随机约束线性规划在水库综合利用中的应用

由于水库入流的不确定性，各用水目标的基本要求（目标放水量）将体现在年内各时期水库放水的随机约束上，配合水库线民生蓄泄水决策规则，将全部随机约束进行确定性等效转换，得到线性规划模型，经多次解析，就可得到水主加容量一定情况下的最优运行规则，针对大型水资源工程综合利用的多目标要求，研究建立了随机约束线性规划模型，以求解水库最优运行规划的方法，并以西南地区某大型综合利用水库为例，对模型进行求解，该方法随机     

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.     

Evaluation of Real-Time Operation Rules in Reservoir Systems Operation

Reservoir operation rules are logical or mathematical equations that take into account system variables to calculate water release from a reservoir based on inflow and storage volume values. In fact, previous experiences of the system are used to balance reservoir system parameters in each operational period. Commonly, reservoir operation rules have been considered to be linear decision rules (LDRs) and constant coefficients developed by using various optimization procedures. This paper addresses the application of real-time operation rules on a reservoir system whose purpose is to supply total downstream demand. Those rules include standard operation policy (SOP), stochastic dynamic programming (SDP), LDR, and nonlinear decision rule (NLDR) with various orders of inflow and reservoir storage volume. Also, a multi-attribute decision method, elimination and choice expressing reality (ELECTRE)-I, with a combination of indices, objective functions, and reservoir performance criteria (reliability, resiliency, and vulnerability) are used to rank the aforementioned rules. The ranking method employs two combinations of indices: (1) performance criteria and (2) objective function and performance criteria by using the same weights for all criteria. Results show that the NLDR gives an appropriate rule for real-time operation. Moreover, NLDR validation is presented by testing predefined curves for dry, normal, and wet years.     

Real-Time Operation of Reservoir System by Genetic Programming

Reservoir operation policy depends on specific values of deterministic variables and predictable actions as well as stochastic variables, in which small differences affect water release and reservoir operation efficiency. Operational rule curves of reservoir are policies which relate water release to the deterministic and stochastic variables such as storage volume and inflow. To operate a reservoir system in real time, a prediction model may be coupled with rule curves to estimate inflow as a stochastic variable. Inappropriate selection of this prediction model increases calculations and impacts the reservoir operation efficiency. Thus, extraction of an operational policy simultaneously with inflow prediction helps the operator to make an appropriate decision to calculate how much water to release from the reservoir without employing a prediction model. This paper addresses the use of genetic programming (GP) to develop a reservoir operation policy simultaneously with inflow prediction. To determine a water release policy, two operational rule curves are considered in each period by using (1) inflow and storage volume at the beginning of each period and (2) inflow of the 1^st, 2^nd, 12^th previous periods and storage volume at the beginning of each period. The obtained objective functions of those rules have only 4.86 and 0.44?% difference in the training and testing data sets. These results indicate that the proposed rule based on deterministic variables is effective in determining optimal rule curves simultaneously with inflow prediction for reservoirs.     

Reservoir operation policies for optimizing energy generation at the Shiroro Dam

Reservoir water release policies are computed for the Shiroro Dam hydroelectric power scheme in Northern Nigeria, using a probabilistic dynamic programming model. The state variable is the reservoir storage volume, while the uncertain nature of the inflow process is accounted for in the model by considering different possible inflow volumes and their inflow probabilities. Simulation of the reservoir operations with the derived policies show that on the average the hydrosystem has acceptable reliability when two units are in use, at 45% design power plant factor. At 70% power plant factor, which is the desired optimum for the power system in Nigeria, system failures are frequent and, in most cases, severe. For normal operation of the Shiroro Dam hydroelectric power system, two or three generating units, running at 40–50% power plant factor is recommended.     

串联供水库群优化调度的模糊规划模型

针对随机动态规划在解决多个水库联合优化调度时存在“维数灾”问题,尝试基于模糊集理论来解决该优化调度问题。以4个串联供水水库系统为例,目标为各供水片区最小的缺水率最大,将水库的入流过程视为模糊集,而需水过程视为确定性的,建立了模糊规划模型,并引入可靠度和满意度对优化调度结果进行评价。实例分析表明,该模型既可以刻画入流的不确定性,又可以简化问题,具有一定的实用性。     

Derivation of Optimal Hedging Rules for a Water-supply Reservoir through Compromise Programming

This study derives optimal hedging rules for simultaneously minimizing short- and long-term shortage characteristics for a water-supply reservoir. Hedging is an effective measure to reduce a high-percentage single period shortage, but at a cost of more frequent small shortages. Thus simultaneously minimizing the maximum monthly shortage and the shortage ratio (defined as the ratio of total shortages to total demands) over the analysis horizon is the operation goal of a water-supply reservoir to derive optimal hedging rules. Two types of hedging are explored in this study: the first uses water availability defined as storage plus inflow, while the second depends on the potential shortage conditions within a specific future lead-time period. The compromise programming is employed to solve this conflicting multiobjective problem. The optimal hedging rules under given reservoir inflow are derived first. Because future inflow cannot be known exactly in advance, the monthly decile inflows are suggested as a surrogate for forecast of future inflows in hedging rules for real-time reservoir operations. The results show that the suggested method can effectively achieve the reservoir operation goal. The merits of the proposed methodology are demonstrated with an application to the Shihmen reservoir in Taiwan.     

Adaptive Reservoir Management by Reforming the Zone-based Hedging Rules against Multi-year Droughts

In this study, the zone-based hedging rule, which is the main operating policy adopted from multipurpose reservoirs in Korea is adjusted to reflect the multi-year droughts caused by climate change. Annual synthetic inflow series with different magnitudes of long memory were generated using the autoregressive fractional integrated moving average (ARFIMA) model. The generated inflow series were then disaggregated into 10-day series and utilized as input variables to derive the alternative hedging rules. The alternative hedging rules from this study were used in adaptive reservoir management by newly updated information. Finally, the performance of the suggested policy is measured in terms of frequency and magnitude under the historical inflow series. As a result, adaptive reservoir management demonstrated improvements in the following terms of the frequency of critical failures (water deficit ratio greater than 30%): 6.14% of the simulation period in the status quo (SQ) policy, and 2.99% in the adaptive management. However, the overall reliability of the reservoir during the simulation horizon was better when operated with the SQ policy (41.19%) than the results from adaptive management (26.42%). Because this result is in a good agreement with the original objective of the hedging rules, the adaptive policy suggested in this study holds promise and may be utilized in further reservoir management with an increase of potential drought risk from climate change.

     

Optimization of Multi-Reservoir Operating Rules for a Water Supply System

To obtain the optimal releases of the multi-reservoir system, two sets of joint operating rules (JOR-I and JOR-II) are presented based on the aggregation-disaggregation approach and multi-reservoir approach respectively. In JOR-I, all reservoirs are aggregated to an equivalent reservoir, the operating rules of which, the release rule of the system is optimized following operating rule curves coupled with hedging rules. Then the system release is disaggregated into each reservoir according to water supply priorities and the dynamic demand partition approach. In JOR-II, a two-stage demand partition approach is applied to allocate the different demand priorities to determine the release from each reservoir. To assess the reliability and effectiveness of the joint operating rules, the proposed rules are applied to a multi-reservoir system in Liaoning province of China. Results demonstrate that JOR-I is suitable for high-dimensional multi-reservoir operation problems with large-scale inflow data, while JOR-II is suitable for low-dimensional multi-reservoir operation problems with small-scale inflow data, and JOR-II performs better than JOR-I but requires more computation time. The research provides guidelines for the management of multi-reservoir system.     

Reservoir Operation Modelling with Fuzzy Logic

In this article, a fuzzy rule based model is developed for the operation of a single purpose reservoir. The model operates on an 'if – then' principle, where the 'if' is a vector of fuzzy premises and the 'then' is a vector of fuzzy consequences. The steps involved in the development of the model include, construction of membership functions for the inflow, storage, demand and the release, formulation of fuzzyrules, implication and defuzzification. The methodology is illustrated through the case study of the Malaprabha irrigation reservoir in Karnataka, India. Reservoir storage, inflow, and demands are used as premises and the release as the consequence.Simulated reservoir operation with a steady state policy provides the knowledge base necessary for the formulation of the Fuzzy rules.     

Water Supply Reservoir Operation by Combined Genetic Algorithm – Linear Programming (GA-LP) Approach

Multi-reservoir operation planning is a complex task involving many variables, objectives, and decisions. This paper applies a hybrid method using genetic algorithm (GA) and linear programming (LP) developed by the authors to determine operational decisions for a reservoir system over the optimization period. This method identifies part of the decision variables called cost reduction factors (CRFs) by GA and operational variables by LP. CRFs are introduced into the formulation to discourage reservoir depletion in the initial stages of the planning period. These factors are useful parameters that can be employed to determine operational decisions such as optimal releases and imports, in response to future inflow predictions. A part of the Roadford Water Supply System, UK, is used to demonstrate the performance of the GA-LP method in comparison to the RELAX algorithm. The proposed approach obtains comparable results ensuring non zero final storages in the larger reservoirs of the Roadford Hydrosystem. It shows potential for generating operating policy in the form of hegging rules without a priori imposition of their form.     

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.     

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.     

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.     

Deriving Reservoir Refill Operating Rules by Using the Proposed DPNS Model

The dynamic programming neural-network simplex (DPNS) model, which is aimed at making some improvements to the dynamic programming neural-network (DPN) model, is proposed and used to derive refill operating rules in reservoir planning and management. The DPNS model consists of three stages. First, the training data set (reservoir optimal sequences of releases) is searched by using the dynamic programming (DP) model to solve the deterministic refill operation problem. Second, with the training data set obtained, the artificial neural network (ANN) model representing the operating rules is trained through back-propagation (BP) algorithm. These two stages construct the standard DPN model. The third stage of DPNS is proposed to refine the operating rules through simulation-based optimization. By choosing maximum the hydropower generation as objective function, a nonlinear programming technique, Simplex method, is used to refine the final output of the DPN model. Both the DPNS and DPN models are used to derive operating rules for the real time refill operation of the Three Gorges Reservoir (TGR) for the year of 2007. It is shown that the DPNS model can improve not only the probability of refill but also the mean hydropower generation when compare with that of the DPN model. It's recommended that the objective function of ANN approach for deriving refill operating rules should maximize the yield or minimize the loss, which can be computed from reservoir simulation during the refill period, rather than to fit the optimal data set as well as possible. And the derivation of optimal or near-optimal operating rules can be carried out effectively and efficiently using the proposed DPNS model.     

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.     

Long-Term Planning of Water Systems in the Context of Climate Non-Stationarity with Deterministic and Stochastic Optimization

Seasonal inflow variability, climate non-stationarity and climate change are matters of concern for water system planning and management. This study presents optimization methods for long-term planning of water systems in the context of a non-stationary climate with two levels of inflow variability: seasonal and inter-annual. Deterministic and stochastic optimization models with either one time-step (intra-annual) or two time-steps (intra-annual and inter-annual) were compared by using three water system optimization models. The first model used one time-step sampling stochastic dynamic programming (SSDP). The other models with two time-steps are long-term deterministic dynamic programming (LT-DDP) and long-term sampling stochastic dynamic programming (LT-SSDP). The study area is the Manicouagan water system located in Quebec, Canada. The results show that there will be an increase of inflow to hydropower plants in the future climate with an increase of inflow uncertainty. The stochastic optimization with two time-steps was the most suitable for handling climate non-stationarity. The LT-DDP performed better in terms of reservoir storage, release and system efficiency but with high uncertainty. The SSDP had the lowest performance. The SSDP was not able to deal with the non-stationary climate and seasonal variability at the same time. The LT-SSDP generated operating policies with smaller uncertainty compared to LT-DDP, and it was therefore a more appropriate approach for water system planning and management in a non-stationary climate characterized by high inflow variability.     

Adaptive irrigation management for subsistence farming

Irrigation management authorities in Sri Lanka have often failed to incorporate historical information in the decision‐making process in a systematic manner. The objective of this study is to develop a water model to combine prior information systematically. The decision rule developed is based on a single‐season linear programming model, using real‐time forecasting model inflows. The forecasts are based on the most current information (via Kalman filtering) available to the forecaster. The forecasting method used is vector autoregression with Bayesian priors, allowing the reservoir management to include subjective information into the decision matrix. This adaptive technique was examined for various seasonal inflow scenarios and found to be superior to the existing water allocation method.     

Modeling the Yield–Evaporation–Spill in the Reservoir Storage Process: The Regulation Triangle Diagram

From the dimensionless reservoir water budget equation, a graphical method to model the yield–spill–evaporation loss trade-off in the reservoir storage process was built. The reservoir inflows were transformed into three parts that sum to the total mean inflow for long-term operation: evaporation, spill and yield. A regulation triangle diagram (RTD) has been proposed to provide a better understanding of the reservoir storage process as a function of reservoir capacity, hydrological river regime, evaporation and reservoir morphology. The inflows were assumed to be serially uncorrelated and to originate from a Gamma probability distribution function. The diagrams were developed using the Monte Carlo method, while the graphics were developed for intermittent rivers with a coefficient of variation of annual inflows that ranges from 0.6 to 1.6. In the model, the reservoir is a single over-year system, and the values are referenced to the steady state conditions.     

Reservoir Operation Incorporating Hedging Rules and Operational Inflow Forecasts

Reservoir operation incorporating a naïve hedging strategy and operational inflow forecasting is studied in this paper. Gridded precipitation forecasts from climate model, ECHAM4.5, are used as potential predictors for reservoir inflow forecasting. In building a statistical predicting model, principal component analysis (PCA) is used to reduce the dimension of the regression model. Performance evaluation indices, including water supply satisfaction ratio, environmental flow satisfaction ratio, end-of-month storage satisfaction ratio and flood prevention capacity index, are defined. Three scenarios where a naïve hedging operation rule under different set of reservoir inflow are investigated. These are evaluated for a water supply reservoir, Falls Lake Reservoir, at Neuse River in the southeast United State. Reservoir simulation with monthly average inflow serves as a benchmark. The utility of operational inflow forecasts is quantified by the improvements of performance indices. Results show that reservoir operation under perfect inflow forecasting has the highest values for most indices. Compared to climatology, operational inflow forecasts result in higher index values. Among all the performance indices, end-of-month storage satisfaction ratio is the most sensitive index to inflow information. Limitation of this study and further work is also discussed.