Optimal Allocation of Flood Control Capacity for Multi-Reservoir Systems Using Multi-Objective Optimization Approach

Operation of multi-reservoir systems during flood periods is of great importance in the field of water resources management. This paper proposes a multi-objective optimization model with new formulation for optimal operation of multi-reservoir systems. In this model, the release rate and the flood control capacity of each reservoir is considered as decision variable and the resulting nonlinear non-convex multi-objective optimization problem is solved with ε-constraint method through the mixed integer linear programming (MILP). Objective functions of the model are minimizing the flood damage at downstream sites and the loss of hydropower generation. The developed model is used to determine optimal operating strategies for Karkheh multi-reservoir system in southwestern Iran. For this purpose, the model is executed in two scenarios based on “two-reservoir” and “six-reservoir” systems and for floods with return periods of 25 and 50 years. The results show that in two-reservoir system, flood damage is at least about 114 million dollars and cannot be mitigated any further no matter how hydropower generation is managed. But, in the case of developing all six reservoirs, optimal strategies of coordinated operation can mitigate and even fully prevent flood damage.     

水库群系统发电调度的合作博弈研究

水资源的竞争性和非排他性导致水库管理者基于个体利益进行发电调度,使得水库在满足个体利益的同时往往忽略了系统的整体效益。为了在保证个体利益的基础上实现系统总效益的最大化,建立了梯级水库群发电调度合作博弈模型;采用改进后的水循环算法对模型进行分层求解。以金沙江两库与三峡梯级构成的梯级水库群为研究对象,选取典型年进行实例计算。计算结果表明：梯级水库群发电调度的合作博弈模型在获得系统最大效益的同时使得个体利益达到Pareto最优状态,实现水库群总效益和单库个体效益的双赢,既优于联合优化调度模型又优于单库优化调度模型。该合作博弈模型及其新解法可为水库群调度决策分析开创一种新思路。     

Hydropower Optimization for the Lower Seyhan Basin System in Turkey using dynamic programming

Abstract

Dynamic programming with successive approximation has been used in the past for optimizing multi-reservoir water resources systems. In this study, a State Incremental Dynamic Programming (SIDP) model is developed for energy optimization of multi-reservoir systems. A random file access method is used to generate initial and intermediate data and cope with the curse of dimensionality of dynamic programming. The conventional dynamic programming method is used for each single reservoir to find the initial trajectory of the reservoirs. Then, the computer program developed in the study is applied to the multipurpose-multi-reservoir system in lower Seyhan basin, which comprises six reservoirs, some serial and some parallel. Extended historical flows are used to first maximize firm energy in the critical period, and then total energy over the entire period of flow records. The program is run with 50-year long segments (20 flow scenarios) of the synthetic flow data generated by using the hec-4 generalized computer program to account for the stochastic nature of streamflows. A 20% approximate increase in total energy is obtained by using the developed model for the lower seyhan basin system as compared to that calculated previously by conventional methods.     

Hydropower Optimization for the Lower Seyhan System in Turkey using Dynamic Programming

Abstract

Dynamic programming with successive approximation has been used in the past for optimizing multi-reservoir water resources systems. In this study, the State Incremental Dynamic Programming (SIDP) model is developed for energy optimization of multi-reservoir systems. A random file access method is used for reaching initial and intermediate data to cope with the curse of dimensionality of dynamic programming. A conventional dynamic programming method is used for each single reservoir to find the initial trajectory of the reservoirs. Then, the computer program developed in the study is applied to the multipurpose-multi-reservoir system in Lower Seyhan Basin, which has six reservoirs, some of which are serial and some parallel. First, extended historical flows were used to maximize firm energy in the critical period, and then total energy in the total flows. The program was run with 50-year long segments (20 flow scenarios) of the synthetic flow data generated by using the HEC-4 generalized computer program to take into account the stochastic nature of stream flows. An increment of approximately 20 percent in total energy was obtained by using the model for the Lower Seyhan System, as compared to that calculated previously by conventional methods.     

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.     

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.     

Chaotic Evolutionary Algorithms for Multi-Reservoir Optimization

The water sharing dispute in a multi-reservoir river basin forces the water resources planners to have an integrated operation of multi-reservoir system rather than considering them as a single reservoir system. Thus, optimizing the operations of a multi-reservoir system for an integrated operation is gaining importance, especially in India. Recently, evolutionary algorithms have been successfully applied for optimizing the multi-reservoir system operations. The evolutionary optimization algorithms start its search from a randomly generated initial population to attain the global optimal solution. However, simple evolutionary algorithms are slower in convergence and also results in sub-optimal solutions for complex problems with hardbound variables. Hence, in the present study, chaotic technique is introduced to generate the initial population and also in other search steps to enhance the performance of the evolutionary algorithms and applied for the optimization of a multi-reservoir system. The results are compared with that of a simple GA and DE algorithm. From the study, it is found that the chaotic algorithm with the general optimizer has produced the global optimal solution (optimal hydropower production in the present case) within lesser generations. This shows that coupling the chaotic algorithm with evolutionary algorithm will enrich the search technique by having better initial population and also converges quickly. Further, the performances of the developed policies are evaluated for longer run using a simulation model to assess the irrigation deficits. The simulation results show that the model satisfactorily meets the irrigation demand in most of the time periods and the deficit is very less.     

Optimal Operation of Multi-reservoir Systems Considering Time-lags of Flood Routing

Operations of multi-reservoir systems are nonlinear and high-dimensional problems, which are difficult to find the optimal or near-optimal solution owing to the heavy computation burden. This study focuses on flood control operation of multi-reservoir systems considering time-lags caused by Muskingum flood routing of river channels. An optimal model is established to jointly minimize the flood peak on the downstream flood control station for the multi-reservoir systems. A hybrid algorithm, Progressive Optimality Algorithm and Successive Approximation (POA-SA), is improved to solve the multi-reservoir operation model by modifying the POA. The POA-SA uses the DPSA to reduce the spatial dimensionality due to the multiple reservoirs, and adopts an improved POA to alleviate the temporal dimensionality caused by the time-lags of the Muskingum flood routing. Linear programming is then implemented to verify the solution of the POA-SA method with a linear approximation of the discharge capacity curve. The multi-reservoir systems of China’s Xijiang River is selected for a case study. Results show that the flood peak of Wuzhou station can be averagely decreased by 6730 m³/s (12.8 %) for the 100-year return period floods, indicating that the proposed method is efficient to operate the multi-reservoir systems and resolve the time-lags issues.     

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.     

Generation of Clean Hydropower Energy in Multi-Reservoir Systems Based on a New Evolutionary Algorithm

Lingering droughts and shortage of water sources signify the importance of optimal utilization of water reservoirs such as multi-reservoir systems. These systems could be employed not only as a storage system to manage the water utilization but also as a power generation system. To rise the generated power besides the management of water utilization, an optimization algorithm should be used. In this study, the kidney algorithm in three different scenarios, namely the wet, normal, and dry years is employed to fulfill such an engineering operation in a four-reservoir system in China. Simulations show well compatibility of the water level inside the reservoir with real statistical indices in terms of RMSE and MAE. Results also reveal that using the kidney algorithm not only reduces the required calculation but also increases the convergence pace with respect to other algorithms that have been used (bat, shark, abundance of particles, and genetic algorithms). Moreover, it increases the amount of the generated energy by a factor of 2.2–3.2 with respect to the aforementioned algorithms. Results indicate the capability of the kidney algorithm in the management of water sources and engineering operations.

     

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.

     

A Study on the Large-scale System Decomposition—Coordination Method Used in Optimal Operation of a Hydroelectric System

Abstract

The optimal operation problem of multiple hydroelectric reservoir systems is very complex because of the large dimensions. Large-scale system decomposition-coordination methods, which can simplify complex problems into several interrelated sub-problems to avoid the “curse of dimensionality” and to obtain the global optimum on the global through coordination among sub-systems, is particularly well suited for optimizing large-scale, multi-reservoir systems. Applying this kind of theory and method, this paper studies and analyzes the problems of optimal operation of multiple hydroelectric reservoir systems in series, and sets up the optimal operation model of hydroelectric reservoir systems in series. On this basis, a practical example of two hydroelectric reservoirs in series on the upper reaches of the Yellow River in China is calculated and analyzed and the results are satisfactory. It is believed that applying this model can cut down the dimensions of the problem notably and that the theory and method are effective for real time operation.     

江西省“五河”流域水量分配数学模型研究

基于江西水资源特点,提出了适合于多节点、多水库水量分配的逆序多水库联合调度法计算模型,实现了江西五大河流及“五河’外的水量分配计算．     

Investigating Energy Flow in Water-Energy Storage for Hydropower Generation in Water Distribution Systems

Quantifying excess energy using an energy balance model is the key to designing and operating an energy-efficient water distribution system (WDS). Excess energy, which can be recovered instantly or stored in a water-energy storage is the basis to estimate hydropower potential in the system. For a given WDS with its demand, how the excess energy can be managed efficiently to design a water-energy storage to maximize hydropower generation is the focus of this paper. A single-objective optimization model has been developed to optimize the dimensions for up to six water-energy storages for maximizing hydropower generation while minimizing the pumping energy. While the ratio of total energy recovered to total pumping energy is found to be about 40% for all water-energy configurations, the recovered specific energy ranges from 0.116 kWh/m³ to 0.121 kWh/m³ showing the potential use of WDS as an energy storage. Results show that hydropower generation increases with the increase of number of storages up to a certain number representing the constraints of constant drinking water demand and storage dimensions. In-pipe turbines with pump operation for minimizing pumping energy can offer the optimal solution for WDS energy management. A higher number of storages with in-pipe turbines offers uniformity in pressure distribution resulting increase in system robustness.

     

我国水库(群)调度理论方法研究应用现状与展望

水库(群)调度理论方法是防洪减灾与水资源高效利用的热点研究问题,其研究成果的应用可以在不改变水库工程规模前提下显著增加防洪与兴利效益,因而也受到工程界的高度关注。我国对水库(群)调度比较系统的研究始于20世纪70年代,现已取得大量高水平研究成果。本文基于复杂巨系统的构架,从调度的可利用信息、调度模型构建及求解技术、调度决策方案评价、实时调度系统开发设计与应用等方面综述我国水库(群)调度理论方法研究应用现状,展望水库调度理论研究与工程实践所亟待解决的问题及其发展趋势,以期对于相关研究具有一定参考价值。     

Optimization of Exclusive Release Policies for Hydropower Reservoir Operation by Using Genetic Algorithm

The efficient utilization of hydropower resources play an important role in the economic sector of power systems, where the hydroelectric plants constitute a significant portion of the installed capacity. Determination of daily optimal hydroelectric generation scheduling is a crucial task in water resource management. By utilizing the limited water resource, the purpose of hydroelectric generation scheduling is to specify the amount of water releases from a reservoir in order to produce maximum power, while the various physical and operational constraints are satisfied. Hence, new forms of release policies namely, BSOPHP, CSOPHP, and SHPHP are proposed and tested in this research. These policies could only use in hydropower reservoir systems. Meanwhile, to determine the optimal operation of each policy, real coded genetic algorithm is applied as an optimization technique and maximizing the total power generation over the operational periods is chosen as an objective function. The developed models have been applied to the Cameron Highland hydropower system, Malaysia. The results declared that by using optimal release policies, the output of power generation is increased, while these policies also increase the stability of reservoir system. In order to compare the efficiency of these policies, some reservoir performance indices such as reliability, resilience, vulnerability, and sustainability are used. The results demonstrated that SHPHP policy had the highest performance among the tested release policies.     

Reliability-based Operation of Reservoirs Using Combined Monte Carlo Simulation Model and a Novel Nature-inspired Algorithm

One of the critical issues in surface water resources management is the optimal operation of dam reservoirs. In recent decades, meta-heuristics algorithms have gained attention as a powerful tool for finding the optimal program for the dam reservoir operation. Increasing demand due to population growth and lack of precipitation for reasons such as climate change has caused uncertainties in the affecting parameters on the planning of reservoirs, which invalidates the operational plans of these reservoirs. In this study, a novel optimization algorithm with the combination of genetic algorithm (GA) and multi-verse optimizer (MVO) called multi-verse genetic algorithm (MVGA) has been developed to solve the optimal dam reservoir operation issue under influence of the joint uncertainties of inflow, evaporation and demand. After validating the performance of MVGA by solving several benchmark functions, MVGA was used to find the optimal operation program of the Amirkabir Dam reservoir in 132 months, in both deterministic and probabilistic states. Minimizing the deficit between downstream demand and release from the reservoir during the operation period was considered as the objective function. Also, the limitations of the reservoir continuity equation, storage volume, and reservoir release equation were applied to the objective function. For modeling the effect of uncertainty, Monte Carlo simulation (MCS) is coupled to MVGA. The results of model implementations showed that the MVGA-MCS model with the best value of the objective function equal to 26 in the 1st rank and MVGA, MVO, and GA, with 15%, 34%, and 46% increase in the value of the objective function compared to the MVGA-MCS stood in the second to fourth ranks, respectively. Also, the results of the resiliency, and vulnerability indices of the reservoir operation showed that MVGA-MCS and MVGA models have better performance than other models.

     

An Improved Genetic Algorithm-Simulated Annealing Hybrid Algorithm for the Optimization of Multiple Reservoirs

A hybrid evolutionary search algorithm is developed to optimize the classical single-criterion operation of multi-reservoir systems. The proposed improved genetic algorithm-simulated annealing (IGA-SA) which combines genetic algorithms (GAs) and the simulated annealing (SA) is a new global optimization algorithm. The algorithm is capable of overcoming the premature convergence of GAs and escaping from local optimal solutions. In addition, it is faster than a traditional unimproved GA-SA algorithm. A case study of optimization operation on generation electricity of a 3-reservoir system in series over 41-year (from May 1940 to April 1981) time periods in Wujiang River, one branch of Yangtze River in China, was performed. The objective is to maximize generation output from the system over each 12-month operating periods. Trade-off analyses on binary coding representation and real-value coding representation of GAs are performed. Sensitivity to some parameters of the GA, the SA and the IGA-SA is analyzed, respectively, and the appropriate values of parameters are suggested. The performance of the proposed algorithm is compared with that of the existing genetic algorithm, the simulated annealing and the dynamic programming (DP). Results demonstrate that the GA is better than the DP, the SA performs better than the GA and the IGA-SA is more efficient than SA. The IGA-SA produces higher quality solutions and costs less computation time compared with the traditional GA-SA. The results obtained from these applications have proved that the IGA-SA has the ability of addressing large and complex problems and is a new promising search algorithm for multi-reservoir optimization problems.     

Multi-reservoir Operation Rules: Multi-swarm PSO-based Optimization Approach

Reservoir operation rules are intended to help an operator so that water releases and storage capacities are in the best interests of the system objectives. In multi-reservoir systems, a large number of feasible operation policies may exist. System engineering and optimization techniques can assist in identifying the most desirable of those feasible operation policies. This paper presents and tests a set of operation rules for a multi-reservoir system, employing a multi-swarm version of particle swarm optimization (MSPSO) in connection with the well-known HEC-ResPRM simulation model in a parameterization–simulation–optimization (parameterization SO) approach. To improve the performance of the standard particle swarm optimization algorithm, this paper incorporates a new strategic mechanism called multi-swarm into the algorithm. Parameters of the rule are estimated by employing a parameterization–simulation–optimization approach, in which a full-scale simulation model evaluates the objective function value for each trial set of parameter values proposed with an efficient version of the particle swarm optimization algorithm. The usefulness of the MSPSO in developing reservoir operation policies is examined by using the existing three-reservoir system of Mica, Libby, and Grand Coulee as part of the Columbia River Basin development. Results of the rule-based reservoir operation are compared with those of HEC-ResPRM. It is shown that the real-time operation of the three reservoir system with the proposed approach may significantly outperform the common implicit stochastic optimization approach.     

Reservoir Flood Season Segmentation and Risk–benefit Cooperative Decision of Staged Flood Limited Water Level

Investigation of seasonal inconsistency between water consumption and rainfall variation is important for more efficient use of floodwater resources. Adjustment of the flood limited water level (FLWL) is an effective way to improve the floodwater use efficiency. Flood season segmentation provides the basis for determining the FLWL and tapping the potential use of floodwater resources. Compromise between the benefit of floodwater use and flood control is crucial to FLWL decision. We use the circular distribution method for flood season segmentation and the relative frequency method for verification. We select the performances of water supply and hydropower generation as the benefit index and the extreme risk rate as the risk index. On the basis of the game theory, we establish a multi-objective cooperative decision-making model and obtain a Nash negotiation solution of staged FLWL. An optimal scheme is determined according to the fuzzy pattern recognition theory. When the risk and benefit are equally valued, the resulting FLWLs of the optimal scheme are 129.0 m, and 128.5 m for a selected reservoir in the pre-flood season and the post-flood season, respectively. By adjusting the preference values of the risk and benefit indexes, we determine the optimal FLWL scheme under different preferences to risk and benefit for each stage.