Reservoir group flood control optimization scheduling method and system based on quadratic programming

Abstract

The invention 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, and the method comprises the following steps: systematically combing the spatial distribution and hydraulic connection of key nodes according to hydraulic engineering facilities and hydrological elements in a drainage basin, constructing a flood control scheduling topology network, and constructing a flood control scheduling topology network; a reservoir group flood control optimization scheduling topological graph is obtained; establishing a reservoir group flood control optimal scheduling quadratic programming model according to the reservoir group flood control optimal scheduling topological graph; and on the basis of the MINOS library of the GAMS, performing optimization solution on the reservoir group flood control optimization scheduling quadratic programming model by using an approximate gradient method and a quasi-Newton method. According to the method, propagation of the flood among the reservoir groups is coupled into the mathematical equation set, complex simulation sequence coding is avoided, modeling is easy, universality is good, the model is easy to seek an optimal solution, the flood control capacity and the peak clipping effect of the reservoir and reasonable scheduling of the water storage capacity of the reservoir can be balanced, and the flood control precision and efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of flood control optimization scheduling, and in particular to a method and system for flood control optimization scheduling of a reservoir group based on quadratic programming. Background Art

[0002] As the core infrastructure of the modern water conservancy system, reservoirs play a multifunctional and synergistic role in river basin flood control safety, water resource allocation, clean energy supply, agricultural irrigation security, and ecological and environmental protection. Reservoir-based flood control scheduling is an important non-engineering measure to reduce flood losses in areas downstream of reservoirs. By scientifically regulating the relationship between storage and discharge, it effectively alleviates downstream flood control pressure. Flood control scheduling not only includes the scheduling of a single reservoir, but also involves the joint scheduling of reservoir groups, river channels, levees, and other water conservancy projects. It is a complex decision-making process with multiple objectives and phased characteristics. It has strong flexibility and dynamic adjustment capabilities, and can be adjusted according to forecast results. It is suitable for responding to complex scenarios such as extreme weather events, flood forecasting, and optimal water resource allocation.

[0003] Reservoir flood control scheduling methods have gradually shifted from conventional scheduling to optimized scheduling. The scheduling targets have expanded from single reservoirs to cascade reservoir groups, and the scheduling objectives have evolved from single functions to multi-objective coordination. Single-objective optimized scheduling constructs a single objective function based on specific performance indicators (such as maximizing power generation benefits and optimizing shipping economics). By setting constraints, it uses mathematical programming models to solve the problem. Multi-objective optimized scheduling breaks through the limitations of a single objective and coordinates multiple dimensions such as flood control safety, power generation benefits, and ecological flow protection. It establishes a multi-objective optimization theoretical framework and achieves optimal equilibrium decisions in complex systems through the configuration of objective weights. 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 then provide support for reservoir scheduling decisions.

[0004] Current research on flood control and operation of reservoir clusters has developed a multidisciplinary research framework encompassing intelligent algorithm innovation, multi-objective coupling modeling, and dynamic risk assessment. Significant progress has been made in improving the effectiveness of coordinated flood control across reservoir clusters and optimizing basin risk management strategies. However, due to the complex nonlinear relationships among multiple objectives within a reservoir cluster, spatiotemporal conflicts, and the curse of dimensionality, further exploration is needed to develop more accurate collaborative optimization methods. Summary of the Invention

[0005] In view of the defects in the prior art, the present invention provides a method and system for optimizing flood control scheduling of a reservoir group based on quadratic programming.

[0006] To achieve the above objectives, in a first aspect, the present invention provides a method for optimizing flood control and scheduling of a reservoir group based on quadratic programming. The method comprises the following steps: systematically sorting out the spatial distribution of key nodes and their hydraulic connections based on water conservancy engineering facilities and hydrological elements within the basin, constructing a multi-level, multi-node flood control and scheduling topology network, and obtaining a reservoir group flood control and scheduling topology map; establishing a reservoir group flood control and scheduling quadratic programming model based on the reservoir group flood control and scheduling topology map; and optimizing and solving the reservoir group flood control and scheduling quadratic programming model using the reduced gradient method and quasi-Newton method based on the MINOS library of GAMS. The present invention couples the propagation of floods between reservoirs into a set of mathematical equations, avoiding complex simulation sequence coding. This method is easy to model and has good versatility. The model is easy to find optimal solutions, can balance the flood control capacity and peak shaving effect of the reservoirs with the reasonable scheduling of the reservoir water storage capacity, and improves 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 constraints.

[0008] Optionally, the objective function includes 7 sub-objective functions and 1 overall objective function.

[0009] Optionally, the seven sub-objective functions are respectively the maximum peak shaving objective function, the minimum excess water objective function, the minimum flood control storage capacity mobilization objective function, the minimum discharge flow fluctuation objective function, the flood regulation end-stage water level objective function, the reservoir water level and 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, 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 water storage capacity constraint, the sub-reservoir discharge capacity constraint, the river water balance equation, the river channel storage equation and the node water balance equation.

[0011] Optionally, the maximum peak shaving objective function, the minimum excess water volume objective function, the minimum flood control reservoir capacity mobilization objective function, the minimum downstream flow fluctuation objective function, the flood regulation end-stage water level objective function, the reservoir water level and storage capacity relationship constraint penalty function, and the reservoir water level discharge relationship constraint penalty function are sequentially shown as follows: in, is the maximum peak shaving, T is the number of time periods, is the flow rate of the node section downstream of reservoir r in time period t, Excess water volume, is the difference in the maximum safe discharge flow of the downstream control section. To use the flood control storage capacity, is the water storage capacity of reservoir r in time period t, The downstream flow fluctuation is is the flow rate of the node section downstream of reservoir r in time period t-1, To regulate the water level at the end of flood season, is the water level of reservoir r at time period t, is the target water level of reservoir r at the end of flood regulation, is the constraint penalty for the reservoir water level and storage capacity relationship, is the maximum water storage capacity of the n-1th sub-reservoir of reservoir r, is the water storage capacity of the n-1th sub-reservoir of reservoir r in time period t, is the water storage capacity of the nth sub-reservoir of reservoir r in time period t, It is the constraint penalty for the relationship between reservoir water level and discharge. is the maximum flow of the node section m-1 downstream of reservoir r, is the flow rate of the node section m-1 downstream of reservoir r in time period t, is the flow rate of node section m downstream of reservoir r in time period t.

[0012] 7. The method for optimizing flood control and dispatching of a reservoir group based on quadratic programming according to claim 6, wherein the overall objective function is as follows: in, is the maximum objective function value, is the maximum peak clipping, Excess water volume, To use the flood control storage capacity, The downstream flow fluctuation is To adjust the water level at the end of flood season, is the constraint penalty for the reservoir water level and storage capacity relationship, It is the constraint penalty for the relationship between reservoir water level and discharge, 、 、 、 and They are 、 、 、 and The normalized weight of and is the constraint penalty coefficient.

[0013] 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 water storage constraint, the sub-reservoir discharge flow constraint, the river channel water balance equation, the river channel storage equation, and the node water balance equation are sequentially shown as follows: in, 、 and They are respectively represented as the water storage capacity of reservoir r in period t-1, the water storage capacity in period t and the interval water inflow, and are the inflow and discharge of the upstream river section of reservoir r in period t, is the water level of reservoir r at time period t, is the dam bottom elevation of reservoir r, and are the water storage depth and corresponding water storage capacity of the nth sub-reservoir of reservoir r in time period t, is the relationship function between the storage depth and storage capacity of the nth sub-reservoir of reservoir r, is the water storage capacity of the nth sub-reservoir of reservoir r, is the discharge flow of the nth sub-reservoir of reservoir r in time period t, is the relationship function between the storage depth and discharge flow of the nth sub-reservoir of reservoir r, is the maximum discharge of reservoir r in period t, and are the highest and lowest water levels of reservoir r, is the maximum water storage capacity of the nth sub-reservoir of reservoir r, is the maximum flow at node section m downstream of reservoir r, and are the water storage of river channel s at time period t and t-1, and are the upstream inflow and downstream discharge of river s in time period t, is the reach propagation time of reach C under steady flow conditions, is the flow proportion factor of section C, and are the upstream inflow and downstream flow of node h in time period t respectively.

[0014] Optionally, based on the Saint-Venant equation as the basic principle and coupled with the 10 constraints, a quadratic programming model for flood control optimization scheduling of a reservoir group is established with maximum peak shaving, minimum excess water volume, minimum flood control storage capacity utilization, minimum downstream flow fluctuation and water level at the end of flood regulation as scheduling objectives.

[0015] In the second aspect, the present invention provides a reservoir group flood control optimization scheduling system based on quadratic planning, the reservoir group flood control optimization scheduling system based on quadratic planning includes: a data acquisition device, a data output device, a processor and a storage, the storage includes a computer-readable storage medium, the computer-readable storage medium stores a computer program, the computer program includes program instructions, and when the program instructions are executed by the processor, the processor implements a reservoir group flood control optimization scheduling method based on quadratic planning provided by the present invention.

[0016] The present invention has at least the following beneficial effects: 1. This method uses the Saint-Venant equation as its basic principle, couples the propagation of floods between reservoirs 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. 2. This method is based on the principle of water balance, and all constraints are linear equations, making it easy to find the optimal solution for flood control optimization scheduling of reservoir groups based on quadratic programming; 3. Through the study of multi-objective scheduling strategies, this method constructs a quadratic programming model for flood control optimization scheduling of reservoir groups, which can balance the flood control capacity, peak shaving effect and reasonable scheduling of reservoir water storage capacity, thereby improving the accuracy and efficiency of flood control. 4. A system compatible with the method is provided, which can improve the practicability of the method and facilitate the promotion of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 Schematic diagram of a flow chart of a reservoir group flood control optimization scheduling method based on quadratic programming according to an embodiment of the present invention; Figure 2 This is a flood control optimization scheduling topology diagram of reservoir group B according to an embodiment of the present invention; Figure 3 Schematic diagram of a framework of a reservoir group flood control optimization scheduling method based on quadratic programming according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] Specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the present invention. In the following description, numerous specific details are set forth to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that these specific details are not necessarily required to practice the present invention. In other instances, well-known circuits, software, or methods are not specifically described to avoid obscuring the present invention.

[0020] Throughout this specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with the embodiment or example is included in at least one embodiment of the present invention. Therefore, appearances of the phrases "in one embodiment," "in an embodiment," "an example," or "an example" in various places throughout this specification are not necessarily all referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics may be combined in any suitable combinations and / or subcombinations in one or more embodiments or examples. Furthermore, those of ordinary skill in the art will appreciate that the figures provided herein are for illustrative purposes only and are not necessarily drawn to scale.

[0021] It should be noted in advance that, in an optional embodiment, except for independent explanations, the same symbols or letters appearing in all formulas have the same meanings and values.

[0022] In an alternative embodiment, see Figure 1 The present invention provides a method for optimizing flood control and scheduling of a reservoir group based on quadratic programming, the method comprising the following steps: S1. Based on the water conservancy engineering 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.

[0023] Specifically, in this example, the construction of a reservoir cluster flood control optimization scheduling topology is a crucial foundation for optimizing a river basin's flood control system. Its core is to systematically analyze the spatial distribution of key nodes, such as reservoirs, river channels, tributary confluences, and downstream control sections, and their upstream and downstream hydraulic connections, based on the water conservancy facilities and hydrological elements within the basin. By clarifying the topological relationships between nodes and integrating them with the natural flow paths of water, a network of connections between nodes is constructed, which can intuitively reflect the flow direction and dynamic interaction processes within the basin, thereby providing a clear structured framework for flood control scheduling.

[0024] The construction of the topological map of flood control optimization scheduling of a reservoir group first requires the identification of key nodes in the basin, including reservoirs, river intersections, tributary confluences and downstream control sections. These nodes play a connecting role in flood control scheduling. They are both the gathering and distribution points of water flow and the implementation points of scheduling strategies. The hydraulic connection between nodes is described by the water balance equation and the flow propagation equation. The water balance equation is used to describe the water conservation relationship between reservoirs, nodes and rivers, while the flow propagation equation is used to simulate the propagation process of flood waves in the river. After clarifying the spatial distribution and hydraulic connection of each node, the topological network of flood control optimization scheduling of the reservoir group is constructed by graph theory. The network can intuitively reflect the transmission direction of water flow in the basin and provide a clear structured framework support for flood control scheduling. The production method and steps are as follows: 1. Based on the reservoir flood control and allocation objectives and the research questions, the river system, including the river main and tributary and generalized rivers, is mapped in a way close to the actual geographical location of the project area; 2. Determine and mark administrative sections, reservoirs, flood protection nodes and water catchments based on the river system; 3. Draw the boundaries of the watershed sub-divisions, generalizing only one section for each sub-watershed sub-division; 4. Repeatedly check and modify the generalized topological structure diagram of the hill irrigation area until it meets the requirements, and finally obtain the reservoir group flood control optimization scheduling topological network, that is, the reservoir group flood control optimization scheduling topological diagram.

[0025] For more details, see Figure 2This example uses Reservoir Group B in a river basin as an example to perform 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 multiple existing reservoir groups within Reservoir 2's catchment area, including Reservoir 3, Reservoir 4, Reservoir 5, Reservoir 6, Reservoir 7, and Reservoir 8. Reservoirs 1 and 2 are connected in parallel. Twelve key nodes are marked at key sections downstream of Reservoir 2: 1.6 km section (Section 1), Section 7 (Section 3), Community 1, Highway 1, Street 1, a village, Highway 2, Hydrological Station 2, Community 2, River Dam, Street 2, and Street 3. Three key nodes are added upstream of the confluence of two tributaries: 1 km section (Section 2), 3 km section (Section 4), and Hydrological Station 1. Upstream of Reservoir 2, six small reservoirs, including Reservoir 3, Reservoir 4, Reservoir 5, Reservoir 6, Reservoir 7 and Reservoir 8, are connected in series, forming a multi-level, multi-node reservoir group flood control optimization scheduling topology network.

[0026] S2. Establishing a reservoir group flood control optimization scheduling quadratic programming model based on the reservoir group flood control optimization scheduling topology map.

[0027] Specifically, in this embodiment, the quadratic programming model for optimal flood control scheduling of a reservoir group includes eight objective functions and ten constraints. The eight objective functions include seven sub-objective functions and one overall objective function. The seven sub-objective functions are: maximum peak shaving objective function, minimum excess water volume objective function, minimum flood control storage capacity utilization objective function, minimum downstream flow fluctuation objective function, final flood regulation water level objective function, reservoir water level and capacity relationship constraint penalty function, and reservoir water level and discharge relationship constraint penalty function. The ten constraints are: reservoir water balance equation, water level and capacity relationship constraint, water level and 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 node water balance equation. The following describes in detail the eight objective functions, ten constraints, and the specific modeling process of the quadratic programming model for optimal flood control scheduling of a reservoir group.

[0028] Maximum peak reduction target. For large floods that approach or exceed the basin flood control standards, it is often difficult for reservoirs to preserve the flood control safety of the downstream. In this case, the reservoir's scheduling strategy is to first ensure the flood control safety of the dam body, and secondly to reduce the peak flow of the downstream flood control section as much as possible to reduce the flood pressure of the downstream flood control objects. Under the premise of ensuring the flood control safety of the reservoir, by minimizing the maximum outflow of the downstream river, reservoir or node, the peak can be reduced to the greatest extent and the flood control pressure downstream can be reduced. That is, the smaller the combined flow of each reservoir flood control section and the downstream common flood control section, the better, and the shorter the duration of the high water level, the better. The maximum peak reduction objective function is shown in the following formula: in, is the maximum peak shaving, T is the number of time periods, is the flow rate at the node section downstream of reservoir r in time period t.

[0029] Minimum excess water flow objective. During flood control operations, to ensure the safety of downstream flood control targets, it is necessary to ensure that the reservoir discharge does not exceed the warning flow or a certain safe discharge flow at the downstream control section. The smaller the combined flow of the downstream flood control section of the reservoir group exceeds the safe flow, the better. The minimum excess water flow objective function is shown in the following formula: in, Excess water volume, It is the difference between the maximum safe discharge flow of the downstream control section.

[0030] Minimum flood control reservoir capacity is used. This is to reserve as much flood control reservoir capacity as possible for possible future floods. While ensuring downstream flood control safety, the reservoir's high water level should be as low as possible to reduce flood control pressure upstream of the reservoir. The minimum flood control reservoir capacity objective function is shown below: in, To use the flood control storage capacity, is the water storage capacity of reservoir r in time period t.

[0031] Minimize the downstream flow fluctuation objective. Ensure that the flood discharge equipment of the reservoir group is not frequently opened and closed, and stabilize the discharge process. The objective function for minimizing downstream flow fluctuation is as follows: in, The downstream flow fluctuation is is the flow rate of the node section downstream of reservoir r in time period t-1.

[0032] Target water level at the end of flood control operation. During the final period of flood control operation, the reservoir water level is controlled to return to the specified level. If the target water level at the end of the operation period is not required, this objective function can be flexibly canceled. The target water level at the end of flood control operation is shown as follows: in, To regulate the water level at the end of flood season, is the water level of reservoir r at time period t, is the target water level of reservoir r at the end of flood regulation.

[0033] The penalty function for the relationship between reservoir water level and storage capacity and the penalty function for the relationship between reservoir water level and discharge are shown in the following formulas: in, is the constraint penalty for the reservoir water level and capacity relationship, is the maximum water storage capacity of the n-1th sub-reservoir of reservoir r, is the water storage capacity of the n-1th sub-reservoir of reservoir r in time period t, is the water storage capacity of the nth sub-reservoir of reservoir r in time period t, It is the constraint penalty for the relationship between reservoir water level and discharge, is the maximum flow of the node section m-1 downstream of reservoir r, is the flow rate of the node section m-1 downstream of reservoir r in time period t, is the flow rate of node section m downstream of reservoir r in time period t.

[0034] Based on the above sub-objectives, the overall objective function of the reservoir group flood control optimization operation quadratic programming model is: in, is the maximum objective function value, 、 、 、 and They are 、 、 、 and The normalized weight of and is the constraint penalty coefficient.

[0035] The reservoir water balance equation, water level and storage capacity relationship constraint, water level and 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 node water balance equation are shown in the following order: in, and They are respectively represented as the water storage capacity of reservoir r in period t-1 and the interval water inflow in period t, is the water inflow from the upstream river section of reservoir r in period t, is the dam bottom elevation of reservoir r, is the water storage depth of the nth sub-reservoir of reservoir r in time period t, is the relationship function between the storage depth and storage capacity of the nth sub-reservoir of reservoir r, is the water storage capacity of the nth sub-reservoir of reservoir r, is the discharge flow of the nth sub-reservoir of reservoir r in time period t, is the relationship function between the storage depth and discharge flow of the nth sub-reservoir of reservoir r, is the maximum discharge of reservoir r in period t, and are the highest and lowest water levels of reservoir r, is the maximum water storage capacity of the nth sub-reservoir of reservoir r, is the maximum flow at node section m downstream of reservoir r, and are the water storage of river channel s at time period t and t-1, and are the upstream inflow and downstream discharge of river s in time period t, is the reach propagation time of reach C under steady flow conditions, is the flow proportion factor of section C, and are the upstream inflow and downstream flow of node h in time period t respectively.

[0036] Assume that the reservoir is divided into N sub-reservoirs from the top to the bottom of the dam. As shown in the first relation from top to bottom in the water level and storage capacity relationship constraint, the reservoir water level is equal to the dam bottom elevation plus the sum of the water storage depths of each sub-reservoir. The total water storage capacity of the reservoir is the sum of the water storage capacity of each layered sub-reservoir, as shown in the third relation from top to bottom in the water level and storage capacity relationship constraint. The functional relationship between the water storage depth and water storage capacity of each sub-reservoir is assumed to be a linear relationship, as shown in the second relation from top to bottom in the water level and storage capacity relationship constraint. If the water level and storage capacity relationship data of the reservoir are accurate enough, the number of sub-reservoirs divided will increase until the flood scheduling accuracy requirements are met. The water storage principle of each sub-reservoir is: first fill the lower sub-reservoir, and then fill the upper layer reservoir in turn. This can be achieved through the following water storage constraint equation: only or In order for the water storage constraint equation to hold. , then you must , meaning that in order for the upper sub-reservoir to store water, the lower sub-reservoir must first be filled. The water storage constraint equation is a nonlinear constraint equation, incorporated into the objective function as a penalty function, ultimately forming the reservoir water level and storage capacity relationship constraint penalty function. The same approach is applied to the flood discharge of each sub-reservoir. The sum of the flood discharges from all sub-reservoirs is the total flood discharge of the reservoir, ultimately forming the reservoir water level and discharge relationship constraint penalty function. It can be understood that when the constraint penalty coefficient is sufficiently large, when the overall objective function is optimized, the objective function composed of the seven sub-objective functions is the global optimal one.

[0037] The default time scale for 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 construction of the reservoir group flood control optimization scheduling topology map, the Saint-Venant equation is used as the basic principle, 10 constraints are coupled, and the scheduling objectives are maximum peak shaving, minimum excess water volume, minimum flood control storage capacity utilization, minimum downstream flow fluctuation, and final flood control water level. The specific modeling process of the reservoir group flood control optimization scheduling quadratic programming model is as follows: 1. Input of basic elements such as river basin and reservoir groups. Encode the river basin divisions, reservoirs, river flood control sections, and calculation period information and input them into the model in the form of a set.

[0038] 2. Input the upstream and downstream topological relationships of the river basin system. Encode the river channel and input it into the model as a set. Link the upstream and downstream river sections of the reservoir, and the upstream and downstream river sections of the flood control section of the river channel in sequence as a two-dimensional set.

[0039] 3. Input of characteristic parameters of natural water system connection, including river section confluence parameters, maximum flow capacity of flood control section, etc.

[0040] 4. Input of reservoir group and flood control section information, including reservoir characteristic parameters, reservoir and node section inflow, water level-storage capacity relationship, water level-gate-discharge relationship, maximum discharge capacity, etc.

[0041] S3. Based on the MINOS library of GAMS, the reduced gradient method and the quasi-Newton method are used to optimize and solve the quadratic programming model of flood control optimal scheduling of the reservoir group.

[0042] On the basis of the reservoir group flood control optimization scheduling topology network, computer modeling is performed using the modeling process described in step S2. Based on the MINOS library of GAMS, the reduced gradient method and the quasi-Newton method are used for optimization solution to conduct a single reservoir multi-objective flood control optimization scheduling analysis. Then, a reservoir 1-reservoir 2 multi-objective parallel flood control scheduling analysis and a reservoir group B multi-objective series-parallel flood control optimization scheduling analysis are conducted.

[0043] Furthermore, based on a multi-objective joint optimization strategy for reservoir operations, the authors quantitatively evaluated the impact of different weighted combinations of three scenarios—maximum peak reduction, maximum remaining storage capacity, and minimum excess water—on the model's operation performance, targeting potential risks in flood control operations. This led to the development of a comprehensive flood control risk assessment system encompassing flood control effectiveness, reservoir safety and stability, and downstream protection. This system includes five core indicators: peak flood reduction rate, water level exceedance rate, water level fluctuation amplitude, final water level deviation, and peak shifting.

[0044] Using the above-mentioned flood control risk assessment system, a comprehensive evaluation was conducted on the results of the multi-objective series-parallel flood control optimization scheduling of reservoir group B under three schemes: maximum peak reduction scheme, maximum remaining storage capacity scheme, and minimum excess water volume scheme. The evaluation results are shown in Table 1: Table 1 Comprehensive evaluation results of multi-objective series-parallel flood control optimization operation of reservoir group B The data in Table 1 shows that under the 100-year and 150-year design flood conditions, all three options meet water level control requirements and do not exceed the restricted water level. The maximum remaining storage capacity option performs best in terms of water level fluctuation amplitude and terminal water level deviation, effectively maintaining reservoir water level stability and reducing water level fluctuations. This is particularly true in the later stages of a flood, enabling better control of the terminal water level and ensuring the reservoir's water storage capacity and flood control reserves.

[0045] The Minimum Excess Flow option offers significant advantages in peak-shifting scheduling, effectively reducing excess water discharge. By optimizing reservoir flood discharge scheduling, it prevents excess water from flowing into the downstream jointly controlled river sections, mitigating downstream water level fluctuations and flood risks. The Maximum Peak Reduction option achieves the best results in reducing flood peak flows, effectively lowering peak flood flows and minimizing the impact of floods on downstream areas, particularly during peak flood periods, thereby maximizing flood relief.

[0046] Overall, under the 100-year design flood conditions, the maximum peak reduction scheme performed most effectively, particularly in reducing flood peaks and mitigating downstream impacts. Under the 50-year design flood conditions, the minimum excess flow scheme performed even better, particularly in reducing excess flow, staggering peak flow, and mitigating flood risks.

[0047] It should be noted that, in some cases, the actions described in the specification can be performed in a different order and still achieve the desired results. In this embodiment, the order of steps given is only to make the embodiment appear clearer and easier to explain, rather than to limit it.

[0048] In an alternative embodiment, see Figure 3In order to improve the practicality of the method and facilitate the promotion of the method, 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 4. The storage 4 includes a computer-readable storage medium. The computer-readable storage medium stores a computer program. The computer program includes program instructions. When the program instructions are executed by the processor 3, the processor 3 implements the contents described in steps S1 to S3.

[0049] In summary, this method takes the Saint-Venant equation as the basic principle, couples the propagation of floods between reservoir groups into a set of mathematical equations, and then constructs a quadratic programming model for flood control optimization scheduling of reservoir groups, avoiding complex simulation sequence coding, easy modeling, and the ability to flexibly add sections and reservoir nodes, with good versatility; this method takes water balance as the basic principle, and all constraints are linear equations, making it easy to find optimal solutions for flood control optimization scheduling of reservoir groups based on quadratic programming; this method, through the study of multi-objective scheduling strategies, constructs a quadratic programming model for flood control optimization scheduling of reservoir groups that can balance the flood control capacity, peak shaving effect and reasonable scheduling of reservoir water storage capacity, thereby improving the accuracy and efficiency of flood control; this method can not only be used for flood control scheduling of a single reservoir, but can also be extended to the joint scheduling of reservoir groups, providing scientific support for basin flood control; a system compatible with the method is provided, which can improve the practicality of the method and facilitate the promotion of the method.

[0050] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and description of the present invention.

Claims

1. A flood control optimization scheduling method for a reservoir group based on quadratic programming, characterized in that: The steps include: Based on the water conservancy facilities and hydrological elements within the basin, the spatial distribution of key nodes and their hydraulic connections are systematically sorted out, and a multi-level, multi-node flood control and scheduling topology network is constructed to obtain a flood control optimization scheduling topology map for the reservoir group. Establishing a reservoir group flood control optimization scheduling quadratic programming model according to the reservoir group flood control optimization scheduling topology map; Based on the MINOS library of GAMS, the reduced gradient method and quasi-Newton method are used to optimize and solve the quadratic programming model of flood control optimal operation of the reservoir group.

2. The method for optimizing flood control and scheduling of a reservoir group based on quadratic programming according to claim 1 is characterized in that: The reservoir group flood control optimization scheduling quadratic programming model includes 8 objective functions and 10 constraints.

3. The method for optimizing flood control and scheduling of a reservoir group based on quadratic programming according to claim 2 is characterized in that: The objective function includes 7 sub-objective functions and 1 overall objective function.

4. The method for optimizing flood control and scheduling of a reservoir group based on quadratic programming according to claim 3 is characterized in that: The seven sub-objective functions are respectively the maximum peak shaving objective function, the minimum excess water volume objective function, the minimum flood control storage capacity mobilization objective function, the minimum discharge flow fluctuation objective function, the water level objective function at the end of flood regulation, the reservoir water level and storage capacity relationship constraint penalty function and the reservoir water level discharge relationship constraint penalty function.

5. The method for optimizing flood control and scheduling of a reservoir group based on quadratic programming according to claim 2 is characterized in that: The 10 constraints are respectively 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 water storage capacity constraint, the sub-reservoir discharge capacity constraint, the river channel water balance equation, the river channel storage equation and the node water balance equation.

6. The method for optimizing flood control and dispatching of a reservoir group based on quadratic programming according to claim 4 is characterized in that: The maximum peak shaving objective function, the minimum excess water volume objective function, the minimum flood control storage capacity mobilization objective function, the minimum downstream flow fluctuation objective function, the flood regulation end-stage water level objective function, the reservoir water level and storage capacity relationship constraint penalty function, and the reservoir water level discharge relationship constraint penalty function are sequentially shown as follows: in, is the maximum peak shaving, T is the number of time periods, is the flow rate of the node section downstream of reservoir r in time period t, Excess water volume, is the difference in the maximum safe discharge flow of the downstream control section. To use the flood control storage capacity, is the water storage capacity of reservoir r in time period t, The downstream flow fluctuation is is the flow rate of the node section downstream of reservoir r in time period t-1, To regulate the water level at the end of flood season, is the water level of reservoir r at time period t, is the target water level of reservoir r at the end of flood regulation, is the constraint penalty for the reservoir water level and capacity relationship, is the maximum water storage capacity of the n-1th sub-reservoir of reservoir r, is the water storage capacity of the n-1th sub-reservoir of reservoir r in time period t, is the water storage capacity of the nth sub-reservoir of reservoir r in time period t, It is the constraint penalty for the relationship between reservoir water level and discharge, is the maximum flow of the node section m-1 downstream of reservoir r, is the flow rate of the node section m-1 downstream of reservoir r in time period t, is the flow rate of node section m downstream of reservoir r in time period t.

7. The method for optimizing flood control and dispatching of a reservoir group based on quadratic programming according to claim 6 is characterized in that: The overall objective function is shown below: in, is the maximum objective function value, is the maximum peak clipping, Excess water volume, To use the flood control storage capacity, The downstream flow fluctuation is To adjust the water level at the end of flood season, is the constraint penalty for the reservoir water level and storage capacity relationship, It is the constraint penalty for the relationship between reservoir water level and discharge. 、 、 、 and They are 、 、 、 and The normalized weight of and is the constraint penalty coefficient.

8. The method for optimizing flood control and dispatching of a reservoir group based on quadratic programming according to claim 5 is 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 node water balance equation are shown in the following order: in, 、 and They are respectively represented as the water storage capacity of reservoir r in period t-1, the water storage capacity in period t and the interval water inflow, and are the inflow and discharge of the upstream river section of reservoir r in period t, is the water level of reservoir r at time period t, is the dam bottom elevation of reservoir r, and are the water storage depth and corresponding water storage capacity of the nth sub-reservoir of reservoir r in time period t, is the relationship function between the storage depth and storage capacity of the nth sub-reservoir of reservoir r, is the water storage capacity of the nth sub-reservoir of reservoir r, is the discharge flow of the nth sub-reservoir of reservoir r in time period t, is the relationship function between the storage depth and discharge flow of the nth sub-reservoir of reservoir r, is the maximum discharge of reservoir r in period t, and are the highest and lowest water levels of reservoir r, is the maximum water storage capacity of the nth sub-reservoir of reservoir r, is the maximum flow at node section m downstream of reservoir r, and are the water storage of river channel s at time period t and t-1, and are the upstream inflow and downstream discharge of river s in time period t, is the reach propagation time of reach C under steady flow conditions, is the flow proportion factor of section C, and are the upstream inflow and downstream flow of node h in time period t respectively.

9. The method for optimizing flood control and dispatching of a reservoir group based on quadratic programming according to claim 2, characterized in that: Based on the Saint-Venant equation, coupled with the 10 constraints, a quadratic programming model for flood control optimization scheduling of reservoir groups is established with the maximum peak shaving, minimum excess water volume, minimum flood control storage capacity utilization, minimum downstream flow fluctuation and water level at the end of flood regulation as the scheduling objectives.

10. 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, the storage includes a computer-readable storage medium, the computer-readable storage medium stores a computer program, the computer program includes program instructions, and when the program instructions are executed by the processor, the processor implements the reservoir group flood control optimization scheduling method based on quadratic programming as described in any one of claims 1-9.

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