A random optimization method and system for flood-end storage level of a multi-year regulation reservoir

Abstract

The application discloses a kind of multi-year regulation reservoir flood-end storage level random optimization method and system, belong to reservoir optimization scheduling technical field.The application first obtains cascade reservoir basic data and constructs runoff edge distribution model;Second, the joint probability distribution function of each reservoir inflow runoff is established using Vine Copula theory, and the random runoff scenario sequence with space-time correlation is generated;Subsequently, with the maximum expected value of total power generation of cascade reservoir group in scheduling period and the maximum expected value of multi-year regulation reservoir flood-end storage capacity as the goal, a multi-objective random optimization scheduling model is constructed, and the Pareto non-inferior solution set is obtained by iterative solution using AR-MOEA algorithm;Finally, the VIKOR multi-attribute decision method is introduced to compromise the non-inferior solution set evaluation, determine the optimal flood-end storage level target value and scheduling process, to guide the actual operation of reservoir.The application effectively quantifies the influence of runoff space-time uncertainty on the flood-end storage capacity of multi-year regulation reservoir, scientifically balances the contradiction between current power generation and future energy storage, and can significantly improve the water resource utilization rate and comprehensive power generation benefit of cascade reservoir group.

Description

Technical Field

[0001] This invention relates to a multi-objective joint optimization scheduling technology for cascade reservoir systems, and in particular to a stochastic optimization method and system for the end-of-flood water level of multi-year regulating reservoirs. Background Technology

[0002] Cascade reservoir systems are crucial projects for the comprehensive utilization of water resources and the supply of clean energy. Among them, multi-year regulating reservoirs, characterized by their large storage capacity and strong regulation capabilities, play a leading role in the cascade reservoir system. Determining the end-of-flood season water level of multi-year regulating reservoirs is a key aspect of reservoir operation. The level of the end-of-flood season water level directly determines the available water volume and power generation head of the reservoir during the dry season. If the water level is too low, it will lead to insufficient water volume during the dry season and reduced power generation efficiency; if the water level is too high, although it can increase power generation during the dry season, water storage during the flood season may reduce power generation during the flood season, thus reducing the power generation efficiency for the current year. Therefore, scientifically and rationally determining the end-of-flood season water level is of great significance for balancing the relationship between the current year's power generation and future power generation of the reservoir system.

[0003] Currently, although some progress has been made in the research on the optimal scheduling of reservoir water levels at the end of the flood season, the following obvious shortcomings still exist: First, the uncertainty of runoff is not adequately characterized. Traditional optimization scheduling methods are mostly deterministic, typically using historical measured runoff or averages as input. However, influenced by factors such as climate change, actual runoff exhibits a high degree of randomness and uncertainty. While some studies have introduced stochastic hydrological generation methods, they often focus only on a single reservoir or a single time period, neglecting the complex interdependence between upstream and downstream areas of cascade reservoir groups (spatial correlation) and between different months (temporal correlation). This results in generated runoff scenarios that deviate significantly from reality, making it difficult to support reliable scheduling decisions.

[0004] Second, the multi-objective optimization trade-off mechanism is not perfect. The scheduling of water storage levels at the end of the flood season is essentially a game between current power generation benefits and future energy storage benefits. Traditional methods mostly take the single objective of maximizing total power generation, failing to effectively quantify and highlight the impact of water storage levels at the end of the flood season on the long-term power generation potential (i.e., energy storage) of the cascade reservoir group. This leads to scheduling schemes that easily overdraw on current conditions.

[0005] Third, the selection of the optimal solution lacks objective decision support. After obtaining the Pareto non-dominated solution set using a multi-objective evolutionary algorithm, traditional methods rely heavily on the subjective experience of dispatchers to select from numerous non-dominant scheduling schemes. There is a lack of a scientific and quantitative method to weigh the contradiction between annual power generation and end-of-flood energy storage, making it difficult to guarantee the rationality and optimality of the final selected scheme.

[0006] In view of the shortcomings of the existing technologies, there is an urgent need for a stochastic optimization method for the end-of-flood water level of multi-year regulating reservoirs that can accurately characterize the spatiotemporal uncertainty of runoff, scientifically weigh current and future power generation benefits, and objectively select the best decision-making scheme. Summary of the Invention

[0007] Purpose of the invention: The purpose of this invention is to provide a method and system for stochastic optimization of the water level at the end of the flood season in a multi-year regulating reservoir.

[0008] Technical solution: The present invention provides a method and system for stochastic optimization of the end-of-flood water level of a multi-year regulating reservoir, comprising the following steps: S1: Obtain historical runoff data, reservoir characteristic curves, and reservoir characteristic parameters of the cascade reservoir group; S2: Construct a runoff edge distribution function based on the historical runoff data; S3: Utilize Vine Copula theory to establish a joint distribution of runoff across multiple time periods, generating a sequence of random runoff scenarios that satisfy spatiotemporal correlation; S4: Taking the maximum expected total power generation within the scheduling cycle of the cascade reservoir group and the maximum expected energy storage at the end of the flood season of the multi-year regulating reservoir as the objective functions, a multi-objective stochastic optimization scheduling model for reservoir water level at the end of the annual flood season is constructed; wherein, the expected energy storage at the end of the flood season is obtained by conversion from the water level at the end of the flood season of the multi-year regulating reservoir based on the principle of electrical equivalent. S5: The AR-MOEA multi-objective evolutionary algorithm is used to iteratively solve the multi-objective optimization scheduling model to obtain a Pareto non-dominated solution set containing multiple scheduling schemes; S6: Using annual power generation and end-of-flood storage as decision indicators, construct the SMAA-VIKOR model, conduct a compromise evaluation on the Pareto non-dominated solution set, and determine the optimal end-of-flood storage water level target value and the corresponding monthly scheduling process for each reservoir. S7: Based on the monthly scheduling process of each reservoir, guide the actual water storage and power generation discharge operations of the cascade reservoir group.

[0009] Furthermore, step S2 includes the following steps: S21: Perform interpolation processing on the historical inflow data of the cascade reservoir group; S22: Select alternative probability distribution functions and fit the marginal distributions of historical runoff data for each reservoir and each time period; the alternative probability distribution functions include normal distribution, log-normal distribution, Pearson type III distribution and generalized extreme value distribution; S23: Calculate the parameters of each alternative probability distribution function using the maximum likelihood estimation method; S24: The goodness-of-fit results are tested using the Kolmogorov-Smirnov test or the AIC / BIC information criterion, and the optimal probability distribution function is selected as the runoff marginal distribution model for the corresponding cross section and time period.

[0010] Furthermore, step S3 includes the following steps: S31: Transform the runoff edge distribution model obtained in step S2 into a uniform distribution sequence in the interval [0,1]. S32: Based on spatiotemporal correlation analysis, determine the vine structure between runoff variables in multiple time periods and construct a C-Vine or D-Vine tree structure; S33: Select an alternative family of binary Copula functions, and combine the maximum likelihood estimation method to fit the Pair-Copula function parameters between nodes in the tree structure to construct a multi-period runoff joint distribution model; S34: Based on the constructed joint distribution model, Monte Carlo random sampling is used to generate a [0,1] uniformly distributed random scenario that satisfies spatiotemporal correlation; S35: Using the runoff edge distribution model in step S2, perform an inverse transformation on the uniformly distributed random scenario to obtain a sequence of random runoff scenarios under actual physical dimensions (see...). Figure 3 ).

[0011] Furthermore, the multi-objective stochastic optimization scheduling model for reservoir water level at the end of the flood season constructed in step S4 includes: Objective function 1: Maximize the expected total power generation of the cascade reservoir group during the scheduling period. The calculation formula is as follows: In the formula, E[⋅] represents the expected value; M This represents the total number of reservoirs. T This represents the number of time periods in the scheduling cycle. I Number of runoff scenarios; For the first i The first runoff scenario m The output of each reservoir; P i For the first i The probability of a runoff scenario occurring; k m For the first m The output coefficient of each reservoir; For the first i The first runoff scenario m The reservoir during the period t The power generation flow rate; No. i The first runoff scenario m The reservoir during the period t Hydropower head; Δ tThe time period is long; Objective function 2: Maximize the expected energy storage capacity of the multi-year regulating reservoir at the end of the flood season. The calculation formula is as follows: In the formula, For the first i The flood season water level of multi-year regulating reservoirs under various runoff scenarios; To regulate the dead water level of the reservoir for many years; This is a function representing the water level-storage capacity relationship of a multi-year regulating reservoir. The average electrical equivalent coefficient of the reservoir during the non-flood season over many years; The constraints include: water balance constraints, reservoir water level boundary constraints, reservoir discharge boundary constraints, power plant output boundary constraints, and non-negative variable constraints.

[0012] Furthermore, step S5 includes the following steps: S51: Initialize the AR-MOEA algorithm parameters, including population size and maximum number of iterations, and randomly generate an initial population, where each individual in the population represents a reservoir scheduling scheme; S52: Using the stochastic runoff scenario sequence as input to the stochastic optimization model, calculate the fitness of the expected total power generation and the expected energy storage at the end of the flood season for each individual in the population; S53: Based on the reference point update strategy, perform crossover and mutation operations on the current population to generate offspring populations; S54: Merge the parent and offspring populations and use an environmental selection strategy based on an adaptive reference point to retain high-performing non-inferior individuals to form a new generation of population. S55: Determine if the maximum number of iterations has been reached. If yes, output the current Pareto non-dominated solution set; otherwise, return to step S52 to continue iterating; obtain the common Pareto front. J One scheduling scheme (see Figure 4 ).

[0013] Furthermore, step S6 includes the following steps: S61: Extract the annual power generation and flood season storage index values ​​of each scheduling scheme in the Pareto non-dominated solution set, and construct the decision matrix; determine the probability density functions of the stochastic decision matrix and the stochastic weights, denoted as follows: and ; S62: In the Decision Space X and weight space W Latin hypercube sampling is used to obtain random samples of attribute values ​​and weight values ​​for each scheduling scheme. These samples are then substituted into the VIKOR method to calculate the utility function value of each scheme. ; S63: Based on the utility function value Define a ranking function to quantitatively express the ranking of each scheduling scheme. The formula for calculating the ranking function is: In the formula, when the condition is true... When the condition is false ; j The scheme number currently being evaluated; d Number the other scheduling schemes; x This represents a random representation of the scheme's attribute values; w The weight vector; the range of values ​​for rank(·) This indicates the scheduling scheme j The order of the sorting.

[0014] S64: Define the scheduling scheme based on the calculation result of the sorting function. j Ranked as r Favorable weight space at time : S65: Integrate the obtained weight space information and calculate the ranking acceptability index. With global acceptability index : In the formula, Representation scheduling scheme j Get the specified sort r The probability of; Overall description of the scheduling scheme j The level of acceptability; The weights are secondary, using centroid weights, which reflect the contribution of each ranking acceptability index of the scheme to the overall acceptability index. S66: Based on global acceptability metrics The size of the water level is used to optimize all scheduling schemes, and the scheduling scheme with the highest global acceptability index is selected as the optimal compromise solution. The corresponding flood season water level is taken as the target value of the optimal flood season water level, and the corresponding monthly scheduling process is extracted (see...). Figure 5 ).

[0015] Based on the same inventive concept, the present invention provides a stochastic optimization system for the end-of-flood-season water level of a multi-year regulating reservoir, comprising the following modules: The data acquisition module is used to acquire historical runoff data, reservoir characteristic curves, and reservoir characteristic parameters of the cascade reservoir group; The edge distribution fitting module is used to construct a runoff edge distribution model based on the historical runoff data; The random scenario generation module is used to establish a joint distribution using Vine Copula theory and generate a sequence of random runoff scenarios that satisfy spatiotemporal correlation. The multi-objective model construction module is used to construct a multi-objective stochastic optimization scheduling model for reservoir water level at the end of the flood season, with the objective functions being to maximize the expected total power generation and the expected end-of-flood-season energy storage. The algorithm solution module is used to iteratively solve the model using the AR-MOEA algorithm to obtain the Pareto non-dominated solution set; The multi-attribute decision module is used to evaluate the non-dominated solution set using the SMAA-VIKOR method, and to determine the optimal target value of the flood season water storage level and the monthly scheduling process of each reservoir. The scheduling guidance execution module is used to output operation instructions to guide actual water storage and power generation release based on the determined monthly scheduling process.

[0016] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) Accurately characterizing the spatiotemporal correlation of runoff improves the robustness of the scheduling scheme. This invention breaks through the limitations of traditional deterministic runoff input and introduces Vine Copula theory to construct a multi-time period and multi-section runoff joint distribution model. Based on this scenario, stochastic optimization is performed, which effectively reduces the impact of hydrological uncertainty on scheduling, making the resulting flood season water level scheme more adaptable and resilient to future extreme water conditions.

[0017] (2) By comprehensively considering both current benefits and future energy storage, the benefits of water resource utilization are maximized. In constructing the multi-objective stochastic optimization scheduling model, this invention not only considers maximizing the expected total power generation during the scheduling period, but also transforms the end-of-flood water level of the multi-year regulating reservoir into the expected end-of-flood energy storage value as an independent objective. This effectively prevents the model from excessively consuming water in pursuit of short-term power generation, thus achieving a balance between current power generation and future energy storage.

[0018] (3) The introduction of a stochastic multi-attribute decision-making method eliminates the subjective blindness in scheme selection. Addressing the challenge of scheme selection for Pareto non-dominated solution sets, this invention introduces the SMAA-VIKOR decision-making method. Annual power generation and end-of-flood-season energy storage are used as decision indicators to screen for the optimal solution that represents a compromise. This ensures that the final determined end-of-flood-season water level target and the monthly scheduling process meet the comprehensive interests of the actual project.

[0019] (4) It has good engineering application value. The method and system provided by this invention are logically rigorous and highly operable. They can directly output the monthly scheduling process of each reservoir. This not only provides a quantitative scientific basis for the management departments of multi-year regulating reservoirs to formulate flood season water storage plans, but also directly guides the actual water storage and discharge operations of cascade reservoir groups. It has high practical value for improving the level of refined management of watershed hydropower resources. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention; Figure 2 It is a generalized diagram of the reservoir system in the study area; Figure 3 Schematic diagram of inflow runoff scenarios; Figure 4 It is the Pareto front obtained by solving a multi-objective stochastic optimization model; Figure 5 It is a multi-year process of randomly optimizing the water level of the reservoir. Detailed Implementation

[0021] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0022] Example 1 The main steps of the stochastic optimization method and system for the end-of-flood water level of a multi-year regulating reservoir are as follows: Figure 1 As shown. Taking the Longyangxia and Liujiaxia interconnected reservoir system in the upper reaches of the Yellow River as an example, the Longyangxia Reservoir is a multi-year regulating reservoir. Figure 2 In China, the total number of reservoirs M =2.

[0023] The present invention provides a method and system for stochastic optimization of the end-of-flood water level of a multi-year regulating reservoir, comprising the following steps: S1: Obtain historical runoff data, reservoir characteristic curves, and reservoir characteristic parameters for Longyangxia and Liujiaxia reservoirs.

[0024] S2: Based on the historical runoff data, construct the marginal distribution function of the inflow runoff at Longyangxia and Liujiaxia reservoirs. Specifically: S21: Perform interpolation processing on the historical inflow data of the cascade reservoir group; S22: Select alternative probability distribution functions and fit the marginal distributions of historical runoff data for each reservoir and each time period; the alternative probability distribution functions include normal distribution, log-normal distribution, Pearson type III distribution and generalized extreme value distribution; in this embodiment, Pearson type III distribution is selected; S23: Calculate the parameters of each alternative probability distribution function using the maximum likelihood estimation method; S24: The goodness-of-fit results are tested using the Kolmogorov-Smirnov test or the AIC / BIC information criterion, and the optimal probability distribution function is selected as the runoff marginal distribution model for the corresponding cross section and time period.

[0025] S3: Utilize Vine Copula theory to establish a joint distribution of runoff across multiple time periods, generating a sequence of stochastic runoff scenarios that satisfy spatiotemporal correlation. Specifically: S31: Transform the runoff edge distribution model obtained in step S2 into a uniform distribution sequence in the interval [0,1]. S32: Based on spatiotemporal correlation analysis, determine the vine structure between runoff variables in multiple time periods and construct a C-Vine or D-Vine tree structure; S33: Select an alternative family of binary Copula functions, and combine the maximum likelihood estimation method to fit the Pair-Copula function parameters between nodes in the tree structure to construct a multi-period runoff joint distribution model; S34: Based on the constructed joint distribution model, Monte Carlo random sampling is used to generate a [0,1] uniformly distributed random scenario that satisfies spatiotemporal correlation; S35: Using the runoff edge distribution model in step S2, perform an inverse transformation on the uniformly distributed random scenario to obtain a sequence of random runoff scenarios under actual physical dimensions (see...). Figure 3 ).

[0026] S4: A multi-objective stochastic optimization scheduling model for reservoir water levels at the end of the annual flood season is constructed, with the objective functions being to maximize the expected total power generation within the cascade reservoir group's scheduling cycle and the expected energy storage at the end of the flood season in multi-year regulating reservoirs. The expected energy storage at the end of the flood season is calculated from the water level at the end of the flood season in multi-year regulating reservoirs based on the principle of electrical equivalent. The objective functions and constraints are as follows: Objective function 1: Maximize the expected total power generation of the cascade reservoir group during the scheduling period. The calculation formula is as follows: In the formula, E[⋅] represents the expected value; M The total number of reservoirs is 2 in this embodiment; T The number of time periods in the scheduling cycle is 12 months in this embodiment; I To determine the number of runoff scenarios, 500 runoff scenarios are randomly generated in this embodiment; For the first i The first runoff scenario m The output of each reservoir; P i For the first i The probability of a runoff scenario occurring; k m For the first mThe output coefficient of each reservoir; For the first i The first runoff scenario m The reservoir during the period t The power generation flow rate; No. i The first runoff scenario m The reservoir during the period t Hydropower head; Δ t The time period is long; Objective function 2: Maximize the expected energy storage capacity of the multi-year regulating reservoir at the end of the flood season. The calculation formula is as follows: In the formula, For the first i The flood season water level of multi-year regulating reservoirs under various runoff scenarios; To regulate the dead water level of the reservoir for many years; This is a function representing the water level-storage capacity relationship of a multi-year regulating reservoir. The average electrical equivalent coefficient of the reservoir during the non-flood season over many years; The constraints include: water balance constraints, reservoir water level boundary constraints, reservoir discharge boundary constraints, power plant output boundary constraints, and non-negative variable constraints.

[0027] S5: The AR-MOEA multi-objective evolutionary algorithm is used to iteratively solve the multi-objective optimization scheduling model to obtain a Pareto non-dominated solution set containing multiple scheduling schemes. Specifically: S51: Initialize the AR-MOEA algorithm parameters, including population size and maximum number of iterations, and randomly generate an initial population. Each individual in the population represents a reservoir scheduling scheme. In this embodiment, the population size is set to 50 and the number of iterations is set to 1000. S52: Using the stochastic runoff scenario sequence as input to the stochastic optimization model, calculate the fitness of the expected total power generation and the expected energy storage at the end of the flood season for each individual in the population; S53: Based on the reference point update strategy, perform crossover and mutation operations on the current population to generate offspring populations; S54: Merge the parent and offspring populations and use an environmental selection strategy based on an adaptive reference point to retain high-performing non-inferior individuals to form a new generation of population. S55: Determine if the maximum number of iterations has been reached. If yes, output the current Pareto non-dominated solution set; otherwise, return to step S52 to continue iteration; 50 scheduling schemes are obtained in total for the Pareto front, such as... Figure 4 As shown.

[0028] S6: Using annual power generation and end-of-flood-season energy storage as decision indicators, a SMAA-VIKOR model is constructed to evaluate the Pareto non-dominated solution set, determining the optimal end-of-flood-season water level target value and the corresponding monthly scheduling process for each reservoir. Specifically: S61: Extract the annual power generation and flood season storage index values ​​of each scheduling scheme in the Pareto non-dominated solution set, and construct the decision matrix; determine the probability density functions of the stochastic decision matrix and the stochastic weights, denoted as follows: and ; S62: In the Decision Space X and weight space W Latin hypercube sampling is used to obtain random samples of attribute values ​​and weight values ​​for each scheduling scheme. These samples are then substituted into the VIKOR method to calculate the utility function value of each scheme. ; S63: Based on the utility function value Define a ranking function to quantitatively express the ranking of each scheduling scheme. The formula for calculating the ranking function is: In the formula, when the condition is true... When the condition is false ; j The scheme number currently being evaluated; d Number the other scheduling schemes; x This represents a random representation of the scheme's attribute values; w The weight vector; the range of values ​​for rank(·) This indicates the scheduling scheme j The order of the sorting.

[0029] S64: Define the scheduling scheme based on the calculation result of the sorting function. j Ranked as r Favorable weight space at time : S65: Integrate the obtained weight space information and calculate the ranking acceptability index. With global acceptability index : In the formula, Representation scheduling scheme j Get the specified sort r The probability of; Overall description of the scheduling scheme j The level of acceptability; The weights are secondary, using centroid weights, which reflect the contribution of each ranking acceptability index of the scheme to the overall acceptability index. S66: Based on global acceptability metrics The size of the scheduling scheme is used to optimize all scheduling schemes. The scheduling scheme with the largest global acceptability index is selected as the optimal compromise solution. The corresponding flood season water level is taken as the optimal flood season water level target value, and the corresponding monthly scheduling process is extracted.

[0030] In this embodiment, the optimal compromise solution selected by the SMAA-VIKOR method is as follows: Figure 4 As shown by the red dot, the monthly scheduling process of the Longyangxia Reservoir, a multi-year regulating reservoir, is as follows: Figure 5 As shown.

[0031] S7: Based on the monthly scheduling process of each reservoir, guide the actual water storage and power generation discharge operations of the cascade reservoir group.

[0032] Example 2 Based on the same inventive concept, the present invention provides a stochastic optimization system for the end-of-flood-season water level of a multi-year regulating reservoir, comprising the following modules: The data acquisition module is used to acquire historical runoff data, reservoir characteristic curves, and reservoir characteristic parameters of the cascade reservoir group; The edge distribution fitting module is used to construct a runoff edge distribution model based on the historical runoff data; The random scenario generation module is used to establish a joint distribution using Vine Copula theory and generate a sequence of random runoff scenarios that satisfy spatiotemporal correlation. The multi-objective model construction module is used to construct a multi-objective stochastic optimization scheduling model for reservoir water level at the end of the flood season, with the objective functions being to maximize the expected total power generation and the expected end-of-flood-season energy storage. The algorithm solution module is used to iteratively solve the model using the AR-MOEA algorithm to obtain the Pareto non-dominated solution set; The multi-attribute decision module is used to evaluate the non-dominated solution set using the SMAA-VIKOR method, and to determine the optimal target value of the flood season water storage level and the monthly scheduling process of each reservoir. The scheduling guidance execution module is used to output operation instructions to guide actual water storage and power generation release based on the determined monthly scheduling process.

Claims

1. A method and system for stochastic optimization of the end-of-flood-season water level of a multi-year regulating reservoir, characterized in that, Includes the following steps: S1: Obtain historical runoff data, reservoir characteristic curves, and reservoir characteristic parameters of the cascade reservoir group; S2: Construct a runoff edge distribution function based on the historical runoff data; S3: Utilize Vine Copula theory to establish a joint distribution of runoff across multiple time periods, generating a sequence of random runoff scenarios that satisfy spatiotemporal correlation; S4: Taking the maximum expected total power generation within the scheduling cycle of the cascade reservoir group and the maximum expected energy storage at the end of the flood season of the multi-year regulating reservoir as the objective functions, a multi-objective stochastic optimization scheduling model for reservoir water level at the end of the annual flood season is constructed; wherein, the expected energy storage at the end of the flood season is obtained by conversion from the water level at the end of the flood season of the multi-year regulating reservoir based on the principle of electrical equivalent. S5: The AR-MOEA multi-objective evolutionary algorithm is used to iteratively solve the multi-objective optimization scheduling model to obtain a Pareto non-dominated solution set containing multiple scheduling schemes; S6: Using annual power generation and end-of-flood storage as decision indicators, construct the SMAA-VIKOR model, conduct a compromise evaluation on the Pareto non-dominated solution set, and determine the optimal end-of-flood storage water level target value and the corresponding monthly scheduling process for each reservoir. S7: Based on the monthly scheduling process of each reservoir, guide the actual water storage and power generation discharge operations of the cascade reservoir group.

2. The method for stochastic optimization of the flood-end water level of a multi-year regulating reservoir according to claim 1, characterized in that, Step 2 specifically includes: S21: Perform interpolation processing on the historical inflow data of the cascade reservoir group; S22: Select alternative probability distribution functions and fit the marginal distributions of historical runoff data for each reservoir and each time period; the alternative probability distribution functions include normal distribution, log-normal distribution, Pearson type III distribution and generalized extreme value distribution; S23: Calculate the parameters of each alternative probability distribution function using the maximum likelihood estimation method; S24: The goodness-of-fit results are tested using the Kolmogorov-Smirnov test or the AIC / BIC information criterion, and the optimal probability distribution function is selected as the runoff marginal distribution model for the corresponding cross section and time period.

3. The method for stochastic optimization of the flood-end water level of a multi-year regulating reservoir according to claim 1, characterized in that, Step S3 specifically includes: S31: Transform the runoff edge distribution model obtained in step S2 into a uniform distribution sequence in the interval [0,1]. S32: Based on spatiotemporal correlation analysis, determine the vine structure between runoff variables in multiple time periods and construct a C-Vine or D-Vine tree structure; S33: Select an alternative family of binary Copula functions, and combine the maximum likelihood estimation method to fit the Pair-Copula function parameters between nodes in the tree structure to construct a multi-period runoff joint distribution model; S34: Based on the constructed joint distribution model, Monte Carlo random sampling is used to generate a [0,1] uniformly distributed random scenario that satisfies spatiotemporal correlation; S35: Using the runoff edge distribution model in step S2, perform an inverse transformation on the uniformly distributed random scenario to obtain a sequence of random runoff scenarios under actual physical dimensions.

4. The method for stochastic optimization of the flood-end water level of a multi-year regulating reservoir according to claim 1, characterized in that, In step S4, the constructed multi-objective stochastic optimization scheduling model for reservoir water level at the end of the flood season specifically includes: Objective function 1: Maximize the expected total power generation of the cascade reservoir group during the scheduling period. The calculation formula is as follows: In the formula, E[⋅] represents the expected value; M This represents the total number of reservoirs. T This represents the number of time periods in the scheduling cycle. I Number of runoff scenarios; For the first i The first runoff scenario m The output of each reservoir; P i For the first i The probability of a runoff scenario occurring; k m For the first m The output coefficient of each reservoir; For the first i The first runoff scenario m The reservoir during the period t The power generation flow rate; No. i The first runoff scenario m The reservoir during the period t Hydropower head; Δ t The time period is long; Objective function 2: Maximize the expected energy storage capacity of the reservoir group at the end of the flood season. The calculation formula is as follows: In the formula, For the first i The flood season water level of multi-year regulating reservoirs under various runoff scenarios; To regulate the dead water level of the reservoir for many years; This is a function representing the water level-storage capacity relationship of a multi-year regulating reservoir. The average electrical equivalent coefficient of the reservoir during the non-flood season over many years; The constraints include: water balance constraints, reservoir water level boundary constraints, reservoir discharge boundary constraints, power plant output boundary constraints, and non-negative variable constraints.

5. The method for stochastic optimization of the flood-end water level of a multi-year regulating reservoir according to claim 1, characterized in that, Step S5 specifically includes: S51: Initialize the AR-MOEA algorithm parameters, including population size and maximum number of iterations, and randomly generate an initial population, where each individual in the population represents a reservoir scheduling scheme; S52: Using the stochastic runoff scenario sequence as input to the stochastic optimization model, calculate the fitness of the expected total power generation and the expected energy storage at the end of the flood season for each individual in the population; S53: Based on the reference point update strategy, perform crossover and mutation operations on the current population to generate offspring populations; S54: Merge the parent and offspring populations and use an environmental selection strategy based on an adaptive reference point to retain high-performing, non-inferior individuals to form a new generation of population. S55: Determine if the maximum number of iterations has been reached. If yes, output the current Pareto non-dominated solution set; otherwise, return to step S52 to continue iterating; obtain the common Pareto front. J One scheduling scheme.

6. The stochastic optimization method for the end-of-flood-season water level of a multi-year regulating reservoir as described in claim 1, characterized in that, Step S6 specifically includes: S61: Extract the annual power generation and flood season storage index values ​​of each scheduling scheme in the Pareto non-dominated solution set, and construct the decision matrix; determine the probability density functions of the stochastic decision matrix and the stochastic weights, denoted as follows: and ; S62: In the Decision Space X and weight space W Latin hypercube sampling is used to obtain random samples of attribute values ​​and weight values ​​for each scheduling scheme. These samples are then substituted into the VIKOR method to calculate the utility function value of each scheme. ; S63: Based on the utility function value Define a ranking function to quantitatively express the ranking of each scheduling scheme. The formula for calculating the ranking function is: In the formula, when the condition is true... When the condition is false ; j The scheme number currently being evaluated; d Number the other scheduling schemes; x This represents a random representation of the scheme's attribute values; w The weight vector; the range of values ​​for rank(·) This indicates the scheduling scheme j The order of the sorting; S64: Define the scheduling scheme based on the calculation result of the sorting function. j Ranked as r Favorable weight space at time : S65: Integrate the obtained weight space information and calculate the ranking acceptability index. With global acceptability index : In the formula, Representation scheduling scheme j Get the specified sort r The probability of; Overall description of the scheduling scheme j The level of acceptability; The weights are secondary, using centroid weights, which reflect the contribution of each ranking acceptability index of the scheme to the overall acceptability index. S66: Based on global acceptability metrics The size of the scheduling scheme is used to optimize all scheduling schemes. The scheduling scheme with the largest global acceptability index is selected as the optimal compromise solution. The corresponding flood season water level is taken as the optimal flood season water level target value, and the corresponding monthly scheduling process is extracted.

7. A stochastic optimization system for the end-of-flood-season water level of a multi-year regulating reservoir, used to implement the method described in any one of claims 1 to 6, characterized in that, include: The data acquisition module is used to acquire historical runoff data, reservoir characteristic curves, and reservoir characteristic parameters of the cascade reservoir group; The edge distribution fitting module is used to construct a runoff edge distribution model based on the historical runoff data; The random scenario generation module is used to establish a joint distribution using Vine Copula theory and generate a sequence of random runoff scenarios that satisfy spatiotemporal correlation. The multi-objective model construction module is used to construct a multi-objective stochastic optimization scheduling model for reservoir water level at the end of the flood season, with the objective functions being to maximize the expected total power generation and the expected end-of-flood-season energy storage. The algorithm solution module is used to iteratively solve the model using the AR-MOEA algorithm to obtain the Pareto non-dominated solution set; The multi-attribute decision module is used to evaluate the non-dominated solution set using the SMAA-VIKOR method, and to determine the optimal target value of the flood season water storage level and the monthly scheduling process of each reservoir. The scheduling guidance execution module is used to output operation instructions to guide actual water storage and power generation release based on the determined monthly scheduling process.

Images