聚合分解随机动态规划模型在梯级水库群发电调度中的应用研究

本文首先采用聚合分解思想将梯级水库群来水量和库容聚合等效为单库，从而简化水库群径流过程的描述和降低高维计算空间，使随机动态规划模型（SDP）在梯级水库群的应用中可以考虑更多的信息来提高模型效率；然后在径流预报中考虑美国全球预报系统（GFS）发布的未来10天降雨预报信息，来提高中期径流预报精度；最后在考虑径流预报不确定性的基础上建立了聚合分解贝叶斯随机动态规划模型（AD-BSDP）。同时与传统调度图、聚合来水量的随机动态规划模型（AF-SDP）和聚合来水量、库容的聚合分解随机动态规划模型（AD-SDP）进行了对比分析来验证模型的有效性，分析结果表明考虑预报信息不确定性的AD-BSDP模型比其他模型具有更高的效率和稳定性。     

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.     

Bayesian Stochastic Dynamic Programming for Hydropower Generation Operation Based on Copula Functions

Bayesian stochastic dynamic programming (BSDP) has been widely used in hydropower generation operation, as natural inflow and forecast uncertainties can be easily determined by transition probabilities. In this study, we propose a theoretical estimation method (TEM) based on copula functions to calculate the transition probability under conditions of limited historical inflow samples. The explicit expression of the conditional probability is derived using copula functions and then used to calculate prior and likelihood probabilities, and the prior probability can be revised to the posterior probability once new forecast information is available by Bayesian formulation. The performance of BSDP models in seven forecast scenarios and two extreme conditions considering no or perfect forecast information is evaluated and compared. The case study in the Ertan hydropower station in China shows that (1) TEM can avoid the shortcomings of empirical estimation method (EMM) in calculating the transition probability, so that the prior and likelihood probability matrices can be distributed more uniformly with less zeros, and the problem that the posterior probability cannot be calculated can be avoided; (2) there is a positive correlation between operating benefit and forecast accuracy; and (3) the operating policy considering reliable forecast information can improve hydropower generation. However, an incorrect decision may be made in the case of low forecast accuracy.

     

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.     

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.     

一种考虑径流预报及其不确定性的水库优化调度模型

鉴于纯随机径流描述或确定性径流预报的水库(群)优化调度模型,未考虑径流预报及其不确定性,导致优化计算结果与水库实际运行情况存在较大差异.本文提出了一种利用后验的径流状态转移概率和径流预报的可预测性概率来描述径流预报及其不确定性的优化调度模型.依据二滩水电站径流及其预报的实际状况,考虑不同预见期的径流预报信息,建立了考虑...     

An Optimal Operation Model for Hydropower Stations Considering Inflow Forecasts with Different Lead-Times

To make full use of inflow forecasts with different lead times, a new reservoir operation model that considers the long-, medium- and short-term inflow forecasts (LMS-BSDP) for the real-time operation of hydropower stations is presented in this paper. First, a hybrid model, including a multiple linear regression model and the Xinanjiang model, is developed to obtain the 10-day inflow forecasts, and ANN models with the circulation indexes as inputs are developed to obtain the seasonal inflow forecasts. Then, the 10-day inflow forecast is divided into two segments, the first 5 days and the second 5 days, and the seasonal inflow forecast is deemed as the long-term forecast. Next, the three inflow forecasts are coupled using the Bayesian theory to develop LMS-BSDP model and the operation policies are obtained. Finally, the decision processes for the first 5 days and the entire 10 days are made according to their operation policies and the three inflow forecasts, respectively. The newly developed model is tested with the Huanren hydropower station located in China and compared with three other stochastic dynamic programming models. The simulation results demonstrate that LMS-BSDP performs best with higher power generation due to its employment of the long-term runoff forecast. The novelties of the present study lies in that it develops a new reservoir operation model that can use the long-, medium- and short-term inflow forecasts, which is a further study about the combined use of the inflow forecasts with different lead times based on the existed achievements.

     

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.     

Effect of inflow forecast accuracy and operating time horizon in optimizing irrigation releases

In this study, application of Genetic Algorithms (GA) is demonstrated to optimize reservoir release policies to meet irrigation demand and storage requirements. As it is commonly recognized that accuracy of inflow forecast and operating time horizon affects the optimal policies, a trial-and-error approach is suggested to identify the appropriate trade-off between forecast accuracy and operating horizon. The flexibility offered by GA to set up and evaluate objective functions is exploited towards this end. The results are also compared with Linear Programming (LP) model. It is concluded that forecasts models of high accuracy are desirable, particularly when the system is to be operated for periods of high demand. In such cases, the optimization with longer time horizon ensures achievement of the objective more uniformly over the period of operation. The performance of GA is found to be better than LP, when forecast model of higher accuracy and longer period of operating horizon are considered for optimization.     

基于Copula函数的多变量水文不确定性处理器

传统的水文不确定性处理器(HUP)属于单变量结构类型,只能独立地给出各预见期实际流量的贝叶斯后验概率密度,没有考虑它们之间的内在相关性。本文利用Copula函数推导了贝叶斯转移预报(BTF)方法中后验转移密度的解析表达式,提出了基于Copula函数的贝叶斯转移预报(CBTF)方法和基于Copula函数的多变量水文不确定性处理器(CMHUP),进而发展了基于Copula函数的贝叶斯极值预报(CBEF)方法,并应用于三峡水库入库洪水预报中。结果表明:所提方法实用有效,CBTF方法和CMHUP可以定量地评估三峡水库入库流量转移预报的不确定性,准确揭示了水文预报不确定性在时间上的演变特征,CBEF方法则提供了预见期时段内最大入库流量预报的不确定性信息。所提方法不需要进行线性-正态假设,能够很好地捕捉流量过程的非线性和非正态特征,适用范围更加广泛,对于支撑防洪减灾和水库运行调度具有重要的参考价值。     

基于贝叶斯统计与MCMC思想的水库随机优化调度研究

针对马尔柯夫随机动态规划中的维数灾问题,提出一种改进马尔柯夫随机动态规划方法,基于贝叶斯统计原理,采用马尔柯夫链蒙特卡洛方法(Markov Chain Monte Carlo,MCMC)从数学角度出发,推求出一定预报级别下的实际来流概率密度函数,建立与预报级别相关的实际来流概率矩阵,在考虑预报误差发生的情况下进行不确定性优化调度,并且将该方法计算结果与有无预报时段相结合的马尔柯夫随机动态规划方法计算结果进行比较。结果表明,该方法所得到的结果比马尔柯夫随机动态规划结果更加贴近实际多年平均发电量,并且能够有效地减少计算量,缩短计算时间,从一定程度上解决了维数灾问题,本方法为不确定性优化调度提供重要理论参考。     

洪水预报中不确定性分析

通过对未来降雨、出流、损失方面的预测及基于预测模型运行过程中不确定性因素的分析,阐述了洪水预报中的不确定性,把贝叶斯的推断过程的真正范畴与"非等效性"概念联系到一起可得到更高的后验密度.     

Integrated Artificial Neural Network (ANN) and Stochastic Dynamic Programming (SDP) Model for Optimal Release Policy

Complexicity in reservoir operation poses serious challenges to water resources planners and managers. These challenges of water reservoir operation are illustrated using a simulation to aid the development of an optimal operation policy for dam and reservoir. To achieve this, a Comprehensive Stochastic Dynamic Programming with Artificial Neural Network (SDP-ANN) model were developed and tested at Sg. Langat Reservoir in Malaysia. The nonlinearity of the natural physical processes was a major problem in determining the simulation of the reservoir parameters (elevation, surface-area, storage). To overcome water shortages resulting from uncertainty, the SDP-ANN model was used to evaluate the input variable and the performance outcome of the Model were compared with the Stochastic Dynamic Programming integrated with auto-regression (SDP-AR) model. The objective function of the models was set to minimize the sum of squared deviation from the desired targeted supply. Comparison result on the performance between SDP-AR model policy with SDP-ANN model found that the SDP-ANN model is a reliable and resilience model with a lesser supply deficit. The study concludes that the SDP-ANN model performs better than the SDP-AR model in deriving an optimal operating policy for the reservoir.     

Robust Methods for Identifying Optimal Reservoir Operation Strategies Using Deterministic and Stochastic Formulations

Water allocation in a competing environment is a major social and economic challenge especially in water stressed semi-arid regions. In developing countries the end users are represented by the water sectors in most parts and conflict over water is resolved at the agency level. In this paper, two reservoir operation optimization models for water allocation to different users are presented. The objective functions of both models are based on the Nash Bargaining Theory which can incorporate the utility functions of the water users and the stakeholders as well as their relative authorities on the water allocation process. The first model is called GA–KNN (Genetic Algorithm–K Nearest Neighborhood) optimization model. In this model, in order to expedite the convergence process of GA, a KNN scheme for estimating initial solutions is used. Also KNN is utilized to develop the operating rules in each month based on the derived optimization results. The second model is called the Bayesian Stochastic GA (BSGA) optimization model. This model considers the joint probability distribution of inflow and its forecast to the reservoir. In this way, the intrinsic and forecast uncertainties of inflow to the reservoir are incorporated. In order to test the proposed models, they are applied to the Satarkhan reservoir system in the north-western part of Iran. The models have unique features in incorporating uncertainties, facilitating the convergence process of GA, and handling finer state variable discretization and utilizing reliability based utility functions for water user sectors. They are compared with the alternative models. Comparisons show the significant value of the proposed models in reservoir operation and supplying the demands of different water users.     

基于k-最近邻筛选的BMA集合预报模型研究

针对冗余训练样本会降低BMA参数求解效率与精度问题,本文提出在BMA运算之前采用k-最近邻(k-nearest neighbor)算法筛选有价值训练样本,并用于BMA参数求解的改进模型。模拟试验在淮河王家坝站进行,分别以k-最近邻筛选、不筛选两种方案为BMA提供训练样本,统计分析两种方案中王家坝站流量模拟结果,评价BMA改进法的性能。模拟结果显示,采用k-最近邻样本筛选方法后,BMA模型对洪水过程以及洪峰的预报精度提升明显;概率预报结果的离散程度降低的同时,可靠性程度获得提升。k-最近邻样本筛选方法的引入,能够有效去除BMA模型训练样本中的冗余数据,以少量的样本获得更可靠的模型参数,改善集合预报性能。     

XI World Water Congress of IWRA “Water Resources Management in the 21st Century”

Abstract

Stochastic Dynamic Programming and Deterministic Dynamic Programming techniques are used in this study to optimize a reservoir system under a max-min type of objective function to maximize the on-peak firm energy generation. This paper shows that SDP is not appropriate for the optimization as it significantly overestimates the firm energy targets while DDP resulted in very reasonable on-peak firm energy targets. An advantage of this objective function under DDP optimization is that it facilitates the sequential optimization of complex reservoir systems and successfully avoids the problem of dimensionality. The local optimum achieved by the sequential optimization is comparable with the global optimum. Implicit stochastic schemes are used to incorporate the stochastic behavior of the system in optimization. Simulation of the system with the optimum on-peak firm energy targets and synthetic flow series have resulted in high reliabilities for targets from DDP while those from SDP are very low.     

基于Copula函数的三峡工程供水期丰枯遭遇分析

针对三峡工程供水期各时段的丰枯遭遇对制定供水期调度方案的影响,以及统计方法的不足,提出了比较真实反映供水期相邻时段丰枯遭遇联系的Copula联合分布函数。以基于Copula函数建立的贝叶斯网络模型,分别分析了先验概率和后验推理对丰枯遭遇状态。Copula函数计算结果和统计方法统计的结果基本吻合,证明了所建立的联合分布函数的合理性。先验概率分析结果显示相邻时段不利调度概率较小,而后验推理分析结果表明不利调度的概率较大。综合考虑,有效利用后验推理分析的信息,能在一定程度上减少来水不确定性对供水调度方案制定带来的影响,提高三峡工程供水期的综合效益。     

Lake Superior water level fluctuation and climatic factors: A dynamic linear model analysis

We use Dynamic Linear Models (DLM) to analyze the time series of annual average Lake Superior water levels from 1860 to 2007, as well as annual averages of climate drivers including precipitation (1900–2007), evaporation and net precipitation (1951–2007). Our results indicate strong evidence favoring the presence of a systematic trend over a random walk for Lake Superior water levels, and this trend has been negative in recent decades. We then show decisive evidence, in terms of improved predictive performance, favoring a model in which the trend component is replaced with regression components consisting of climatic drivers as predictor variables. Because these models use lagged values of precipitation or net precipitation as predictors, the models can be used to forecast water levels, with the associated uncertainty, several years into the future. We use several of the best fit models and compare one (2008) and two step-ahead (2009) forecasts. The 2008 forecasts compare very well with the observed 2008 water level; the two step-ahead 2009 forecasts are offered as testable hypotheses. The Bayesian context in which these models are developed provides a rigorous framework for data assimilation and regular model updating.     

Multi-Stage Dynamic Programming Method for Short-Term Cascade Reservoirs Optimal Operation with Flow Attenuation

In Short-term Cascade Reservoirs Optimal Operation (SCROO), the flow from upstream reservoir to downstream reservoir which propagates in the natural channel can be generalized as not only transposition but also attenuation. In order to get the relative accurate inflow series of downstream reservoir, the paper tries to adopt the Muskingum model to simulate the inflow of the downstream reservoir instead of the easier processing in most papers of SCROO: ignoring the flow attenuation in natural channel. Considering the flow attenuation between the cascade reservoirs, the SCROO problem do not satisfy the “Principe of Optimality” anymore, so the Dynamic Programming(DP) is no longer applicable. The paper proposes a new improved DP named Multi-Stage Dynamic Programming (MSDP) based on DP. In MSDP, multi-stage’s outflow of upstream reservoir is taken into account at the same time and then inflow of downstream reservoir can be calculated by the Muskingum model, which can include much more flow information than the easier processing with DP, and the inflow of downstream reservoir will be closer to the actual one. The paper takes the cascade hydro-power stations consisting of Jindong and Guandi in Yalong river basin as an example to solve the SCROO problem with MSDP. By comparing the operation result of MSDP and DP with the easier processing, the operation strategy of MSDP can gain further benefits than DP’s in actual operation.     

Water Resources Allocation in Transboundary River Basins Based on a Game Model Considering Inflow Forecasting Errors

Dynamic transboundary water resources allocation based on inflow prediction results is an important task for water resources management in river basins. This paper takes the watershed management agency as the leader and the associated area as the follower, and proposes a two-level asymmetric Nash-Harsanyi Leader-Follower game model considering inflow forecasting errors. In the proposed model, the Monte Carlo method is used to analyze the uncertainty of various stakeholder allocation results and the response regularity to the total water resource uncertainty. The quantitative relationship between the allocation results of stakeholders and the mean and standard deviation of total water resource uncertainty is subsequently established. The Huaihe River basin in China is selected as a case study. The results show the following: (1) the water allocated to the watershed management agency and three provinces has a normal distribution when the inflow forecasting error obeys the normal distribution; (2) the sum of the mean of the water allocated to stakeholders equals the mean of the forecast water resource and the sum of the standard deviations of the water allocated to stakeholders equals the standard deviation of the forecast water resource; (3) the mean and standard deviation of the allocation results have a good linear relationship with the mean and standard deviation of forecast water resource; (4) the distribution parameters of the stakeholder allocation results can be directly derived from the distribution parameters of the forecast information, thus aiding the stakeholders in making decisions and improving the practical value of the method.