Multi-objective Optimal Operation Model Research Articles

Multi-Objective Optimal Operation Decision for Parallel Reservoirs Based on NSGA-II-TOPSIS-GCA Algorithm: A Case Study in the Upper Reach of Hanjiang River

The parallel reservoirs in the upper reach of the Hanjiang River are key projects for watershed management, development, and protection. The optimal operation of parallel reservoirs is a multiple-stage, multiple-objective, and multiple-decision attributes complex decision problem. Taking Jiaoyan–Shimen parallel reservoirs as an example, a method of multi-objective optimal operation decision of parallel reservoirs (MOODPR) was proposed. The multi-objective optimal operation model (MOOM) was constructed. The new algorithm coupling NSGA-II, TOPSIS, and GCA was used to solve the MOODPR problem. The method of MOODPR was formed by coupling problem identification, model construction, an optimization solution, and scheme evaluation. The results show that (1) combining the Euclidean distance with the grey correlation degree to construct a new hybrid closeness degree makes the multi-attribute decision making method more scientific and feasible. (2) The NSGA-II-TOPSIS-GCA algorithm is applied to obtain decision schemes, which provide decision support for management. (3) It can be seen from the Pareto chart that for the Jiaoyan–Shimen parallel reservoirs, the comprehensive water supply was negatively related to ecology. (4) The comprehensive water supply and ecological AAPFD value in the extraordinarily dry year was 4.212 × 108 m3 and 4.953. The number of maximum continuous water shortage periods was 4 and 6. The maximum ten-day water shortage was 4.46 × 107 m3 and 2.3 × 106 m3. The research results provide technical support and reference value to multi-objective optimal operation decisions for parallel reservoirs in the upper reach of the Hanjiang River.

Impact on traditional hydropower under a multi-energy complementary operation scheme: An illustrative case of a ‘wind–photovoltaic–cascaded hydropower plants’ system

Establishing a wind–photovoltaic (PV)–hydro hybrid system is a new method to utilize wind and PV power, but how multi-energy complementation affects the working modes of cascaded hydropower plants (CHP) has not been fully revealed. In this study, a wind–PV–CHP system was considered as an example and a multi-objective optimal operation model was constructed considering the maximization of both the power generation and the minimum power output. Simulation and comparison results showed that (1) the regulation capability of the hydropower was mainly used for two purposes: one was to drive the early water storage (or water release reduction) of CHP to improve the overall utilization efficiency of water resources, and the other was to drive the hydropower output to cooperate with the non-regulatable wind–PV power output in order to achieve a complementary output; (2) the different minimum outputs determined the regulation capacity for complementing the wind–PV power output, which represents the degree of complementation; and (3) complementation would significantly affect the minimum output and slightly affect the average output of CHP. Overall, this study improves our understanding of wind–PV–hydro complementary operation and can serve as a reference for actual project operation.

Energy saving based on a multi-objective optimization model of the tidal pumping station along the coastal area

The operation of tidal pumping station has an energetic impact on energy course of massive water pumping for a long time. Thus, a multi-objective optimal operation model was developed to optimize the operation scheme and reduce the energy consumption of the tidal pumping station. In the model, a day is divided into several sub-periods according to the regulation of water level in tidal reach. The partition of sub-periods, the number and blade angle of operating units in each sub-period are adjusted to minimize daily operation energy consumption. And the less switching times, the better the reliability and durability of the unit, the lower the failure rate. Therefore, the reduction of wearing parts’ service life is quantified for each switching time in the form of cost. A case study is performed with the tidal pumping station of the South-to-North Water Transfer Project in China. In this paper, energy consumption and switching times are quantified as costs respectively, and the result shows that the daily energy consumption could be saved about 2.28%–6.56%, and the switching times reduced at least 60%. Therefore, this paper could provide an effective optimal operation scheme for the tidal pumping station whose operation is affected by tides.

Deriving operating rules for inter-basin water transfer projects incorporating a scenario reduction strategy

Streamflow uncertainty is one of the main challenges in managing reservoir systems. To accurately characterize the streamflow uncertainty in a reservoir operation model, numerous streamflow scenarios should be considered, but this results in a huge computational burden for multi-objective optimization. Here, we propose a methodology for deriving the operating rules for an inter-basin water transfer project (IBWT). The methodology adopts a scenario-reduction strategy to balance accuracy against the computational burden. The proposed method first reduces a large number of streamflow scenarios to several typical scenarios and the corresponding occurrence probabilities using a simultaneous backward reduction method. A multi-objective optimal operation model is then formulated to optimize the expected values of performance indices of the IBWT system under the typical scenarios. Finally, a simulation-based optimization framework is adopted to derive the multi-objective operating rules. To test the method, the Han to Wei IBWT project in northwest China is considered as a case study. The results show that the proposed methodology produces effective reservoir operating rules with a relatively low computational burden. After the initial 1,000 streamflow scenarios have been reduced to 20, the model solution time decreases significantly, from 49.17 h to 1.05 h, while the changes in mean value (0.47%) and standard deviation (0.93%) of these scenarios are less than 1%. Compared with an operation scheme that uses only historical streamflow data, the operation performance is further improved in terms of energy production, energy consumption, and water shortage index when the streamflow uncertainty is considered.

Cascade reservoirs operation rules derivation using integrated decision-making method and combinatorial evolution network

Implicit reservoir operation rules map known reservoir conditions to discharge flow or water level decisions to guide reservoir operation. Existing data-driven operation rule extraction models are influenced by both features and hyperparameters, and lack subjective-objective coordination, hindering the formulation of reasonable water energy utilization strategies. To improve the comprehensive benefits of cascade reservoirs, this study proposes a novel multi-objective cascade reservoir operation rule derivation framework. First, a multi-objective optimal operation model for cascade reservoirs (MOOMCR) considering power generation, environment, and navigation is constructed and solved using a Speed-constrained Multi-objective Particle Swarm Optimization algorithm (SMPSO). The relationships among the requirements were explained using a four-dimensional Pareto front visualization analysis. Then, an Integrated Decision-making Method based on Multilevel Subspace Domination (IDMSD) is proposed to circumvent the subjective defects of single decision-making models and reliably select the optimal scheme with the most significant comprehensive benefits from all typical years. Finally, a feature-hyperparameter combination optimization technique based on the differential evolutionary algorithm (FHCC-DE/best/1) is proposed, which exhibits its strength in the identification of key influencing factors on the optimal discharge flow from the IDMSD. The method was embedded in a deep learning model to construct a Combinatorial Evolution Network (CEN) to extract the implicit reservoir operation rules from the optimal IDMSD schemes for the MOOMCR. The results show that the RMSE of the CEN simulating the optimal discharge flow is improved by 5.98%, 28.03%, and 27.89% for the XLD reservoir and by 11.01%, 1.66%, and 60.98% for the XJB reservoir, respectively, over the best results of all benchmark models. Meanwhile, the operation simulation results confirmed that the CEN outperforms conventional reservoir scheduling, with advanced multi-objective comprehensive effects. This suggests that multimethod integrated decision-making and deep learning evolution optimization can help improve the accuracy, generalization, and reliability of implicit reservoir operation rules.

Multi-objective optimization operation of micro energy network with energy storage system based on improved weighted fuzzy method

As a terminal type of micro integrated energy system, micro energy network is small in scale and easy to implement, which meets the needs of developing an integrated energy system. Consequently, it has great promotion value. In order to better coordinate the economy, energy conservation and environmental protection of micro energy network, this paper first establishes a multi-objective optimal operation model considering the factors of economy, energy and environment. Second, an improved weighted fuzzy method is proposed to transform the above model into a single-objective one, which can be solved by the particle swarm algorithm. Then, the results and satisfaction of single-objective and multi-objective optimization are compared and analyzed in the example. By optimizing the membership function and multi-objective weight setting method of the traditional weighted fuzzy method, not only the importance of different objectives can be reflected, but also the relationship between single-objective and multi-objective optimization results can be reflected. The proposed improved weighted fuzzy method can improve the comprehensive coordination among multiple objectives and the robustness of the algorithm, optimize the output of each device and realize the coordinated development of energy, environment and economic benefits. It is not only suitable for solving multi-objective optimization problems of micro-energy network, but also for other scenarios.

Regulating outflow temperature for multi-objective operation of cascade reservoirs: A case study

Thermal stratification widely exists in large reservoirs, causing significant inflow-outflow temperature difference (IOTD), which goes against the downstream ecology. Reservoir optimal operation has recently been conducted to regulate the outflow temperature, while its effects for cascade reservoirs urgently needed to be illuminated. Taking the typical Xiluodu-Xiangjiaba cascade reservoirs (XXCR) as study case, this paper had built a multi-objective optimal operation model combing the non-dominated sorting genetic algorithm II (NSGA-II) and a hydrodynamic-temperature model, and the total power generation (TPG) and IOTD were simultaneously considered. The effects of different inflow discharge and global warming scenarios were analyzed. This paper showed the following: (1) The IOTD and TPG of XXCR showed a positively linear relationship with the water level of the superior Xiluodu Reservoir (XLD), instead of the inferior Xiangjiaba Reservoir (XJB). (2) The reservoir with larger water volume and depth (such as XLD) determined the thermal structure and hydropower generation in cascade reservoirs, compared with the inferior reservoir (such as XJB). (3) As the inflow discharge or air temperature increased, the slope between the IOTD and TPG in the Pareto front curve increased. The results of this paper could support the ecological operation for cascade reservoir to regulate the outflow temperature.

Research on distribution network optimal operation with a novel medium voltage photovoltaic power generation device with the soft open point function

Soft open point (SOP) realizes the normal and flexible interconnection between distribution network feeders, leading to the improvement of the flexibility and rapidity of the distribution network control. However, drawbacks such as high cost and low utilization rate limit its application. A novel medium voltage photovoltaic power generation device with the SOP function is proposed in this paper. There are two grid-connected interfaces, and both of them adopt the cascaded H-bridge topology. A common DC-link is used for both H-bridge inverters belonging to the two grid-connected interfaces respectively. The proposed device eliminates the step-up transformers, and can be connected directly to the medium voltage distribution network. Therefore, advantages such as simple structure, low cost, low power loss and fault-tolerant operation capability are able to be obtained. The stability and flexibility of the distribution network operation are improved. The topology and power flow mode of the proposed medium voltage photovoltaic power generation device with the SOP function are analyzed, and the distribution network multi-objective optimal operation model with the proposed device is established. The proposed medium voltage photovoltaic power generation device with the SOP function is connected to the modified IEEE 33-node distribution network, and the network optimal operation with the device in terms of the power flow optimization and voltage improvement is analyzed.

Multi-Objective Optimal Long-Term Operation of Cascade Hydropower for Multi-Market Portfolio and Energy Stored at End of Year

Taking into account both market benefits and power grid demand is one of the main challenges for cascade hydropower stations trading on electricity markets and secluding operation plan. This study develops a multi-objective optimal operation model for the long-term operation of cascade hydropower in different markets. Two objectives were formulated for economics benefits and carryover energy storage. One was to maximize the market utility value based on portfolio theory, for which conditional value at risk (CVaR) was applied to measure the risk of multi-markets. Another was the maximization of energy storage at the end of a year. The model was solved efficiently through a multi-objective particle swarm optimization (MOPSO). Under the framework of the MOPSO, the chaotic mutation search mechanism and elite individual retention mechanism were introduced to diversify and accelerate the non-inferior solution sets. Lastly, a dynamic updating of archives was established to collect the non-inferior solution. The proposed model was implemented on the hydropower plants on the Lancang River, which traded on the Yunnan Electricity Market (YEM). The results demonstrated non-inferior solution sets in wet, normal and dry years. A comparison in solution sets revealed an imbalanced mutual restriction between objectives, such that a 2.65 billion CNY increase in market utility costs a 13.96 billion kWh decrease in energy storage. In addition, the non-inferior solution provided various schemes for actual demands based on other evaluating indexes such as the minimum output, power generation and spillage.

Optimal reservoir operation and risk analysis of agriculture water supply considering encounter uncertainty of precipitation in irrigation area and runoff from upstream

The precipitation in irrigation area and the runoff from upstream can reflect the natural and irrigated agriculture water supply situations. The wetness–dryness encounter uncertainty of precipitation and runoff, affected by the different microclimate in the basin, can lead to the potential water supply risk of reservoir dispatching, which poses a threat to food security. This study develops an innovative integrated modeling framework by coupling Copula joint distribution of precipitation and runoff, the reservoir multi–objective optimal operation model, and multi–criteria decision–making CECG–VIKOR method to assess agriculture water supply risk in the Baojixia Irrigation Area (BIA) of Northwest China. The results indicated that the integrated methodology is an important tool for assessing agriculture water supply risk, which has comprehensive, advanced, and efficient features. The correlation between the precipitation in BIA and runoff from upstream is weak, which can lead to a high uncertainty of the natural and irrigated agriculture water supply conditions. The Clayton copula was more suitable for estimating the joint distribution of precipitation and runoff. And there was a large probability of an unfavorable water balance situation in the BIA, with the extreme water shortage encounter condition of precipitation and runoff had the maximum joint distribution probability of 23.50%. The 9 scheduling schemes were set up according to encounter scenarios and whose optimal scheduling results are R104, R116, R66, R95, R5, R28, R117, R89, and R110, respectively. Among the 9 optimal scheduling results, the water supply risk in BIA increased with the decrease of available water supply and the increase of water demand. Below middle and middle water supply risk were mainly faced by scheme A and B with an occurrence probability of 62.47%, while scheme C had a high risk with an occurrence probability of 37.53% in BIA. The research results can provide a scientific basis for reservoir dispatching risk research and new ideas for making dispatching plans.

Research on optimal operation of grid-connected microgrid based on improved whale algorithm

In this paper, a small microgrid system is composed of wind turbines, photovoltaic generators, micro gas turbines, fuel cells and battery energy storage devices. In order to realize the optimal operation of the grid-connected microgrid, a multi-objective optimal operation model with economical and environmental friendliness is established. Secondly, an adaptive strategy is introduced for the whale optimization algorithm (WOA) to improve the optimization accuracy and convergence speed of the whale algorithm. The improved whale algorithm is used to solve the target model, and the optimal operation scheme of each distributed power source in the microgrid is obtained, and the simulation analysis results are compared to verify the rationality of the improved whale algorithm.

Optimal Operation Strategy of PV-Charging-Hydrogenation Composite Energy Station Considering Demand Response

Traditional charging stations have a single function, which usually does not consider the construction of energy storage facilities, and it is difficult to promote the consumption of new energy. With the gradual increase in the number of new energy vehicles (NEVs), to give full play to the complementary advantages of source-load resources and provide safe, efficient, and economical energy supply services, this paper proposes the optimal operation strategy of a PV-charging-hydrogenation composite energy station (CES) that considers demand response (DR). Firstly, the operation mode of the CES is analyzed, and the CES model, including a photovoltaic power generation system, fuel cell, hydrogen production, hydrogen storage, hydrogenation, and charging, is established. The purpose is to provide energy supply services for electric vehicles (EVs) and hydrogen fuel cell vehicles (HFCVs) at the same time. Secondly, according to the travel law of EVs and HFCVs, the distribution of charging demand and hydrogenation demand at different periods of the day is simulated by the Monte Carlo method. On this basis, the following two demand response models are established: charging load demand response based on the price elasticity matrix and interruptible load demand response based on incentives. Finally, a multi-objective optimal operation model considering DR is proposed to minimize the comprehensive operating cost and load fluctuation of CES, and the maximum–minimum method and analytic hierarchy process (AHP) are used to transform this into a linearly weighted single-objective function, which is solved via an improved moth–flame optimization algorithm (IMFO). Through the simulation examples, operation results in four different scenarios are obtained. Compared with a situation not considering DR, the operation strategy proposed in this paper can reduce the comprehensive operation cost of CES by CNY 1051.5 and reduce the load fluctuation by 17.8%, which verifies the effectiveness of the proposed model. In addition, the impact of solar radiation and energy recharge demand changes on operations was also studied, and the resulting data show that CES operations were more sensitive to energy recharge demand changes.

A Method of Multi-Objective Optimization and Multi-Attribute Decision-Making for Huangjinxia Reservoir

The objectives of flood control, power generation, water supply and ecology for reservoir operation are neither completely coordinated nor completely opposed, and its optimal operation and decision-making is very complicated. This study proposed a method of multi-objective optimization and multi-attribute decision making for reservoir operation (MODRO). The correlation analysis method was used to analyze the competitive relationship among the extracted objectives, and the multi-objective optimal operation model was constructed. The NSGA-II-SEABODE algorithm was applied to solve the MODRO problem. The objective extraction, model construction, optimization solution and scheme selection were coupled to form a multi-objective optimization and multi-attribute decision making method with the whole process of “Objective-Modeling-Optimization-Selection”. Huangjinxia Reservoir, which is located in Shaanxi, China, was selected as the case study. The results show that: (1) Quantifying the degree of conflict among objectives makes the construction of the multi-objective optimal operation model more reasonable. (2) The NSGA-II-SEABODE algorithm are used to obtain the decision-making scheme, which provides decision-making basis for managers. (3) For Huangjinxia Reservoir, water diversion is negatively related to power generation and ecology, and power generation is positively related to ecology. The results can promote the efficient utilization of water resources, improve the comprehensive benefits of reservoirs, and provide decision-making support for actual reservoir operation.

Multi-Objective Optimal Source–Load Interaction Scheduling of Combined Heat and Power Microgrid Considering Stable Supply and Demand

With the development of smart grids, it has become possible to take demand-side resource utilization into account to improve the comprehensive benefits of combined heat and power microgrids (CHP-MGs). In order to improve the benign interaction between the source and the load of the system, the source side decouples the thermoelectric linkage through energy storage devices and improves the system multi-energy supply capacity by introducing various energy flow forms of energy devices. On the demand side, considering the elasticity of electric heating load and the diversity of heating mode, an integrated demand response (IDR) model is established, and a flexible IDR price compensation mechanism is introduced. On this basis, aiming at the optimal stability of supply and demand and the minimum operating cost of the system, a multi-objective optimal operation model of combined heat and power source–load interaction is constructed, taking into account the user satisfaction with energy consumption and the internal equipment load constraints of the system. Finally, an improved multi-objective optimization algorithm is used to solve the model. The analysis of the algorithm shows that the source–load interaction multi-objective optimal scheduling of the cogeneration microgrid considering the stability of supply and demand can effectively improve the stability of supply and demand and the economy of the system.

A framework for adaptive control of multi-reservoir systems under changing environment

The changing environment has led to significant changes in the supply and demand of runoff, directly affecting the benefits of the multi-reservoir systems. Adaptive operation and quantitative control can hedge against the negative effects of changing environment for multi-reservoir systems, while studies related to the general theory and methods or models of such operations are inadequate. In this context, an adaptive control framework for multi-reservoir systems is proposed from a supply and demand perspective. Under this framework, a multi-objective optimal operation model is first established for adaptive control analysis, and the adaptive control measures based on supply-side, demand-side, and supply-demand linkage perspectives are designed. The effects of different control measures are further evaluated through scenario simulation analysis to recommend control schemes, using a multi-reservoir system in the Upper Yangtze River Basin of China as an example. The results suggest that the supply-demand linkage is an effective method to minimize the negative effects of changing environment on multi-reservoir systems, such as changes in runoff, increasing demands in water supply, population growth and socioeconomic development, etc. The proposed framework is shown to be feasible and effective in developing control measures for multi-reservoir systems to adapt to changing environments, which can provide a theoretical basis for the management of multi-reservoir systems under changing environments.

Multi-objective synergetic reservoir operation in a sediment-laden river

Multi-objective requirements including water supply, hydropower generation, water–sediment regulation (WSR), and inner-river ecosystem maintenance should be fully valued in the operation of reservoirs located on a sediment-laden river. In order to balance the satisfaction of multiple objectives with intense competition and guarantee the primary requirements preferentially, this paper presents a novel framework that incorporates the recognition and classification of primary and secondary requirements of multiple operation targets, a set of principles for multi-objective synergetic regulation of reservoirs (MOSRR) following the theory of synergetics, and the optimization model construction of MOSRR considering the maximization synergetic degree of multi-objective. The Analytic Hierarchy Process and Particle Swarm Optimization algorithm are employed to determine the weight and solve the MOSRR model, respectively. MOSRR is applied to a system of cascade reservoirs along the Upper Yellow River in China considering climatic and hydrologic variability. The results from MOSRR are compared to those from a traditional multi-objective optimal operation model. It is found that the guarantee of multi-objective requirements from MOSRR have been improved visibly compare with the traditional model at the expense of a slight reduction in the hydropower generation (especially the secondary requirement of the energy output in the dry season). Also, MOSRR can mitigate the effects of runoff reduction through minimizing the damage of primary requirements, which is more appropriate for multi-objective reservoir operation with limited water in sediment-laden river. The proposed MOSRR framework can be applied to other large-scale reservoir systems with stiff competition in water resources.

Application of a Novel Jaya Algorithm Based on Chaotic Sequence and Opposition-based Learning in the Multi-objective Optimal Operation of Cascade Hydropower Stations System

The traditional operation of the cascade hydropower stations system (CHPS) mainly focus on the maximization of power generation benefits, but ignores the interference of CHPS operation to the river ecosystem, therefore, carrying out the multi-objective optimal operation (MOOP) of CHPS considering ecological demands is crucial. In this paper, a MOOP model considering the ecological objective is established. To effectively solve the MOOP problems, a novel multi-objective Jaya algorithm (MOCOM-Jaya) is proposed, where the quality of the initial population is enhanced based on the chaotic sequence, the later disturbance term and Gaussian mutation are incorporated to improve the local search ability, the elite opposition-based learning is adopted to broaden the optimization space. The proposed algorithm is applied to the study of MOOP of CHPS in the Wujiang river, and the results show that compared with MOPSO and NSGA-II, MOCOM-Jaya can gain the solution set with better convergence and distribution for the MOOP. The competition relationship between the power generation objective (PGO) and the ecological objective (ECO) is revealed based on the partial replacement ratio method. The results show that the competitiveness of PGO and ECO experienced a trade lead with the increase of power generation. The mean competitiveness ratios of PGO to ECO ( $\overline {CP{R_{P - E}}} $ ) in three typical years (dry, normal, wet) are 3.22, 3.17 and 3.15, indicating that the PGO is dominant in the competition with the ECO as a whole.

Risk analysis of water supply-hydropower generation-environment nexus in the cascade reservoir operation

Water supply, hydropower generation and environment are three main subsystems in water resources managements. Reservoir operation is an effective tool for water supply, hydropower generation and improvement of environment and ecology. During the cascade reservoirs operation, the subsystems are inextricably linked and interrelated, which can be conceptualized as a nexus. Complicated interrelationships in the nexus can lead to higher uncertainties in water resources system. Limited research has been carried out to study the water supply-hydropower generation-environment nexus in the reservoir operation processes. Research on water supply-hydropower generation-environment nexus has becoming a hot issue, which has been supported by National Natural Science Foundation of China. The purpose of this paper is to explore the interdependencies and further to evaluate the risk of water supply-hydropower generation-environment nexus of the upper Yangtze River Basin. The multi-objective optimal operation model considering the objectives of water supply, hydropower generation and environment was developed. The risk indicators concerning the nexus were identified. In order to overcome the shortcomings that the previous studies cannot consider the interrelationships in the nexus, copulas were used to quantitatively assess the multiple and conditional risk in the nexus. Furthermore, the conditional entropy was introduced for the first time to assess the systematic risk in the nexus. Case studies demonstrate that water supply upstream of reservoir has a weak correlation with the hydropower generation and river habitat downstream of the reservoir, and hydropower generation has a significant impact on river habitat downstream of reservoir. Higher hydropower generation increases the risk of river habitat downstream of reservoir in non-flood season. Conversely, higher hydropower generation reduces the risk of river habitat downstream of reservoir in flood season. The systemic risk of water supply-hydropower generation-environment system during the cascade reservoirs optimal operation process can maintain at a lower level in non-flood and flood seasons based on different combinations of guarantee rates of water supply, hydropower generation and environment subsystems.

Multi-Objective Joint Optimal Operation of Reservoir System and Analysis of Objectives Competition Mechanism: A Case Study in the Upper Reach of the Yangtze River

The multi-objective optimal operation and the joint scheduling of giant-scale reservoir systems are of great significance for water resource management; the interactions and mechanisms between the objectives are the key points. Taking the reservoir system composed of 30 reservoirs in the upper reaches of the Yangtze River as the research object, this paper constructs a multi-objective optimal operation model integrating four objectives of power generation, ecology, water supply, and shipping under the constraints of flood control to analyze the inside interaction mechanisms among the objectives. The results are as follows. (1) Compared with single power generation optimization, multi-objective optimization improves the benefits of the system. The total power generation is reduced by only 4.09% at most, but the water supply, ecology, and shipping targets are increased by 98.52%, 35.09%, and 100% at most under different inflow conditions, respectively. (2) The competition between power generation and the other targets is the most obvious; the relationship between water supply and ecology depends on the magnitude of flow required by the control section for both targets, and the restriction effect of the shipping target is limited. (3) Joint operation has greatly increased the overall benefits. Compared with the separate operation of each basin, the benefits of power generation, water supply, ecology, and shipping increased by 5.50%, 45.99%, 98.49%, and 100.00% respectively in the equilibrium scheme. This study provides a widely used method to analyze the multi-objective relationship mechanism, and can be used to guide the actual scheduling rules.

Short-Term Multi-Objective Optimal Operation of Reservoirs to Maximize the Benefits of Hydropower and Navigation

Traditional reservoir operation mainly focuses on economic benefits, while ignoring the impacts on navigation. Thus, the economic operation of reservoirs considering navigational demands is of great significance for improving benefits. A navigation capacity evaluation method (NCEM), which evaluates the navigation capacity considering the influence of flow velocity and water level variation on navigation, is proposed to more effectively evaluate the navigation capacity. Based on two-dimensional hydrodynamic numerical simulation, the NCEM accurately calculates the navigation capacity according to detailed flow velocity and water level changes. In addition, a short-term multi-objective optimal operation model considering the upstream and downstream navigation and power generation is established. Then, the Strength Pareto Evolutionary Algorithm (SPEA2) is used to solve the model. To verify the rationality of the method and model, they are applied to the case study of the Xiangjiaba reservoir. The results demonstrate that the method and model can not only provide a series of operation schemes for decision makers of reservoirs, but also direct the ship to pass safely through the approach channel, implying a certain practical value and significance as a reference for the short-term optimal operation of reservoirs in the future.