A method and system for optimal flood control scheduling of a reservoir group based on quadratic programming

Abstract

The present application relates to the technical field of flood control optimal scheduling, in particular to a reservoir group flood control optimal scheduling method and system based on quadratic programming, the method comprising the following steps: according to the water conservancy facilities and hydrological elements in the basin, the system sorts out the spatial distribution of key nodes and their hydraulic connection, constructs a flood control scheduling topological network, and obtains a reservoir group flood control optimal scheduling topological graph; a reservoir group flood control optimal scheduling quadratic programming model is established according to the reservoir group flood control optimal scheduling topological graph; based on the MINOS library of GAMS, the least gradient method and quasi-Newton method are used to optimize and solve the reservoir group flood control optimal scheduling quadratic programming model. The present application couples the propagation of flood between reservoir groups in the mathematical equation set, avoids complex simulation sequential coding, is easy to model, has good universality, and the model is easy to seek an optimal solution, can balance the reasonable scheduling of the flood control capacity, peak shaving effect and reservoir storage capacity of the reservoir, and improve the accuracy and efficiency of flood regulation.

Description

A method and system for optimal flood control scheduling of reservoir groups based on quadratic programming Technical Field

[0001] This invention relates to the field of flood control optimization scheduling technology, and in particular to a method and system for optimizing flood control scheduling of reservoir groups based on quadratic programming. Background Technology

[0002] As a core infrastructure of the modern water conservancy system, reservoirs play a multi-functional and collaborative role in basin flood control, water resource allocation, clean energy supply, agricultural irrigation, and ecological environment maintenance. Flood control scheduling, with reservoirs as the main body, is an important non-engineering measure to mitigate flood damage in downstream areas, effectively alleviating downstream flood pressure through scientific regulation of storage and release relationships. Flood control scheduling not only includes the scheduling of individual reservoirs but also involves the joint scheduling of reservoir groups, rivers, dikes, and other water conservancy projects. It is a complex decision-making process with multiple objectives and phased characteristics, possessing strong flexibility and dynamic adjustment capabilities. It can be adjusted based on forecast results and is suitable for responding to extreme weather events, flood forecasting, and optimizing water resource allocation in complex scenarios.

[0003] Reservoir flood control scheduling methods have gradually shifted from conventional scheduling to optimized scheduling, the scheduling objects have expanded from single reservoirs to cascade reservoir groups, and the scheduling objectives have evolved from single-function to multi-objective coordination. Single-objective optimized scheduling constructs a single objective function with specific performance indicators (such as maximizing power generation benefits and optimizing navigation economics), and solves it using mathematical programming models by setting constraints. Multi-objective optimized scheduling breaks through the limitations of single objectives, taking into account multiple dimensions such as flood control safety, power generation benefits, and ecological flow protection, establishing a multi-objective optimization theoretical framework, and achieving optimal equilibrium decisions in complex systems through objective weight configuration. Data-driven decision-making methods, based on machine learning and artificial intelligence technologies, extract implicit patterns from historical scheduling data through knowledge discovery mechanisms, realize the dynamic optimization of scheduling rules and the coupled iteration of mechanism models, and thus provide support for reservoir scheduling decisions.

[0004] Current research on flood control scheduling of reservoir groups has formed a multidisciplinary research system encompassing intelligent algorithm innovation, multi-objective coupled modeling, and dynamic risk assessment, achieving significant progress in improving the collaborative flood control efficiency of reservoir groups and optimizing watershed risk management strategies. However, due to the complex nonlinear relationships and spatiotemporal conflict characteristics among multiple objectives in reservoir groups, as well as the impact of problems such as the curse of dimensionality, further exploration is needed to establish more accurate collaborative optimization methods. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for optimizing flood control scheduling of reservoir groups based on quadratic programming.

[0006] To achieve the above objectives, in a first aspect, this invention provides a method for optimizing flood control scheduling of reservoir groups based on quadratic programming. The method includes the following steps: Based on the water conservancy facilities and hydrological elements within the basin, systematically analyze the spatial distribution and hydraulic connections of key nodes, construct a multi-level, multi-node flood control scheduling topology network, and obtain a reservoir group flood control optimization scheduling topology map; establish a quadratic programming model for reservoir group flood control optimization scheduling based on the reservoir group flood control optimization scheduling topology map; and optimize and solve the reservoir group flood control optimization scheduling quadratic programming model using the MINOS library of GAMS and the reduced gradient method and quasi-Newton method. This invention couples the propagation of floodwaters among reservoir groups into a system of mathematical equations, avoiding complex simulation sequence coding. It is easy to model, has good versatility, and the model is easy to optimize. It can balance the flood control capacity, peak shaving effect, and water storage capacity of reservoirs through reasonable scheduling, improving the accuracy and efficiency of flood control.

[0007] Optionally, the reservoir group flood control optimization scheduling quadratic programming model includes 8 objective functions and 10 constraint conditions.

[0008] Optionally, the objective function includes seven sub-objective functions and one overall objective function.

[0009] Optionally, the seven sub-objective functions are respectively the maximum peak reduction objective function, the minimum excess water volume objective function, the minimum flood control storage capacity utilization objective function, the minimum discharge flow fluctuation objective function, the water level objective function at the end of the flood regulation period, the reservoir water level-storage capacity relationship constraint penalty function, and the reservoir water level-discharge relationship constraint penalty function.

[0010] Optionally, the 10 constraints are respectively the reservoir water balance equation, water level-storage capacity relationship constraint, water level-discharge relationship constraint, reservoir discharge capacity constraint, reservoir water level constraint, sub-reservoir storage capacity constraint, sub-reservoir discharge capacity constraint, river channel water balance equation, river channel storage equation, and nodal water balance equation.

[0011] Optionally, the objective functions for the maximum peak reduction, the minimum excess water volume, the minimum flood control storage capacity, the minimum discharge flow fluctuation, the final water level during flood regulation, the reservoir water level-storage capacity relationship constraint penalty function, and the reservoir water level-discharge relationship constraint penalty function are as follows:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] in, To maximize peak reduction, T represents the number of time periods. Let t be the flow rate at the downstream node section of reservoir r during time period t. For excess water, The difference between the maximum safe discharge flow at the downstream control section and the maximum safe discharge flow. In order to utilize flood control reservoir capacity, Let r be the water storage capacity of reservoir during time period t. To account for fluctuations in the outflow, Let be the flow rate at the downstream node section of reservoir r during time period t-1. To regulate the water level at the end of the flood season, Let r be the water level of reservoir r during time period t. The target water level for reservoir r at the end of the flood control period. The relationship between reservoir water level and storage capacity is a constraint and penalty. Let r be the maximum water storage capacity of the (n-1)th sub-reservoir of reservoir r. Let be the water storage capacity of the (n-1)th sub-reservoir of reservoir r during time period t. Let be the water storage capacity of the nth sub-reservoir of reservoir r during time period t. Constraints and penalties related to reservoir water level and discharge relationship. Let m be the maximum flow rate at section m-1 downstream of reservoir r. Let m-1 be the flow rate at section m-1 downstream of reservoir r during time period t. Let m be the flow rate at the downstream node section m of reservoir r during time period t.

[0020] The overall objective function is shown in the following equation:

[0021]

[0022] in, To maximize the objective function value, To maximize peak reduction, For excess water, In order to utilize flood control reservoir capacity, To account for fluctuations in the outflow, To regulate the water level at the end of the flood season, The relationship between reservoir water level and storage capacity is a constraint and penalty. Constraints and penalties related to reservoir water level and discharge relationship. , , , and They are respectively , , , and Normalized weights, and This is a constraint penalty coefficient.

[0023] Optionally, the reservoir water balance equation, the water level-storage capacity relationship constraint, the water level-discharge relationship constraint, the reservoir discharge capacity constraint, the reservoir water level constraint, the sub-reservoir storage capacity constraint, the sub-reservoir discharge capacity constraint, the river channel water balance equation, the river channel storage equation, and the nodal water balance equation are as follows:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] in, , and Let these represent the water storage capacity of reservoir r at time t-1, the water storage capacity at time t, and the inflow during the interval, respectively. and These represent the inflow and outflow of the reservoir (r) in the upstream river section during time period (t). Let r be the water level of reservoir r during time period t. Let r be the elevation of the dam base. and Let represent the water depth and corresponding water volume of the nth sub-reservoir of reservoir r during time period t. Let r be the function relating the water depth and water volume of the nth sub-reservoir of reservoir r. Let be the water storage capacity of the nth sub-reservoir of reservoir r. Let be the discharge flow of the nth sub-reservoir of reservoir r in time period t. Let r be the function relating the water depth of the nth sub-reservoir to the outflow rate. Let r be the maximum discharge flow of reservoir r during time period t. and Let r be the highest and lowest water levels of the reservoir. Let r be the maximum water storage capacity of the nth sub-reservoir. Let m be the maximum flow rate at the downstream node section m of reservoir r. and Let be the water storage capacity of river channel s at time intervals t and t-1, respectively. and These represent the upstream inflow and downstream discharge of river channel s at time t, respectively. The propagation time in river segment C under steady flow conditions. For the proportion of river flow in river segment C, and These represent the upstream inflow and downstream outflow of node h during time period t, respectively.

[0035] Optionally, based on the Saint-Venant equation and coupled with the 10 constraints, a secondary programming model for optimal flood control scheduling of a reservoir group is established with the scheduling objectives of maximizing peak reduction, minimizing excess water volume, minimizing the use of flood control storage capacity, minimizing the fluctuation of downstream flow, and minimizing the water level at the end of the flood control period.

[0036] Secondly, the present invention provides a reservoir group flood control optimization scheduling system based on quadratic programming. The reservoir group flood control optimization scheduling system based on quadratic programming includes: a data acquisition device, a data output device, a processor, and a storage device. The storage device includes a computer-readable storage medium storing a computer program. The computer program includes program instructions. When the program instructions are executed by the processor, the processor enables the processor to implement the reservoir group flood control optimization scheduling method based on quadratic programming provided by the present invention.

[0037] The present invention has at least the following beneficial effects:

[0038] 1. This method uses the Saint-Venant equation as its basic principle, couples the propagation of floods among reservoir groups into a set of mathematical equations, and then constructs a quadratic programming model for optimal flood control scheduling of reservoir groups. This avoids complex simulation sequence coding, is easy to model, and has good versatility.

[0039] 2. This method is based on the principle of water balance, and all constraints are linear equations, which makes it easy to find the optimal solution for flood control optimization scheduling of reservoir groups based on quadratic programming.

[0040] 3. Through the study of multi-objective scheduling strategies, this method constructs a secondary programming model for optimal flood control scheduling of reservoir groups, which can balance the flood control capacity, peak reduction effect and water storage capacity of reservoirs, thereby improving the accuracy and efficiency of flood control.

[0041] 4. A system adapted to the method is provided, which can improve the practicality of the method and facilitate its promotion. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 is a flowchart illustrating a reservoir group flood control optimization scheduling method based on quadratic programming according to an embodiment of the present invention;

[0044] Figure 2 is a topology diagram of flood control optimization scheduling of reservoir group B according to an embodiment of the present invention;

[0045] Figure 3 is a schematic diagram of the framework of a reservoir group flood control optimization scheduling method based on quadratic programming according to an embodiment of the present invention. Detailed Implementation

[0046] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0047] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0048] It should be noted in advance that, in one alternative embodiment, except for independent descriptions, the same symbols or letters appearing in all formulas have the same meaning and value.

[0049] In an optional embodiment, referring to Figure 1, the present invention provides a reservoir group flood control optimization scheduling method based on quadratic programming, the method comprising the following steps:

[0050] S1. Based on the water conservancy facilities and hydrological elements in the basin, the spatial distribution of key nodes and their hydraulic connections are systematically sorted out, and a multi-level, multi-node flood control scheduling topology network is constructed to obtain the flood control optimization scheduling topology map of the reservoir group.

[0051] Specifically, in this embodiment, the construction of the reservoir group flood control optimization scheduling topology map is an important foundation for the optimization of the basin flood control system. Its core lies in relying on the water conservancy facilities and hydrological elements within the basin to systematically analyze the spatial distribution and upstream-downstream hydraulic connections of key nodes such as reservoirs, river channels, tributary confluences, and downstream control sections. By clarifying the topological relationships of each node and combining them with the natural flow paths of water, a connection network between nodes is constructed. This network can intuitively reflect the direction of water flow transmission and dynamic interaction processes within the basin, thus providing a clear and structured framework for flood control scheduling.

[0052] The construction of the reservoir group flood control optimization scheduling topology map first requires identifying key nodes within the watershed, including reservoirs, river confluences, tributary inlets, and downstream control sections. These nodes play a crucial role in flood control scheduling, serving as both water flow distribution points and implementation points for scheduling strategies. The hydraulic connections between nodes are described using the water balance equation and the flow propagation equation. The water balance equation describes the water conservation relationship between reservoirs, nodes, and rivers, while the flow propagation equation simulates the propagation process of flood waves in the river channel. After clarifying the spatial distribution and hydraulic connections of each node, the reservoir group flood control optimization scheduling topology network is constructed using graph theory methods. This network can intuitively reflect the direction of water flow transmission within the watershed, providing a clear structured framework for flood control scheduling. The construction method and steps are as follows:

[0053] 1. Based on the reservoir flood control and allocation objectives and the depth of the research questions, generalize the main and tributary river system and draw the river system in a way that closely approximates the actual geographical location of the project area, including the main and tributary rivers and generalized rivers;

[0054] 2. Based on the river system, identify and mark administrative region sections, reservoirs, flood control protection nodes, and watercourses;

[0055] 3. Draw the boundaries of the watershed divisions, and only generalize one cross section for each sub-watershed division;

[0056] 4. Repeatedly check and modify the generalized topology diagram of the hilly irrigation area until it meets the requirements, and finally obtain the flood control optimization scheduling topology network of the reservoir group, that is, the flood control optimization scheduling topology diagram of the reservoir group.

[0057] More specifically, please refer to Figure 2. This embodiment takes a reservoir group B in a river basin as an example to conduct a flood control optimization scheduling simulation analysis. The main reservoirs involved in reservoir group B include reservoir 1 and reservoir 2 located in the basin. In addition, it also includes several existing reservoir groups within the catchment area of ​​reservoir 2, including reservoir 3, reservoir 4, reservoir 5, reservoir 6, reservoir 7, and reservoir 8. Among them, reservoir 1 and reservoir 2 are connected in parallel. Twelve key nodes are marked at the key cross-section downstream of reservoir 2, namely, 1.6km cross-section (cross-section 1), cross-section 7 (cross-section 3), community 1, highway 1, street 1, a village, highway 2, hydrological station 2, community 2, river dam, street 2, and street 3. At the same time, three key nodes are added upstream of the confluence of the two tributaries, namely, 1km cross-section (cross-section 2), 3km cross-section (cross-section 4), and hydrological station 1. Upstream of Reservoir 2 are six smaller reservoirs: Reservoir 3, Reservoir 4, Reservoir 5, Reservoir 6, Reservoir 7, and Reservoir 8, forming a multi-level, multi-node reservoir group flood control optimization scheduling topology network.

[0058] S2. Establish a secondary programming model for flood control optimization scheduling of the reservoir group based on the topology map of the reservoir group.

[0059] Specifically, in this embodiment, the quadratic programming model for optimal flood control scheduling of a reservoir group includes 8 objective functions and 10 constraints. The 8 objective functions include 7 sub-objective functions and 1 overall objective function. The 7 sub-objective functions are: maximum peak reduction objective function, minimum excess water volume objective function, minimum flood control storage capacity utilization objective function, minimum discharge flow fluctuation objective function, water level objective function at the end of flood regulation, reservoir water level-storage capacity relationship constraint penalty function, and reservoir water level-discharge relationship constraint penalty function. The 10 constraints are: reservoir water balance equation, water level-storage capacity relationship constraint, water level-discharge relationship constraint, reservoir discharge capacity constraint, reservoir water level constraint, sub-reservoir storage capacity constraint, sub-reservoir discharge flow constraint, river water balance equation, river channel storage equation, and nodal water balance equation. The following sections will detail the specific modeling process of the 8 objective functions, 10 constraints, and the quadratic programming model for optimal flood control scheduling of a reservoir group.

[0060] Maximum peak reduction objective. For major floods approaching or exceeding the basin's flood control standard, reservoirs often struggle to ensure downstream flood control safety. In such cases, the reservoir's operational strategy prioritizes ensuring the dam's flood control safety, followed by minimizing the peak flow at downstream flood control sections to alleviate the flood pressure on downstream flood-prone areas. Under the premise of ensuring reservoir flood control safety, minimizing the maximum outflow from downstream channels, reservoirs, or nodes can maximize peak reduction and alleviate downstream flood pressure. That is, the smaller the combined flow at each reservoir's flood control section and the downstream common flood control section, the better, and the shorter the duration of high water levels, the better. The maximum peak reduction objective function is shown in the following equation:

[0061]

[0062] in, To maximize peak reduction, T represents the number of time periods. Let t be the flow rate at the downstream node section of reservoir r during time period t.

[0063] Minimum Excess Water Volume Target. During flood control scheduling, to ensure the safety of downstream flood control targets, it is necessary to ensure that the reservoir's discharge flow does not exceed the warning flow or a specific safe discharge flow at the downstream control section. The smaller the combined discharge at the downstream flood control sections of the reservoir group exceeds the safe flow, the better. The objective function for minimizing excess water volume is shown in the following formula:

[0064]

[0065] in, For excess water, This is the difference between the maximum safe discharge flow rate at the downstream control section.

[0066] The minimum objective of utilizing flood control reservoir capacity is to reserve as much flood control capacity as possible for potential future floods. While ensuring downstream flood control safety, the lower the reservoir's flood control high water level, the better, to reduce upstream flood control pressure. The minimum objective function for utilizing flood control reservoir capacity is shown in the following equation:

[0067]

[0068] in, In order to utilize flood control reservoir capacity, Let r be the water storage capacity of reservoir r during time period t.

[0069] The objective is to minimize fluctuations in the discharge flow. This ensures that the flood discharge equipment of the reservoir group is not frequently opened and closed, and that the discharge process is stable. The objective function for minimizing fluctuations in the discharge flow is shown in the following equation:

[0070]

[0071] in, To account for fluctuations in the outflow, Let be the flow rate at the downstream node section of reservoir r during time period t-1.

[0072] Target water level at the end of the flood control period. During the final stage of flood control operations, the goal is to control the reservoir water level back to the designated level. If a target water level at the end of the control period is not required, this objective function can be flexibly cancelled. The target water level at the end of the flood control period is shown in the following formula:

[0073]

[0074] in, To regulate the water level at the end of the flood season, Let r be the water level of reservoir r during time period t. This represents the target water level of reservoir r at the end of the flood control period.

[0075] The penalty functions for the reservoir water level-capacity relationship and the reservoir water level-discharge relationship are shown in the following equations:

[0076]

[0077]

[0078] in, The relationship between reservoir water level and storage capacity is a constraint and penalty. Let r be the maximum water storage capacity of the (n-1)th sub-reservoir of reservoir r. Let be the water storage capacity of the (n-1)th sub-reservoir of reservoir r during time period t. Let be the water storage capacity of the nth sub-reservoir of reservoir r during time period t. Constraints and penalties related to reservoir water level and discharge relationship. Let m be the maximum flow rate at section m-1 downstream of reservoir r. Let m-1 be the flow rate at section m-1 downstream of reservoir r during time period t. Let m be the flow rate at the downstream node section m of reservoir r during time period t.

[0079] Based on the above sub-objectives, the overall objective function of the quadratic programming model for optimal flood control scheduling of the reservoir group is:

[0080]

[0081] in, To maximize the objective function value, , , , and They are respectively , , , and Normalized weights, and This is a constraint penalty coefficient.

[0082] The reservoir water balance equation, water level-storage capacity relationship constraint, water level-discharge relationship constraint, reservoir discharge capacity constraint, reservoir water level constraint, sub-reservoir storage capacity constraint, sub-reservoir discharge capacity constraint, river channel water balance equation, river channel storage equation, and nodal water balance equation are shown in the following equations:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] in, and Let r represent the water storage volume of reservoir r during time period t-1 and the inflow volume during time period t, respectively. Let r be the inflow of water into the upstream river section of reservoir t. Let r be the elevation of the dam base. Let be the water depth of the nth sub-reservoir of reservoir r during time period t. Let r be the function relating the water depth and water volume of the nth sub-reservoir of reservoir r. Let be the water storage capacity of the nth sub-reservoir of reservoir r. Let be the discharge flow of the nth sub-reservoir of reservoir r in time period t. Let r be the function relating the water depth of the nth sub-reservoir to the outflow rate. Let r be the maximum discharge flow of reservoir r during time period t. and Let r be the highest and lowest water levels of the reservoir. Let r be the maximum water storage capacity of the nth sub-reservoir. Let m be the maximum flow rate at the downstream node section m of reservoir r. and Let be the water storage capacity of river channel s at time intervals t and t-1, respectively. and These represent the upstream inflow and downstream discharge of river channel s at time t, respectively. The propagation time in river segment C under steady flow conditions. For the proportion of river flow in river segment C, and These represent the upstream inflow and downstream outflow of node h during time period t, respectively.

[0094] Assume the reservoir is divided into N sub-reservoirs from dam crest to dam base. As shown in the first equation from top to bottom in the water level-capacity relationship constraint, the reservoir water level equals the dam base elevation plus the sum of the water depths of each sub-reservoir. The total water storage capacity of the reservoir is the sum of the water storage capacities of all sub-reservoirs, as shown in the third equation from top to bottom in the water level-capacity relationship constraint. The functional relationship between the water depth and water storage capacity of each sub-reservoir is assumed to be linear, as shown in the second equation from top to bottom in the water level-capacity relationship constraint. If the water level-capacity relationship data of the reservoir is sufficiently accurate, the number of sub-reservoirs can be increased until the accuracy requirements for flood control are met. The water storage principle of each sub-reservoir is: first fill the lower-level sub-reservoir, then fill the upper-level sub-reservoir sequentially. This can be achieved through the following water storage constraint equation:

[0095]

[0096] only or Only then can the water storage constraint equation hold. If Then it is necessary In other words, to impound water in the upper sub-reservoir, the lower sub-reservoir must first be filled. The impoundment constraint equation is a nonlinear constraint equation, which is added to the objective function as a penalty function, ultimately forming the reservoir level-capacity relationship constraint penalty function. The same approach is used to handle the flood discharge of each sub-reservoir; the sum of the flood discharges of all sub-reservoirs is the total flood discharge of the reservoir, ultimately forming the reservoir level-discharge relationship constraint penalty function. It can be understood that, with sufficiently large constraint penalty coefficients, when the overall objective function reaches its optimum, the objective function composed of the seven sub-objective functions is globally optimal.

[0097] The default timescale of the reservoir group flood control optimization scheduling quadratic programming model is hours, but the scheduling time step can be flexibly set according to specific accuracy requirements. Based on the constructed reservoir group flood control optimization scheduling topology, and using the Saint-Venant equation as the fundamental principle, coupled with 10 constraints, the model is established with the scheduling objectives of maximizing peak reduction, minimizing excess water volume, minimizing the use of flood control capacity, minimizing downstream flow fluctuations, and minimizing the water level at the end of the flood control period. The specific modeling process of the reservoir group flood control optimization scheduling quadratic programming model is as follows:

[0098] 1. Input of basic elements such as watershed reservoir groups. Encode the watershed divisions, reservoirs, river flood control sections, and calculation period information, and input them into the model in the form of sets.

[0099] 2. Input of upstream and downstream topological relationships of the watershed system. The river channel is encoded and input into the model in the form of a set; in a two-dimensional set, the following are linked sequentially: upstream river segment of the reservoir, downstream river segment of the reservoir; upstream river segment of the river channel flood control section, downstream river segment of the river channel flood control section.

[0100] 3. Input of natural water system connection characteristic parameters, including river section confluence parameters, maximum flow capacity of flood control sections, etc.

[0101] 4. Input of information on reservoir groups and flood control sections, including reservoir characteristic parameters, inflow to reservoirs and node sections, water level-storage capacity relationship, water level-gate-discharge relationship, maximum discharge capacity, etc.

[0102] S3. Using the MINOS library based on GAMS, the reduced gradient method and quasi-Newton method are used to optimize and solve the quadratic programming model for flood control scheduling of the reservoir group.

[0103] Based on the topology network of flood control optimization scheduling of reservoir group, computer modeling is performed using the modeling process described in step S2. Based on the MINOS library of GAMS, the reduced gradient method and quasi-Newton method are used for optimization solution. Multi-objective flood control optimization scheduling analysis of a single reservoir is carried out. Then, multi-objective parallel flood control scheduling analysis of reservoir 1-reservoir 2 and multi-objective serial-parallel flood control optimization scheduling analysis of reservoir group B are carried out.

[0104] Furthermore, based on a multi-objective reservoir group joint optimization scheduling strategy, and addressing potential risks in flood control scheduling, this study quantitatively assesses the impact of different weight combinations of three scenarios—maximum peak reduction, maximum remaining reservoir capacity, and minimum excess water volume—on the model's scheduling effectiveness. A comprehensive flood control risk assessment system is constructed, encompassing flood control efficiency, reservoir area safety and stability, and downstream protection effectiveness. This indicator system includes five core indicators: peak reduction rate, water level exceedance rate, water level fluctuation amplitude, final water level deviation, and peak shifting degree.

[0105] Using the aforementioned flood control risk assessment system, a comprehensive evaluation was conducted on the results of the multi-objective series and parallel flood control optimization scheduling of reservoir group B under three schemes: maximum peak reduction scheme, maximum remaining reservoir capacity scheme, and minimum excess water volume scheme. The evaluation results are shown in Table 1.

[0106] Table 1. Comprehensive Evaluation Results of Multi-Objective Series-Parallel Flood Control Optimization Scheduling for Reservoir Group B

[0107]

[0108] As can be seen from the data in Table 1, under the design flood conditions of a 100-year return period and a 50-year return period, all three schemes can meet the water level control requirements and do not exceed the limit water level. The scheme with the largest remaining reservoir capacity performs best in terms of water level fluctuation range and deviation of the water level at the end of the flood, effectively maintaining the stability of the reservoir's water level and reducing water level fluctuations. Especially in the later stages of the flood, it can better control the water level at the end of the flood, ensuring the reservoir's water storage capacity and flood control reserves.

[0109] The minimum excess water volume scheme has a significant advantage in peak-shaving scheduling, effectively reducing the discharge of excess water. By optimizing the flood discharge scheduling of reservoirs, it avoids excessive water flow flowing into the downstream shared river sections, mitigating downstream water level fluctuations and flood risks. The maximum peak reduction scheme achieves the best results in reducing flood peaks, effectively reducing peak flood flow and minimizing the impact of floods on downstream areas, especially during peak flood periods, thus alleviating flood pressure to the greatest extent.

[0110] In summary, under the design flood condition of a 100-year return period, the scheme with the largest peak shaving performance is the most outstanding, especially in reducing the flood peak and mitigating downstream impact. Under the design flood condition of a 50-year return period, the scheme with the smallest excess water volume performs even better, particularly in reducing excess water volume, staggering peak flow, and mitigating flood risk.

[0111] It should be noted that in some cases, the actions described in the specification can be performed in different orders and still achieve the desired results. In this embodiment, the order of steps is given only to make the embodiment clearer and easier to explain, and not to limit it.

[0112] In an optional embodiment, please refer to Figure 3. To improve the practicality of this method and facilitate its promotion, the present invention also provides a reservoir group flood control optimization scheduling system based on quadratic programming. The reservoir group flood control optimization scheduling system based on quadratic programming includes: a data acquisition device 1, a data output device 2, a processor 3, and a storage device 4. The storage device 4 includes a computer-readable storage medium storing a computer program. The computer program includes program instructions, which, when executed by the processor 3, cause the processor 3 to implement the contents described in steps S1 to S3.

[0113] In summary, this method, based on the Saint-Venant equation, couples the propagation of floodwaters among reservoir groups into a set of mathematical equations, thereby constructing a quadratic programming model for optimal flood control scheduling of reservoir groups. This avoids complex simulation sequence coding, is easy to model, allows for flexible addition of cross sections and reservoir nodes, and has good versatility. Based on the principle of water balance, all constraints are linear equations, making it easy to find optimal solutions for optimal flood control scheduling of reservoir groups based on quadratic programming. Through research on multi-objective scheduling strategies, the constructed quadratic programming model for optimal flood control scheduling of reservoir groups can achieve a reasonable scheduling of reservoir flood control capacity, peak shaving effect, and water storage capacity, improving the accuracy and efficiency of flood control. This method can be used not only for flood control scheduling of single reservoirs but also extended to the joint scheduling of reservoir groups, providing scientific support for watershed flood control. A system adapted to the method is provided, which enhances its practicality and facilitates its promotion.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for optimizing flood control scheduling of reservoir groups based on quadratic programming, characterized in that, The process includes the following steps: Based on the water conservancy facilities and hydrological elements within the basin, systematically sort out the spatial distribution of key nodes and their hydraulic connections, construct a multi-level, multi-node flood control scheduling topology network, and obtain the reservoir group flood control optimized scheduling topology map; A quadratic programming model for flood control optimization scheduling of the reservoir group is established based on the aforementioned reservoir group flood control optimization scheduling topology. This model includes 8 objective functions and 10 constraint conditions. The objective functions consist of 7 sub-objective functions and 1 overall objective function. The 7 sub-objective functions are: maximum peak reduction objective function, minimum excess water volume objective function, minimum flood control capacity utilization objective function, minimum discharge flow fluctuation objective function, final flood control water level objective function, reservoir water level-capacity relationship constraint penalty function, and reservoir water level-discharge relationship constraint penalty function. The maximum peak reduction objective function, the minimum excess water volume objective function, the minimum flood control capacity utilization objective function, the minimum discharge flow fluctuation objective function, the final flood control water level objective function, the reservoir water level-capacity relationship constraint penalty function, and the reservoir water level-discharge relationship constraint penalty function are shown in the following equations: in, To maximize peak reduction, T represents the number of time periods. Let t be the flow rate at the downstream node section of reservoir r during time period t. For excess water, The difference between the maximum safe discharge flow at the downstream control section and the maximum safe discharge flow. In order to utilize flood control reservoir capacity, Let r be the water storage capacity of reservoir during time period t. To account for fluctuations in the outflow, Let be the flow rate at the downstream node section of reservoir r during time period t-1. To regulate the water level at the end of the flood season, Let r be the water level of reservoir r during time period t. The target water level for reservoir r at the end of the flood control period. The relationship between reservoir water level and storage capacity is a constraint and penalty. Let r be the maximum water storage capacity of the (n-1)th sub-reservoir of reservoir r. Let be the water storage capacity of the (n-1)th sub-reservoir of reservoir r during time period t. Let be the water storage capacity of the nth sub-reservoir of reservoir r during time period t. Constraints and penalties related to reservoir water level and discharge relationship. Let m be the maximum flow rate at section m-1 downstream of reservoir r. Let m-1 be the flow rate at section m-1 downstream of reservoir r during time period t. Let m be the flow rate at section m downstream of reservoir r during time period t; the overall objective function is shown in the following equation: in, To maximize the objective function value, To maximize peak reduction, For excess water, In order to utilize flood control reservoir capacity, To account for fluctuations in the outflow, To regulate the water level at the end of the flood season, The relationship between reservoir water level and storage capacity is a constraint and penalty. Constraints and penalties related to reservoir water level and discharge relationship. 、 、 、 and They are respectively 、 、 、 and Normalized weights, and To constrain the penalty coefficient, the quadratic programming model for flood control scheduling of the reservoir group is optimized and solved using the MINOS library of GAMS and the reduced gradient method and quasi-Newton method.

2. The reservoir group flood control optimization scheduling method based on quadratic programming according to claim 1, characterized in that: The 10 constraints are: reservoir water balance equation, water level-storage capacity relationship constraint, water level-discharge relationship constraint, reservoir discharge capacity constraint, reservoir water level constraint, sub-reservoir storage capacity constraint, sub-reservoir discharge capacity constraint, river channel water balance equation, river channel storage equation, and nodal water balance equation.

3. The reservoir group flood control optimization scheduling method based on quadratic programming according to claim 2, characterized in that, The reservoir water balance equation, the water level-storage capacity relationship constraint, the water level-discharge relationship constraint, the reservoir discharge capacity constraint, the reservoir water level constraint, the sub-reservoir storage capacity constraint, the sub-reservoir discharge capacity constraint, the river channel water balance equation, the river channel storage equation, and the nodal water balance equation are shown in the following equations: in, 、 and Let these represent the water storage capacity of reservoir r at time t-1, the water storage capacity at time t, and the inflow during the interval, respectively. and These represent the inflow and outflow of the reservoir (r) in the upstream river section during time period (t). Let r be the water level of reservoir r during time period t. Let r be the elevation of the dam base. and Let represent the water depth and corresponding water volume of the nth sub-reservoir of reservoir r during time period t. Let r be the function relating the water depth and water volume of the nth sub-reservoir of reservoir r. Let be the water storage capacity of the nth sub-reservoir of reservoir r. Let be the discharge flow of the nth sub-reservoir of reservoir r in time period t. Let r be the function relating the water depth of the nth sub-reservoir to the outflow rate. Let r be the maximum discharge flow of reservoir r during time period t. and Let r be the highest and lowest water levels of the reservoir. Let r be the maximum water storage capacity of the nth sub-reservoir. Let m be the maximum flow rate at the downstream node section m of reservoir r. and Let be the water storage capacity of river channel s at time intervals t and t-1, respectively. and These represent the upstream inflow and downstream discharge of river channel s at time t, respectively. The propagation time in river segment C under steady flow conditions. For the proportion of river flow in river segment C, and These represent the upstream inflow and downstream outflow of node h during time period t, respectively.

4. The reservoir group flood control optimization scheduling method based on quadratic programming according to claim 1, characterized in that: Based on the Saint-Venant equation and coupled with the 10 constraints, a quadratic programming model for optimal flood control scheduling of a reservoir group is established with the scheduling objectives of maximizing peak reduction, minimizing excess water volume, minimizing the use of flood control capacity, minimizing the fluctuation of downstream flow, and minimizing the water level at the end of the flood control period.

5. A reservoir group flood control optimization scheduling system based on quadratic programming, characterized in that, The reservoir group flood control optimization scheduling system based on quadratic programming includes: a data acquisition device, a data output device, a processor, and a storage device. The storage device includes a computer-readable storage medium storing a computer program. The computer program includes program instructions, which, when executed by the processor, cause the processor to implement the reservoir group flood control optimization scheduling method based on quadratic programming as described in any one of claims 1-4.

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