Mixed-Integer Programming Model for Reservoir Performance Optimization
01 Sep 1999-Journal of Water Resources Planning and Management (American Society of Civil Engineers)-Vol. 125, Iss: 5, pp 298-301
TL;DR: In this paper, a mixed-integer programming model for the operation of a water supply reservoir during critical periods has been presented in the literature that incorporates reliability, resilience, and vulnerability, and an improved formulation of this model that represents resilience more completely is discussed.
Abstract: Failures in operation of water supply reservoir systems are often unavoidable during critical hydrologic periods. The failure characteristics of such systems can be represented by performance indicators such as reliability, resilience, and vulnerability. A mixed-integer programming model for the operation of a water supply reservoir during critical periods has been presented in the literature that incorporates these performance indicators. An improved formulation of this model that represents resilience more completely is discussed herein. In addition, a set of constraints with binary integer variables are included to account for reservoir spills. The improvements achieved with the modified model is demonstrated using the same example as presented with the original model.
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TL;DR: In this article, an inexact two-stage stochastic integer programming (ISIP) model is developed for capacity planning of flood diversion under uncertainty, which can facilitate dynamic analysis of capacityexpansion planning when uncertainties are presented in terms of probabilistic distributions and discrete intervals.
Abstract: An inexact two-stage stochastic integer programming (ISIP) model is developed for capacity planning of flood diversion under uncertainty. It incorporates the concepts of two-stage stochastic programming and chance-constrained programming within an interval-parameter integer programming framework. ISIP can facilitate dynamic analysis of capacity-expansion planning when uncertainties are presented in terms of probabilistic distributions and discrete intervals. Moreover, it can be used for examining various policy scenarios associated with different levels of economic penalties when the promised targets are violated. The developed method is applied to a case study of flood-diversion planning under uncertainty. Reasonable solutions are generated for binary and continuous variables. They provide the desired capacity-expansion schemes and flood-diversion patterns, which are related to a variety of trade-offs between system cost and constraint-violation risk. Decisions with a lower-risk level imply a higher syst...
10 citations
Cites background from "Mixed-Integer Programming Model for..."
...Previously, several studies of flood management by means of MILP were reported (van Dantzig 1956, Kumar et al. 1979, Windsor 1981, Randall 1997, Srinivasan et al. 1999, Needham et al. 2000)....
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TL;DR: In this paper, a case study for hydropower reservoir operation of Indirasagar reservoir system in India is presented and the performances of optimal hedging rules were compared with that of a new standard operation policies and the superiority (reliability increases by about 10%) of the hedging rule are presented.
9 citations
Cites background from "Mixed-Integer Programming Model for..."
...However, using this resilience indicator alone may have some drawbacks [40]....
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...Hence, with the total number of failure periods remaining xed, continuous failures are undesirable compared to intermittent failures [40]....
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...The ability of the system to recover from failure state to success state will be de ned as resilience [40]....
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TL;DR: Wang et al. as discussed by the authors applied a monotonic test to three fundamental single drought indices, namely reliability, vulnerability and resilience, to demonstrate that indices showing non-monotonic behaviour can potentially give misleading information regarding the effects of drought to water resources systems.
Abstract: In this study, innovative drought indices are developed to accurately quantify the characteristics of drought events and their possible impacts to the water resources system of the Tsengwen Reservoir of Taiwan. We applied a monotonic test to three fundamental single drought indices, namely reliability, vulnerability and resilience, to demonstrate that indices showing non-monotonic behaviour can potentially give misleading information regarding the effects of drought to water resources systems. We further tested two newly proposed single drought indices, Vul
system
and Res
weighted
, to the study site, of which Vul
system
showed monotonic behaviour but Res
weighted
still behaved non-monotonically, even though in a suppressed manner. Next, we proposed and tested three composite drought indices, sustainability index (SI), drought risk index (DRI) and the water shortage index (WSI), of which only the WSI behaved monotonically. As a result, WSI was applied to investigate the potential impact of climate change to the future drought risk of the study site. On the basis of WSI values derived from runoffs simulated by the modified HBV and a reservoir operation (water balance) model driven with 18 sets of climate changes scenarios of IPCC (2007) statistically downscaled using the MarkSim GCM model, it seems that there is a 20 % chance that climate change impact could lead to more severe droughts in the study site. However, under the combined impact of climate change and the effect of sedimentation to the Tsengwen Reservoir, which could decrease its storage capacity by about 12 % (i.e., s = 0.88), it seems more severe drought impacts will increase to 2/3 of the 18 test cases. Lastly, a direct relationship was developed between WSI and the multifractal strength, which implies that runoff data with a stronger multifractal strength could lead to more severe droughts and vice versa.
8 citations
Cites background from "Mixed-Integer Programming Model for..."
...On the other hand, by a simple example, Srinivasan et al. (1999) showed that the maximum CDDE may not be a representative measure of resilience and other researchers also presented drawbacks of different definitions about resilience....
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TL;DR: In this article, the authors used an ANFIS model to estimate monthly volumes by using the data of 1986-2008 for Sandikli Kestel dam, where the number of clusters used for the inputs was obtained by the method of K-means.
Abstract: Correct planning of water resources is important for the efficient use of rapidly decreasing water resources in the future. Flow modeling and flow estimations in the planning of water resource are the basis of studies. In this study, it is aimed to estimate monthly volumes by using ANFIS model based on the data of 1986-2008 for Sandikli Kestel dam. In the system, the volume of the previous months, the volume of the incoming and outgoing volumes and the amount of evaporation were used as input variables. In ANFIS method, the number of clusters used for the inputs was obtained by the method of K-means. Different clusters formed by K-averages were modeled in ANFIS and the results were compared. The optimal number of clusters for each input value is determined. Models have been established in this way. As a result, it has been found that the models made according to the optimal number of clusters yield results with lower error percentage compared to randomly generated models.
6 citations
Cites background from "Mixed-Integer Programming Model for..."
...[3] Srinivasan K, Neelakantan TR, Narayan PS, Nagarajukumar C....
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TL;DR: A new methodology for analyzing and computing the overall hydraulic performance for each single component in the network and for the whole water distribution system is introduced.
6 citations
References
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TL;DR: In this paper, three criteria for evaluating the performance of water resource systems are discussed, i.e., reliability, resilience, and vulnerability, which describe how likely a system is to fail, how quickly it recovers from failure, and how severe the consequences of failure may be.
Abstract: Three criteria for evaluating the possible performance of water resource systems are discussed. These measures describe how likely a system is to fail (reliability), how quickly it recovers from failure (resiliency), and how severe the consequences of failure may be (vulnerability). These criteria can be used to assist in the evaluation and selection of alternative design and operating policies for a wide variety of water resource projects. The performance of a water supply reservoir with a variety of operating policies illustrates their use.
1,458 citations
TL;DR: In this paper, a linear decision rule is proposed to specify the release during any period of reservoir operation as the difference between the storage at the beginning of the period and a decision parameter for the period.
Abstract: With the aid of a linear decision rule, reservoir management and design problems often can be formulated as easily solved linear programing problems. The linear decision rule specifies the release during any period of reservoir operation as the difference between the storage at the beginning of the period and a decision parameter for the period. The decision parameters for the entire study horizon are determined by solving the linear programing problem. Problems may be formulated in either the deterministic or the stochastic environment.
290 citations
TL;DR: In this article, the tradeoffs between reliability, vulnerability, and resilience were examined using multiobjective mixed-integer, linear programming, and it was found that as reliability is increased or as the maximum length of consecutive shortfalls decreases (resilience increases), the vulnerability of the water system to larger deficits increases.
Abstract: Reliability in water supply reservoir operation is commonly thought of as the probability of failing to achieve some target release. Here we explore two additional proposed descriptions of reservoir performance: the maximum shortfall from the target (system vulnerability) and the maximum number of consecutive periods of deficit during a record (system resilience). The larger the maximum shortfall, the greater the vulnerability. The shorter the maximum length of deficits, the more resilient the system. Using multiobjective mixed-integer, linear programming, the tradeoffs between reliability, vulnerability, and resilience are examined. It is found that as reliability is increased or as the maximum length of consecutive shortfalls decreases (resilience increases), the vulnerability of the water system to larger deficits increases.
267 citations
TL;DR: In this article, a polytope search algorithm using a combination of simulation and optimization is compared to an iterative mixed integer programming method to determine the parameters of continuous demand management rules.
Abstract: Demand-management policy rules are sought during drought and impending drought for a water system consisting of a reservoir dedicated only to water supply. The creation of such rules requires solution of a nonlinear, nonseparable mathematical programming problem. A polytope search algorithm using a combination of simulation and optimization is compared to an iterative mixed integer programming method to determine the parameters of continuous demand management rules. The signal used for calling rationing is a trigger volume given in terms of months of demand (as a volume) that are needed in storage. When the sum of actual storage plus anticipated inflow is less than the trigger volume, rationing is initiated. The extent of rationing or demand reduction that is required is determined by the ration of the sum of storage plus inflow to the trigger volume. The two methodologies for parameter determination are compared using as a criteria the maximum shortage that occurs over some planning period.
145 citations
TL;DR: A mixed integer programming model is constructed for the operation of a single water supply reservoir during drought and impending drought and determines trigger volumes of storage plus anticipated inflow which signal the need for each of the several phases of rationing.
113 citations