Joint operation method of flood control storage capacity of cascade reservoirs based on approximate equal proportion impoundment

Abstract

The present application relates to the technical field of cascade reservoir flood control scheduling, and discloses a cascade reservoir flood control storage capacity joint operation method based on approximate equal proportion impoundment, comprising the following steps: collecting basic data; carrying out equal proportion impoundment joint flood control scheduling to obtain an initial trajectory; introducing a deviation coefficient to obtain an approximate equal proportion distribution coefficient, constructing an objective function and a constraint condition; taking a step-by-step optimization method as a framework to decompose into two-stage sub-problems, embedding a variable spiral search strategy to optimize, and iteratively outputting a final scheduling trajectory. The cascade reservoir flood control storage capacity joint operation method based on approximate equal proportion impoundment solves the strictness and mechanicalness of the equal proportion impoundment distribution coefficient, improves the flexibility and variability of the cascade reservoir flood control storage capacity joint operation, and overcomes the defects of dimension disaster and insufficient search capability faced by POA when solving the cascade reservoir flood control storage capacity optimization operation problem.

Description

Technical Field

[0001] This invention relates to the field of flood control scheduling technology for cascade reservoirs, specifically to a method for the joint use of flood control capacity of cascade reservoirs based on approximately proportional water storage. Background Technology

[0002] In recent years, a large number of reservoir projects have been built and put into operation in major river basins, which have significantly improved the flood control capacity of the basins. The joint use of flood control capacity of cascade reservoirs has become the norm. The core of this is to form a cascade flood control and peak reduction chain by the coordinated relay of cascade reservoirs in the main stream and tributaries. This includes upstream reservoirs releasing water in advance to intercept the initial flood peak, midstream reservoirs receiving and regulating the passing flood, and downstream reservoirs reserving capacity to cope with the tail flood. This achieves complementary flood control capacity of cascade reservoirs and reduces the risk of floods exceeding the standard for a single reservoir.

[0003] To implement the joint operation of flood control capacity of cascade reservoirs, a joint flood control scheduling strategy based on proportional water storage is generally adopted (He Xiaocong, Ding Yi, Li Shufei. Joint flood control scheduling strategy of three reservoirs in the middle and upper reaches of the Yangtze River based on proportional water storage [J]. Hydropower Energy Science, 2013, 31(4):38-41.). In essence, this strategy rationally allocates flood control tasks to each reservoir, avoiding unfavorable situations such as some reservoirs prematurely occupying flood control capacity due to early flood interception, and some reservoirs failing to play their flood control role due to late flood interception. This provides a solution for the allocation of flood control capacity in cascade reservoirs.

[0004] In view of this, starting from the principle of proportional water storage, Li Ningning et al. (Li Ningning, Wang Liping, Wu Jiajie, et al. Research on flood storage mode of cascade reservoirs based on the concept of spatial risk hedging [J]. China Rural Water Resources and Hydropower, 2020, (9): 138-142+147.) derived the flood storage and detention volume allocation rule of cascade reservoirs based on the concept of risk hedging, and allocated the total amount of flood storage in cascade reservoirs according to the proportion of each reservoir's flood control capacity in the total flood control capacity. However, the above proportional water storage strategy calculates the allocation coefficient according to the proportion of each reservoir's flood control capacity in the total flood control capacity, which is generally difficult to accurately meet in actual scheduling, and is relatively strict and mechanical. It is advisable to consider floating optimization and adjustment based on the proportional allocation coefficient to improve the flexibility of joint use of flood control capacity.

[0005] Meanwhile, the joint operation and optimization scheduling of flood control capacity of cascade reservoirs mainly focuses on optimizing the water level control during the flood season. Mathematically, it shares many similarities with scheduling models such as cascade reservoir power generation optimization scheduling and flood control optimization scheduling, belonging to the complex optimization problem of water level control in cascade reservoirs, which is multi-stage, high-dimensional, strongly constrained, and nonlinear. The successive optimization method (POA), as an improved dynamic programming method for solving multi-stage complex optimization problems, decomposes the multi-stage problem into multiple two-stage sub-problems. In each calculation, iterative optimization is performed only on the current stage, and so on, iterating stage by stage until the final solution is obtained. This method reduces the discrete combination of feasible solutions and can significantly improve computational efficiency compared to dynamic programming methods. It has been widely used in problems such as single-reservoir power generation optimization scheduling and flood control optimization scheduling. However, when the number of reservoirs is large, it still faces shortcomings such as the curse of dimensionality and insufficient search capability.

[0006] The variable spiral search strategy originates from the whale optimization algorithm, in which whales use bubble nets to surround prey, thus completing their foraging and hunting behavior. The curved path of these bubble nets is spiral-shaped. Furthermore, during the computation process, adjusting the variable parameters of the spiral search improves the diversity and globality of the search, allowing for a faster approximation of the optimal solution. Inspired by this search process, this invention proposes embedding the variable spiral search strategy into the solution of each two-stage sub-optimization problem in the POA (Problem-Oriented Algorithm) to generate diverse search information and enhance the global search capability of the POA. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of the above-mentioned technologies by providing a method for the joint operation of flood control capacity of cascade reservoirs based on approximately equal-proportion water storage. This method solves the problems of the strictness and mechanical nature of equal-proportion water storage allocation coefficients, improves the flexibility and variability of the joint operation of flood control capacity of cascade reservoirs, and overcomes the defects of dimensionality curse and insufficient search capability faced by POA in solving the problem of optimizing the operation of flood control capacity of cascade reservoirs.

[0008] To achieve the above objectives, the present invention provides a method for the combined use of flood control capacity of cascade reservoirs based on approximately equal-proportion water storage, comprising the following steps: S1) Collect basic data on the joint operation of cascade reservoirs; S2) In accordance with the joint operation plan of cascade reservoirs, carry out joint flood control operation of cascade reservoirs based on proportional water storage, obtain the total interception flow process of the joint use of flood control capacity of cascade reservoirs, and obtain the proportional allocation coefficient and initial trajectory of each reservoir at each stage according to the proportional water storage strategy of flood control capacity ratio. S3) Introduce an approximate proportional water storage strategy, and optimize and adjust it by floating up and down based on the original proportional allocation coefficient. Introduce a deviation coefficient to obtain a new approximate proportional allocation coefficient for each reservoir. Construct an objective function and constraints for the joint operation and optimization scheduling of flood control capacity of cascade reservoirs based on approximate proportional water storage. S4) Start iterating, execute the stepwise optimization method several times, generate the trajectory and store it into the historical trajectory library in sequence; S5) Continue iterating. In each iteration, the problem of optimizing the joint use of flood control capacity of cascade reservoirs is decomposed into several two-stage sub-problems. A variable spiral search strategy is embedded in the calculation process of each two-stage sub-problem. A variable spiral search is performed on the current trajectory and the historical trajectory in the historical trajectory library to generate a spiral trajectory. The current trajectory and the spiral trajectory are compared, and the better trajectory is retained as the current trajectory. This process continues until all two-stage sub-problems are completed, the iteration is completed, the final optimal trajectory is obtained, and the joint use and scheduling process of flood control capacity of cascade reservoirs that takes into account the optimal benefits within the feasible space is output.

[0009] Preferably, in step S1), the basic data for the scheduling of the cascade reservoir group includes the characteristic parameters of each reservoir, the water level and storage capacity curves of each reservoir, typical flood processes, and the joint scheduling scheme of the cascade reservoirs.

[0010] Preferably, in step S2), the total interception flow process is as follows: ,in For the stage j The total flow intercepted by the cascade reservoirs T The total number of reservoirs during the scheduling period is calculated based on a proportional water storage strategy according to the flood control capacity ratio. i In the stage j The proportional distribution coefficient is ,have , N The total number of reservoirs, For fixed values, For reservoir i Total flood control capacity The total flood control capacity of the cascade reservoirs, combined with a proportional water storage strategy, is [the following information is missing from the original text]. i In the stage j The interception flow value is Given the inflow and retention processes of each reservoir, and based on the water balance equations for each reservoir, the initial scheduling trajectory of the water level process for the joint operation of the flood control capacity of the cascade reservoirs under proportional impoundment can be obtained as follows: , For reservoir i In the stage j The initial trajectory.

[0011] Preferably, in step S3), the original proportional allocation coefficient is used. Based on this, and through upward and downward adjustments, new approximate proportional allocation coefficients for each reservoir are obtained. ,have ,in For reservoir i In the stage j Deviation coefficient, approximate proportional distribution coefficient of each stage of the cascade reservoir. It is 1, that is, it satisfies By introducing a controllable deviation coefficient, the allocation coefficient is given a certain floating space while maintaining the overall framework of the proportional water storage strategy. This not only meets the needs of the opening and closing time of the water discharge facilities and the regulation of the power station in actual scheduling, but also ensures the overall balance and flexibility of the joint use of flood control capacity.

[0012] Preferably, the objective function is: In the formula, F This represents the total power generation during the dispatch period. For reservoir i The output coefficient, For reservoir i In the stage j Power generation flow, in m³ 3 / s, For reservoir i In the stage j Average hydroelectric head after deducting head loss, in meters. The duration of the stage is measured in days.

[0013] Preferably, the constraints include one or more of the following: water balance constraints of each reservoir, hydraulic connection constraints of each reservoir, water level constraints of each reservoir, outflow constraints of each reservoir, discharge capacity constraints of each reservoir, power output constraints of each reservoir, interception flow constraints of each reservoir, total interception flow constraints of cascade reservoirs, approximately proportional distribution coefficient constraints of cascade reservoirs, total power output constraints of cascade reservoirs, and non-negative constraints.

[0014] Preferably, in step S4), the number of iterations is initialized. , The stepwise optimization method is used to calculate Y Each time, the trajectory is calculated and generated. The trajectories are then sequentially stored in the historical trajectory database. By establishing a historical trajectory database containing sufficient historical trajectory information before the variable spiral search, a reliable prior knowledge base is provided for the subsequent variable spiral search, enabling the spiral search to perform effective trajectory combination transformation based on sufficient historical optimization information.

[0015] Preferably, step S5) includes the following steps: S51) Set the iteration count ; S52) decomposes the problem of optimized scheduling of joint use of flood control capacity of cascade reservoirs into... A two-stage sub-problem; S53) For each two-stage subproblem, perform a variable spiral search sequentially and output the optimal trajectory; S54) Order ,like , M If the maximum number of iterations is reached, proceed to step S55; otherwise, store the optimal trajectory output in step S53) into the historical trajectory database, and then proceed to step S52. S55) Stop the calculation and output the final optimal trajectory.

[0016] Preferably, when performing the variable spiral search sequentially for each two-stage sub-problem, the following steps are included: S531) A two-stage sub-problem, set ; S532) Initialize the variable spiral search count ; S533) Randomly generated from 1 to Y Positive integers between y ,have ; S534) for the stage j Current trajectory and historical trajectories in the historical trajectory database Perform a variable spiral search to generate a spiral trajectory. The calculation formula is as follows: , In the formula, L A random number between -1 and 1. The variable spiral shape parameter is composed of an exponential function and a cosine function, and it varies with the number of iterations. m The spiral's size and amplitude are dynamically adjusted based on the function's properties to control the randomness, directionality, and effectiveness of the spiral search process. This allows the search to maintain a large exploration range in the early stages and enable refined development in the later stages. The calculation formula is as follows: ; S535) Comparison of spiral trajectories and current trajectory ,if Superior If the current trajectory is correct, then replace it with a spiral trajectory; otherwise, do nothing. S536) Order ,if , K(If the maximum number of variable spiral searches is reached, proceed to step S533); otherwise, proceed to step S537. S537) Order ,if (If not, proceed to step S532); otherwise, proceed to step S538. (S538) The iteration is complete, and the optimal trajectory is output.

[0017] A system for the joint operation of flood control capacity of cascade reservoirs based on approximately proportional water storage, comprising: The initialization module is used to generate the initial trajectory for the joint operation of flood control capacity of cascade reservoirs based on the proportional water storage strategy. The scheduling model construction module is used to adjust the proportional allocation coefficients up and down according to the approximately proportional water storage strategy, and to construct the objective function and constraints for the joint operation optimization scheduling of flood control capacity of cascade reservoirs. The historical trajectory library module is used to store and retrieve trajectories during the iteration process, and to update the storage by combining the optimal trajectory of each iteration; The progressive optimization decomposition module is used to decompose the problem of joint utilization and scheduling of flood control capacity of cascade reservoirs in the current iteration number into several two-stage sub-problems; The variable spiral search module, based on the stepwise optimization decomposition module, performs a variable spiral search, including historical trajectory reading, variable spiral morphology parameter generation, spiral trajectory generation, trajectory optimization and replacement, and stopping condition judgment functions, in order to obtain a better optimized trajectory. The output module is used to repeatedly execute the historical trajectory library module, the stepwise optimization decomposition module, and the variable spiral search module until the preset iteration stopping condition is met, to obtain the optimal trajectory, and to serve as the final scheduling process for the joint operation of flood control capacity of the cascade reservoirs.

[0018] Compared with the prior art, the present invention has the following advantages: 1. Based on the conventional proportional water storage strategy, an approximate proportional water storage strategy for the joint use of flood control capacity of cascade reservoirs is proposed. The approximate proportional allocation coefficient of each reservoir can be obtained by floating optimization adjustment, which improves the flexibility and variability of the joint use of flood control capacity of cascade reservoirs, making the scheduling process more realistic and robust. 2. A variable spiral stepwise optimization method is proposed, which has the characteristics of fewer control parameters, strong search capability and fast computation efficiency. It increases the diversity and speed of global search, avoids the dimensionality curse problem of the stepwise optimization method with full combination of discrete states, and effectively reduces the computational complexity. 3. An objective function for the joint operation and optimization of flood control capacity of cascade reservoirs based on approximately proportional water storage was constructed. While satisfying the total interception flow process of cascade reservoirs, the benefits of joint operation were expanded. Under the premise of ensuring flood control safety, the benefits of cascade reservoirs can be improved, providing a new approach for optimizing the use of flood control capacity and maximizing flood control benefits of cascade reservoirs. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the method for the combined use of flood control storage capacity of cascade reservoirs based on approximately equal water storage ratios, as per the present invention. Figure 2 This is a diagram showing the calculation results of the flood control scheduling and storage process of cascade reservoirs in an embodiment of the present invention; Figure 3 This is a diagram showing the calculation results of the reservoir impoundment process in an embodiment of the present invention; Figure 4 This is the scheduling process of Reservoir A in this embodiment of the invention; Figure 5 This describes the scheduling process of Reservoir B in this embodiment of the invention. Figure 6 This is the scheduling process of Reservoir C in this embodiment of the invention; Figure 7 This describes the scheduling process of Reservoir D in this embodiment of the invention. Detailed Implementation

[0020] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] This invention, based on the premise of obtaining the total interception flow process of the joint operation of flood control capacity in cascade reservoirs, addresses the optimization problem of flood control scheduling and interception processes in each reservoir within the cascade reservoirs. While ensuring that flood control capacity remains unchanged, it proposes an optimized utilization strategy for flood control capacity based on approximately proportional water storage. Simultaneously, addressing the optimization of the beneficial effects of the joint operation of flood control capacity in cascade reservoirs, it constructs an optimized scheduling objective function for the joint operation of flood control capacity in cascade reservoirs based on approximately proportional water storage. This function aims to rationally allocate the scheduling process and flood control capacity input of each reservoir, thereby further improving the beneficial scheduling efficiency of cascade reservoirs.

[0022] Based on the above, the optimized scheduling model for the joint operation of flood control capacity of cascade reservoirs based on approximately proportional water storage can be described as follows: Given the total intercepted flow process of the cascade reservoirs, the approximately proportional distribution coefficients of each reservoir, and the initial water level, inflow flood process, and interval flood process of each reservoir during the scheduling period, under the premise of ensuring the effective distribution of the total intercepted flow among the cascade reservoirs, and under the complex constraints such as water level and flow of each reservoir and flood control station, the optimal water level process for the joint operation of flood control capacity of the cascade reservoirs is determined to rationally allocate the scheduling process and flood control capacity input of each reservoir, and to maximize the utilization of water energy resources to achieve the maximum total power generation of the cascade reservoirs during the scheduling period.

[0023] like Figure 1 As shown, a method for the joint operation of flood control capacity of cascade reservoirs based on approximately equal-proportion water storage includes the following steps: S1) Collect basic data on the joint operation of cascade reservoirs. The basic data on the operation of the cascade reservoir group includes the characteristic parameters of each reservoir, the water level and storage capacity curves of each reservoir, typical flood processes, and the joint operation scheme of the cascade reservoirs. S2) According to the joint operation plan of the cascade reservoirs, joint flood control operation of the cascade reservoirs based on proportional water storage is carried out to obtain the total interception flow process of the joint use of flood control capacity of the cascade reservoirs. Furthermore, according to the proportional water storage strategy based on the proportion of flood control capacity, the proportional allocation coefficient and initial trajectory of each reservoir at each stage are obtained. Specifically, the total interception flow process is as follows: ,in For the stage j The total flow intercepted by the cascade reservoirs T The total number of reservoirs during the scheduling period is calculated based on a proportional water storage strategy according to the flood control capacity ratio. i In the stage j The proportional distribution coefficient is ,have , N The total number of reservoirs, This is a fixed value, representing the ratio of the total flood control capacity of the reservoir to the total flood control capacity of the cascade reservoirs. It is difficult to precisely meet this requirement during scheduling and necessitates flexible adjustments. For reservoir i Total flood control capacity The total flood control capacity of the cascade reservoirs, combined with a proportional water storage strategy, is [the following information is missing from the original text]. i In the stage j The interception flow value is Given the inflow and retention processes of each reservoir, and based on the water balance equations for each reservoir, the initial scheduling trajectory of the water level process for the joint operation of the flood control capacity of the cascade reservoirs under proportional impoundment can be obtained as follows: , For reservoir i In the stage jThe initial trajectory; S3) An approximate proportional water storage strategy is introduced, which is optimized and adjusted by floating up and down based on the original proportional allocation coefficient. A deviation coefficient is introduced to obtain new approximate proportional allocation coefficients for each reservoir. An objective function and constraints for the joint operation and optimization scheduling of flood control capacity of cascade reservoirs based on approximate proportional water storage are constructed. Specifically, based on the original proportional allocation coefficient... Based on this, and through upward and downward adjustments, new approximate proportional allocation coefficients for each reservoir are obtained. ,have ,in For reservoir i In the stage j The deviation coefficient, generally ranging from 0 to 0.1, controls the degree of deviation of the approximate proportional allocation coefficient from the proportional allocation coefficient. The approximate proportional allocation coefficients for each stage of the cascade reservoir are... It is 1, that is, it satisfies Furthermore, the objective function is: In the formula, F This represents the total power generation during the dispatch period. For reservoir i The output coefficient, For reservoir i In the stage j Power generation flow, in m³ 3 / s, For reservoir i In the stage j Average hydroelectric head after deducting head loss, in meters. The stage length is in days, and the constraints are one or more of the following: Water balance constraints in each reservoir: In the formula, For reservoir i In the stage j Final storage capacity, in meters (m) 3 , For reservoir i In the stage j Inbound flow rate, in m 3 / s, For reservoir i In the stage j Outbound flow rate, in m³ 3 / s; Hydraulic constraints of the reservoir: In the formula, For reservoir i In the stage j Interval flow rate, in m 3 / s; Water level constraints for each reservoir: In the formula, For reservoir i In the stage j The water level in front of the dam, in meters. and Reservoirs i In the stage j The lowest and highest water levels in front of the dam, in meters; Outflow constraints for each reservoir: In the formula, and Reservoirs i In the stage j Minimum and maximum outbound flow rates, in meters. 3 / s, For reservoir i In the stage j The discharge flow rate, in meters 3 / s; Constraints on the discharge capacity of each reservoir: , For reservoir i In the stage j Corresponding to water level Maximum discharge capacity, unit m 3 / s; Output constraints of each reservoir: , and Reservoirs i In the stage j Minimum and maximum output power, in kW; Reservoir flow control constraints: ; Total storage capacity constraint of cascade reservoirs: ; Constraints on the approximate proportional distribution coefficients for cascade reservoirs: ; Total output constraints of cascade reservoirs: ;, For cascade reservoirs in stages j The minimum total output, expressed in kW.

[0024] Non-negativity constraint: All variables must be non-negative. S4) Begin iteration, executing the stepwise optimization method several times. In this embodiment, it is executed 6 to 12 times, generating trajectories and storing them sequentially in the historical trajectory database. Specifically, initialize the number of iterations. , The stepwise optimization method is used to calculate Y Each time, the trajectory is calculated and generated. The trajectories are then sequentially stored in the historical trajectory database. ; S5) Continue iterating. In each iteration, the problem of optimizing the joint use of flood control capacity of cascade reservoirs is decomposed into several two-stage sub-problems. A variable spiral search strategy is embedded in the calculation process of each two-stage sub-problem. A variable spiral search is performed on the current trajectory and the historical trajectory in the historical trajectory library to generate a spiral trajectory. The current trajectory and the spiral trajectory are compared, and the better trajectory is retained as the current trajectory. This process continues until all two-stage sub-problems are completed, the iteration is completed, the final optimal trajectory is obtained, and the joint use and scheduling process of flood control capacity of cascade reservoirs that takes into account the optimal benefits within the feasible space is output.

[0025] Overall, step S5 includes the following steps: S51) Set the iteration count ; S52) decomposes the problem of optimized scheduling of joint use of flood control capacity of cascade reservoirs into... A two-stage sub-problem; S53) For each two-stage subproblem, perform a variable spiral search sequentially and output the optimal trajectory; S54) Order ,like , M If the maximum number of iterations is reached, proceed to step S55; otherwise, store the optimal trajectory output in step S53) into the historical trajectory database, and then proceed to step S52. S55) Stop the calculation and output the final optimal trajectory.

[0026] In step S53), the variable spiral search is performed sequentially for each two-stage sub-problem, including the following steps: S531) A two-stage sub-problem, set ; S532) Initialize the variable spiral search count ; S533) Randomly generated from 1 to Y Positive integers between y ,have In this embodiment, y The value range is 4 to 8; S534) for the stage j Current trajectory and historical trajectories in the historical trajectory database Perform a variable spiral search to generate a spiral trajectory. The calculation formula is as follows: , In the formula, L A random number between -1 and 1. The variable spiral shape parameter is composed of an exponential function and a cosine function, and it varies with the number of iterations. m The spiral's size and amplitude are dynamically adjusted based on the function's properties to control the randomness, directionality, and effectiveness of the spiral search process. The calculation formula is as follows: ; S535) Comparison of spiral trajectories and current trajectory ,if Superior If the current trajectory is correct, then replace it with a spiral trajectory; otherwise, do nothing. S536) Order ,if , K (If the maximum number of variable spiral searches is reached, proceed to step S533); otherwise, proceed to step S537. S537) Order ,if (If not, proceed to step S532); otherwise, proceed to step S538. (S538) The iteration is complete, and the optimal trajectory is output.

[0027] In addition, this embodiment also provides a system for the joint operation of flood control capacity of cascade reservoirs based on approximately equal-proportion water storage, and a method for the joint operation of flood control capacity of cascade reservoirs based on approximately equal-proportion water storage, including: The initialization module is used to generate the initial trajectory for the joint operation of flood control capacity of cascade reservoirs based on the proportional water storage strategy. The scheduling model construction module is used to adjust the proportional allocation coefficients up and down according to the approximately proportional water storage strategy, and to construct the objective function and constraints for the joint operation optimization scheduling of flood control capacity of cascade reservoirs. The historical trajectory library module is used to store and retrieve trajectories during the iteration process, and to update the storage by combining the optimal trajectory of each iteration; The progressive optimization decomposition module is used to decompose the problem of joint utilization and scheduling of flood control capacity of cascade reservoirs in the current iteration number into several two-stage sub-problems; The variable spiral search module, based on the stepwise optimization decomposition module, performs a variable spiral search, including historical trajectory reading, variable spiral morphology parameter generation, spiral trajectory generation, trajectory optimization and replacement, and stopping condition judgment functions, in order to obtain a better optimized trajectory; The output module is used to repeatedly execute the historical trajectory library module, the stepwise optimization decomposition module, and the variable spiral search module until the preset iteration stopping condition is met, to obtain the optimal trajectory, and to serve as the final scheduling process for the joint operation of flood control capacity of the cascade reservoirs.

[0028] Next, a case study will be conducted using a cascade reservoir system consisting of four reservoirs (A, B, C, and D) in the upper reaches of a certain river basin. This cascade reservoir system is a key component in constructing the basin's flood control and disaster reduction system, playing a significant comprehensive role in flood control, power generation, navigation, ecology, and dry season water replenishment. Due to the high peak volume and large flow of floods during the flood season, the limited flood control capacity of a single reservoir makes it difficult to cope with the risks of extreme floods. However, the joint operation of the cascade reservoirs can integrate the overall flood control capacity, improving overall flood control capabilities and protecting the lives and property of people along the river through temporal and spatial peak shifting and tiered water volume regulation. Simultaneously, the joint operation of the cascade reservoirs' flood control capacity can organically coordinate flood control and water resource utilization, achieving safe flood control in the basin while also taking into account the utilization of flood resources.

[0029] According to the joint flood control scheduling scheme of the basin, when there is a need for flood control scheduling in the middle and lower reaches of the basin, the flood control capacity of cascade reservoirs is jointly utilized, and flood control scheduling is implemented in a manner of equal discharge. After obtaining the total interception flow of the cascade reservoirs, the optimization scheduling problem of the joint operation of the flood control capacity of the cascade reservoirs deserves special attention. This invention takes a typical major flood that actually occurred in the basin as the implementation condition and conducts research on the optimization problem of the joint operation of the flood control capacity of cascade reservoirs based on approximately equal-proportion water storage. Specifically, in late July of the year of the major flood, there was a need for flood control scheduling in the basin during this scheduling period, and the cascade reservoirs implemented joint flood control scheduling. After obtaining the total interception flow of the cascade reservoirs, a comparative analysis was conducted using equal-proportion water storage strategy and approximately equal-proportion water storage strategy. In the approximately equal-proportion water storage strategy, the optimization scheduling of the joint operation of the flood control capacity of the cascade reservoirs was solved using POA and the method of this invention.

[0030] This cascade of reservoirs has a total reserved flood control capacity of 15.493 billion cubic meters. 3 The flood control capacity of reservoirs A, B, C, and D is 2.44 billion cubic meters. 3 7.5 billion m 3 4.65 billion m 3 and 903 million m 3 According to the proportional water storage strategy, the proportional allocation coefficients for flood control storage capacity utilization are 0.17, 0.53, 0.24, and 0.06. Considering the opening and closing time of the spillway facilities and the regulation needs of the power station, these proportional allocation coefficients are difficult to precisely meet in actual scheduling and usually need to fluctuate. Therefore, in order to enhance the flexibility and variability of the joint use of flood control storage capacity during the flood control scheduling of cascade reservoirs, the scheduling decision-making experts believe that the deviation coefficients of each reservoir at all stages are 0.02, 0.04, 0.02, and 0.01, respectively. Thus, the approximate proportional allocation coefficients of each reservoir are distributed in the ranges of 0.15–0.19, 0.49–0.57, 0.22–0.26, and 0.05–0.07, respectively. Based on this, an optimized scheduling model for the joint use of flood control storage capacity of cascade reservoirs based on approximate proportional water storage was constructed. The calculation and analysis were carried out using both POA and the method of this invention. The calculation results are shown in Table 1.

[0031] Table 1. Comparison of the method of the present invention and the calculation results of POA As shown in the table, compared with the proportional water storage strategy, considering the joint optimization of flood control capacity of cascade reservoirs based on approximately proportional water storage can improve the power generation and efficiency of cascade reservoirs. This indicates that in actual scheduling, the flow distribution coefficient of each reservoir can be adjusted by combining expert decisions and floating optimization to improve the flexibility and variability of the joint operation of flood control capacity of cascade reservoirs.

[0032] Furthermore, in the approximate proportional water storage strategy, the advantages of the method of this invention compared to POA are as follows: 1. Compared with the equal-proportion water storage strategy, the approximate equal-proportion water storage strategy can further optimize the use of flood control capacity of cascade reservoirs. Compared with the conventional equal-proportion water storage strategy, the power generation and power generation benefits of the method of this invention are increased by 2.48 million kWh and the power generation benefits are approximately RMB750,000, indicating that the approximate equal-proportion water storage strategy proposed in this invention is effective. 2. If an approximate proportional water storage strategy is considered simultaneously, the power generation and power generation benefits of the method of this invention are better than those of POA compared to the solution method. The power generation is increased by 240,000 kWh, and the power generation benefits are approximately RMB 80,000. If the flood control scheduling period is longer, the power generation and power generation benefits that the method of this invention can increase will be even greater. 3. The computation time of the method of the present invention is only about 15% of that of POA. If the reservoir size, computation stages and discrete states are more numerous, the computational performance advantage of the method of the present invention will be more prominent.

[0033] Combination Figure 2 , Figure 3 and Figures 4-7 The present invention provides the flood control scheduling calculation results of the method of the present invention during a major flood. The flood control scheduling results all meet the constraints. Based on the proportional water storage strategy, the water storage capacity of each reservoir is optimized and adjusted based on the approximate proportional water storage strategy, realizing the joint optimization of the flood control capacity of cascade reservoirs.

[0034] In summary, the main advantages of the method of this invention are as follows: First, by proposing an approximately proportional water storage strategy, the joint operation of flood control capacity in cascade reservoirs becomes more realistic and robust, improving the beneficial effects of cascade reservoirs while ensuring flood control safety. Second, by embedding a variable spiral search strategy, the diversity and speed of the global search are increased, avoiding the dimensionality curse problem of comprehensive discrete state combinations and effectively reducing computational complexity. The method of this invention possesses excellent robustness and optimization capabilities, providing a new approach for optimizing the use of flood control capacity in cascade reservoirs and maximizing flood control benefits. It can also be further extended to the problem of joint optimization and scheduling of reservoir capacity in cascade reservoirs with joint water storage and drawdown.

[0035] Finally, it should be noted that the above description is a further detailed explanation of the invention in conjunction with specific embodiments. It should not be considered that the specific implementation of the invention is limited to these descriptions. For those skilled in the art, any simple substitutions made without departing from the concept of the invention should be considered within the scope of protection of this invention. The above embodiments are merely representative examples of the invention. Obviously, the invention is not limited to the above embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the invention should be considered within the scope of protection of this invention.

[0036] Furthermore, the description of the above technical solutions is exemplary, and this specification may be embodied in different forms and should not be construed as limiting it to the technical solutions set forth herein. Rather, providing these descriptions will ensure that the disclosure of this invention is thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Moreover, the technical solutions of this invention are defined only by the scope of the claims. Features of various embodiments of the invention may be combined or spliced ​​together in part or in whole, and may be implemented in various different configurations as will be fully understood by those skilled in the art. Embodiments of the invention may be implemented independently of each other or may be implemented together in an interdependent relationship.

[0037] For those skilled in the art, without departing from the concept of this invention, several simple deductions or substitutions can be made, and all of these should be considered to fall within the protection scope of this invention.

Claims

1. A method for the combined use of flood control storage capacity of cascade reservoirs based on approximately proportional water storage, characterized in that: Includes the following steps: S1) Collect basic data on the joint operation of cascade reservoirs; S2) In accordance with the joint operation plan of cascade reservoirs, carry out joint flood control operation of cascade reservoirs based on proportional water storage, obtain the total interception flow process of the joint use of flood control capacity of cascade reservoirs, and obtain the proportional allocation coefficient and initial trajectory of each reservoir at each stage according to the proportional water storage strategy of flood control capacity ratio. S3) Introduce an approximate proportional water storage strategy, and optimize and adjust it by floating up and down based on the original proportional allocation coefficient. Introduce a deviation coefficient to obtain a new approximate proportional allocation coefficient for each reservoir. Construct an objective function and constraints for the joint operation and optimization scheduling of flood control capacity of cascade reservoirs based on approximate proportional water storage. S4) Start iterating, execute the stepwise optimization method several times, generate the trajectory and store it into the historical trajectory library in sequence; S5) Continue iterating. In each iteration, the problem of optimizing the joint use of flood control capacity of cascade reservoirs is decomposed into several two-stage sub-problems. A variable spiral search strategy is embedded in the calculation process of each two-stage sub-problem. A variable spiral search is performed on the current trajectory and the historical trajectory in the historical trajectory library to generate a spiral trajectory. The current trajectory and the spiral trajectory are compared, and the better trajectory is retained as the current trajectory. This process continues until all two-stage sub-problems are completed, the iteration is completed, the final optimal trajectory is obtained, and the joint use and scheduling process of flood control capacity of cascade reservoirs that takes into account the optimal benefits within the feasible space is output.

2. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal-proportion water storage as described in claim 1, characterized in that: In step S1), the basic data for the scheduling of the cascade reservoir group includes the characteristic parameters of each reservoir, the water level and storage capacity curves of each reservoir, typical flood processes, and the joint scheduling scheme of the cascade reservoirs.

3. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal-proportion water storage as described in claim 1, characterized in that: In step S2), the total flow interception process is as follows: ,in For the stage j The total flow intercepted by the cascade reservoirs T The total number of reservoirs during the scheduling period is calculated based on a proportional water storage strategy according to the flood control capacity ratio. i In the stage j The proportional distribution coefficient is ,have , N The total number of reservoirs, For fixed values, For reservoir i Total flood control capacity The total flood control capacity of the cascade reservoirs, combined with a proportional water storage strategy, is [the following information is missing from the original text]. i In the stage j The interception flow value is Given the inflow and retention processes of each reservoir, and based on the water balance equations for each reservoir, the initial scheduling trajectory of the water level process for the joint operation of the flood control capacity of the cascade reservoirs under proportional impoundment can be obtained as follows: , For reservoir i In the stage j The initial trajectory.

4. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal water storage ratio as described in claim 3, characterized in that: In step S3), the original proportional allocation coefficient is used. Based on this, and through upward and downward adjustments, new approximate proportional allocation coefficients for each reservoir are obtained. ,have ,in For reservoir i In the stage j Deviation coefficient, approximate proportional distribution coefficient for each stage of the cascade reservoir. It is 1, that is, it satisfies .

5. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal-proportion water storage as described in claim 4, characterized in that: The objective function is: In the formula, F This represents the total power generation during the dispatch period. For reservoir i The output coefficient, For reservoir i In the stage j Power generation flow, in m³ 3 / s, For reservoir i In the stage j Average hydroelectric head after deducting head loss, in meters. The duration of the stage is measured in days.

6. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal-proportion water storage as described in claim 5, characterized in that: The constraints include one or more of the following: water balance constraints of each reservoir, hydraulic connection constraints of each reservoir, water level constraints of each reservoir, outflow constraints of each reservoir, discharge capacity constraints of each reservoir, power output constraints of each reservoir, interception flow constraints of each reservoir, total interception flow constraints of cascade reservoirs, approximately proportional distribution coefficient constraints of cascade reservoirs, total power output constraints of cascade reservoirs, and non-negative constraints.

7. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal water storage as described in claim 5, characterized in that: In step S4), the number of iterations is initialized. , The stepwise optimization method is used to calculate Y Each time, the trajectory is calculated and generated. The trajectories are then sequentially stored in the historical trajectory database. .

8. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal-proportion water storage as described in claim 7, characterized in that: Step S5) includes the following steps: S51) Set the iteration count ; S52) decomposes the problem of optimized scheduling of joint use of flood control capacity of cascade reservoirs into... A two-stage sub-problem; S53) For each two-stage subproblem, perform a variable spiral search sequentially and output the optimal trajectory; S54) Order ,like , M If the maximum number of iterations is reached, proceed to step S55; otherwise, store the optimal trajectory output in step S53) into the historical trajectory database, and then proceed to step S52. S55) Stop the calculation and output the final optimal trajectory.

9. The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately equal-proportion water storage as described in claim 8, characterized in that: For each two-stage subproblem, the variable spiral search is performed sequentially, including the following steps: S531) A two-stage sub-problem, set ; S532) Initialize the variable spiral search count ; S533) Randomly generated from 1 to Y Positive integers between y ,have ; S534) for the stage j Current trajectory and historical trajectories in the historical trajectory database Perform a variable spiral search to generate a spiral trajectory. The calculation formula is as follows: ， In the formula, L A random number between -1 and 1. The variable spiral shape parameter is composed of an exponential function and a cosine function, and it varies with the number of iterations. m The spiral's size and amplitude are dynamically adjusted based on the function's properties to control the randomness, directionality, and effectiveness of the spiral search process. The calculation formula is as follows: ; S535) Comparison of spiral trajectories and current trajectory ,if Superior If the current trajectory is correct, then replace it with a spiral trajectory; otherwise, do nothing. S536) Order ,if , K (If the maximum number of variable spiral searches is reached, proceed to step S533); otherwise, proceed to step S537. S537) Order ,if (If not, proceed to step S532); otherwise, proceed to step S538. (S538) The iteration is complete, and the optimal trajectory is output.

10. A cascade reservoir flood control capacity joint operation system based on approximately proportional water storage, characterized in that: The method for joint operation of flood control storage capacity of cascade reservoirs based on approximately proportional water storage, as described in any one of claims 1 to 9, includes: The initialization module is used to generate the initial trajectory for the joint operation of flood control capacity of cascade reservoirs based on the proportional water storage strategy. The scheduling model construction module is used to adjust the proportional allocation coefficients up and down according to the approximately proportional water storage strategy, and to construct the objective function and constraints for the joint operation optimization scheduling of flood control capacity of cascade reservoirs. The historical trajectory library module is used to store and retrieve trajectories during the iteration process, and to update the storage by combining the optimal trajectory of each iteration; The progressive optimization decomposition module is used to decompose the problem of joint utilization and scheduling of flood control capacity of cascade reservoirs in the current iteration number into several two-stage sub-problems; The variable spiral search module, based on the stepwise optimization decomposition module, performs a variable spiral search, including historical trajectory reading, variable spiral morphology parameter generation, spiral trajectory generation, trajectory optimization and replacement, and stopping condition judgment functions, in order to obtain a better optimized trajectory; The output module is used to repeatedly execute the historical trajectory library module, the stepwise optimization decomposition module, and the variable spiral search module until the preset iteration stopping condition is met, to obtain the optimal trajectory, and to serve as the final scheduling process for the joint operation of flood control capacity of the cascade reservoirs.

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