An efficient solution method for optimal operation of cascade reservoirs

Abstract

The application discloses a kind of high-efficiency solving methods of cascade reservoir joint power generation optimization scheduling model, comprising: determining the storage capacity of cascade reservoir at the beginning and end of scheduling period, and the inflow of leading reservoir in whole scheduling period, interval inflow between each reservoir, various constraints of cascade reservoir;The storage capacity value of each reservoir is discretized within the upper and lower limits of storage capacity according to the discrete accuracy requirement;In time period t , for all possible storage capacity combinations of cascade reservoir at the beginning of time period, find the corresponding optimal storage capacity combination of cascade reservoir at the end of time period, and store such a correspondence as optimal state transition relationship;Let t = t -1, repeat step 3 until all time periods in scheduling period are traversed;According to the stored optimal state transition relationship, start backtracking from the beginning of the first time period, and obtain the optimal storage capacity process of cascade reservoir in the whole scheduling period;The application can improve the solving efficiency of cascade reservoir optimization scheduling model, while ensuring the quality of solution, so that the calculation result is close to the global optimal solution.

Description

Technical Field

[0001] This invention relates to the field of hydropower system optimization scheduling technology, specifically to an efficient solution method for a cascade reservoir joint power generation optimization scheduling model. Background Technology

[0002] Reservoir scheduling is a classic problem in the field of hydrology and water resources. With the gradual advancement of hydropower development projects in China, the various levels of hydropower stations in a river basin's cascade reservoirs are successively completed and begin generating electricity. How to fully realize the benefits of joint optimal scheduling of these cascade reservoirs is currently a major challenge. However, optimal reservoir scheduling is a non-convex, discontinuous, and multi-constrained optimization problem, and existing solutions generally suffer from low efficiency, poor solution quality, and unstable results. Therefore, there is an urgent need to conduct research on efficient solution methods for the joint optimal scheduling of reservoir power generation.

[0003] Dynamic programming and its improved methods are the most widely used and theoretically mature algorithms in the field of reservoir optimization scheduling. The core idea of ​​dynamic programming is to divide a problem into multiple subproblems and solve them step by step. By analyzing the overlapping subproblems and optimal substructure properties of the model to be optimized, it effectively avoids redundant calculations in ergonomic optimization. Dynamic programming methods do not have specific requirements on the form of the objective and constraints, have a clear structure, strong applicability, and do not require calibrated model parameters. They can obtain theoretically optimal solutions under corresponding discrete precision conditions, thus quickly gaining widespread attention and rapid development in the field of reservoir optimization scheduling. However, dynamic programming methods also have obvious drawbacks. When the number of power stations involved in the scheduling calculation increases, dynamic programming algorithms exhibit a serious "curse of dimensionality" problem. Many experts and scholars have conducted research on improving dynamic programming methods and proposed a series of improved methods. However, apart from the general method of dynamic programming, other improved methods all have their applicable scope and conditions, and the solutions obtained are not globally optimal. Therefore, it is necessary to propose an improved dynamic programming algorithm that utilizes the economic characteristics of the objective of optimizing the scheduling of cascade reservoir power generation. Without changing the structure of the dynamic programming algorithm, the algorithm improves computational efficiency by narrowing the search range, thus providing a feasible method for efficiently solving the optimal scheduling model of cascade reservoir joint power generation. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned shortcomings and provide an efficient solution method for the optimal scheduling model of cascade reservoir joint power generation, aiming to solve the problem of low solution efficiency of existing multidimensional dynamic programming algorithms when solving the scheduling model of cascade reservoir joint power generation.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: an efficient solution method for a cascade reservoir joint power generation optimization scheduling model, which includes the following steps:

[0006] (1) Determine the reservoir capacity of the cascade reservoirs at the beginning and end of the scheduling period as the boundary conditions for scheduling calculation; collect the inflow of the head reservoir and the interval inflow between each reservoir as the input for scheduling calculation; determine the water level, outflow, output and other constraints of the cascade reservoirs during the scheduling period according to the actual operation requirements of the reservoirs, and collect the basic characteristic curve data of each reservoir.

[0007] (2) Discretize the reservoir capacity values ​​of the N reservoirs involved in the calculation within the upper and lower limits of the reservoir capacity according to the discretization precision. The discretization precision is determined according to the actual scheduling calculation requirements. Initialize the time period t = T, where T is the number of calculation time periods in the entire scheduling period.

[0008] (3) At time t, for all possible reservoir capacity combinations S of the cascade reservoirs at the beginning of time. t-1 Quickly find the optimal reservoir capacity combination of cascade reservoirs that meets various constraints at the end of the time period. And S t-1 and This correspondence is stored as the optimal state transition relationship;

[0009] (4) Let t = t-1, and repeat step (3) until all time periods within the scheduling period have been traversed;

[0010] (5) Based on the stored optimal state transition relationship, backtracking is performed starting from the beginning of the first time period to obtain the optimal reservoir capacity process of the cascade reservoirs throughout the entire scheduling period.

[0011] Preferably, in step (3), the initial storage capacity combination S for the time period t-1 The corresponding optimal storage capacity combination at the end of the time period It depends on the following equation:

[0012]

[0013] Among them, b t (S t-1 O t B represents the time-period benefit function of the cascade reservoirs at time t. t (S t S represents the optimal cumulative benefit function from the end of time period t to the end of time period T. t-1 S represents the reservoir capacity combination of the cascade reservoirs at the beginning of time period t. t O represents the combined reservoir capacity of the cascade reservoirs at the end of time period t. t This represents the inflow rate of each reservoir in time period t;

[0014] Preferably, in step (3), for all possible reservoir capacity combinations S of the cascade reservoirs at the beginning of time period t. t-1 Quickly find the optimal reservoir capacity combination of the cascade reservoirs at the end of time period t. The method includes the following steps:

[0015] S1: Combining the reservoir capacities of the cascade reservoirs at the beginning of time period t. t-1 Record Storage capacity combination S at the end of the period t Record in For the j-th reservoir at the beginning of time period t i The storage capacity value corresponding to each discrete point is similar. For the i-th reservoir at the end of time period t, the k-th... i The storage capacity value corresponding to each discrete point, j i and k i The smaller the value, the smaller the corresponding storage capacity; initialize j i =1, where i∈{1,2,…,N};

[0016] S2: Determine the value of j1 in the headwater reservoir. If j1 = 1, then j2, ..., j N-1 ,j N If the value is equal to any value, execute S3; otherwise, execute S4.

[0017] S3: Using a method where the upstream reservoir circulates in the outer layer and the downstream reservoir circulates in the inner layer, iterates through all possible reservoir capacity combinations of the cascade reservoirs when the initial head reservoir j1=1 during this period, i.e. And j1=1, with the goal of maximizing the sum of the time period benefit function of the cascade reservoirs in this period and the optimal cumulative benefit function from the end of this period to the end of the Tth period, we seek the optimal reservoir capacity combination at the end of each period corresponding to each reservoir capacity combination, and save and record this optimal state transition relationship.

[0018] S4: Using a method where the upstream reservoir circulates in the outer layer and the downstream reservoir circulates in the inner layer, iterates through all possible reservoir capacity combinations of the cascade reservoirs at the beginning of this period, excluding the head reservoir j1=1. And j1≠1; for each combination of storage capacity First, calculate the storage capacity difference of the headwater reservoir. Simultaneously obtain the storage capacity combination at the beginning of this period. The corresponding optimal storage capacity combination at the end of the time period and their corresponding optimal discharge flow combinations Then, iterate through all possible combinations of storage capacity at the end of that period. The water balance method is used to calculate the discharge flow combination corresponding to the initial and final reservoir capacity combination of the currently selected time period. And judge If the value is greater than zero and less than N*△, skip the reservoir capacity combination at the end of this period. If it is, calculate the sum of the time-period benefit function of the cascade reservoirs corresponding to the selected initial and final reservoir capacity combination and the optimal cumulative benefit function from the end of this period to the end of the Tth period. Finally, use the maximum value of this sum as the objective function to determine each reservoir capacity combination. The corresponding optimal combination of storage capacity at the end of the time period is determined, and this optimal state transition relationship is saved and recorded.

[0019] Preferably, in step S3, the method for finding the optimal reservoir capacity combination at the end of the time period for all possible reservoir capacity combinations of the cascade reservoirs when j1=1 at the beginning of time period t includes the following steps:

[0020] S3.1: For the initial {j1=1,j2=1,…,j} period, i =1,…,j N =1} The optimal reservoir capacity combination at the end of the time period is obtained by taking the maximum sum of the time period benefit function of the cascade reservoirs and the optimal cumulative benefit function from the end of the time period to the end of the Tth time period as the objective.

[0021] S3.2: When traversing all possible reservoir capacity combinations of the cascade reservoirs when the initial head reservoir j1 = 1 in this time period, if {j1 = 1, ..., j i-1 =1,j i =1}, while {j i+1 ≠1,…,j N-1 ≠1,j N If ≠1}, then for each combination of storage capacity First, calculate the storage capacity difference of the (i+1)th reservoir. Simultaneously obtain the storage capacity combination at the beginning of this period. The corresponding optimal storage capacity combination at the end of the time period and their corresponding optimal discharge flow combinations Then, iterate through all possible combinations of storage capacity at the end of that period. The water balance method is used to calculate the discharge flow combination corresponding to the initial and final reservoir capacity combination of the currently selected time period. And judge Is it greater than zero and less than (Ni)*△? If not, skip the reservoir capacity combination at the end of this period. If yes, calculate the sum of the time-period benefit function of the cascade reservoirs corresponding to the current selected initial and final reservoir capacity combination and the optimal cumulative benefit function from the end of this period to the end of the Tth period. Finally, use the maximum of this value as the objective function to determine each reservoir capacity combination. The corresponding optimal combination of storage capacity at the end of the time period is determined, and this optimal state transition relationship is saved and recorded.

[0022] The beneficial effects of this invention are:

[0023] 1. The method of this invention improves the multidimensional dynamic programming algorithm based on the concavity and convexity of the objective function of the joint power generation optimization scheduling of cascade reservoirs. It significantly reduces the search space of the reservoir capacity combination of cascade reservoirs and greatly improves the solution efficiency of the joint power generation optimization scheduling model of cascade reservoirs, providing a feasible method to alleviate the "curse of dimensionality" problem.

[0024] 2. The method of this invention adopts a computational structure similar to that of multidimensional dynamic programming algorithm. While improving the solution efficiency of the cascade reservoir joint power generation optimization scheduling model, it can also ensure that the solution calculation result of the model is close to the global optimal solution and has good solution stability. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating an efficient solution method for a cascade reservoir joint power generation optimization scheduling model. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0027] like Figure 1 As shown, an efficient solution method for a cascade reservoir joint power generation optimization scheduling model is proposed, which includes the following steps:

[0028] (1) Determine the reservoir capacity of the cascade reservoirs at the beginning and end of the scheduling period as the boundary conditions for scheduling calculation; collect the inflow of the head reservoir and the interval inflow between each reservoir as the input for scheduling calculation; determine the water level, outflow, output and other constraints of the cascade reservoirs during the scheduling period according to the actual operation requirements of the reservoirs, and collect the basic characteristic curve data of each reservoir.

[0029] (2) Discretize the reservoir capacity values ​​of the N reservoirs involved in the calculation within the upper and lower limits of the reservoir capacity according to the discretization precision. The discretization precision is determined according to the actual scheduling calculation requirements. Initialize the time period t = T, where T is the number of calculation time periods in the entire scheduling period.

[0030] (3) At time t, for all possible reservoir capacity combinations S of the cascade reservoirs at the beginning of time. t-1 Quickly find the optimal reservoir capacity combination of cascade reservoirs that meets various constraints at the end of the time period. And S t-1 and This correspondence is stored as the optimal state transition relationship;

[0031] (4) Let t = t-1, and repeat step (3) until all time periods within the scheduling period have been traversed;

[0032] (5) Based on the stored optimal state transition relationship, backtracking is performed starting from the beginning of the first time period to obtain the optimal reservoir capacity process of the cascade reservoirs throughout the entire scheduling period.

[0033] Preferably, in step (3), the initial storage capacity combination S for the time period t-1 The corresponding optimal storage capacity combination at the end of the time period It depends on the following equation:

[0034]

[0035] Among them, b t (S t-1 O t B represents the time-period benefit function of the cascade reservoirs at time t. t (S t S represents the optimal cumulative benefit function from the end of time period t to the end of time period T. t-1 S represents the reservoir capacity combination of the cascade reservoirs at the beginning of time period t. t O represents the combined reservoir capacity of the cascade reservoirs at the end of time period t. t This represents the inflow rate of each reservoir in time period t;

[0036] Preferably, in step (3), for all possible reservoir capacity combinations S of the cascade reservoirs at the beginning of time period t. t-1 Quickly find the optimal reservoir capacity combination of the cascade reservoirs at the end of time period t. The method includes the following steps:

[0037] S1: Combining the reservoir capacities of the cascade reservoirs at the beginning of time period t. t-1 Record Storage capacity combination S at the end of the period t Record in For the j-th reservoir at the beginning of time period t i The storage capacity value corresponding to each discrete point is similar. For the i-th reservoir at the end of time period t, the k-th... i The storage capacity value corresponding to each discrete point, j i and k i The smaller the value, the smaller the corresponding storage capacity; initialize j i =1, where i∈{1,2,…,N};

[0038] S2: Determine the value of j1 in the headwater reservoir. If j1 = 1, then j2, ..., j N-1 ,j N If the value is equal to any value, execute S3; otherwise, execute S4.

[0039] S3: Using a method where the upstream reservoir circulates in the outer layer and the downstream reservoir circulates in the inner layer, iterates through all possible reservoir capacity combinations of the cascade reservoirs when the initial head reservoir j1=1 during this period, i.e. And j1=1, with the goal of maximizing the sum of the time period benefit function of the cascade reservoirs in this period and the optimal cumulative benefit function from the end of this period to the end of the Tth period, we seek the optimal reservoir capacity combination at the end of each period corresponding to each reservoir capacity combination, and save and record this optimal state transition relationship.

[0040] S4: Using a method where the upstream reservoir circulates in the outer layer and the downstream reservoir circulates in the inner layer, iterates through all possible reservoir capacity combinations of the cascade reservoirs at the beginning of this period, excluding the head reservoir j1=1. And j1≠1; for each combination of storage capacity First, calculate the storage capacity difference of the headwater reservoir. Simultaneously obtain the storage capacity combination at the beginning of this period. The corresponding optimal storage capacity combination at the end of the time period and their corresponding optimal discharge flow combinations Then, iterate through all possible combinations of storage capacity at the end of that period. The water balance method is used to calculate the discharge flow combination corresponding to the initial and final reservoir capacity combination of the currently selected time period. And judge If the value is greater than zero and less than N*△, skip the reservoir capacity combination at the end of this period. If it is, calculate the sum of the time-period benefit function of the cascade reservoirs corresponding to the selected initial and final reservoir capacity combination and the optimal cumulative benefit function from the end of this period to the end of the Tth period. Finally, use the maximum value of this sum as the objective function to determine each reservoir capacity combination. The corresponding optimal combination of storage capacity at the end of the time period is determined, and this optimal state transition relationship is saved and recorded.

[0041] Preferably, in step S3, the method for finding the optimal reservoir capacity combination at the end of the time period for all possible reservoir capacity combinations of the cascade reservoirs when j1=1 at the beginning of time period t includes the following steps:

[0042] S3.1: For the initial {j1=1,j2=1,…,j} period, i =1,…,j N =1} The optimal reservoir capacity combination at the end of the time period is obtained by taking the maximum sum of the time period benefit function of the cascade reservoirs and the optimal cumulative benefit function from the end of the time period to the end of the Tth time period as the objective.

[0043] S3.2: When traversing all possible reservoir capacity combinations of the cascade reservoirs when the initial head reservoir j1 = 1 in this time period, if {j1 = 1, ..., j i-1 =1,j i=1}, while {j i+1 ≠1,…,j N-1 ≠1,j N If ≠1}, then for each combination of storage capacity First, calculate the storage capacity difference of the (i+1)th reservoir. Simultaneously obtain the storage capacity combination at the beginning of this period. The corresponding optimal storage capacity combination at the end of the time period and their corresponding optimal discharge flow combinations Then, iterate through all possible combinations of storage capacity at the end of that period. The water balance method is used to calculate the discharge flow combination corresponding to the initial and final reservoir capacity combination of the currently selected time period. And judge Is it greater than zero and less than (Ni)*△? If not, skip the reservoir capacity combination at the end of this period. If yes, calculate the sum of the time-period benefit function of the cascade reservoirs corresponding to the current selected initial and final reservoir capacity combination and the optimal cumulative benefit function from the end of this period to the end of the Tth period. Finally, use the maximum of this value as the objective function to determine each reservoir capacity combination. The corresponding optimal combination of storage capacity at the end of the time period is determined, and this optimal state transition relationship is saved and recorded.

[0044] Example: A case study was conducted using three cascade reservoirs—Wudongde, Baihetan, and Xiluodu—located in the lower reaches of the Jinsha River. Based on the natural inflow sequence of the cascade reservoirs from July 1959 to June 2018, decadal inflow rates for high-water years (25% frequency), normal-water years (50% frequency), and low-water years (75% frequency) were selected as the water input. An experiment was performed to solve the optimal scheduling model for joint power generation of the cascade reservoirs, verifying the computational effectiveness of the method proposed in this invention.

[0045] The scheduling model uses a ten-day period as the calculation step, a hydrological year (from the beginning of July to the end of June of the following year) as the scheduling period, the flood control limit water level as the initial reservoir capacity and the final water level of the scheduling period, and 1m as the discrete precision. The scheduling model is solved by the method of this invention and the multidimensional dynamic programming algorithm respectively, and a comparative analysis is performed.

[0046] Table 1

[0047]

[0048] Table 1 presents the solution results of the proposed method and the multidimensional dynamic programming algorithm for the optimal scheduling model of cascade reservoir joint power generation. It can be seen that, in different years of water inflow, the annual power generation obtained by the proposed method is 250-300 million kWh less than that obtained by the multidimensional dynamic programming algorithm, representing only 0.1% of the result obtained by the multidimensional dynamic programming algorithm. This indicates that the proposed method can obtain a high-quality solution that approximates the global optimum. Furthermore, it can be seen that the proposed method has a significant advantage in computational efficiency, taking only about 3% of the time of the multidimensional dynamic programming algorithm, demonstrating the good performance of the proposed method in solving the "curse of dimensionality" problem.

[0049] In summary, compared with the prior art, the present invention has the following advantages:

[0050] The method of this invention improves the multidimensional dynamic programming algorithm based on the concavity and convexity of the objective function of the joint power generation optimization scheduling of cascade reservoirs. It significantly reduces the search space of the reservoir capacity combination of cascade reservoirs and greatly improves the solution efficiency of the joint power generation optimization scheduling model of cascade reservoirs, providing a feasible method to alleviate the "curse of dimensionality" problem.

[0051] The method of this invention adopts a computational structure similar to that of multidimensional dynamic programming algorithms. While improving the solution efficiency of the cascade reservoir joint power generation optimization scheduling model, it can also ensure that the solution calculation results are close to the global optimal solution and have good solution stability.

[0052] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The embodiments and features described in these embodiments can be arbitrarily combined without conflict. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. An efficient solution method for a cascade reservoir joint power generation optimization scheduling model, characterized in that: It includes the following steps: Step (1): Determine the reservoir capacity of the cascade reservoirs at the beginning and end of the scheduling period as the boundary condition for scheduling calculation; The inflow of the leading reservoir and the inter-reservoir inflow during the scheduling period are collected as inputs for scheduling calculations. Based on the actual operation requirements of the reservoirs, the water level, outflow and output constraints of the cascade reservoirs during the scheduling period are determined, and the basic characteristic curve data of each reservoir are collected. Step (2): Discretize the reservoir capacity values ​​of the N reservoirs involved in the calculation within the upper and lower limits of the reservoir capacity according to the discretization precision. The discretization precision is determined according to the actual scheduling calculation requirements; initialize the time period. t =T, where T is the number of calculation periods in the entire scheduling period; Step (3), during the time period t For all possible reservoir capacity combinations of the cascade reservoirs at the beginning of the period Quickly find the optimal reservoir capacity combination of cascade reservoirs that meets various constraints at the end of the time period. and will and This correspondence is stored as the optimal state transition relationship; Step (4), let t = t -1, repeat step (3) until all time periods within the scheduling period have been traversed; Step (5): Based on the stored optimal state transition relationship, backtracking is performed starting from the beginning of the first time period to obtain the optimal reservoir capacity process of the cascade reservoirs throughout the entire scheduling period; In step (3), for the cascade reservoirs in the first... t All possible storage capacity combinations at the beginning of the period Quickly locate the cascade reservoirs in the first t The optimal storage capacity combination at the end of the period The method includes the following steps: S1: The cascade reservoirs are located in the first... t Initial storage capacity combination Record Storage capacity combination at the end of the period Record ,in For the first t Initial period i The first reservoir j i The storage capacity value corresponding to each discrete point is similar. For the first t End of period i The first reservoir k i The storage capacity value corresponding to each discrete point. j i and k i The smaller the value, the smaller the corresponding storage capacity; initialization j i =1, where ; S2: For the headwater reservoir j 1. Make a judgment, if j 1=1, and j 2, …, j N-1 , j N If the value is equal to any value, execute S3; otherwise, execute S4. S3: Using a method where the upstream reservoir circulates in the outer layer and the downstream reservoir circulates in the inner layer, the initial headwater reservoir of this period is traversed. j All possible reservoir capacity combinations of the cascade reservoirs when 1=1, i.e. With the goal of maximizing the sum of the time-period benefit function of the cascade reservoirs during the time period and the optimal cumulative benefit function from the end of the time period to the end of the Tth time period, we seek the optimal reservoir capacity combination at the end of each time period for each reservoir capacity combination and save and record this optimal state transition relationship. S4: Using a method where the upstream reservoir circulates in the outer layer and the downstream reservoir circulates in the inner layer, the initial removal headwater reservoir is traversed throughout this period. j All possible reservoir capacity combinations of cascade reservoirs other than 1=1, i.e. For each combination of storage capacity First, calculate the storage capacity difference of the headwater reservoir. At the same time, obtain the initial storage capacity combination for that period. The corresponding optimal storage capacity combination at the end of the time period and their corresponding optimal discharge flow combinations Then, iterate through all possible combinations of storage capacity at the end of that period. The water balance method is used to calculate the downstream flow combination corresponding to the initial and final reservoir capacity combination of the currently selected time period. and judge Is it greater than zero and less than zero? If not, skip the reservoir capacity combination at the end of this period; if yes, calculate the sum of the time-period benefit function of the cascade reservoirs corresponding to the selected initial and final reservoir capacity combination and the optimal cumulative benefit function from the end of this period to the end of period T. Finally, use the maximum of this value as the objective function to determine each reservoir capacity combination. The corresponding optimal combination of storage capacity at the end of the time period is determined, and this optimal state transition relationship is saved and recorded.

2. The efficient solution method for the cascade reservoir joint power generation optimization scheduling model according to claim 1, characterized in that: In step (3), the initial storage capacity combination for the time period The corresponding optimal storage capacity combination at the end of the time period It depends on the following equation: ； in, Indicates the first t The time-period benefit function of cascade reservoirs during a given time period. Indicates the first t The optimal cumulative benefit function from the end of time period T to the end of time period T. This indicates that the cascade reservoirs are in the first t Initial storage capacity configuration at the beginning of the period This indicates that the cascade reservoirs are in the first t Storage capacity combination at the end of the period Indicates that each reservoir is in the first... t Inbound flow during a given time period.

3. The efficient solution method for the cascade reservoir joint power generation optimization scheduling model according to claim 1, characterized in that: In step S3, for the first t Initial stage of the Longtou Reservoir j The method for finding the optimal reservoir capacity combination at the end of the time period when 1=1, considering all possible reservoir capacity combinations of the cascade reservoirs, includes the following steps: S3.1: For the initial period of this time The corresponding cascade reservoir capacity combination aims to maximize the sum of the time-period benefit function of the cascade reservoirs during the current period and the optimal cumulative benefit function from the end of the current period to the end of the Tth period, thereby obtaining the optimal capacity combination at the end of the current period. S3.2: During the traversal of the initial headwater reservoir in this period j When considering all possible reservoir capacity combinations of a cascade reservoir with 1=1, if ,and For each combination of storage capacity First, calculate the first... i+ The storage capacity difference of a reservoir At the same time, obtain the initial storage capacity combination for that period. The corresponding optimal storage capacity combination at the end of the time period and their corresponding optimal discharge flow combinations Then, iterate through all possible combinations of storage capacity at the end of that period. The water balance method is used to calculate the downstream flow combination corresponding to the initial and final reservoir capacity combination of the currently selected time period. and judge Is it greater than zero and less than zero? If not, skip the reservoir capacity combination at the end of this period; if yes, calculate the sum of the time-period benefit function of the cascade reservoirs corresponding to the selected initial and final reservoir capacity combination and the optimal cumulative benefit function from the end of this period to the end of period T. Finally, use the maximum of this value as the objective function to determine each reservoir capacity combination. The corresponding optimal combination of storage capacity at the end of the time period is determined, and this optimal state transition relationship is saved and recorded.

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