THE EFFECTS OF RISK AND RELIABILITY ON OPTIMAL RESERVOIR DESIGN1

A chance-constrained linear programming model, which utilizes multiple linear decision rules and is useful for river basin planning, is used to evaluate the effects of risk and reliability on optimal reservoir design. Streamflow forecasts or predictions can be explicitly included in the linear program. The risk associated with the predictions is included in the model through the use of cumulative distribution functions (CDF) of streamflows which are conditioned on the predictions. A multiple-purpose reservoir on the Gunpowder River in Maryland is used to illustrate the effectiveness of the model. In order to provide the decision makers with complete and useful information, trade-off curves relating minimum reservoir capacity (a surrogate for dam costs), water supply and flood control targets, and the reliability of achieving the targets are developed. The trade-off curves may enhance the decision maker's ability to select the best dam capacity, considering technological and financial constraints as well as the trade-offs between targets, risks, and costs.     

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.     

LAND USE CHANGE PATTERNS BY LOCATION WITH RESPECT TO A RESERVOIR1

Much research has been done to determine the benefit of a water resources development to society as a whole. Some research has explored the benefit of such a facility to a region. Very little research exists on the effects of a reservoir on the immediately surrounding area. The general hypothesis of this study is that the spatial patterns of land use change are influenced by economic characteristics of the reservoir and reservoir area. Several hypotheses concerning the effects of relative location on a peninsula are tested using analysis of variance. The data used for the analysis is based on Lake Cumberland, a reservoir in southern Kentucky. The analysis indicates that there exists significant patterns of land use change around the lake and on peninsulas.     

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.     

MULTI-OBJECTIVE RESERVOIR OPERATION INCLUDING TURBIDITY CONTROL1

ABSTRACT: The operational problems of a reservoir are expressed by three coordinates: space, time stage, and objective. The operational procedure is formulated using dynamic programming as a multi-objective problem. After comparing the scalar and the vector optimization, the scalar optimization technique is applied to turbidity analysis in a reservoir.     

PRACTICAL IMPLICATIONS IN THE USE OF STOCHASTIC DYNAMIC PROGRAMMING FOR RESERVOIR OPERATION1

ABSTRACT: A stochastic dynamic programming model is applied to a small hydroelectric system. The variation in number of stage iterations and the computer time required to reach steady state conditions with changes in the number of storage states is investigated. The increase in computer time required to develop the storage probability distributions with increase in the number of storage states is reviewed. It is found that for an average of seven inflow states, the largest number of storage states for which it is computationally feasible to develop the storage probability distributions is nine. It is shown that use of the dynamic program results based on a small number of storage states results in unrealistically skewed storage probability distributions. These skewed distributions are attributed to “trapping” states at the low end of the storage range.     

MULTIOBJECTWE OPTIMIZATION OF RESERVOIR SYSTEMS OPERATION1

ABSTRACT: Development of optimal operational policies for large-scale reservoir systems is often complicated by a multiplicity of conflicting project uses and purposes. A wide range of multiobjective optimization methods are available for appraising tradeoffs between conificting objectives. The purpose of this study is to provide guidance as to those methods which are best suited to dealing with the challenging large-scale, nonlinear, dynamic, and stochastic characteristics of multireservoir system operations. As a case study, the selected methodologies are applied to the Han River Reservoir System in Korea for four principal project objectives: water supply and low flow augmentation; annual hydropower production, reliable energy generation, and minimization of risk of violating firm water supply requirements. Additional objectives such as flood control are also considered, but are imposed as fixed constraints.     

FLOOD CONTROL RESERVOIR OPERATIONS UNDER ENVIRONMENTAL RESTRAINTS1

ABSTRACT: A flood control reservoir protects valuable developments on the downstream flood plain by storing flood waters and releasing them at a rate that will reduce the downstream damage. The water surface level of the flood pool behind the dam can fluctuate considerably during the occurrence of a large magnitude flood causing the inundation of trees, low vegetation, and water based recreation facilities located in those areas of the flood pool area that are normally well above the water level. The amount of damage that will occur in the upper levels of the flood storage area will depend on the depth and duration of the inundation that occurs. This, in turn, is directly related to the operating policy for the reservoir. A dynamic programming optimization model of flood control reservoir operation is presented. This model determines the reservoir operating schedule that minimizes downstream flood damages. Various constraints are added to the model to account for the environmental impacts of long periods of flood storage.     

OPTIMIZING THE PROBABILITIES OF WATER YIELD FOR THE RIDAURA AQUIFER (SPAIN)1

ABSTRACT: Aquifer pumping represents, in many geographical locations, an alternative and/or a complementary source of water to surface water supplies. Several Catalonian coastal towns in the northeastern corner of Spain are in this situation. Also, since pumped water is used to supply drinking water, the main purpose in managing these water resources is to supply, no matter the cost, the amount needed at every moment. In other words, the managers of these aquifers attempt to optimize firm water yield. If we think of these aquifers as underground reservoirs with fixed storage capacity, most of the techniques which are applied to surface reservoirs can be implemented. In this paper we use a Stochastic Dynamic Programming model to optimize the yield from the aquifer of the Ridaura River. The objective function in this model was chosen with the aim of maximizing the reliability of the target yields in each of four seasons.     

MANGANESE OXIDATION RELATED TO THE RELEASES FROM RESERVOIRS1

ABSTRACT: Stratified reservoir waters frequently contain objectionable quantities of dissolved manganese. The oxidation and removal of dissolved manganese during transport below Normandy Dam, Tennessee, was shown to be much more rapid than expected from chemical oxidation. Oxidation took place in only a day of travel time rather than months or years. Laboratory studies showed that removal was associated with a slime found on rock surfaces below the dam and led to the development of column technology as a possible method of treating natural waters containing manganese. Hydraulic loadings on the columns in the range of 390–780 m³/hr.ha accomplished a 90 percent removal rate of soluble manganese over an influent concentration range of 2 to 15 mg/l.     

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.     

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.     

STOCHASTIC DYNAMIC PROGRAMMING FOR OPTIMUM RESERVOIR OPERATION1

ABSTRACT. For a multipurpose single reservoir a deterministic optimal operating policy can be readily devised by the dynamic programming method. However, this method can only be applied to sets of deterministic stream flows as might be used repetitively in a Monte Carlo study or possibly in a historical study. This paper reports a study in which an optimal operating policy for a multipurpose reservoir was determined, where the optimal operating policy is stated in terms of the state of the reservoir indicated by the storage volume and the river flow in the preceding month and uses a stochastic dynamic programming approach. Such a policy could be implemented in real time operation on a monthly basis or it could be used in a design study. As contrasted with deterministic dynamic programming, this method avoids the artificiality of using a single set of stream flows. The data for this study are the conditional probabilities of the stream flow in successive months, the physical features of the reservoir in question, and the return functions and constraints under which the system operates.     

REVIEW OF DETERMINATION OF INSTREAM FLOW REQUIREMENTS WITH SPECIAL APPLICATION TO AUSTRALIA1

ABSTRACT: A critical examination of the techniques used to assess and specify environmental instream flow requirements is provided. The strengths and weaknesses of individual techniques are evaluated on both an absolute and a comparative basis. Particular attention is given to the problem of specifying environmental flow requirements in Australia where the hydrology has distinctly different characteristics to those in countries where most of the models for prediction of instream flow requirements were developed. Broad recommendations as to the suitability and use of the different techniques for different conditions are provided.     

OPTIMAL RESERVOIR MANAGEMENT AND CROP PLANNING UNDER DETERMINISTIC AND STOCHASTIC INFLOWS1

ABSTRACT: This study analyzes planning under deterministic and stochastic inflows for the Mayurakshi project in India. Models are developed to indicate the optimal storage of reservoir water, the transfer of water to the producing regions, and the spillage of water from the reservoir, if needed. A deterministic programming model was first formulated to represent the existing situation. A chance-constrained model then was constructed to evaluate potential violations of the deterministic model. Both models were quantified for the command area. Data were collected from surveys of the area and from government agencies. Both the deterministic and change-constrained models suggest a more intensive cropping program in the region. Both emphasize more dependence on rabi and less on kharif crops. The chance-constrained especially suggests use of more water in the rabi season. Important chances in cropping programs and labor use take place under the chance-constrained model.     

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.     

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.     

A NONLINEAR PROGRAMMING ALGORITHM FOR REAL-TIME HOURLY RESERVOIR OPERATIONS1

ABSTRACT: The optimization of real-time operations for a single reservoir system is studied. The objective is to maximize the sum of hourly power generation over a period of one day subject to constraints of hourly power schedules, daily flow requirement for water supply and other purposes, and the limitations of the facilities. The problem has a nonlinear concave objective function with nonlinear concave and linear constraints. Nonlinear Duality Theorems and Lagrangian Procedures are applied to solve the problem where the minimization of the Lagrangian is carried out by a modified gradient projection technique along with an optimal stepsize determination routine. The dimension of the problem in terms of the number of variables and constraints is reduced by eliminating the 24 continuity equations with a special implicit routine. A numerical example is presented using data provided by the Bureau of Reclamation, Sacramento, California.     

IRRIGATION WATER DELIVERY SYSTEM OPERATION VIA AGGREGATE STATE DYNAMIC PROGRAMMING1

ABSTRACT: A modified dynamic programming (DP) approach that is called aggregate state dynamic programming (ASDP) is presented to optimally operate irrigation water delivery systems. ASDP can be applied to multiple reservoir systems without encountering dimensionality problems. In addition, the random nature of water supply and consumptive crop demands can be incorporated into the technique. A case study is presented to display the application of ASDP. Using a sum-of-squared shortages objective, ASDP out performs a traditional separation technique and approaches the theoretical (ideal) optimum. Problem settings that are conducive to the use of ASDP and limitations of the technique are presented.