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.     

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.     

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.     

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.     

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.     

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.     

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.     

AN OPTIMIZATION MODEL FOR EFFICIENT MANAGEMENT OF URBAN WATER RESOURCES1

ABSTRACT: A mathematical programming model is proposed to determine economically efficient urban water resource allocation and pricing policy by maximizing the sum of the consumer and producer surplus. The optimization of this nonlinear problem is accomplished by the use of linear programming algorithm. The feasibility of using recycled water for municipal purposes is examined in a planning context. The impact of higher water quality discharge standards on pricing and allocation of water is analyzed and the attractiveness of water reuse option is demonstrated.     

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.     

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.     

THE OPTIMALITY OF CAPACITY SHARING IN STOCHASTIC DYNAMIC PROGRAMMING PROBLEMS OF SHARED RESERVOIR OPERATION1

ABSTRACT: This paper is concerned with finding an optimal allocation of water entitlements for each of two users of water who share a reservoir. Two instruments of allocation are considered. The first, release sharing, involves sharing the releases from the reservoir; the second, capacity sharing, is concerned with allocating to each user of water a share of inflows, reservoir capacity and leakage and evaporation losses. Stochastic dynamic programming problems of reservoir operation under each type of sharing arrangement are formulated. It is shown that the maximum discounted expected profit from reservoir operation over the life of the storage using capacity sharing is at least as large as that obtained using release sharing and that release sharing is not Pareto efficient.     

A LINEAR ANALYSIS OF AN URBAN WATER SUPPLY SYSTEM1

The use of linear programming as a planning tool for determining the optimal long-range development of an urban water supply system was explored. A stochastic trace of water demand was synthesized and used as an input to the model. This permitted evaluating the feasibility of imposing demand restrictions as an effective cost reduction mechanism. The City of Lincoln, Nebraska, was used as the urban model. The fundamental problem was to allocate limited water supplies from several sources to an urban load center to minimize costs and comply with system constraints. The study period covered twenty years, and findings indicate the planning direction for stage development during this period. Sensitivity analyses were performed on cost coefficients and demands. Thirteen sources were included in the initial computations. Conclusions were that linear programming and generated demand traces are useful tools for both short- and long-term urban water supply planning. Lowering peak demands results in long-range development of fewer sources of supply and more economic and efficient use of the supplies developed.     

OPTIMAL CAPACITIES OF WATER SUPPLY RESERVOIRS IN SERIES AND PARALLEL1

ABSTRACT: The planning of water supply reservoirs has traditionally been based on the Rippl or sequent peak analysis which applies to the design of a single reservoir. This paper incorporates the sequent peak method as the central feature in establishing a procedure for determining the sizes of several potential reservoirs located in a system of one or more rivers. Separate algorithms are developed for sites on parallel streams and for sites on the same stream. In both cases the approach is to find the combination of reservoirs which can satisfy a given constant monthly demand at a minimum total construction cost. It is shown that both problems can be cast in the form of a dynamic programming problem. A more complex system is then a combination of reservoirs in parallel and in series. An extension is given if the monthly demand is not constant but each reservoir satisfies a constant fraction of the monthly demand.     

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.     

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.     

A NEW METHOD FOR ESTIMATING FUTURE RESERVOIR STORAGE CAPACITIES1

ABSTRACT: A new method has been developed for estimating future reservoir storage capacities, allowing for sediment deposition and compaction. Reservoir sedimentation surveys for 117 reservoirs, conducted by the Illinois State Water Survey over the past 60 years, were used to determine regional constants K to represent the severity of sediment deposition in the reservoirs. More than half of the 82 water supply reservoirs investigated had records of reservoir sedimentation surveys, and their K values were calculated by using data from those sediment surveys. The average K values of the remaining non-surveyed water supply reservoirs were estimated from the regional distribution of the K values. Other important factors considered in the estimation of future reservoir storage capacities are the trap efficiency of the reservoirs and the variation of density of sediment deposits due to compaction. The model can also be used for analyzing the economics of alternative sites and of design features that can be incorporated in dams for reducing reservoir sedimentation.     

RESERVOIR OPERATION THROUGH OBJECTIVE TRADE-OFFS1

ABSTRACT: Water resource development has progressed to the stage where various human factors are now being considered in reservoir design and operation. The introduction of human factor objectives complicates the problem since they are noncommensurate with other objectives and they are difficult to identify quantitatively. Some of the problems that now arise concern the proper methods for consideration of several different, sometimes subjectively identified, objectives in reservoir planning. The classical systems analysis approach to decision making for multiple objective problems is outlined and the inherent difficulties associated with multiple objectives and subjective estimates are identified. Techniques being used in reservoir design and operation are reviewed and discussed. An alternate technique for considering noncommensurate, subjectively identified, objectives, which relates the objectives in terms of real trade-off costs and eliminates the need for a priori estimates of objective worth is then presented. The method is illustrated with three examples, including a reservoir operation problem and a cooling tower design problem.     

A SEPARABLE LINEAR ALGORITHM FOR HYDROPOWER OPTIMIZATION1

ABSTRACT: A deterministic, separable, linear algorithm is presented for maximizing aggregate hydropower production. The method is iterative and amenable to solution using standard LP software. The utility of the technique is demonstrated using several test applications involving a hypothetical single-purpose hydropower reservoir and a monthly increment 20-year flow record from the Gunpowder River in Maryland. The separable linearized forms solved quickly using MPSX on a variety of IBM hardware: 3090-400 VF, 3084 QX, dual processor 4381-3, and an AT/370 personal computer. For comparison purposes, the original nonlinear nonseparable version of the model was also solved using MINOS. This yielded a value of aggregate hydropower marginally higher than that using MPSX. The separable, linearized methodology proved to be a useful and an efficient means of generating good starting points for MINOS. The use of these warm starts effected substantial reductions in MINOS execution times.     

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.