern. The demand for a reliable method for forecasting weekly rainfall is evident in this study.     

AN APPLICATION OF MATHEMATICAL PROGRAMMING IN PLANNING SURFACE WATER STORAGE1

Designing a surface reservoir involves the concept of reservoir yield. This concept embodies three basic information items: hydrologic regime, active storage volume, and reservoir release policy. In the actual case presented below, the magnitude of the active storage was prescribed by a legal procedure, so that the planning issue became that of determining the reservoir yield given the hydrological information. A stochastic dynamic programming model was formulated to derive a schedule of seasonal optimal reservoir releases and their respective probabilities of occurrence. This schedule is the reservoir yield. The yearly cycle was divided into three seasons representing the actual climatic conditions, and conditional probabilities linking streamflows in consecutive seasons were estimated. An operating policy was postulated, based on the same set of legal decisions that prescribed the active storage volume, and target reservoir releases were assumed. Similarly, target storages at the end of each season were set up. The optimizing/ minimizing criterion in the dynamic programming formulation was the sum of squares of deviations of actual releases and final storage volumes from their respective targets.     

IMPLEMENTATION OF AN OPTIMIZATION MODEL FOR OPERATION OF A METROPOLITAN RESERVOIR SYSTEM1

ABSTRACT: A deterministic dynamic programming optimization model with a refining sectioning search procedure is developed and implemented to find least cost withdrawal and release patterns for water supple from a multiple reservoir system serving a metropolitan area. Applications are made to teh four reservoir system operated by the city of Dallas, Texas. A realistic cost structure, including nonlinear power consumption, block rate unit power costs, and flow dependent power consumption for intracity water distribution, is utilized. Applications are made to find least cost operating patterns and, as well, by inclusion of a water loss penalty function, supply patterns which will reduce evaporation water losses for the Dallas system.     

A RESERVOIR OPERATING MODEL WITH INORGANIC QUALITY CONSTRAINTS FOR THE TRUCKEE RIVER1

ABSTRACT: This study investigated low flow augmentation as a means of meeting inorganic water quality standards for the Truckee River at the California-Nevada state line. A digital inorganic water quality model was combined with a deterministic dynamic reservoir operating model in an iterative process which allowed the optimization of releases subject to selected inorganic water quality constraints as well as downstream demands. Results from model runs with varied flow and river loading data indicate that flow augmentation may be a feasible and relatively inexpensive way of meeting standards for this system except in time of severe drought.     

APPLICATION OF THE HEC-4 MONTHLY STREAM FLOW SIMULATION MODEL1

ABSTRACT: The HEC-4 monthly stream flow simulation model, developed by the Hydrologic Engineering Center, Davis, California, is used to extend the available historical stream flow records in the Central Ohio area. The principal objective of this paper is to examine the effectiveness of the HEC-4 model in generating synthetic monthly flows. Important statistical parameters are evaluated in order to relate the statistical properties of the historical and generated flows. In doing so, it is observed that the mean, standard deviation, and skewness of the generated flows are consistently larger than the corresponding estimates based on historical flows. However, results show that these statistics, as well as the lag-1 serial correlation, are generally well maintained by the generated sequences. The degree to which any statistical dissimilarities would be critical, from an engineering design point of view, is demonstrated by utilizing their low flow characteristics. Estimates of reservoir safe-yields, based on a nonsequential mass-curve analysis of the historical and generated low flows, indicate a nominal difference in this particular study.     

MULTIOBJECTIVE DECISION MAKING TECHNIQUES FOR RESERVOIR OPERATION1

ABSTRACT: Six applications of multiobjective decision making techniques for finding optimal or satisfying operating rules for reservoir systems are presented. The examples include situations with hydropower vs. water supply (for irrigation), flood control vs. low flow augmentation, selection of an operating rule, low-flow vs. reliability, and low flow and recreation vs. water quality. The techniques applied include the constraint method, compromise programming, goal programming, Tchebycheff approach (max-mm), Consensus, and ELECTRE I and II.     

OPTIMIZING FLOOD CONTROL ALLOCATION FOR A MULTIPURPOSE RESERVOIR1

ABSTRACT. In the last decade much research has been devoted to applying the systems analysis approach to water resources problems. A popular research goal has been determination of the “best” method of operating a multipurpose reservoir. The goal of this study was to derive the economically optimum flood control diagram for a multipurpose reservoir by systems analysis. The technique employed to optimize the flood control diagram was programmed so that the optimization process could be applied to other multipurpose reservoirs. Two computer programs developed at the U.S. Army Corps of Engineers' Hydrologic Engineering Center were utilized with modifications to simulate the operation of Folsom Reservoir in central California. Economic analyses were incorporated along with an optimization technique into the reservoir operations program; and the resultant program was capable of routing a sequence of monthly reservoir inflows, computing benefits for various flood control diagrams (as dictated by the optimization procedure), and selecting the economically optimum flood control diagram. The univariate gradient technique was the optimization procedure employed. The two computer programs are on file at the Hydrologic Engineering Center in Davis, California.     

WATER QUALITY ALLOCATED COST FOR MULTIPURPOSE RESERVOIRS1

ABSTRACT: Low flow augmentation from multipurpose reservoirs may yield significant water quality benefits. Cost allocation assigns a portion of reservoir expense to water quality consumers, waste water dischargers who benefit from increased receiving flow. Whereas such allocation currently is not authorized for Federal projects, the procedure is increasingly appropriate for efficient multiobjective management. Waste water treatment costs, multipurpose reservoir costs, and water quality are modeled for Oregon's Willamette River. Water quality is expressed as a function of treatment and augmentation levels. Treatment cost necessary to achieve a given water quality without augmentation less treatment cost with augmentation is an alternative cost of water quality maintenance. With a cost allocation procedure, this alternative cost is used to determine water quality's share of reservoir cost. Under current conditions, water quality beneficiaries could be charged approximately seven percent of annualized reservoir expense. This charge is one-fourth the expense of additional treatment facilities required were augmentation not provided.     

Adjusting irrigation abstraction to minimise the impact on stream flow in the East of Scotland

Abstractions of surface and groundwater for irrigation in Scotland are currently subject to control in only two small catchments. Under the terms of the EU Water Framework Directive, it will be necessary to introduce new legislation to control abstractions elsewhere. To help in the development of appropriate policy for Scotland a study has been carried out to examine the significance of irrigation and the effectiveness of different types of control strategies in terms of the economics of potato cropping and stream hydrology in Scotland. This paper presents the findings of the hydrological study and highlights some of the spatial and temporal issues that need to be considered in the selection of control mechanisms, if they are to be successful in achieving objectives for environmental improvement.The study was focussed on two catchments in the east of Scotland, the Tyne and West Peffer. The effectiveness of several different abstraction control strategies was examined to see how stream flows in the catchment would be modified by their implementation. The results of the study demonstrated that the West Peffer catchment in particular is significantly affected by irrigation abstractions. Control mechanisms based on allowable monthly abstraction volumes and flow-based abstraction bans would be of considerable help in restoring stream flows to their natural levels, but would modify the hydrological regime in slightly different ways. A spatial analysis of stream flows demonstrated that implementation of controls based on a single monitoring point may be ineffective at maintaining acceptable levels of flow throughout the catchment and that this may require a tighter control at the monitoring point.     

A DECISION SUPPORT TOOL FOR THE MANAGEMENT OF MULTI‐RESERVOIR SYSTEMS1

ABSTRACT: A decision support tool is developed for the management of water resources, focusing on multipurpose reservoir systems. This software tool has been designed in such a way that it can be suitable to hydrosystems with multiple water uses and operating goals, calculating complex multi‐reservoir systems as a whole. The mathematical framework is based on the parameterization‐simulation‐optimization scheme. The main idea consists of a parametric formulation of the operating rules for reservoirs and other projects (i.e., hydropower plants). This methodology enables the radical decrease of the number of decision variables, making feasible the location of the optimal management policy, which maximizes the system yield and the overall operational benefit and minimizes the risk for the management decisions. The program was developed using advanced software engineering techniques. It is adaptable in a wide range of water resources systems, and its purpose is to support water and power supply companies and related authorities. It already has been applied to two of the most complicated hydrosystems of Greece, the first time as a planning tool and the second time as a management tool.