Parallel Reservoirs Research Articles

Refill and Drawdown Rules for Parallel Reservoirs: Quantity and Quality

This paper presents two operating rules for the refill and drawdown seasons of reservoirs in parallel for water supply, considering water quality. For the refill season a Linear Programming form of the New York City Rule is developed. Another Linear Programming form based on equalizing the probability of emptying each reservoir is developed for the drawdown season. Both formulations are extended to consider stratified water quality in the reservoirs and a water quality requirement for a downstream demand. The refill rule is applied to Shasta and Whiskeytown reservoirs in California (USA). The drawdown rule is applied to Alarcón and Contreras reservoirs in the Júcar Basin (Spain). The results of these applications show the effect of a water quality consideration in water supply operation.

Discussion of “Optimal Operation of Multireservoir Systems: State-of-the-Art Review” by John W. Labadie

A large and long-existing literature employs analytical optimization methods to derive reservoir operating rules for multireservoir systems. These date back to rules for minimizing spill from parallel reservoirs by Bower et al. 1966 and Clark 1950 . Lund and Guzman 1999 summarize such analytically derived optimal operating rules for some simple multireservoir systems under specific conditions and criteria. Lund 2000 uses analytical optimization for hydropower operations with multiple reservoirs. More complex multireservoir problems have been examined analytically and partially analytically using interesting extensions of Varlet’s 1922 and Masse’s 1946 single reservoir methods MorelSeytoux 1999 .

Stochastic multiobjective optimization of reservoirs in parallel

AbstractA stochastic multiobjective optimization method for finding noninferior solutions of the operation problem of reservoirs in parallel is presented. This problem is characterized by a multiobjective optimization, a multireservoir system, and stochasticity of inflows, which represent three difficult aspects in reservoir system planning and operation. In this method, a constraint technique, decomposition iteration, and simulation analysis are employed conjunctively to deal with the three difficult aspects. The constraint technique is intended to transform the multiobjective optimization into a uniobjective one and the decomposition iteration in conjunction with the simulation analysis attempts to alleviate the dimensionality problem. The proposed methodology is applied to a reservoir system in the upper Tone River basin, which consists of three reservoirs in parallel and is operated primarily for three objectives: hydropower, water supply, and flood control. A total of 49 noninferior solutions for the reservoir system are obtained, from which the decision makers may be able to find the most satisfactory operating policy. Copyright © 2005 John Wiley & Sons, Ltd.

Selection of conceptual models for regionalisation of the rainfall-runoff relationship

This study attempts to identify relationships between suitable conceptual rainfall-runoff model structures and catchment types, and demonstrates an objective procedure for selection of model structures for use in model regionalisation studies. 12 conceptual model structures have been tested on 28 UK catchments. The model structures are combinations of three soil moisture accounting modules (the catchment wetness index model structure, a modified Penman model structure, and a probability distributed soil moisture model), and four routing models (two linear reservoirs in parallel, an adaptation that represents macropore flow, three linear reservoirs in parallel, and a model that includes leakage from the groundwater store). The 28 catchments were selected to cover a range of hydrological types based on known catchment characteristics (designed combinations of catchment size, baseflow index, and annual rainfall are used). The important points in objectively selecting model structures for regionalisation are proposed as: performance in calibration and validation, trade-off between high and low flow performance, and model complexity (here represented as the number of parameters). Although, the results in this study provide no evidence of relationships between catchment type and preferred model structure, the study indicates that out of the 12 trial model structures, the following four may be the most suitable for regionalisation across UK catchments: the modified Penman model with two parallel linear routing reservoirs, and the probability distributed soil moisture model with two parallel linear routing reservoirs, three parallel linear routing reservoirs, or the macropore adaptation.

Optimization and simulation of a multiple reservoir system operation

Dynamic programming (DP) optimization and HEC-5 simulation models were developed for planning the long-term operation of the Karoon-Dez multireservoir system in Iran. The well-known dimensionality problem associated with DP was controlled using a heuristic approach to narrow the required search algorithm within the state space of DP. HEC-5 as a common and widely available computer program for studying reservoir systems regulation was also used to simulate operation of the Karoon-Dez system with water supply and hydropower generation objectives. HEC-5 is able to consider flood control, hydropower generation and conservation purposes. Both the DP and HEC-5 models were applied to the Karoon-Dez system consisting of six reservoirs; five reservoirs in series parallel to a sixth one. The results obtained by the HEC-5 and DP models were analysed and compared. The results show that, although the DP results were better than those of HEC-5 in terms of meeting system operating targets and energy generation, HEC-5 as a simulation model demands much less computer time and memory, making it attractive for practical use.

The use of the linear reservoir concept to quantify the impact of changes in land use on the hydrology of catchments in the Andes

Abstract. The high Andes region of South Ecuador (The Páramo) is characterised by a cold and wet climate. Most soils of the Páramo region are Andosols and Histosols, with a very high water retention capacity that is affected irreversibly by drying. This key property of Páramo soils buffers catchment outflow, resulting in an almost uniform outflow pattern which, notwithstanding the variability in rainfall, can be very variable in space and time. These soils serve as the most important reservoir of drinking and irrigation water for the densely populated inter-Andean depression region. The Páramo has long served only as an extensive grazing area but recent population pressure and land scarcity have increased cultivation. Two small Páramo catchments (about 2 km2) were monitored intensively for precipitation and discharge for over a year to assess the effect of such land-use changes on the hydrological properties. One catchment is in an undisturbed area and grazed intensively while in the other, local farmers started intensive drainage for cultivation of potatoes about five years ago. The linear reservoir concept has been used to assess the overall retention capacity of the catchments in terms of both peak response and base flow. In this model, every catchment is considered as a series of independent parallel reservoirs, each characterised by mean residence times (T). In every catchment, three major mean residence times can be distinguished. In the undisturbed catchment, an immediate response, characterised by a T of 5.4 hours, is followed by a slower response with a T of 44.3 h. The base flow has a mean T value of 360 h. The response of the cultivated catchment is similar with T values of 3.6 h, 27.2 h and 175 h, respectively. As a result, in the disturbed catchment, water release is about 40% faster than in the undisturbed catchment, so that the base flow falls rapidly to lower levels. The linear reservoir model is a simple way of quantifying the impact of land use changes on the water regulation capacity of Páramo catchments. Keywords: linear reservoir, Páramo, mountain hydrology, land use changes, Ecuador

Root selection methods in flood analysis

Abstract. In the 1970s, de Laine developed a root-matching procedure for estimating unit hydrograph ordinates from estimates of the fast component of the total runoff from multiple storms. Later, Turner produced a root selection method which required only data from one storm event and was based on recognising a pattern typical of unit hydrograph roots. Both methods required direct runoff data, i.e. prior separation of the slow response. This paper introduces a further refinement, called root separation, which allows the estimation of both the unit hydrograph ordinates and the effective precipitation from the full discharge hydrograph. It is based on recognising and separating the quicker component of the response from the much slower components due to interflow and/or baseflow. The method analyses the z-transform roots of carefully selected segments of the full hydrograph. The root patterns of these separate segments tend to be dominated by either the fast response or the slow response. This paper shows how their respective time-scales can be distinguished with an accuracy sufficient for practical purposes. As an illustration, theoretical equations are derived for a conceptual rainfall-runoff system with the input split between fast and slow reservoirs in parallel. These are solved analytically to identify the reservoir constants and the input splitting parameter. The proposed method, called "root separation", avoids the subjective selection of rainfall roots in the Turner method as well as the subjective matching of roots in the original de Laine method. Keywords: unit hydrograph,identification methods, z-transform, polynomial roots, root separation, fast andslow response, Nash cascade

Derived Power Production and Energy Drawdown Rules for Reservoirs

Theoretical hydropower operation rules are derived and discussed for reservoirs in parallel, in series, and single reservoirs for cases where reservoirs typically refill before they empty and for parallel reservoirs when reservoirs are expected to draw down to empty. These hydropower rules offer a simplified economic basis for allocating storage and energy in multireservoir hydropower systems. The approach is demonstrated for an illustrative example and should be helpful for making decisions regarding hydropower releases over time, subject to the limited conditions under which these rules hold.

Multireservoir System Optimization using Fuzzy Mathematical Programming

For a multireservoir system, where the number of reservoirs is large, the conventional modelling by classical stochastic dynamic programming (SDP) presents difficulty, due to the curse of dimensionality inherent in the model solution. It takes a long time to obtain a steady state policy and also it requires large amount of computer storage space, which form drawbacks in application. An attempt is made to explore the concept of fuzzy sets to provide a viable alternative in this context. The application of fuzzy set theory to water resources systems is illustrated through the formulation of a fuzzy mathematical programming model to a multireservoir system with a number of upstream parallel reservoirs, and one downstream reservoir. The study is aimed to minimize the sum of deviations of the irrigation withdrawals from their target demands, on a monthly basis, over a year. Uncertainty in reservoir inflows is considered by treating them as fuzzy sets. The model considers deterministic irrigation demands. The model is applied to a three reservoir system in the Upper Cauvery River basin, South India. The model clearly demonstrates that, use of fuzzy linear programming in multireservoir system optimization presents a potential alternative to get the steady state solution with a lot less effort than classical stochastic dynamic programming.

Derived Operating Rules for Reservoirs in Series or in Parallel

This paper reviews a variety of derived single-purpose operating policies for reservoirs in series and in parallel for water supply, flood control, hydropower, water quality, and recreation. Such rules are useful for real-time operations, conducting reservoir simulation studies for real-time, seasonal, and long-term operations, and for understanding the workings of multireservoir systems. For reservoirs in series, several additional new policies are derived for special cases of optimal short-term operation for hydropower production and energy storage. For reservoirs in parallel, additional new special-case rules are derived for water quality, water supply, and hydropower production. New operating policies also are derived for reservoir recreation.

Application of the LP-DP approach to Andong and Imha parallel reservoirs, Korea

This paper presents an application of a previously developed linear programming-dynamic programming (LP-DP) methodology to the operation of Andong and Imha parallel reservoirs in South Korea. The model allows for multioptimization of power generation and municipal, industrial, and irrigation water use. It is shown that the annual average energy and the annual average water supply generated from the joint operation of the two parallel reservoirs by the LD-DP approach is 15.2 and 1.7% more than the contracted power production and water supply respectively.

Practical use of analytically derived runoff models based on rainfall point processes

This work reports on the practical usage of the four stochastic rainfall‐runoff models introduced by Bierkens and Puente (1990). These models, which are lumped in space, were analytically derived combining two rainfall point process models with two simple runoff parameterizations. The rainfall models employ rectangular pulses with Poisson (PRP) and Neyman‐Scott (NSRP) arrivals, respectively. The runoff models route individual rainfall pulses via linear reservoirs. One runoff parameterization accounts for surface runoff by using a single linear reservoir (SLR). The other model considers both surface and groundwater runoff employing two linear reservoirs in parallel (PLR). All four representations were tested on two catchments located in the Netherlands and Colombia. Emphasis was placed on the models' ability to (1) give stable parameter values for data sets at alternative averaging (aggregation) lengths (consistency) and (2) preserve historical statistics at alternative averaging lengths when using parameters found from data at other averaging scales (robustness). Results show that the use of alternative rainfall models may have little effect on runoff performance. Specifically, the NSRP model resulted in more robust runoff behavior than the PRP model only when combined to the SLR parameterization. The type of model used to route individual rainfall pulses was found to be important. Runoff representations containing the PLR component were found more robust than those having the SLR model.

A probability treatment of storage, yield and spillage in a system of two reservoirs in series, and in two reservoirs in parallel

The paper examines a system of two discrete stochastic reservoirs in series, and a system of two in parallel. In the ‘series’ case, the downstream reservoirs is fed not only by an inflow from its own catchment but also (after the necessary transit time lag by the controlled release plus the overflow from the upstream facility. If the inflow processes to the two reservoirs from their respective catchments are independent of one another, the pair ( Z t− a , Z′ t ) of water levels in the two constituents form a bivariate Markov chain, the transition probabilities of which are derived. The joint equilibrium distribution of the two storage variables then requires the solution of ( c + 1)( c′ + 1) simultaneous linear algebraic equations, where c, c′ are the capacities of the two reservoirs. The final yield and spillage distributions follow directly from those of the storages. If, however, the inflow processes are both Markovian, defined on the values 0, 1,…, d and 0, 1,…, d′ respectively, the number of equations to be solved increases to the impracticable level of ( c + 1) ( c′ + 1)( d + 1)( d′ + 1). In the ‘parallel’ case, each reservoir receives its own inflow process, and in each the release is controlled by both storage levels. The two yields are then combined. If the inflow processes are mutually independent we find that ( Z t , Z t ′) is bivariate Markov; if, instead, they are themselves Markovian, one has to work in terms of the quadrivariate Markov process ( Z t , Z t ′, X t , X t ′), with consequences for the number of equations to be solved as in the ‘series’ system.

Long-term optimal operation of series parallel reservoirs for critical period with specified monthly generation and average monthly storage

We present in this paper an efficient approach for solving the problem of planning the long-term (multiyear) operation of a multireservoir hydroelectric power system for the critical period with a monthly variable load. This load is equal to a certain percentage of the total generation at the end of the year, subject to satisfying a number of constraints on the hydrosystem, using the minimum norm formulation. The proposed method is efficient in computing time and in calculating the total expected benefits from the system during the critical period. Numerical results are reported for a real system in operation consisting of two rivers. Each river has two series reservoirs.

Modelling and optimization of parallel reservoirs having nonlinear storage curves under critical water conditions for long-term regulation

This paper deals with the problem of parallel reservoirs having nonlinear storage-elevation curves (quadratic functions) for long-term regulation under critical water conditions using the minimum norm formulation. To overcome these nonlinearities, we introduce a set of pseudo-state variables. A set of optimizing equations is obtained. The proposed method is efficient in computing time and in calculating the expected benefits of generation from the system during the critical period. Numerical results are reported for a real system in operation consisting of two rivers; each river has two reservoirs in series.

Multipurpose reservoir operation: 2. Daily operation of a multiple reservoir system

The short-term control of reservoir systems usually calls for numerous updates of the operating policy because of the uncertainties associated with the forecast of inflow. This paper presents and illustrates a daily operation model for maximization of monthly water and energy output from a system of two parallel reservoirs. The model uses optimum monthly water and energy contract levels obtained from the monthly release policy. These contract levels are adjusted to allow for differences between the daily and monthly forecast of inflow. The model is developed using a minicomputer to provide an inexpensive tool for updating purposes. The model is applied to the Shasta and Folsom reservoirs of the California Central Valley Project with computation time requirements of less than 2 min.

Application of Dynamic Team Theory to the Scheduling of Reservoirs in the Presence of Random Inflows

The management of water in a multiple reservoir system constitutes an important element of the operational scheduling problem in electric power systems. The presence of random inflows and system nonlinearities would require stochastic dynamic programming to provide an optimal feedback solution. However, the dimensionality of the hydro-scheduling problem rules out the direct use of stochastic dynamic programming, and leads to the consideration of decomposition methods requiring less computation. This paper uses concepts from dynamic team theory to characterize and develop stochastic spatial decomposition methods to systems of (a) parallel reservoirs, and (b) series reservoirs. These methods can be combined to generate the stochastic spatial decomposition algorithm for the general reservoir configuration. The computational features of these algorithms are discussed and numerical results will be presented at the conference.

Drain Discharge for a Level Agricultural Watershed

A hypothesis was developed that watershed discharge from rainfall, for nonfreezing periods from a tile drained level watershed, was mainly tile flow with negligible amounts of surface runoff and base flow. Daily discharges at the watershed outlet were due to depletion of two parallel linear reservoirs. A fast reacting reservoir, represented by the physical shallow ploughed layer, constituted nearly 40% of the total runoff volume. The slow reacting reservoir, represented by the subsoil zone, contributed nearly 60% of the total runoff volume.

Gains from joint operation of multiple reservoir systems

Synergistic gains are defined as the gains in benefits due to joint operation of a system of reservoirs in excess of the benefits from optimal individual operation. These gains are a result of both the deterministic (regional) and the stochastic diversity of flows into each of the reservoirs. They are captured by the use of flexible reservoir operating rules which base release decisions for a given reservoir on the state of the entire system, not just on the state of that reservoir. One possible operating rule is formulated and is demonstrated to be highly effective in capturing synergistic gains. A hypothetical design problem of sizing three water supply reservoirs in parallel is solved by three methods. The first method assumes that no synergistic gains are achievable. The second and third methods recognize the existence of such gains. The method recommended here incorporates the operating rule into the design process and makes use of the observation that the system yield is a function of system capacity.

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.