Step-by-step optimization method for cascade reservoirs to turn somersaults in water storage and regulation

Abstract

The present application relates to the technical field of efficient utilization of water resources and optimal scheduling of water and electricity, and discloses a flip-flop gradual optimization method for cascade reservoir group water storage scheduling, which takes the gradual optimization method as a calculation framework, divides the multi-stage cascade reservoir group water storage optimization scheduling problem into multiple two-stage sub-problems before each iteration, regards the current trajectory as a fulcrum position and the historical trajectory process as different historical positions in each sub-problem, and performs a flip-flop search action to move back and forth around the search range between the fulcrum position and the different historical positions to find a new position with better results. As the distance between the current trajectory and the historical trajectory becomes closer and closer, the flip-flop search space gradually narrows, so that the global optimal solution is gradually approached. The flip-flop gradual optimization method for cascade reservoir group water storage scheduling solves the problems of insufficient search capability and insufficient calculation accuracy of the gradual optimization method in solving the optimization scheduling of complex water and electricity systems.

Description

Technical Field

[0001] This invention relates to the field of efficient water resource utilization and optimized hydropower scheduling, specifically to a step-by-step optimization method for water storage scheduling of a cascade reservoir group. Background Technology

[0002] Water storage scheduling is a crucial link in ensuring the comprehensive utilization benefits of a river basin's reservoir system. Under the premise of ensuring the flood control safety of reservoirs and upstream and downstream areas, implementing cascade reservoir water storage scheduling can minimize water wastage, raise reservoir water levels, and thus increase hydropower head, reduce water storage during the dry season, and alleviate water shortages in downstream areas. Therefore, to coordinate water resource allocation between upstream and downstream areas, fully realize the comprehensive utilization benefits of the reservoir system, and meet the water demand of the middle and lower reaches, it is urgent to conduct research on the optimized water storage scheduling of cascade reservoir systems while ensuring flood control safety. This research aims to optimize the water storage sequence and process of the cascade reservoir system to improve the overall fullness of the reservoir system, ensure water supply security, and maximize comprehensive utilization benefits.

[0003] However, the impoundment period is the time when multi-objective demands are most concentrated. Under limited water storage capacity, the optimal scheduling of cascade reservoir groups requires comprehensive consideration of each reservoir's flood control role, impoundment tasks, and operational characteristics, as well as factors such as flood control, power generation, navigation, and ecology. This necessitates optimizing the timing and process of impoundment to ensure the optimal level of full storage and comprehensive utilization benefits for each reservoir after the flood season. Therefore, the optimal scheduling of cascade reservoir groups is a complex optimization problem involving multiple stages, dimensions, and constraints, and its efficient solution has attracted widespread attention.

[0004] The Progressive Optimization Approach (POA) is an improved dynamic programming method for solving multi-stage, multi-state optimization problems. Its basic principle is to decompose the multi-stage problem into multiple two-stage subproblems. In each calculation, the variables of other stages are fixed, and the objective function value is iteratively optimized only for the current stage and the two adjacent stages. This process is repeated stage by stage until the final solution is output. This method reduces the discrete states of feasible solutions and significantly improves computational efficiency compared to dynamic programming. However, when the number of reservoirs is large, it still faces a severe curse of dimensionality, and its search capability needs to be strengthened. Therefore, there is an urgent need to effectively improve the computational mechanism of POA to enhance the computational efficiency and solution accuracy of the joint scheduling problem of reservoir groups.

[0005] Somersaulting while hunting is one of the most efficient hunting methods for manta rays in nature. When they find a food source, they perform a series of backward somersaults, circling their prey until they find the optimal solution. Inspired by this phenomenon, Chinese scholars proposed a novel intelligent biomimetic swarm algorithm in 2019, namely the manta ray foraging optimization algorithm. Its basic principle is: first, obtain a manta ray swarm; then, treat the current optimal position as a pivot point; each manta ray updates its position by swimming back and forth through somersaults to perform the search for the optimal solution.

[0006] Since POA lacks the concept of a population, this approach treats the state in a two-stage subproblem as a single manta ray individual, and the historical states of several such subproblems as individual manta rays, thus considering these individuals as a population. To implement the somersault-foraging technique, the current trajectory is considered a pivot point, and the historical trajectory process is considered different historical positions. By performing somersault search actions, the system moves back and forth within the search range between the pivot point and different historical positions to find new positions with better results, thereby generating diverse search information and improving global search capabilities.

[0007] This invention takes into account the knowledge information carried by historical trajectories and combines somersault learning with POA. When updating the position, it mines the knowledge information carried by the historical trajectory process and conducts somersault search around different search ranges. It has strong global search capability and high computational accuracy, effectively overcoming the dimensionality curse problem of traditional methods. It is a new solution for effectively solving the optimization scheduling problem of large-scale cascade reservoir groups. Summary of the Invention

[0008] The purpose of this invention is to address the shortcomings of the aforementioned technologies by providing a step-by-step optimization method for the water storage scheduling of cascade reservoir groups. This method solves the problems of insufficient search capability and low computational accuracy in solving the optimization scheduling of complex hydropower systems.

[0009] To achieve the above objectives, the cascade reservoir group water storage scheduling stepwise optimization method designed in this invention includes the following steps:

[0010] 1) Determine the initial calculation conditions, including the optimization objective function, constraints, and decision variables for the water storage and scheduling of the cascade reservoir group;

[0011] 2) Set the calculation parameters, including the maximum number of iterations M, the maximum number of somersault searches K, the number of reservoir groups N, the number of scheduling periods during the water storage period T, and the upper limit of the water level of reservoir i in time period j. and lower limit of water level Z i,j ;

[0012] 3) Generate initial trajectories for each reservoir that meet the constraints using manual experience-based decision-making or conventional methods, and store the initial trajectories in the historical trajectory database.

[0013] 4) Initialize the number of iterations m = 1;

[0014] 5) The conventional stepwise optimization method is used to iteratively calculate M′ times, where M′ < M. Each calculation generates a scheduling trajectory. This represents the trajectory of reservoir i calculated in stage j during the M′-th iteration. The scheduling trajectories are then sequentially stored in the historical trajectory database.

[0015] 6) Let m = M′ + 1, continue iterating, and execute the somersault-based stepwise optimization method. The specific calculation steps are as follows:

[0016] 6.1) Decompose the optimization scheduling problem into T-1 two-phase problems;

[0017] 6.2) For T-1 two-phase problems, perform a somersault optimization, initializing the time interval j=1;

[0018] 6.3) Initialize the number of somersault searches, k = 1;

[0019] 6.4) Randomly generate a positive integer y between 1 and Y, where 1 ≤ y ≤ Y < m;

[0020] 6.5) Perform a somersault search to optimize the current trajectory;

[0021] 6.6) From the historical trajectory database In the process, read the stored historical trajectory {Z}. m-y};

[0022] 6.7) Combining the upper and lower limits of the water level of each reservoir, determine the current dispatch trajectory for the j-th time period. and historical trajectory After normalization, convert the result to a number between 0 and 1. The calculation formulas are as follows:

[0023]

[0024]

[0025] In the formula, and Z i,j These represent the upper and lower limits of the water level of reservoir i during time period j, respectively. and The water level values ​​of reservoir i in time period j are the current scheduling trajectory and the my-th historical trajectory, respectively. and The normalized value;

[0026] 6.8) Based on the foraging learning strategy of somersaulting, normalize the current scheduling trajectory value. Considered as the fulcrum position, the normalized value around the historical trajectory Moving back and forth, creating a new position The calculation formula is as follows:

[0027]

[0028] In the formula, p and q are random numbers between 0 and 1, and F is the flip factor;

[0029] 6.9) will Inverse normalization yields a new somersault trajectory. The calculation formula is as follows:

[0030]

[0031] 6.10) Compare the somersault trajectory with the current trajectory; if... Superior The current trajectory will be replaced with the trajectory of a somersault; otherwise, no action will be taken.

[0032] 6.11) Let k = k + 1. If k ≤ K, go to step 6.4); otherwise, go to step 6.12.

[0033] 6.12) Let j = j + 1. If j ≤ T - 1, go to step 6.3); otherwise go to step 7).

[0034] 7) Let m = m + 1. If m > M, then go to step 8); otherwise, go to step 6.

[0035] 8) Stop the calculation and output the final optimal trajectory.

[0036] Preferably, in step 5), the value of M′ ranges from 8 to 10.

[0037] Preferably, in step 6.4), Y = 8.

[0038] Preferably, in step 6.8), F = 2.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1. Simple and easy to operate;

[0041] 2. When updating the location, it leverages the knowledge and information carried by the historical trajectory process to conduct somersault searches around different search ranges, which has the advantages of strong global search capabilities and high calculation accuracy;

[0042] 3. By replacing the full enumeration operation in the two-stage subproblem with a flip search optimization, the dimensionality curse problem of traditional methods is effectively overcome, which is a new scheme for effectively solving the large-scale cascade reservoir group optimal scheduling problem. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the step-by-step optimization method for water storage scheduling of cascade reservoir groups according to the present invention.

[0044] Figure 2 This is a diagram showing the calculation results of the water storage period scheduling of Wudongde Reservoir under relatively abundant water conditions;

[0045] Figure 3 This is a diagram showing the calculation results of the water storage period scheduling of Baihetan Reservoir under relatively abundant water conditions;

[0046] Figure 4 This is a diagram showing the calculation results of the water storage period scheduling of Xiluodu Reservoir under relatively abundant water conditions;

[0047] Figure 5 This is a diagram showing the calculation results of the Xiangjiaba Reservoir's water storage period scheduling under relatively abundant water conditions;

[0048] Figure 6 This is a diagram showing the calculation results of the Three Gorges Reservoir's water storage period scheduling under relatively abundant water conditions. Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0050] like Figure 1 As shown, a step-by-step optimization method for water storage scheduling of a cascade reservoir group includes the following steps:

[0051] 1) Determine the initial calculation conditions, including the optimization objective function, constraints, and decision variables for the cascade reservoir group's water storage scheduling. Given the known water storage schedule and control water level during the water storage period, to coordinate the water storage order and process of each reservoir to maximize power generation benefits, the cascade reservoir group's water storage optimization scheduling model can be described as follows: Given the initial water level, final water level, inflow process, and interval flow process of each reservoir during the water storage period, and satisfying the complex constraints such as water level and flow rate related to the comprehensive utilization factors of flood control, navigation, and ecology of each reservoir, with the optimization objective of maximizing the power generation of the cascade reservoir group, the objective function of the cascade reservoir water storage period optimization scheduling mathematical model is as follows:

[0052]

[0053] In the formula: F is the total power generation during the water storage period; N is the number of reservoirs; i is the reservoir number, and i = 1, 2, ..., N; T is the number of scheduling periods during the water storage period; j is the time period number, and j = 1, 2, ..., T; A i Q is the output coefficient of reservoir i; i,j The power generation flow (m³) of reservoir i during time period j 3 / s); H i,j Let Δj be the average power generation head (m) of reservoir i during time period j after deducting head loss; Δj is the length of time period (h).

[0054] The constraints that need to be met for the optimal water storage scheduling of a cascade reservoir group mainly include:

[0055] (1) Water balance constraint:

[0056] V i,j =V i,j-1 +(I i,j-1 -O i,j-1 )×Δj,

[0057] In the formula, V i,j Let m be the reservoir capacity of reservoir i at the end of time period j. 3 );I i,j Let m be the inflow rate of reservoir i during time period j. 3 / s);

[0058] (2) Hydraulic constraint:

[0059]

[0060] In the formula, R i,j Let the interval flow rate (m³) of reservoir i during time period j be... 3 / s); U i Let O be the number of upstream reservoirs of reservoir i; u,j The outflow from upstream reservoir i during time period j (m³) 3 / s);

[0061] (3) Time-based water level constraints:

[0062]

[0063] In the formula, Z i,j Let be the water level (m) in front of the dam of reservoir i during time period j; and These represent the lowest and highest water levels (m) in front of the dam for reservoir i during time period t.

[0064] (4) Outbound flow constraints:

[0065]

[0066] In the formula, and These represent the minimum outflow (m³) of reservoir i during time period j. 3 / s) and maximum outflow (m 3 / s);

[0067] (5) Initial and final water level constraints:

[0068] Z i,0 =Z i,start Z i,T =Z i,end

[0069] In the formula, Z i,star and Z i,end These represent the initial reservoir water level (m) and the final control water level (m) of reservoir i during the scheduling period, respectively.

[0070] (6) Reservoir output constraints:

[0071]

[0072] In the formula, P i,j Let i be the power output (kW) of reservoir i during time period j; and These represent the minimum and maximum power output (kW) of reservoir i during time period j, respectively.

[0073] (7) System output constraints:

[0074]

[0075] In the formula, NP j To calculate the minimum total power output (kW) of the reservoir group during time period j;

[0076] (8) Non-negativity constraint: All variables are non-negative values;

[0077] It is evident that the optimal scheduling of water storage in a cascade reservoir group is a complex coupled optimal control problem with large scale, high dimension, multiple stages, strong constraints, and nonlinearity. It includes numerous constraints such as water level, reservoir capacity, and flow rate. When solving this problem using the stepwise optimization method, the computational complexity increases exponentially with the increase of the number of reservoirs, computation time periods, and discrete numbers, and it will face a serious problem of dimensionality curse. The search capability needs to be strengthened.

[0078] 2) Set the calculation parameters, including the maximum number of iterations M, the maximum number of somersault searches K, the number of reservoir groups N, the number of scheduling periods during the water storage period T, and the upper limit of the water level of reservoir i in time period j. and lower limit of water level Z i,j ;

[0079] 3) Generate initial trajectories for each reservoir that meet the constraints using manual experience-based decision-making or conventional methods, and store the initial trajectories in the historical trajectory database.

[0080] 4) Initialize the number of iterations m = 1;

[0081] 5) The conventional stepwise optimization method is used to iteratively calculate M′ times, where M′ < M, and the value of M′ ranges from 8 to 10. Each calculation generates a scheduling trajectory. This represents the trajectory of reservoir i calculated in stage j during the M′-th iteration. The scheduling trajectories are then sequentially stored in the historical trajectory database. At this time, the historical trajectory database When sufficient historical trajectory information is available, a stepwise optimization method for somersaults can be implemented.

[0082] 6) Let m = M′ + 1, continue iterating, and execute the somersault-based stepwise optimization method. The specific calculation steps are as follows:

[0083] 6.1) Decompose the optimization scheduling problem into T-1 two-phase problems;

[0084] 6.2) For T-1 two-phase problems, perform a somersault optimization, initializing the time interval j=1;

[0085] 6.3) Initialize the number of somersault searches, k = 1;

[0086] 6.4) Randomly generate a positive integer y between 1 and Y, where 1 ≤ y ≤ Y < m. In this embodiment, Y = 8.

[0087] 6.5) Perform a somersault search to optimize the current trajectory;

[0088] 6.6) From the historical trajectory database In the process, read the stored historical trajectory {Z}. m-y};

[0089] 6.7) Combining the upper and lower limits of the water level of each reservoir, determine the current dispatch trajectory for the j-th time period. and historical trajectory After normalization, convert the result to a number between 0 and 1. The calculation formulas are as follows:

[0090]

[0091]

[0092] In the formula, and Z i,j These represent the upper and lower limits of the water level of reservoir i during time period j, respectively. and The water level values ​​of reservoir i in time period j are the current scheduling trajectory and the my-th historical trajectory, respectively. and The normalized value;

[0093] 6.8) Based on the foraging learning strategy of somersaulting, normalize the current scheduling trajectory value. Considered as the fulcrum position, the normalized value around the historical trajectory Moving back and forth, creating a new position The calculation formula is as follows:

[0094]

[0095] In the formula, p and q are random numbers between 0 and 1, and F is the airflip factor. In this embodiment, F = 2.

[0096] 6.9) will Inverse normalization yields a new somersault trajectory. The calculation formula is as follows:

[0097]

[0098] 6.10) Compare the somersault trajectory with the current trajectory; if... Superior The current trajectory will be replaced with the trajectory of a somersault; otherwise, no action will be taken.

[0099] 6.11) Let k = k + 1. If k ≤ K, go to step 6.4); otherwise, go to step 6.12.

[0100] 6.12) Let j = j + 1. If j ≤ T - 1, go to step 6.3); otherwise go to step 7).

[0101] 7) Let m = m + 1. If m > M, then go to step 8); otherwise, go to step 6.

[0102] 8) Stop the calculation and output the final optimal trajectory.

[0103] Taking the Jinsha River in my country as an example, the four cascade reservoirs—Wudongde, Baihetan, Xiluodu, and Xiangjiaba—in the lower reaches of the Jinsha River, together with the Three Gorges Reservoir on the main stream of the Yangtze River, form the world's largest cascade reservoir group. They undertake comprehensive utilization tasks including flood control, power generation, navigation, ecological restoration, and dry season water replenishment, and are a key control project for the management, development, and protection of the Yangtze River basin. The total regulating capacity of the five reservoirs in the cascade reservoir group is 37.321 billion cubic meters. 3 The total installed capacity is 58,960 MW, and the total flood control capacity is 37.643 billion cubic meters. 3These cascade reservoirs possess enormous flood and runoff regulation capabilities, significantly impacting flood control and water resource utilization patterns in the upper reaches of the Yangtze River (Sichuan-Chongqing section) and the middle and lower reaches. Due to the similar impoundment periods and large overlapping reservoir capacities, competitive impoundment exists within this group. Furthermore, the complex relationships between flood control, power generation, navigation, water supply, and ecology must be coordinated during impoundment. Therefore, research on the optimized joint impoundment scheduling of this cascade reservoir group is urgently needed to ensure safe and orderly impoundment, thereby maximizing its comprehensive benefits.

[0104] The selected calculation period is from August 1 to October 30. Among them, Wudongde and Baihetan reservoirs will start impounding water in early August, Xiluodu and Xiangjiaba reservoirs will start impounding water in early September, and the Three Gorges Reservoir will start raising its water level on August 21 when it can undertake flood control scheduling. The water level will be controlled at 150-155m on September 10, and at no more than 162-165m by the end of September. It can be impounded to 175m by the end of October, with scheduling periods in ten-day periods.

[0105] Five typical water inflow rates of 15%, 30%, 50%, 70%, and 90% were selected as high-water years, slightly high-water years, normal-water years, slightly low-water years, and low-water years, respectively, to carry out optimized scheduling of water storage in the cascade reservoir group using the method of this invention and the stepwise optimization method.

[0106] Table 1 lists the calculation results of the reservoir storage period optimization scheduling using the method of this invention and the stepwise optimization method. The calculation results show that the method of this invention has the following advantages over the stepwise optimization method: ① Under all inflow conditions, the calculation results of the method of this invention are better than those of the POA, which can increase power generation by 0.1 to 0.4 billion kWh, resulting in good power generation benefits; ② The calculation time of the method of this invention is shorter than that of the stepwise optimization method. For different types, the calculation time of the method of this invention is about 30% of that of the stepwise optimization method, and the performance advantage becomes more prominent as the reservoir calculation scale and discrete state increase.

[0107] Table 1 Comparison of calculation results between the method of the present invention and the stepwise optimization method.

[0108]

[0109] Figures 2-6 Schematic diagrams of the water storage process and power output changes for each reservoir are presented. As shown in the diagrams, the optimized water storage scheduling results for each reservoir satisfy all constraints, and the water storage process is balanced and coordinated, increasing the power generation benefits of the cascade reservoir group during the water storage period. Similar conclusions are reached from the analysis of the reservoir group optimization results under different inflow conditions during different water storage periods, which is consistent with the actual situation. This indicates that the calculation results of the method of this invention are reasonable and reliable, providing technical support for the scheduling, operation, and management of the cascade reservoir group in the basin.

[0110] This invention presents a stepwise optimization method for the water storage scheduling of cascade reservoir groups. This method is simple and easy to implement. When updating positions, it leverages the knowledge information carried by historical trajectories to conduct stepwise searches around different search ranges, exhibiting strong global search capabilities and high computational accuracy. By replacing the comprehensive enumeration operation in the two-stage subproblems with stepwise search optimization, it effectively overcomes the dimensionality curse problem of traditional methods, providing a novel and effective solution to the large-scale cascade reservoir group optimization scheduling problem.

[0111] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A stepwise optimization method for water storage scheduling of a cascade reservoir group, characterized in that: Includes the following steps: 1) Determine the initial calculation conditions, including the optimization objective function, constraints, and decision variables for the water storage and scheduling of the cascade reservoir group; 2) Set the calculation parameters, including the maximum number of iterations M, the maximum number of somersault searches K, the number of reservoir groups N, the number of scheduling periods during the water storage period T, and the upper limit of the water level of reservoir i in time period j. and lower limit of water level Z i,j ; 3) Generate initial trajectories for each reservoir that meet the constraints using manual experience-based decision-making or conventional methods, and store the initial trajectories in the historical trajectory database. 4) Initialize the number of iterations m = 1; 5) The conventional stepwise optimization method is used to iteratively calculate M′ times, where M′ < M. Each calculation generates a scheduling trajectory. This represents the trajectory of reservoir i calculated in stage j during the M′-th iteration. The scheduling trajectories are then sequentially stored in the historical trajectory database. 6) Let m = M′ + 1, continue iterating, and execute the somersault-based stepwise optimization method. The specific calculation steps are as follows: 6.1) Decompose the optimization scheduling problem into T-1 two-phase problems; 6.2) For T-1 two-phase problems, perform a somersault optimization, initializing the time interval j=1; 6.3) Initialize the number of somersault searches, k = 1; 6.4) Randomly generate a positive integer y between 1 and Y, where 1 ≤ y ≤ Y < m; 6.5) Perform a somersault search to optimize the current trajectory; 6.6) From the historical trajectory database In the process, read the stored historical trajectory {Z} of the my-th record. m -y }; 6.7) Combining the upper and lower limits of the water level of each reservoir, determine the current dispatch trajectory for the j-th time period. and historical trajectory After normalization, convert the result to a number between 0 and 1. The calculation formulas are as follows: In the formula, and Z i,j These represent the upper and lower limits of the water level of reservoir i during time period j, respectively. and The water level values ​​of reservoir i in time period j are the current scheduling trajectory and the my-th historical trajectory, respectively. and The normalized value; 6.8) Based on the foraging learning strategy of somersaulting, normalize the current scheduling trajectory value. Considered as the fulcrum position, the normalized value around the historical trajectory Moving back and forth, creating a new position The calculation formula is as follows: In the formula, p and q are random numbers between 0 and 1, and F is the flip factor; 6.9) will Inverse normalization yields a new somersault trajectory. The calculation formula is as follows: 6.10) Compare the somersault trajectory with the current trajectory; if... Superior The current trajectory will be replaced with the trajectory of a somersault; otherwise, no action will be taken. 6.11) Let k = k + 1. If k ≤ K, go to step 6.4); otherwise, go to step 6.

12. 6.12) Let j = j + 1. If j ≤ T - 1, go to step 6.3); otherwise go to step 7). 7) Let m = m + 1. If m > M, then go to step 8); otherwise, go to step 6. 8) Stop the calculation and output the final optimal trajectory.

2. The stepwise optimization method for water storage scheduling of cascade reservoir groups as described in claim 1, characterized in that: In step 5), the value of M′ ranges from 8 to 10.

3. The stepwise optimization method for water storage scheduling of cascade reservoir groups as described in claim 2, characterized in that: In step 6.4), Y = 8.

4. The step-by-step optimization method for water storage scheduling of cascade reservoir groups as described in claim 1, characterized in that: In step 6.8), F = 2.

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