A Fuzzy Stochastic Dynamic Nash Game Analysis of Policies for Managing Water Allocation in a Reservoir System

In this paper a fuzzy dynamic Nash game model of interactions between water users in a reservoir system is presented. The model represents a fuzzy stochastic non-cooperative game in which water users are grouped into four players, where each player in game chooses its individual policies to maximize expected utility. The model is used to present empirical results about a real case water allocation from a reservoir, considering player (water user) non-cooperative behavior and also same level of information availability for individual players. According to the results an optimal allocation policy for each water user can be developed in addition to the optimal policy of the reservoir system. Also the proposed model is compared with two alternative dynamic models of reservoir optimization, namely Stochastic Dynamic Programming (SDP) and Fuzzy-State Stochastic Dynamic programming (FSDP). The proposed modeling procedures can be applied as an appropriate tool for reservoir operation, considering the interaction among the water users as well as the water users and reservoir operator.     

Modeling Multi-objective Pareto-optimal Reservoir Operation Policies Using State-of-the-art Modeling Techniques

A novel challenge faced by water scientists and water managers today is the efficient management of the available water resources for meeting crucial demands such as drinking water supply, irrigation and hydro-power generation. Optimal operation of reservoirs is of paramount importance for better management of scarce water resources under competing multiple demands such as irrigation, water supply etc., with decreasing reliability of these systems under climate change. This study compares six different state-of-the-art modeling techniques namely; Deterministic Dynamic Programming (DDP), Stochastic Dynamic Programming (SDP), Implicit Stochastic Optimization (ISO), Fitted Q-Iteration (FQI), Sampling Stochastic Dynamic Programming (SSDP), and Model Predictive Control (MPC), in developing pareto-optimal reservoir operation solutions considering two competing operational objectives of irrigation and flood control for the Pong reservoir located in Beas River, India. Set of pareto-optimal (approximate) solutions were derived using the above-mentioned six methods based on different convex combinations of the two objectives and finally the performances of the resulting sets of pareto-optimal solutions were compared. Additionally, key reservoir performance indices including resilience, reliability, vulnerability and sustainability were estimated to study the performance of the current operation of the reservoir. Modeling results indicate that the optimal-operational solution developed by DDP attains the best performance followed by the MPC and FQI. The performance of the Pong reservoir operation assessed by comparing different performance indices suggests that there is high vulnerability (~?0.65) and low resilience (~?0.10) in current operations and the development of pareto-optimal operation solutions using multiple state-of-the-art modeling techniques might be crucial for making better reservoir operation decisions.

     

用增量动态规划法进行联合水资源系统分析

本文应用数学规划技术建立一种适用于多用途和多水源系统的最优运行策略，通常标准动态规划法的“维数灾”问题限制了动态规划法只能用于低阶系统，这里将增量动态规划法用于四维水库系统处理轨迹优化，采用这种方法收到了两种效益，增加生活、工业、灌溉、发电供水的效益和减少计算机时间的效益。     

基于DPSA 的梯级水库群优化调度

动态规划法是一种求解多阶段决策优化问题的常用方法,在水库优化调度计算中应用广泛。该方法最大的缺陷就是用于水库群优化调度时易出现"维数灾"问题。逐次逼近动态规划法(DPSA)可以有效克服这一问题,它采用逐次迭代逼近的思想,将一个多维问题分解为多个一维问题求解。本文以水库运行模拟模型为基础,建立了基于DPSA的梯级水库群中长期优化调度模型,以汉江上游梯级水库群为研究对象,选取发电量最大为目标,对各水库库容进行离散,从而求解水库优化运行过程,其结果对于水库优化调度运行具有指导意义。     

An alternative approach to the operation of multinational reservoir systems: Application to the Amistad &; Falcon system (Lower Rio Grande/Río Bravo)

An optimization approach for the operation of international multi-reservoir systems is presented. The approach uses Stochastic Dynamic Programming (SDP) algorithms – both steady-state and real-time – to develop two models. In the first model, the reservoirs and flows of the system are aggregated to yield an equivalent reservoir, and the obtained operating policies are disaggregated using a non-linear optimization procedure for each reservoir and for each nation's water balance. In the second model a multi-reservoir approach is applied, disaggregating the releases for each country's water share in each reservoir. The non-linear disaggregation algorithm uses SDP-derived operating policies as boundary conditions for a local time-step optimization. Finally, the performance of the different approaches and methods is compared. These models are applied to the Amistad-Falcon International Reservoir System as part of a binational dynamic modeling effort to develop a decision support system tool for a better management of the water resources in the Lower Rio Grande Basin, currently enduring a severe drought.     

Comparison of Policies Derived from Stochastic Dynamic Programming and Genetic Algorithm Models

A comprehensive Genetic Algorithm (GA) model has been developed and applied to derive optimal operational strategies of a multi-purpose reservoir, namely Perunchani Reservoir, in Kodaiyar Basin in Tamil Nadu, India. Most of the water resources problem involves uncertainty, in order to see that the GA model takes care of uncertainty in the input variable, the result of the GA model is compared with the performance of a detailed Stochastic Dynamic Programming (SDP) model. The SDP models are well established and proved that it takes care of uncertainty in-terms of either implicit or explicit approach. In the present study, the objective function of the models is set to minimize the annual sum of squared deviation from desired target release and desired storage volume. In the SDP model the optimal policies are derived by varying the state variables from 3 to 9 representative class intervals, and then the cases are evaluated for their performance using a simulation model for longer length of inflow data, generated using a Thomas–Fiering model. From the performance of the SDP model policies, it is found that the system encountered irrigation deficit, whereas GA model satisfied the demand to a greater extent. The sensitivity analysis of the GA model in selecting optimal population, optimal crossover probability and the optimal number of generations showed the values of 150, 0.76 and 175 respectively. On comparing the performance of SDP model policy with GA model, it is found that GA model has resulted in a lesser irrigation deficit. Thus based on the present case study, it may be concluded that the GA model performs better than the SDP model.     

Medium-Term Hydro Generation Scheduling (MTHGS) with Chance Constrained Model (CCM) and Dynamic Control Model (DCM)

Medium-Term Hydro Generation Scheduling (MTHGS) plays an important role in the operation of hydropower systems. In the first place, this paper presents a Chance Constrained Model for solving the optimal MTHGS problem. The model recognizes the impact of inflow uncertainty and the constraints involving hydrologic parameters subjected to uncertainty are described as probabilistic statements. It aims at providing a more practical technique compared to the traditional deterministic approaches used for MTHGS. The stochastic inflow is expressed as a simple discrete-time Markov chain and Stochastic Dynamic Programming is adopted to solve the model. Then in order to use the information of long-term inflow forecast to improve dispatching decisions, a Dynamic Control Model is developed. Short-term forecast results of the current period and long-term forecast results of the remaining period are treated as inputs of the model. Finally, the two methods are applied to MTHGS of Xiluodu hydro plant in China. The results are compared to those obtained from Deterministic Dynamic Programming with hindsight and advantages and disadvantages of the two methods are analyzed.     

Reliability Improved Stochastic Dynamic Programming for Reservoir Operation Optimization

Stochastic Dynamic Programming (SDP) is widely used in reservoir operation problems. Besides its advantages, a few drawbacks have leaded many studies to improve its structure. Handling the infeasible conditions and curse of dimensionality are two major challenges in this method. The main goal of this paper is proposing a new method to avoid infeasible conditions and enhance the solution efficiency with new discretization procedure. For this purpose, an optimization module is incorporated into regular SDP structure, so that, near optimal values of state variables are determined based on the available constraints. The new method (RISDP) employs reliability concept to maximize the reservoir releases to satisfy the downstream demands. Applying the proposed technique improves the reservoir operating policies compared to regular SDP policies with the same assumptions of discretization. Simulation of reservoir operation in a real case study indicates about 15% improvement in objective function value and elimination of infeasible conditions by using RISDP operating policies.     

Feasibility Improved Stochastic Dynamic Programming for Optimization of Reservoir Operation

Water Resources Management - Stochastic Dynamic Programming (SDP) is a major method for optimizing reservoir operation. Handling non-linear, non-convex and non-differentiable objective functions...     

Monthly Joint Operations for the Nakdong Multi-reservoir System in Korea

Abstract

This study applies a state-of-art optimization technique, SSDP/ESP (Sampling Stochastic Dynamic Programming with Ensemble Streamflow Prediction), to derive a monthly joint operating policy for the Nakdong multi-reservoir system in Korea. A rainfall-runoff model, SSARR (Streamflow Synthesis And Reservoir Regulation), is linked to the SSDP/ESP model to provide ESP scenarios for runoff during the next month in the Nakdong River basin. The primary advantage of the SSDP/ESP is that it updates the derived operating policy as new ESP forecasts become available. Another SSDP model that employs historical runoff scenarios (SSDP/Hist) is also developed. The main difference between the two SSDP models is that SSDP/Hist is an off-line model whereas the SSDP/ESP is on-line. The developed operating policies are tested with a simulation model using an object-oriented simulation software, STELLA. The simulation results show that SSDP/ESP is superior to SSDP/Hist with respect to the water supply criterion, although both models perform similarly with respect to the hydroelectric energy production criterion.     

Optimal Hydropower Generation Under Climate Change Conditions for a Northern Water Resources System

This paper examines climate change impacts on the water resources system of the Manicouagan River (Québec, Canada). The objective is to evaluate the performance of existing infrastructures under future climate projections and the associated uncertainties. The main purpose of the water resources system is hydropower production. A reservoir optimization algorithm, Sampling Stochastic Dynamic Programming (SSDP), was used to derive weekly operating decisions for the existing system subject to reservoir inflows reflecting future climate, for optimum hydropower production. These projections are simulations from the SWAT hydrologic model for climate change scenarios for the period from 2010 to 2099. Results show that the climate change will alter the hydrological regime of the study area: earlier timing of the spring flood, reduced spring peak flow, and increased annual inflows volume in the future compared to the historical climate. The SSDP optimization algorithm adapted the operating policy to the future hydrological regime by adjusting water reservoir levels in the winter and spring, and increasing the release through turbines, which in the end increased power generation. However, there could be more unproductive spills for some power plants, which would decrease the overall efficiency of the existing water resources system.     

Value of Medium-range Precipitation Forecasts in Inflow Prediction and Hydropower Optimization

This paper presents an inflow-forecasting model and a Piecewise Stochastic Dynamic Programming model (PSDP) to investigate the value of the Quantitative Precipitation Forecasts (QPFs) comprehensively. Recently medium-range quantitative precipitation forecasts are addressed to improve inflow forecasts accuracy. Revising the Ertan operation, a simple hydrological model is proposed to predict 10-day average inflow into the Ertan dam using GFS-QPFs of 10-day total precipitation during wet season firstly. Results show that the reduction of average absolute errors (ABE) is of the order of 15% and the improvement in other statistics is similar, compared with those from the currently used AR model. Then an improved PSDP is proposed to generate monthly or 10-day operating policies to incorporate forecasts with various lead-times as hydrologic state variables. Finally performance of the PSDP is compared with alternative SDP models to evaluate the value of the GFS-QPFs in hydropower generation. The simulation results demonstrate that including the GFS-QPFs is beneficial to the Ertan reservoir inflow forecasting and hydropower generation dispatch.     

Environmental Flows in a Human‐Dominated System: Integrated Water Management Strategies for the Rio Grande/Bravo Basin

Water management in the transboundary Rio Grande/Bravo (RGB) Basin, shared by the US and Mexico, is complicated by extreme hydrologic variability, overallocation, and international treaty obligations. Heavy regulation of the RGB has degraded binationally protected ecosystems along the Big Bend Reach of the RGB. This study addresses the need for integrated water management in Big Bend by developing an alternative reservoir operation policy to provide environmental flows while reducing water management trade‐offs. A reach‐scale water planning model was used to represent historical hydrology (1955–2009), water allocation, and reservoir operations, and key human water management objectives (water supply, flood control, and binational treaty obligations) were quantified. Spatially distributed environmental flow objectives and an alternative reservoir rule curve were developed. We simulated current and alternative water management policies and used an iterative simulation–evaluation process to evaluate alternative policies based on water system performance criteria with respect to specified objectives. A single optimal policy was identified that maximized environmental flows while maintaining specified human objectives. By changing the timing but not the volume of releases, the proposed reservoir re‐operation policy has the potential to sustain key ecological and geomorphic functions in Big Bend without significantly impacting current water management objectives. The proposed policy also improved water supply provisions, reduced average annual flood risk, and maintained historical treaty provisions. Copyright © 2014 John Wiley & Sons, Ltd.     

Applying Genetic Algorithm and Neural Network to the Conjunctive Use of Surface and Subsurface Water

The conjunctive use of surface and subsurface water is one of the most effective ways to increase water supply reliability with minimal cost and environmental impact. This study presents a novel stepwise optimization model for optimizing the conjunctive use of surface and subsurface water resource management. At each time step, the proposed model decomposes the nonlinear conjunctive use problem into a linear surface water allocation sub-problem and a nonlinear groundwater simulation sub-problem. Instead of using a nonlinear algorithm to solve the entire problem, this decomposition approach integrates a linear algorithm with greater computational efficiency. Specifically, this study proposes a hybrid approach consisting of Genetic Algorithm (GA), Artificial Neural Network (ANN), and Linear Programming (LP) to solve the decomposed two-level problem. The top level uses GA to determine the optimal pumping rates and link the lower level sub-problem, while LP determines the optimal surface water allocation, and ANN performs the groundwater simulation. Because the optimization computation requires many groundwater simulations, the ANN instead of traditional numerical simulation greatly reduces the computational burden. The high computing performance of both LP and ANN significantly increase the computational efficiency of entire model. This study examines four case studies to determine the supply efficiencies under different operation models. Unlike the high interaction between climate conditions and surface water resource, groundwater resources are more stable than the surface water resources for water supply. First, results indicate that adding an groundwater system whose supply productivity is just 8.67 % of the entire water requirement with a surface water supply first (SWSF) policy can significantly decrease the shortage index (SI) from 2.93 to 1.54. Second, the proposed model provides a more efficient conjunctive use policy than the SWSF policy, achieving further decrease from 1.54 to 1.13 or 0.79, depending on the groundwater rule curves. Finally, because of the usage of the hybrid framework, GA, LP, and ANN, the computational efficiency of proposed model is higher than other models with a purebred architecture or traditional groundwater numerical simulations. Therefore, the proposed model can be used to solve complicated large field problems. The proposed model is a valuable tool for conjunctive use operation planning.     

逐次逼近随机动态规划及库群优化调度

随机动态规划（SDP）在水库水电站长期优化调度中有着较为广泛的应用,它的最大缺陷就是用于库群优化调度时的“维数灾”问题,逐次逼近胡机动态规划可有效克服这一问题。该方法采用逐次迭代逼近的思想,每次仅对一个水库采用SDP求解,并假设其它水库的蓄水过程已确定为多年平均蓄水过程,对某水库进行SDP求解后,通过多年历史径流过程的模拟调度可对各水库的多年平均蓄水过程进行更新,最后以福建省闽江流域水电系统为例进行了实例应用。     

Basin/Reservoir System Integration for Real Time Reservoir Operation

This paper demonstrates the basin/reservoir system integration as a decision support system for short term operation policy of a multipurpose dam. It is desired to re-evaluate and improve the current operational regulation of the reservoir with respect to water supply and flood control especially for real time operation. The most innovative part of this paper is the development of a decision support system (DSS) by the integration of a hydrological (HEC-HMS) and reservoir simulation model (HEC-ResSim) to guide the professional practitioners during the real time operation of a reservoir to meet water elevation and flood protection objectives. In this context, a hybrid operating strategy to retain maximum water elevation is built by shifting between daily and hourly decisions depending on real time runoff forecasts. First, a daily hydro-meteorological rule based reservoir simulation model (HRM) is developed for both water supply and flood control risk. Then, for the possibility of a flood occurrence, hourly flood control rule based reservoir simulation model (FRM) is used. The DSS is applied on Yuvac?k Dam Basin which has a flood potential due to its steep topography, snow potential, mild and rainy climate in Turkey. Numerical weather prediction based runoff forecasts computed by a hydrological model together with developed reservoir operation policy are put into actual practice for real time operation of the reservoir for March – June, 2012. According to the evaluations, proposed DSS is found to be practical and valuable to overcome subjective decisions about reservoir storage.     

A Bayesian Stochastic Optimization Model for a Multi-Reservoir Hydropower System

This paper presents the development of an operating policy model for a multi-reservoir system for hydropower generation by addressing forecast uncertainty along with inflow uncertainty. The stochastic optimization tool adopted is the Bayesian Stochastic Dynamic Programming (BSDP), which incorporates a Bayesian approach within the classical Stochastic Dynamic Programming (SDP) formulation. The BSDP model developed in this study considers, the storages of individual reservoirs at the beginning of period t, aggregate inflow to the system during period t and forecast for aggregate inflow to the system for the next time period t + 1, as state variables. The randomness of the inflow is addressed through a posterior flow transition probability, and the uncertainty in flow forecasts is addressed through both the posterior flow transition probability and the predictive probability of forecasts. The system performance measure used in the BSDP model is the square of the deviation of the total power generated from the total firm power committed and the objective function is to minimize the expected value of the system performance measure. The model application is demonstrated through a case study of the Kalinadi Hydroelectric Project (KHEP) Stage I, in Karnataka state, India.     

Technical Communication: Two-Phase Stochastic Dynamic Programming Model for Optimal Operation of Irrigation Reservoir

A two-phase stochastic dynamic programming model is developed for optimal operation of irrigation reservoirs under a multicrop environment. Under a multicrop environment, the crops compete for the available water whenever the water available is less than the irrigation demands. The performance of the reservoir depends on how the deficit is allocated among the competing crops. The proposed model integrates reservoir release decisions with water allocation decisions. The water requirements of crops vary from period to period and are determined from the soil moisture balance equation taking into consideration the contribution of soil moisture and rainfall for the water requirements of the crops. The model is demonstrated over an existing reservoir and the performance of the reservoir under the operating policy derived using the model is evaluated through simulation.     

梯级水库短期优化调度模型的精细化与GPU并行实现

目前制约梯级水库短期优化调度在实际工程中应用的主要瓶颈有:所构建的优化模型存在不合理的简化策略,所选择的求解算法无法保证解的质量以及模型的计算时间远超规定时长。为解决上述问题,本文首先构建精细至水电站各机组工作特性的优化调度模型,接着通过二重嵌套动态规划(DP)计算给定模拟精度下的高质量解,并针对算法固有的"维数灾"问题,一方面通过数据压缩与数据库技术降低程序的内存占用量,另一方面将GPU并行加速技术首次引入水库调度领域,通过OpenACC实现算法的GPU并行以减少计算时间。最后通过潘口、小漩梯级水库日优化调度的实例研究与对比分析得出:精细模型较传统模型能更好地贴合电站的实际工况,提高梯级系统的发电效益;内存占用缩减策略的引入能有效降低算法的空间复杂度;GPU并行较传统的CPU并行能大幅提升算法的求解速度。由此为短期优化调度的理论发展与算法"维数灾"的处理提供借鉴。     

A Novel Solution for Stochastic Dynamic Game of Water Allocation from a Reservoir Using Collocation Method

In this study, a continuous model of stochastic dynamic game for water allocation from a reservoir system was developed. The continuous random variable of inflow in the state transition function was replaced with a discrete approximant rather than using the mean of the random variable as is done in a continuous model of deterministic dynamic game. As a result, a new solution method was used to solve the stochastic model of game based on collocation method. The collocation method was introduced as an alternative to linear-quadratic (LQ) approximation methods to resolve a dynamic model of game. The collocation method is not limited to the first and second degree approximations, compared to LQ approximation, i.e. Ricatti equations. Furthermore, in spite of LQ related problems, consideration of the stochastic nature of game on the action variables in the collocation method would be possible. The proposed solution method was applied to the real case of reservoir operation, which typically requires considering the effect of uncertainty on decision variables. The results of the solution of the stochastic model of game are compared with the results of a deterministic solution of game, a classical stochastic dynamic programming model (e.g. Bayesian Stochastic Dynamic Programming model, BSDP), and a discrete stochastic dynamic game model (PSDNG). By comparing the results of alternative methods, it is shown that the proposed solution method of stochastic dynamic game is quite capable of providing appropriate reservoir operating policies.