Identifying Explicit Formulation of Operating Rules for Multi-Reservoir Systems Using Genetic Programming

Operating rules have been widely used to handle the inflows uncertainty for reservoir long-term operations. Such rules are often expressed in implicit formulations not easily used by other operators and/or reservoirs directly. This study presented genetic programming (GP) to derive the explicit nonlinear formulation of operating rules for multi-reservoir systems. Steps in the proposed method include: (1) determining the optimal operation trajectory of the multi-reservoir system using the dynamic programming to solve a deterministic long-term operation model, (2) selecting the input variables of operating rules using GP based on the optimal operation trajectory, (3) identifying the formulation of operating rules using GP again to fit the optimal operation trajectory, (4) refining the key parameters of operating rules using the parameterization-simulation-optimization method. The method was applied to multi-reservoir system in China that includes the Three Gorges cascade hydropower reservoirs (Three Gorges and Gezhouba reservoirs) and the Qing River cascade hydropower reservoirs (Shuibuya, Geheyan and Gaobazhou reservoirs). The inflow and storage energy terms were selected as input variables for total output of the aggregated reservoir and for decomposition. It was shown that power energy term could more effectively reflect the operating rules than water quantity for the hydropower systems; the derived operating rules were easier to implement for practical use and more efficient and reliable than the conventional operating rule curves and artificial neural network (ANN) rules, increasing both average annual hydropower generation and generation assurance rate, indicating that the proposed GP formulation had potential for improving the operating rules of multi-reservoir system.     

Derivation of Aggregation-Based Joint Operating Rule Curves for Cascade Hydropower Reservoirs

Operating rule curves have been widely applied to reservoir operation, due to their ease of implementation. However, these curves are generally used for single reservoirs and have rarely been applied to cascade reservoirs. This study was conducted to derive joint operating rule curves for cascade hydropower reservoirs. Steps in the proposed methodology include: (1) determining the optimal release schedule using dynamic programming to solve a deterministic long-term operation model, (2) identifying the forms of operating rule curves suitable for cascade hydropower reservoirs based on the optimal release schedule, (3) constructing a simulation-based optimization model and then using the non-dominated sorting genetic algorithm-II (NSGA-II) to identify the key points of the operating rule curves, (4) testing and verifying the efficiency of the generated joint operating rule curves using synthetic inflow series. China’s Qing River cascade hydropower reservoirs (the Shuibuya, Geheyan and Gaobazhou reservoirs) were selected for a case study. When compared with the conventional operating rule curves, the annual power generation can be increased by 2.62% (from 7.27 to 7.46 billion kWh) using the observed inflow from 1951 to 2005, as well as by about 1.77% and 2.52% using the synthetic inflows generated from two alternative hydrologic simulation methods. Linear operating rules were also implemented to simulate coordinated operation of the Qing River cascade hydropower reservoirs. The joint operating rule curves were more efficient and reliable than conventional operating rule curves and linear operating rules, indicating that the proposed method can greatly improve hydropower generation and work stability.     

Operating Rules Derivation of Jinsha Reservoirs System with Parameter Calibrated Support Vector Regression

The reservoir optimal operation depends on not only specific characteristics of reservoirs and hydropower stations but also stochastic inflows. The key issue of actual hydropower operation is to make an approximate optimal decision triggered by limited inflow forecasts. To implement actual optimal operation of hydropower system with limited inflows forecast, this paper makes use of Support Vector Regression (SVR) to derive optimal operating rules. To improve the performance of SVR, parameters in SVR model are calibrated with grid search and cross validation techniques. The trained SVR model describes the complex nonlinear relationships between reservoir operation decisions and factors by considering both generalization and regression performance, which overcomes local optimization and over fitting deficits. Hybrid programming platform is further developed to implement system simulation. This SVR model along with simulation platform is applied to the largest hydropower base in China – Jinsha system. Three scenarios are developed for comparison: deterministic optimal operation, SVR based simulation with calibrated parameters, SVR based simulation with default parameters. Comprehensive evaluation indicates that, operating rules derived from SVR presents a reliable performance in system power generation and output processes with respect to ideal deterministic results, especially when the parameters are calibrated. Hybrid programming technique provides a feasible and compatible platform for future research.     

溪洛渡-向家坝-三峡梯级水库联合蓄水方案与多目标决策研究

为协调好梯级水库联合蓄水调度过程中防洪、发电、蓄水和航运等目标之间的矛盾,实现各水库蓄水时机与蓄水进程的协同优化,以溪洛渡-向家坝-三峡梯级水库为例,推求了可权衡防洪与兴利之间矛盾的梯级水库联合蓄水方案,主要研究内容主要包括以下3个部分:(1)风险分析,推求了汛末各分期内坝前最高安全水位约束和联合蓄水方案的防洪风险;(2)兴利效益分析,分析了联合蓄水方案的发电和蓄水等兴利效益;(3)多目标决策,评价了联合蓄水方案的防洪风险、发电和蓄水效益,得出了最优非劣质蓄水方案。研究结果表明:溪洛渡-向家坝-三峡梯级水库的较优联合蓄水方案,分别为9月5日起蓄的同步起蓄方案和9月1日-9月5日-9月10日起蓄的异步起蓄方案,较原设计蓄水方案,年均发电量可分别增加23.76和20.43亿k W·h,增幅分别为3.25%和2.78%;蓄水率可由96.73%分别提高至97.51%和97.57%,两者均可在不降低原防洪标准的前提下,提高梯级水库的综合效益,前者的发电效益较优,而后者的蓄水效益较优。     

Deriving the optimal refill rule for multi-purpose reservoir considering flood control risk

For most multi-purpose reservoirs, there is a conflict between the flood control and refill operations. Refill before the end of the flood season is a valuable and effective solution to the conflict. In this paper, we present a method to derive the optimal refill rule for multi-purpose reservoir considering flood control risk. The paper begins with an investigation of the temporal trends of historical reservoir inflow series during refill period by the methods of linear regression, Mann–Kendall and Spearman's rho test. Six refill rules are then proposed. A procedure to couple a flood control risk module with utilization benefits analysis module is then developed to derive the optimal refill rule. China's Three Gorges Reservoir (TGR) is selected as a case study. The application results show that the optimal refill rule is that refill begins on September 1 with storage level reaching 160 m on September 30 linearly. Compared with the original rule, the optimal refill rule can increase hydropower generation by 7.19%, decrease spilled water by 25.07%, and improve the fullness storage rate to 95.35%, without increasing flood control risk.     

Deriving Optimal Operating Rules of a Multi-Reservoir System Considering Incremental Multi-Agent Benefit Allocation

Joint multi-reservoir operation is one of the most efficient measures to meet the demand for increasing economic benefits. Operating rules have been widely used in long-term reservoir operations. However, reservoirs belong to multiple agents in most cases, which imposes difficulties on benefit allocation. This motivated us to derive optimal operating rules for a multi-reservoir system, considering incremental benefit allocation among multiple agents. Fairness of incremental benefits for multiple agents is proposed as one of the objective functions, and then optimal joint operating rules with fairness are derived. The optimal joint operating rules with fairness are compared with conventional, optimal individual, and joint operating rules. The Three Gorges (Three Gorges and Gezhouba) and Qing River (Shuibuya, Geheyan and Gaobazhou) cascade reservoirs are selected for case study. The optimal joint operating rules with fairness not only encourage agents to participate in joint operation, but also increase average annual hydropower generation and the assurance rate of hydropower generation relative to those of the conventional operating rules. Furthermore, the proposed optimal operating rules with fairness are easier to implement in practice than the optimal joint rules. This indicates that the proposed method has potential for improving operating rules of a multi-reservoir system.     

Operating rules of irrigation reservoir under climate change and its application for the Dongwushi Reservoir in China

Since agriculture development would be affected by climate change, the reservoir operation for agricultural irrigation should be adjusted. However, there are to date few literatures addressing how to design adaptive operating rules for an irrigation reservoir. This study aims to analyze the adaption of fixed operating rules and to derive adaptive operating rules under climate change. The deterministic optimization model is established with the solving method of two-dimensional dynamic programming (TDDP), and its optimal trajectory is supplied to derive reservoir operating rules at time intervals of crop growth periods. Then, two alternative operating rules, including fixed operating rules based on historical data and adaptive operating rules based on climate change data, are extracted using the fitting method with the multiple linear regression model. The alteration of reservoir inflow under climate change is calculated by the Budyko formula. A case study of the China’s Dongwushi Reservoir shows that: (1) fixed operating rules are unable to adapt climate change in the future scenario. Thus, adaptive operating rules should be established, (2) adaptive operating rules can reduce profits loss resulting from climate change, and improve field soil water storages, and (3) precipitation reduction by 7%/40a is the major cause for agricultural profits loss, whereas, the decrement of agricultural profits is less than that of precipitation, which indicates agricultural crops have the resilience to resist the adverse influence from precipitation decrease. These findings are helpful for adaptive operation of irrigation reservoirs under climate change.     

Deriving Optimal Refill Rules for Multi-Purpose Reservoir Operation

This paper focuses on deriving optimal refill rules for a multi-purpose reservoir, and aims to maximize utilization benefits under the condition of flood control safety. The entire flood season is divided into multiple sub-seasons (i.e. pre-flood season, main-flood season and post-flood season). By advancing the start of the refill period to the beginning of the post-flood season, seasonal design flows during the new refill period are estimated. A multi-objective refill operation model is proposed by combining flood control and conservation together. The simulation–optimization-test framework and hybrid multi-objective genetic algorithms are developed and used to optimize the rule curves. China’s Three Gorges Reservoir is selected as a case study and the application results show that the proposed model can increase the hydropower generation by 17.4%, decrease spilled water by 43.9%, and improve the refill probability greatly without decreasing the flood control standard and navigation probability during the refill period.     

水电站水库长期优化调度模型及调度图

为绘制高效可靠的水库运行调度图,以平衡保证出力保证率与发电量矛盾的惩罚系数为优化变量、以保证出力设计保证率满足条件下发电量最大为目标函数,综合集成以黄金分割法为时段决策优选法的随机动态规划核心模型,以及评估调度方案优劣时历法长系列模拟计算模块,利用遗传算法的并行计算能力,结合电站调度方案制定与有效性检验,构建水电站水库长期优化调度模型。应用结果表明:所建模型具有不受年调节和多年调节库容机械划分约束、快速获得满足发电保证率所要求的优化调度图的优秀特性;较之常规调度方法,可增发电量2.0%以上,保证率更高,决策信息更丰富。     

Reservoir Operation Using a Dynamic Programming Fuzzy Rule–Based Approach

A dynamic programming fuzzy rule–based (DPFRB) model for optimal operation of reservoirs system is presented in this paper. In the first step, a deterministic dynamic programming (DP) model is used to develop the optimal set of inflows, storage volumes, and reservoir releases. These optimal values are then used as inputs to a fuzzy rule–based (FRB) model to establish the general operating policies in the second step. Subsequently, the operating policies are evaluated in a simulation model. During the simulation step, the parameters of the FRB model are optimized after which the algorithm gets back to the second step in a feedback loop to establish the new set of operating rules using the optimized parameters. This iterative approach improves the value of the performance function of the simulation model and continues until the satisfaction of predetermined stopping criteria. This method results in deriving the operating policies, which are robust against the uncertainty of inflows. These policies are derived by using long-term synthetic inflows and an objective function that minimizes its variance. The DPFRB performance is tested and compared to a model, which uses the commonly used multiple regression–based operating rules. Results show that the DPFRB performs well in terms of satisfying the system target performances and computational requirements.     

Multi-Objective Operating Rules for Danjiangkou Reservoir Under Climate Change

The natural variations of climatic system, as well as the potential influence of human activity on global warming, have changed the hydrologic cycle and threatened current water resources management. And the conflicts between different objectives in reservoir operation may become more and more challenging because of the impact of climate change. This study aims at deriving multi-objective operating rules to adapt to climate change and alleviate the conflicts. By combining the reservoir operation function and operating rule curves, an adaptive multi-objective operation model was proposed and developed. The optimal operating rules derived both by dynamic programming and NSGA-II method were compared and discussed. The projection pursuit method was used to select the best operating rules. The results demonstrate that the reservoir operating rules obtained by NSGA-II can increase the power generation and water supply yield and reliability, and the rules focusing on water supply can significantly increase the reservoir annual water supply yield (by 18.7 %). It is shown that the proposed model would be effective in reservoir operation under climate change.     

寺坪水电站优化调度模型

随着社会经济的快速发展,水资源供需矛盾日趋尖锐,如何合理调度有限的水资源已成为水资源管理中的现实而紧迫的任务。通过进一步研究水库调度的机理,采用非线性规划作为优化求解方法构建了水库优化调度模型,非线性规划结合了线性规划和动态规划各自的优点,并将水库调度中的各种因素融入数学模型中,较准确地计算模拟期间各种优化变量数值条件下的目标函数值,并比较得出最优值。之后,基于多目标思想,给出了一组Pareto前沿解集,通过寺坪水电站的应用,构建不同的目标函数,得到一系列决策方案,以便决策者选择偏好的决策方案。     

水电站水库防洪优化调度的模型与方法

水库防洪调度是一种确保水库及下游安全的控制运行方法，通过建立水电站水库优化调度模型，利用动态规划方法，可以计算单一水库或者梯级水电站群的最优调度方案，从而确保水库工程安全，有效利用防洪库容拦蓄洪水，削减洪峰，减免洪水灾害，充分发挥水库的综合效益。通过建立水库防洪调度的数学模型，利用动态规划方法对单一水电站水库的防洪调度进行了研究。     

Structural and Non-Structural Climate Change Adaptation Strategies for the Péribonka Water Resource System

This paper discusses the possibility for a privately managed hydro-power system to adapt to a projected increase in water flow in their central-Québec watersheds by adding power generation potential. Runoffs simulated by a lumped rainfall-runoff model were fed into a stochastic dynamic programming (SDP) routine to generate reservoir operating rules. These rules were optimized for maximum power generation under maximal and minimal reservoir level constraints. With these optimized rules, a power generation simulator was used to predict the amount of generated hydropower. The same steps, excluding calibration, were performed on 60 climate projections (from 23 general circulation models and 3 greenhouse gas emission scenarios) for future horizons 2036–2065 and 2071–2100. Reservoir operation rules were optimized for every climate change projection for the 3 power plants in the system. From these simulations, it was possible to determine hydropower numbers for both horizons. The same steps were performed under a modified system in which an additional turbine was added to each power plant. Results show that both the non-structural (optimizing reservoir rules) and structural (adding turbines) adaptation measures allow for increased power production, but that adapting operating rules is sufficient to reap the most of the benefits of increased water availability.     

Assessment of Stochastic Operation Optimization for Reservoirs of Contrasting Scales

Deriving optimal release policies for dams and corresponding reservoirs is crucial for the sustainable water resources management of a region as they directly control the distribution of water to several users. Mathematical optimization algorithms can help in finding efficient reservoir operating strategies taking into account complex system constraints and hydrologic uncertainty. The robustness of operation optimization models may be influenced by physical reservoir characteristics such as size and scale and the effectiveness of a model for a particular case study does not always guarantee the same level of success for another application. This research focused on assessing the applicability of an implicit stochastic optimization (ISO) procedure to derive rule curves for two different dams of contrasting reservoir scales in terms of physical and operational characteristics. The results demonstrated the feasibility of the proposed technique for both small- and large-scale systems in view of the lower vulnerability provided by the ISO-derived policies in contrast to operations carried out by the standard reservoir operating policy as well as the proximity of the ISO operations with those by perfect-forecast deterministic optimization. The ISO procedure also provided operating rules similar to, and even less vulnerable than, those derived by stochastic dynamic programming.     

Reservoir Operation Optimization: A Nonstructural Solution for Control of Seepage from Lar Reservoir in Iran

Abstract

In this paper, the results of utilizing a deterministic dynamic programming model for operation of Lar Reservoir in Iran are discussed. This reservoir has experienced extensive seepage from the start of its operation. The optimization model consists of a three-step cycle, which began with the optimization of reservoir operation for a given set of streamflows. The optimal policies are then analyzed in a regression procedure to obtain a set of operating rules. After the first run, operating rules from the previous run were placed as a new constraint on the water releases with some pre-assigned tolerance and the cycle continues. The model also consisted of mathematical functions for modeling the seepage from Lar Reservoir as a function of storage head in the reservoir. The loss function in the model was also modified in order to incorporate parameters that reduce the seepage. Results of different scenarios showed the significant effect of optimal policies on reduction of seepage and increasing the reliability of water supply to Tehran Metropolitan Area. A pumping station was also proposed to utilize the inactive part of the reservoir, in access of over 100 MCM, in order to reduce the seepage. The effectiveness of different pumping capacities to reduce the seepage was also investigated.     

Optimal Operation of Reservoir Systems using Simulated Annealing

A stochastic search technique, simulated annealing (SA), is used to optimize the operation of multiple reservoirs. Seminal application of annealing technique in general to multi-period, multiple-reservoir systems, along with problem representation and selection of different parameter values used in the annealing algorithm for specific cases is discussed. The search technique is improved with the help of heuristic rules, problem-specific information and concepts from the field of evolutionary algorithms. The technique is tested for application to a benchmark problem of four-reservoir system previously solved using a linear programming formulation and its ability to replicate the global optimum solution is examined. The technique is also applied to a system of four hydropower generating reservoirs in Manitoba, Canada, to derive optimal operating rules. A limited version of this problem is solved using a mixed integer nonlinear programming and results are compared with those obtained using SA. A better objective function value is obtained using simulated annealing than the value from a mixed integer non-linear programming model developed for the same problem. Results obtained from these applications suggest that simulated annealing can be used for obtaining near-optimal solutions for multi-period reservoir operation problems that are computationally intractable.     

Predictive Temporal Data-Mining Approach for Evolving Knowledge Based Reservoir Operation Rules

The persistent problem in reservoir operation is that the derived optimal releases fail to incorporate the decision maker or reservoir operators’ knowledge into reservoir operation models. The reservoir operators’ knowledge is specific to that particular reservoir and incorporating such an experienced knowledge will help to derive field reality based operation rules. The available historical reservoir operation databases are the representative samples of reservoir operators’ knowledge or experience. Thus, an attempt has been made that deals with the development of a methodological framework to recover or explore the historical reservoir operation database to derive the reservoir operators’ knowledge as operational rules. The developed methodological framework utilizes the strength and capability of recently developed predictive datamining algorithms to recover the knowledge from large historical database. Predictive data-mining algorithms such as a) classifier: Artificial Neural Network (ANN), and b) regression: Support Vector Regression (SVR) have been used for single reservoir operation data-mining (SROD) modelling framework to explore the temporal dependence between different variables of reservoir operation. The rules of operation or knowledge learned from the training database have been used as guiding rules for predicting the future reservoir operators’ decision on operating the reservoir for the given condition on the inflow, initial storage, and demand requirements. The developed SROD model was found to be efficient in exploring the hidden relationships that exist in a single reservoir system.     

基于耗水率动态规划模型的水电站水库优化调度

目前水电站水库优化调度常侧重于提高算法的精度和计算的速度,往往忽视了优化调度模型本身的合理性和准确性。综合耗水率是衡量水电站经济运行情况的重要指标。基于耗水率动态规划模型的水电站水库优化调度方法,依据水电站长期运行的历史资料,采用水电站综合耗水率参数作为水电站水库优化计算的基础,使优化结果更符合水库经济运行的实际要求。     

三峡梯级电站短期优化调度的模糊多目标动态规划

针对三峡梯级电站的短期优化调度是一个具有复杂约束条件的大型、动态、有时滞、模糊非线性的优化问题，本文建立了模糊优化调度模型，并对其进行了求解。由于常规模糊动态规划的方法在库容变化大的时候会出现维数灾，因此本文利用模糊多目标动态规划法，并结合逐次逼近方法，来求解梯级短期优化调度问题。实例仿真结果表明，它不仅可以根据不同的参数选择生成非劣解集，还可以推荐满意解，为决策支持提供依据。