State-of-the-Art Review on Operation of Multi-Reservoir System
Water resources engineers and hydrologists understand that the combined operation of multiple reservoirs can yield greater benefits than operating each reservoir independently Independent operation means that the release decisions for one reservoir do not consider the conditions of other reservoirs, whereas joint operation involves making release decisions based on the conditions of all reservoirs in the system, as highlighted by Robert et al.
Reservoir operation primarily involves determining the optimal amount of water to release immediately versus what to conserve for future needs, based on available data and forecasts at the start of the current period Typically, operators adhere to rule curves that dictate specific actions based on the system's current condition.
1.1.1 Analytical Analysis of Multi-Reservoir Optimal Operation
Analytical analysis plays a crucial role in the joint operation of multi-reservoir systems, offering valuable insights for practical applications Extensive literature has explored analytical optimization methods to establish operating rules for these systems, tracing back to early rules aimed at minimizing spill in parallel reservoirs Recent advancements have highlighted significant progress in this field, with researchers like Lund and Guzman summarizing optimal operating rules for simple multi-reservoir systems Lund's work on theoretical hydropower operation rules provides a simplified economic framework for energy and storage allocation Additionally, Draper and Lund's exploration of optimal hedging for water supply releases emphasizes the analytical relationship between water release decisions and carryover storage value You and Cai expanded on this by developing a two-period model that incorporates uncertain future inflows, contributing to both intuitive and new insights in reservoir operations Their method further derived hedging rules using a Markov hydrology model, while Zhao and Cai analyzed optimality conditions for a two-stage reservoir operation, addressing various constraints Shiau's research on optimal hedging for water supply reservoirs balances beneficial releases with carryover storage, applying the methodology to the Shihmen Reservoir in Taiwan, thus demonstrating the impact of optimal hedging on reservoir performance.
1.1.2 Numerical Simulation and Optimization of Multi-Reservoir
The optimization of reservoir operations has been a widely researched topic in recent decades, focusing primarily on deterministic models that overlook uncertainties like future inflows Most optimization approaches rely on various mathematical programming techniques, with linear programming (LP) being a fundamental classification within these methods.
Dynamic programming (DP) and nonlinear programming (NLP) are two optimization techniques applicable in both deterministic and stochastic environments Reservoir optimization models serve planning and real-time operational purposes, necessitating an objective function, decision variables, and constraints The objective function measures performance based on changes in decision variables, which dictate system operations such as water release schedules and storage levels Constraints ensure adherence to physical laws, economic factors, and social obligations, including conservation equations and legal requirements Research on optimizing reservoir storage capacities and operating policies is extensive, with significant contributions from Yeh, Wurbs, Labadie, and Rani and Moreira Yeh's review highlights theories and applications of systems analysis techniques, while Wurbs expands upon this with an annotated bibliography Labadie evaluates current practices in reservoir management optimization and suggests future research directions, whereas Rani and Moreira survey various modeling approaches, including simulation and optimization, to address reservoir operation challenges.
Multi-reservoir optimization operation faces stochastic characteristics primarily due to the uncertainty of reservoir inflows, which can lead to expected inflow values failing to capture highly variable hydrologic conditions or unreliable long-term forecasts Stochastic optimization methodologies are categorized into explicit stochastic optimization (ESO) and implicit stochastic optimization (ISO).
The ESO approach integrates probabilistic inflow methods into the optimization problem, typically handled by stochastic dynamic programming (SDP), which effectively manages single reservoirs with correlated inflows while accounting for streamflow uncertainty A key challenge in applying SDP to reservoir operations is representing future streamflow uncertainty, leading to various studies focused on this issue For instance, Kelman et al introduced sampling SDP (SSDP) to incorporate inflow scenarios into the DP recursive equation, reflecting streamflow characteristics across the basin Faber and Stedinger utilized SSDP for multi-reservoir systems by integrating Ensemble Streamflow Prediction (ESP) forecasts, allowing for optimal release updates with new ESP data Recent advancements by Kim and Heo showcased state-of-the-art optimization models using SSDP with ESP Zhao et al proposed an algorithm to enhance the computational efficiency of both deterministic and stochastic dynamic programming for reservoir operations with concave objective functions However, applying SDP to multi-reservoir cases incurs higher computational costs due to the curse of dimensionality, prompting the use of heuristic methods like aggregation-disaggregation and one-at-a-time successive decomposition Arunkumar and Yeh developed a one-at-a-time decomposition SDP approach for multi-reservoir systems, while Wang et al presented a combined methodology for multi-objective SDP optimization Additionally, Rani and Moreira provided a comprehensive review of the SDP literature.
Unlike ESO, ISO employs deterministic optimization to manage reservoirs across various probable inflow scenarios, leading to the development of rule curves based on optimal operating data Young's pioneering work introduced ISO for reservoir operating policies through dynamic programming, which allowed optimal release calculations based on current storage and projected inflow Karamouz and Houck advanced this method by incorporating a constraint to ensure releases align with established operating policies Kim and Heo further utilized ISO with linear equations for monthly operating rules in multipurpose reservoirs Alternatively, Willis et al focused on the probability mass function of optimal releases in relation to storage and inflow Contemporary methods, such as artificial neural networks and fuzzy rule-based modeling, offer modern alternatives to traditional regression analysis, with fuzzy logic providing flexibility and the ability to integrate expert insights, enhancing operator acceptance Many studies indicate that these advanced techniques surpass regression-based ISO and SDP in performance.
Numerical Simulation Combined with Optimization Models
The rapid advancement of modern evolutionary algorithms has made numerical simulation combined with optimization models a leading method in the field, often referred to as the Parameterization–Simulation–Optimization (PSO) methodology, as noted by Celeste and Billib The PSO technique involves predefining a shape for the rule curve based on specific parameters, then utilizing heuristic strategies to identify the optimal parameter combinations for reservoir performance under varying inflow scenarios Numerous studies have successfully implemented the PSO principle to derive effective reservoir rule curves For instance, Cancelliere et al developed monthly operating rules for an irrigation reservoir using dynamic programming and artificial neural networks, validating their results through simulations Neelakantan and Pundarikanthan employed a combined neural network simulation-optimization model with multiple hedging rules to evaluate operational policies Koutsoyiannis and Economou introduced a low-dimensional PSO approach based on parametric rules, optimizing performance measures through nonlinear optimization Tung et al applied a genetic algorithm to optimize operation rules for the LiYuTan Reservoir in Taiwan, while Momtahen and Dariane utilized a real-coded genetic algorithm for direct search optimization of reservoir operating policies Additionally, Kangrang et al proposed a heuristic algorithm integrated with simulation models to find optimal reservoir rule curves.
Multi-Reservoir Construction and Management Practice in China
China boasts a rich history of dam construction, dating back nearly 2,600 years to the first reservoir, Anfeng Pond, in Shou County, Anhui Province Prior to the establishment of the People's Republic of China (PRC), the development of dam building was relatively slow, with only 22 dams exceeding 15 meters in height However, since the founding of the PRC, particularly over the past 30 years, significant advancements in dam construction technology have been achieved Today, China accounts for a substantial share of the world's dams, maintaining a rapid construction rate These reservoirs are essential for the effective utilization of water resources and play a critical role in flood control.
To meet energy demands and environmental protection goals, the Chinese government has outlined a hydropower development plan targeting 2050, featuring 13 key hydropower energy bases Most of this hydropower potential is concentrated in Southwest China, influenced by the region's topography and water resource distribution.
Total number of large dams
Fig 1.1 The construction process of large dams in China and in the world (1: the number of large dams in the world, 2: in China, 3: in other countries)
The construction of numerous reservoirs has brought the challenge of effective reservoir management to the forefront, particularly the multi-reservoir joint operation issue, which is a critical concern for both reservoir managers and researchers Key areas of focus include the multi-objective optimization of reservoir operations, the development of operational rules and derivation methods, the joint operation of multiple reservoirs in inter-basin water transfer projects, and the forecasting of inflows for effective reservoir management These topics hold significant theoretical and practical importance and will be explored in detail in the following sections.
2 Multi-Reservoir Operation Within Theory
Framework of Dualistic Water Cycle
Dualistic Water Cycle Theory
As the economy develops and the population grows, the water cycle has evolved from a purely natural model to a "natural-artificial" dualistic model The traditional natural water cycle encompasses processes such as precipitation, canopy interception, evapotranspiration, infiltration, surface runoff, overland flow, river flow, and groundwater flow, all driven by natural forces like radiation, gravity, and wind In contrast, the "natural-artificial" dualistic water cycle integrates these natural hydrological processes with human-induced activities, including water extraction, conveyance, distribution, utilization, consumption, and drainage, influenced by both natural and artificial driving forces.
The dualistic characteristics of the water cycle can be summarized in three key aspects First, the driving force has transitioned from a centralized natural system to a "natural-artificial" dualistic model, incorporating both natural elements like gravity, capillary force, and solar evaporation, along with artificial inputs such as electrical, mechanical, and chemical energy Second, the structure of the water cycle has evolved to include a modern complete cycle that integrates the natural processes of the atmosphere, slope, underground, and river systems with artificial collateral cycles.
The water cycle involves key processes such as water intake, transportation, consumption, and drainage Additionally, the overall response of a basin's water cycle to changes in environmental conditions and precipitation is influenced not only by natural hydrological and geological factors but also by the development and management of water resources and socio-economic factors Addressing water resource and environmental issues in a basin requires a comprehensive analysis of the dualistic nature of the water cycle and the evolution of its associated processes.
The world comprises interconnected social-economic and ecological-environmental systems that engage in mutual interactions and feedback mechanisms Within these systems, water serves as a crucial medium for material and energy exchange, embodying five key attributes: resources, ecology, environment, economy, and society The fundamental attribute of water is its resource aspect, while the other attributes arise from the interactions between water and the two overarching systems Understanding these attributes is essential for effectively simulating and regulating the dualistic water cycle.
Intense human activity and climate variation have created dualistic driving forces in the water cycle, leading to significant issues such as water scarcity, flooding, and environmental degradation To address these water crises and promote sustainable societal and economic development, it is crucial to understand the evolution of the water cycle and its driving mechanisms By applying complex water resource system operation theories, we can maximize the economic, social, environmental, and ecological benefits of water resources, fostering harmony between humanity and nature This article introduces a theoretical framework for dualistic water cycle simulation and regulation to guide these efforts.
The watershed water cycle encompasses both the natural and artificial water cycles, with their dynamic interaction facilitated by hydraulic projects The natural water cycle consists of three key segments: meteorology-hydrology, hydrology-water quality, and hydrology-water ecology In contrast, the artificial water cycle is divided into two main components: flood control and the ecological, environmental, economic, and societal aspects of water resource management.
Fig 1.3 The relationship between water and society, economy, ecology, environment system rainfall radiation wind humidity natural water cycle Social water cycle hydrology water quality ecology simulation
Flood control regulation topology land use soil
Water quality economic equity ecology
Hydro- power multi -objective optimization technology
Water quality ecology Flood control
Hydro- power tempera meteorology parameters rule input objective process
Fig 1.4 Theoretical framework of dualistic water cycle simulation and regulation profiting operation For reservoir operation, profiting operation takes into account water supply, hydropower generation, ecology and navigation.
The coupling simulation foundation of the "natural and artificial" water cycle system represents the physical mechanism of the dualistic water cycle and the derivative effect theory of water resources The dualistic water cycle simulation and regulation model, illustrated in Fig 1.5, plays a crucial role in multi-reservoir systems by offering reservoir inflow predictions that inform optimal operation models, thereby assessing the effectiveness of system operating policies.
The dualistic water cycle simulation and regulation model encompasses two key components: the simulation theory of the watershed's dualistic water cycle processes and the multi-objective operation theory for complex multi-reservoir systems This model effectively illustrates the dynamics of the dualistic water cycle system.
Society water cycle simulation model
Natural water cycle simulation model
Multi-reservoir programming operation model
Multi-reservoir real-time operation model
Fig 1.5 The model system of dualistic water cycle simulation and regulation
Watershed dualistic water cycle multi-process simulation theory
Multi-objective operation theory for complex multi-reservoir system
The dualistic water cycle simulation and regulation model integrates human intervention into the social water cycle process, as depicted in Fig 1.6 By optimizing hydraulic project operations, this model enhances the utilization of water resources for economic and social development while minimizing disruptions to the natural water cycle system.
Main Technologies
This section presents three key technologies essential for simulating and regulating the dualistic water cycle These include coupling technology for the dualistic model, distributed hydrological modeling for inflow prediction, and the technology that facilitates the operation of multi-reservoir policies.
2.2.1 Coupling Technology for Dualistic Model
The dualistic model system effectively integrates natural evolution factors, human activities, urbanization, and hydraulic project regulations to analyze the water cycle and the evolution of water ecosystems It highlights the distinct transformation processes in mountainous and plain areas, as well as between surface and underground water systems in urban and rural settings By simulating the water cycle under various historical and planning scenarios, this model identifies key impacts and potential countermeasures, thereby guiding scientists in addressing water resource challenges and supporting comprehensive management objectives for basin water resources.
The Dualistic Model, developed by the China Institute of Water Resources and Hydropower Research (IWHR), integrates various components to enhance water and energy management This model combines the Water and Energy Transfer Processes Model (WEP), the Rules-based Object-oriented Water Allocation Simulation Model (ROWAS), and the Decision Analysis for Multi-Objective System (DAMOS), creating a comprehensive framework for effective resource allocation and decision-making.
The Dualistic Model System is a specialized software designed for managing dualistic model operations, encompassing a platform for data management and model calculations Its data management capabilities handle a variety of attribute and spatial data, hydrological data, water environment data, and socio-economic data Additionally, the model calculation functions include essential processes such as pre-processing, multi-model coupling, and post-processing, all crucial for effective model computation.
Characteristics of the Dualistic Model
Dualistic system model is a huge software project The system has the following characteristics:
Developing a dualistic model system is challenging due to the complexity and diversity of individual models, each implemented in different programming languages and methods The DAMOS model utilizes GAMS for optimizing multi-objective water resource allocation, while the ROWAS model, developed in C++, simulates the balance of water supply and demand The WEP model employs Fortran to simulate the coupling of natural and artificial water cycles To create an integrated dualistic model, it is essential to transform each model for seamless integration, such as adapting the DAMOS model from GAMS to Java for better application compatibility Additionally, data management varies across models, with DAMOS and WEP using text mode, while ROWAS combines text and database management A unified management approach is necessary to effectively couple these models into a cohesive system.
Water supply, water consumption water to sea of predefined economic scenario
Rational Water distribution among region and time
(runoff, evaporation, seepage) and control section
Time : Day(hour) series Space : Sub-basin:
Water distribution and Hydraulic facilities operation Information distribution
Operation of hydraulic facilities and decision- making
Time : Month series Space : hydrological region : municipalities
Water alloction by users and provinces Information distribution
(Economy gross, Et and water to sea)
Decision- making mode and Optimization mechanism
Time : Annual Space : Basin, Province Macrostructure
Adjusting objective Adjusting decision-making
Fig 1.7 Dualistic model structure and output data of every model, and build the unified data management module of multiple models on the unified database platform.
The dualistic model system integrates a variety of software technologies to enhance innovation and effectively manage complex calculations and data Utilizing a rich client/server model, it combines the advantages of both fat and thin client/server architectures, allowing users to perform complex calculations directly on the system interface without needing to access additional platforms This approach supports enhanced user interaction and responsiveness Developed using the open-source Eclipse RCP framework and pure Java, with SQL Server 2000 as the database server and Hibernate for data access, the system is designed for seamless integration with practical applications, paving the way for future development of a web-based dualistic model system.
The dualistic model system incorporates various software technologies, such as GAMS for optimization, MS SQL Server for database management, Hibernate for database connectivity, Supermap for spatial display, and ArcGIS SDE for spatial data management, along with several open-source GIS components like MapWindow.
Function of Dualistic Model System
To enhance system development and streamline user familiarity with the interface, we have implemented a versatile data management interface for efficient data input and output This interactive system allows users to visualize data through graphs, charts, and various formats, ensuring a comprehensive understanding of the information presented.
The dualistic model system enhances the calculation capabilities of various models, including DAMOS, ROWAS, and WEP, by tailoring packaging and transformation to the unique characteristics of each model For instance, the DAMOS model, originally developed using the GAMS optimization software, faced limitations for application system development To address this, a versatile water resources optimization model construction and solving package called Lp_Solve was developed, allowing for the rewriting of the DAMOS model using this more suitable software.
The dualistic model system facilitates the integration and automated data exchange among three models: DAMOS, ROWAS, and WEP The DAMOS model operates on an annual time scale at the provincial level, while ROWAS functions on a multi-month time scale across three-stage districts and cities, and WEP works daily within sub-basin contours In the forthcoming decades, the DAMOS model optimizes industrial and agricultural structures, water usage, pollution control, and engineering measures, providing these results to ROWAS and WEP for further simulations ROWAS, in turn, offers feedback to DAMOS regarding water supply and guarantee rates, while also sharing details on water utilization and drainage after its calculations This information is essential for WEP's simulations, which operate on a finer time and spatial scale Additionally, WEP sends resource volume feedback, including surface inflow and groundwater status, back to ROWAS Given the differing time and spatial scales of these models, we have developed data distribution procedures to ensure effective coupling and coordination among them.
2.2.2 Developing Distributed Hydrological Model for Inflow Prediction
The WEP-L model is a physically-based distributed hydrological tool designed to simulate both natural hydrological processes and human water usage, enabling the assessment of water resource variations in heavily impacted basins To enhance its applicability to large river basins and mitigate the computational challenges associated with small grid sizes and overly rough grids, the WEP-L modeling scheme utilizes contour bands within sub-basins This approach integrates spatial information on terrain, river networks, vegetation, soil, and land use, ensuring a more accurate representation of hydrological dynamics.
Despite the advancements in distributed hydrological models, several challenges persist, such as complexity in operation and modification, as well as limitations in application to small basins due to high computational and data preparation demands Key disadvantages contributing to these issues include low modularization, low generalization of pre-processing programs, and low automation To address these limitations, the AutoWEP modeling scheme was developed, featuring enhanced generalization and expandability, improved pre-processing modules, and an automatic parameter identification module This section outlines the significant improvements and modeling approach of AutoWEP, which is designed for effective inflow prediction.
To enhance the WEP-L modeling method, a new algorithm has been developed to streamline the modeling and calibration processes, minimizing repetitive tasks in the creation of distributed hydrological models This innovation aims to improve modeling efficiency and achieve optimal simulation accuracy.
AutoWEP has been developed with significant enhancements, including a restructured coding framework, revised input/output parameters, and improved pre-processing programs Key new features such as parameter sensitivity analysis and automatic parameter calibration have been introduced The most notable advancement in the AutoWEP algorithm is the integration of “AUTO” modules, which greatly enhance the efficiency of the WEP modeling and calibration process The modeling process of Auto-WEP is illustrated in Fig 1.8.
The AutoWEP algorithm has undergone significant enhancements, with its modeling codes being restructured for greater generalization and expandability Additionally, multiple modeling modules have been updated to improve functionality Key advancements in the AutoWEP modeling method are highlighted below.
Fortran 90 Is Used to Rebuild Modeling Codes
Dualistic Hydrology Simulation and Regulation System for Upper Reaches
The upper reaches of the Yangtze River are home to numerous large reservoirs, with the Three Gorges Reservoir being a key player due to its significant capacity and strategic location at the river's boundary The regulation of this multi-reservoir system leads to distinct dualistic characteristics in the natural water cycle To ensure the sustainable utilization of water resources in the Yangtze River watershed, we have developed a dualistic hydrology simulation and regulation system, grounded in dualistic hydrology simulation and multi-reservoir operation theory.
Application of reservoir simulation model with operation policies
Generation new parameters set using particle swarm algorithm
Fig 1.9 Framework to derive the proposed optimal operating rule
Fig.1.10, the system is devised from the perspective of multi-scale, multi-process and multi-level for simulating and regulating water resources system of Yangtze River upper reaches.
The dualistic hydrology simulation and water resources regulation in the upper reaches of the Yangtze River require research across multiple temporal and spatial scales This involves analyzing both the entire watershed and specific study areas to understand hydrological variation characteristics as scale changes As illustrated in Fig 1.11, it is essential to model and generate hydrological time series at monthly, daily, and hourly scales for effective real-time and planned operations of the multi-reservoir system in this region.
For achieving the whole process and all element simulation of the water cycle, the system needs to be able to model the water cycle and its accompanying process.
The system encompasses various processes, including atmospheric, land surface, and operational processes, as illustrated in Fig 1.12 Specifically, the atmospheric numerical simulation and forecasting models consist of global climate models (GCM), weather research and forecasting models (WRF), and mesoscale models.
The distributed water cycle and its simulation model include the EasyDHM hydrological model, the EasyWQ water pollution model, and the EasyRiv hydrodynamic model Additionally, the multi-reservoir multi-objective joint operation model comprises a joint simulation model, a multi-objective optimization model, and a real-time operation model Effective coupling technology among these various process simulations is crucial for the comprehensive simulation of the upper reaches of the Yangtze River.
Fig 1.10 Dualistic simulation and regulation system for upper reaches of Yangtze River
Month scale Day scale Hour scale
Upper reaches of Yangtze River Three Gorges Reservoir region
Fig 1.11 Multi-scale modeling technology for upper reaches of Yangtze River
Atmosphere numerical simulation and forecast model Global Climate Model (GCM) Weather Research and Forecasting Model (GCM) Mesa-scale Model 5 (MM5)
Distributed water cycle and its accompanying process simulated model Distributed Hydrological model EasyDHM Water pollution model EasyWQ Hydrodynamic model Easy Riv
Multi-reservoir multi-objective joint operation model Joint simulation model Multi-objective optimization model Real time operation model
Coupling hydrology and reservoir system operation
Land surface process operation process
Fig 1.12 Multi-process simulation of upper reaches of Yangtze River
The joint operation model for the multi-reservoir system in the upper reaches of the Yangtze River is categorized into two levels: real-time operation and planned operation The planned operation model focuses on analyzing the evolution of water resources, assessing the impacts of multi-reservoir operations, and determining optimal policies for the system In contrast, real-time operation is essential for managing floods and short-term profit operations, relying on inflow prediction data Profit operations involve reservoir management aimed at beneficial outcomes such as hydropower generation, water supply, and navigation.
3 Operation Rule Curves for Multi-Reservoir Operation
Historically, reservoirs were managed separately, but due to practical and environmental challenges, there is a shift towards multi-reservoir water resource management systems Extensive research has been conducted on multi-reservoir operation strategies, as reviewed by Yeh, Wurbs, and Labadie Notably, Oliveira and Loucks employed genetic search algorithms to establish operating policies that optimize system releases and individual reservoir storage based on total storage across multiple periods Similarly, Nalbantis and Koutsoyiannis introduced a parametric rule to enhance planning and management of multi-reservoir systems, addressing various operational objectives.
Flood prediction Flood operation Profiting operation
Water resources evolution law and tendency analysis
Impact assessment of multi -reservoir operation
Optimal policy determination of multi -reservoir
Fig 1.13 Multi-level operation of multi-reservoir system in upper reaches of Yangtze River
The parametric rule simplifies reservoir management by utilizing a limited set of control variables throughout the control period, allowing for efficient distribution of storage targets and calculation of water releases Unlike traditional methods that rely on numerous control variables, this approach significantly reduces complexity while still delivering effective solutions However, it depends on the System Operating Policy (SOP) to meet demand, which can lead to critical shortages during prolonged droughts, extreme weather events, or unexpected shifts in water demand.
Equivalent Reservoir Rule Curves
This article proposes an innovative operating policy for multi-reservoir water supply systems, integrating a hedging rule with a parametric rule to mitigate severe water shortages The policy consists of two main steps: first, it specifies water releases based on the hedging rule, which utilizes the initial storage levels of reservoirs to address overall water demand and local needs Second, the parametric rule determines specific release amounts from each reservoir to align with the hedging requirements To optimize this policy, a Particle Swarm Optimization (PSO) algorithm, coupled with a simulation model, fine-tunes the hedging curves and parametric parameters A case study of the Guanyinge, Shenwo, and Tanghe (G-S-T) multi-reservoir system in China's Taize River basin illustrates the effectiveness of this approach, demonstrating a significant reduction in decision variables and improved control over severe water shortages during droughts compared to traditional methods.
Operating policies for multi-reservoir systems should detail both the total release from the system and the specific amounts to be released from each individual reservoir The proposed operating rule incorporates a hedging rule that determines the total release based on the current storage volume, while a parametric rule is utilized to allocate the release amounts among the member reservoirs, ensuring that they collectively meet the total specified by the hedging rule.
Droughts are a natural aspect of the climate, making their occurrence unavoidable Therefore, it is crucial to focus on the water shortages caused by droughts Implementing strategies like the hedging rule for reservoir management can help alleviate the negative effects associated with drought conditions.
The hedging rule for reservoir operations has been explored through various methodologies Srinivasan and Philipose developed hedging parameters to assess their impact on reservoir performance indicators Shih and ReVelle focused on identifying trigger values for both continuous and discrete hedging rules Neelakantan and Pundarikanthan introduced a simulation-optimization approach that utilized neural networks alongside multiple hedging rules to enhance reservoir operation efficiency Additionally, Tu et al examined rule curves based on current storage levels to initiate hedging in multi-purpose, multi-reservoir systems.
The hedging rule outlined here includes specific hedging rule curves and rationing factors tailored to various water demands For a comprehensive understanding, refer to Fig 1.14 and Table 1.1, which provide detailed illustrations of the hedging rule curves alongside their associated water-supply operating rules.
In previous works [56,57] on hedging rule curves, all planned water demands are
In water-supply operations, demand is categorized into irrigation, industrial, and municipal needs, each requiring varying levels of reliability and hedging during droughts This study assigns distinct hedging rule curves and rationing factors to these categories, prioritizing lower-demand uses for rationing first The degree of hedging for lower-priority demands must exceed that of higher-priority ones, as outlined by the proposed hedging rule curves Rationing factors play a crucial role in managing hedging levels during droughts, with their values derived either through optimization methods or expert knowledge.
In multi-reservoir operations, water demand is categorized into local and common demands Local water demand is fulfilled by specific reservoirs, while common water demand can be met by any reservoir in the system The supply for common demand depends on the total water storage across all reservoirs, whereas local demand is tied to the storage of individual reservoirs This study introduces an equivalent reservoir to symbolize the entire multi-reservoir system, using its initial storage level to trigger the hedging process for meeting common water supply needs A simplified model of an equivalent reservoir for hydroelectric systems was initially proposed by Arvanitidis and Rosing.
Branda˜o [59] examines the effectiveness of a method for optimizing the operation of multi-reservoir hydroelectric systems In the context of water supply, Robert et al [1] introduced the concept of an equivalent reservoir, representing a fictitious system Unlike typical water demands, the hedging rule curve for local water demand is tailored to the storage levels of specific member reservoirs Ultimately, the desired water releases for both common and local demands depend on the existing storage volumes in the equivalent or specific member reservoirs, the season, and overall water demand, which is illustrated through hedging rule curves.
Table 1.1 Water-supply operating rule implied by hedging rule curves
Water supply for each demand
3.1.2 Parametric Rule to Determine the Reservoir Release
The hedging rule is designed to ascertain the necessary water supply for various demands, yet the specific water release from each reservoir to meet these demands remains unclear This section modifies the parametric rule introduced by Nalbantis and Koutsoyiannis to effectively determine water release from each reservoir during any given period The parametric rule involves three key computational stages: first, it allocates the overall target storage among the system's reservoirs; second, it adjusts each reservoir's target storage to ensure compliance with physical constraints; and third, it calculates the actual storage and release amounts for each reservoir.
The system target storage S tþ1 T for a certain period is obtained through the continuity equation of equivalent reservoir by
The equivalent reservoir model is defined by key variables including the beginning-of-period storage (S_T_t), stream inflows (I_T_t), reservoir releases for water demand (R_T_t), water spills (SU_T_t), and water losses due to evaporation and seepage (L_T_t) Similar to individual reservoirs, the equivalent reservoir has a storage capacity that ranges from full to dead storage, with its total capacity being the sum of the capacities of all individual reservoirs The water balance terms—S_T_t, I_T_t, and L_T_t—are also derived from the individual reservoirs in the system and can be calculated or estimated Under the standard operating procedure (SOP) governed by parametric rules, R_T_t meets demand only when sufficient water is available in the equivalent reservoir However, if water is insufficient, demand will be rationed, resulting in R_T_t being lower than the actual demand to prevent severe shortages Initially, water spills (SU_T_t) are set to zero, with potential adjustments made in subsequent steps.
The water balance terms of the equivalent reservoir, as outlined in Eq (1.1), can be determined using various methods, allowing for the calculation of the system target storage S t T + 1 Subsequently, the target storage S t+1 i for each individual reservoir at stage t+1 can be derived using Eq (1.2).
The article discusses a system of individual reservoirs, denoted by ordinal numbers i and j, which represent their respective positions within a defined annual cycle It specifies m as the total number of individual reservoirs in the system and n as the number of stages within a water year.
In the optimization process, parameters a_ij and b_ij are crucial components of the parametric rule Each reservoir is governed by a water balance equation, similar to equation (1.1), specifically outlined in equation (1.3) This equation is essential for calculating the specific release from each individual reservoir, ensuring that their total release aligns with the overall requirement represented by R_T_t in equation (1.1).
The total target storage of all individual reservoirs matches the target storage of the equivalent reservoir, as indicated in equation (1.4) Therefore, the parameters a_ij and b_ij in equation (1.2) must adhere to the constraints outlined in equations (1.5) and (1.6).
1ẳX m iẳ1 aij iẳ1, 2 .m,jẳ1, 2 .n ð1:5ị
0ẳX m iẳ1 bi j iẳ1, 2 .m,jẳ1, 2 .n ð1:6ị
The individual reservoir responsible for meeting local water demands must adhere to a minimum release threshold, denoted as R tmin i, in accordance with the hedging rule Additionally, the target storage allocated to this reservoir, as specified by Equation (1.2), must not exceed the maximum storage capacity, S max tỵ1 i, outlined in Equation (1.7).
S max tỵ1 i ð ị ẳS t i ỵI t i R tmin i L t i iẳ1, 2 .m ð1:7ị
Two-Dimension (2D) Rule Curves for Dual-Reservoir System
3.2.1 The Function of 2D Rule Curves
In multi-reservoir water-supply joint operations, water supply decisions should prioritize the overall storage state of the entire system rather than individual reservoirs To effectively manage this, we introduce a two-dimensional reservoir rule curve for a two-reservoir system addressing a single water demand This model, illustrated in Fig 1.15, features coordinate axes representing the water storage levels of each reservoir The symbols max 1 and max 2 indicate the storage capacities of reservoir 1 and reservoir 2, respectively The lines x 1 and y 1 depict hedging rule curves that trigger water supply adjustments when reservoir storage dips below these thresholds Additionally, lines x 2 and y 2 represent rule curves that facilitate increased water supply based on current storage levels.
1 and reservoir 2 For one dimension reservoir rule curve, the water supply will be increased more than water demand if the reservoir storage is higher the hedging rule curve.
Unlike one-dimensional reservoir rule curves, two-dimensional reservoir rule curves determine water supply based on the interplay between the storage levels of two reservoirs and their operational zones As illustrated in Fig 1.15, the hedging rule curves (x1, y1) and the increasing water supply curves (y2) segment the reservoir capacity into nine distinct zones, comprising three hedging zones, three normal zones, and three increment zones In these zones, the water supply rules for hedging and increment zones align with those of one-dimensional rule curves When the combined storage of the two reservoirs falls within the normal zone, the water supply matches the water demand Fig 1.15 depicts the two-dimensional rule curves for a single operational period each year, with potential variations in the hedging rule curves across different periods Ultimately, two-dimensional reservoir rule curves offer a framework for water supply in a dual-reservoir system, effectively accounting for overall system storage For practical implementation, these curves should be utilized alongside a specific allocation rule to manage water supply distribution among the member reservoirs.
3.2.2 2D Rule Curves with Variable Allocation Ratios
The 2D rule curves illustrated in Fig 1.15 are tailored for a dualistic reservoir system with a single water demand, featuring a hedging zone, normal zone, and increment zone Building on prior research, we introduce a new set of 2D rule curves for a dualistic reservoir system accommodating two water demands, as depicted in Fig 1.16 This new model maintains the hedging and normal zones but omits the increment zone Notably, in this framework, water demand 1 is assigned a lower supply priority compared to water demand 2.
The water supply policy will prioritize hedging based on the reservoir system's storage levels, particularly when there is insufficient water available.
Water supply decisions can be categorized into three types: no hedging, hedging for demand 1 only, and hedging for both demand 1 and demand 2 These categories correspond to the initial section of Fig 1.16.
To optimize the water supply management in a dualistic reservoir system, the concept of variable allocation ratios is introduced, allowing for effective distribution of water resources between the reservoirs As illustrated in the second and third sections of Fig 1.16, the allocation ratios remain constant during each operational period, with 'y' representing the ratio for reservoir one and 'z' for reservoir two.
Hedging zone Normal zone Increment zone
Hedging zone Normal zone Increment zone
Fig 1.15 Two dimension reservoir rule curves for dual-reservoir system
In an optimization model, the sum of ratio y and ratio z at a given square equals 1, serving as a key constraint Typically, these allocation ratios are established using optimization algorithms.
The operation of reservoir systems using 2D rule curves with variable allocation ratios involves two key steps: initially, the system manager determines the water supply needed based on the 2D rule curves Subsequently, this water supply is allocated among specific member reservoirs according to variable ratios, ensuring precise water release from each reservoir A detailed analysis of this methodology will be presented in the following case study.
3.2.3 The Optimization Model and Result Analysis for 2D Rule Curves
This study evaluates the effectiveness of 2D rule curves with variable allocation ratios by examining the dualistic water supply reservoir system in Northeast China, which includes Reservoir A and Reservoir B operating in parallel to meet the water demands of downstream agriculture and industry Each reservoir not only fulfills its water supply obligations but also ensures the maintenance of environmental flow downstream The flood season in the region occurs from July to August, with Reservoir A having a capacity of 13,218.9 ten thousand m³ and Reservoir B holding 7,345.5 ten thousand m³ Relevant reservoir inflow and water demand data are illustrated in accompanying figures.
To achieve optimal performance in a dualistic reservoir system, we have developed an optimization model that identifies the ideal 2D rule curves and allocation ratios This model incorporates risk indexes, specifically focusing on water supply reliability (REL) and the resiliency coefficient (RES), to ensure effective water management.
The two-dimensional reservoir rule curves illustrate variable allocation ratios for assessing the water supply disk Utilizing the analytical hierarchy process (AHP), diverse indices from various water users are consolidated into a single comprehensive index, R The primary optimization goal is to enhance water supply reliability and resiliency, as outlined in the objective function maxR = ω1RELindu + ω2RESindu + ω1RELagri + ω2RESagri.
Industry and agriculture water demand
Fig 1.17 One dualistic reservoir system in
The monthly average inflow of the reservoir is illustrated in Fig 1.18, highlighting the water supply reliability for industrial (RELindu) and agricultural (RELagr) demands Additionally, the water supply resiliency coefficients for these sectors are represented as RESindu and RESagr The analysis incorporates weighting factors, ω1 and ω2, which balance various water supply risk indexes, alongside windu and wagri, reflecting the weighting factors between industrial and agricultural water demands.
The optimization model incorporates several constraints, including the water balance equation, reservoir storage capacity, and requirements for the hedging factor and hedging rule curve position To solve this model, the SCE algorithm is employed, integrating a simulation model with an optimization algorithm.
The model's optimal solution features 2D reservoir rule curves with varying allocation ratios for each operational period, as illustrated in Fig 1.20 Additionally, Table 1.2 presents the specific allocation ratios for reservoir A and reservoir B, which are derived from the simulation model's results.
1 month as a time step and one piece of 2D reservoir rule curves is used for 2 months.
In Fig 1.20, demand 1 and demand 2 represent water requirements for agriculture and industry, respectively Throughout the year, the 2D reservoir rule curves exhibit notable variations in their rule zones Specifically, the hedging zones are larger during the drought season compared to the flood season, which is influenced by changes in reservoir inflow In the flood season, reservoir storage is nearly at full capacity, eliminating the need for water supply restrictions Conversely, during the drought season, limited water storage necessitates an increased hedging strategy to prevent severe water shortages in the future.