A Simple and Effective Method for Modelling a Catchment: A Case Study

Abstract Considering the scarcity of water all over the world and need t

A Simple and Effective Method for Modelling a Catchment: A Case Study

Abstract Considering the scarcity of water all over the world and need t

Folded Dynamic Programming for Optimal Operation of Multireservoir System

Dynamic Programming (DP) is considered as a good technique for optimal reservoir operation due to the sequential decision making and ease in handling non-linear objective functions and constraints. But the application of DP to multireservoir system is not that encouraging due to the problem `curse of dimensionality'. Incremental DP, discrete differential DP, DP with successive approximation, incremental DP with successive approximation are some of the algorithms evolved to tackle this curse of dimensionality for DP. But in all these cases, it is difficult to choose an initial trial trajectory, to get at an optimal solution and there is no control over the number of iterations required for convergence. In this paper, a new algorithm, Folded DP, is proposed, which overcomes these difficulties. Though it is also an iterative process, no initial trial trajectory is required to start with. So, the number of iterations is independent of any initial condition. The developed algorithm is applied to a hypothetical reservoir system, solved by earlier researchers. Operating policy obtained using the present algorithm has compared well with that of the earlier algorithm

Stochastic Linear Programming for Optimal Reservoir Operation: A Case Study

Optimal reservoir operating policy should consider the uncertainty associated with the uncontrolled inflow to the reservoir. In the present study, Stochastic Linear Programming (SLP) model is developed to obtain optimal operating policy for the existing multipurpose reservoir. The objective of the model is to maximise the expected value of the system performance which is the sum of the all performance value times the respective joint probabilities. The decision variables are the probabilities of reservoir release, PR k,i,l,t , which are the joint probabilities of the reservoir release, R k,i,l,t , with an initial reservoir storage volume of S k,t , inflow of Q i,t and the final storage volume of S l,t+1 for a given time period t. The joint probabilities are influenced by the target reservoir storages, releases and the stochastic nature of inflows. This objective is subject to a set of stochastic constraints to maintain continuity. Historic inflow data is used to consider the stochastic nature of inflows in the form of inflow transition probability matrices. A computer program is developed in LINGO (Language for INteractive General Optimisation) to perform stochastic optimisation. The model gives the steady state probabilities of reservoir storage and inflow as output. The model is applied to Hirakud reservoir in Mahanadi river basin of orissa state, India, for development of an optimal reservoir operating policy. The steady state optimal operating policy and its implications are discussed in this paper

Folded Dynamic Programming for Optimal Operation of Multireservoir System

Dynamic Programming (DP) is considered as a good technique for optimal reservoir operation due to the sequential decision making and ease in handling non-linear objective functions and constraints. But the application of DP to multireservoir system is not that encouraging due to the problem ‘curse of dimensionality’. Incremental DP, discrete differential DP,DP with successive approximation, incremental DP with successive approximation are some of the algorithms evolved to tackle this curse of dimensionality for DP. But in all these cases, it is difficult to choose an initial trial trajectory, to get at an optimal solution and there is no control over the number of iterations required for convergence. In this paper, a new algorithm, Folded DP, is proposed, which overcomes these difficulties. Though it is also an iterative process, no initial trial trajectory is required to start with. So, the number of iterations is independent of any initial condition. The developed algorithm is applied to a hypothetical reservoir system, solved by earlier researchers. Operating policy obtained using the present algorithm has compared well with that of the earlier algorithm

Extended Muskingum method for flood routing

Routing of floods is essential to control the flood flow at the flood control station such that it is within the specified safe limit. In this paper, the applicability of the extended Muskingum method is examined for routing of floods for a case study of Hirakud reservoir, Mahanadi river basin, India. The inflows to the flood control station are of two types-one controllable which comprises of reservoir releases for power and spill and the other is uncontrollable which comprises of inflow from lower tributaries and intermediate catchment between the reservoir and the flood control station. Muskingum model is improved to incorporate multiple sources of inflows and single outflow to route the flood in the reach. Instead of time lag and prismoidal flow parameters, suitable coefficients for various types of inflows were derived using Linear Programming. Presently, the decisions about operation of gates of Hirakud dam are being taken once in 12 h during floods. However, four time intervals of 24, 18, 12 and 6 h are examined to test the sensitivity of the routing time interval on the computed flood flow at the flood control station. It is observed that mean relative error decreases with decrease in routing interval both for calibration and testing phase. It is concluded that the extended Muskingum method can be explored for similar reservoir configurations such as Hirakud reservoir with suitable modifications. (C) 2010 International Association of Hydro-environment Engineering and Research. Asia Pacific Division. Published by Elsevier By. All rights reserved

Optimal Reservoir Operation for Flood Control Using Folded Dynamic Programming

Folded Dynamic Programming (FDP) is adopted for developing optimalnreservoir operation policies for flood control. It is applied to a case study of Hirakud Reservoir in Mahanadi basin, India with the objective of deriving optimal policy for flood control. The river flows down to Naraj, the head of delta where a major city is located and finally joins the Bay of Bengal. As Hirakud reservoir is on the upstream side of delta area in the basin, it plays an important role in alleviating the severity of the flood for this area. Data of 68 floods such as peaks of inflow hydrograph, peak of outflow from reservoir during each flood, peak of flow hydrograph at Naraj and d/s catchment contribution are utilized. The combinations of 51, 54, 57 thousand cumecs as peak inflow into reservoir and 25.5, 20, 14 thousand cumecs respectively as,peak d/s catchment contribution form the critical combinations for flood situation. It is observed that the combination of 57 thousand cumecs of inflow into reservoir and 14 thousand cumecs for d/s catchment contribution is the most critical among the critical combinations of flow series. The method proposed can be extended to similar situations for deriving reservoir operating policies for flood control