An Adaptive Scheduling Method for Agricultural Water Supply Systems

Abstract

The present invention provides an adaptive scheduling method for an agricultural water supply system, constructs a reservoir scheduling model for flood seasons and non-flood seasons, and adaptively schedules reservoir decisions according to different focuses in flood seasons and non-flood seasons; among them, for the reservoir scheduling in flood seasons, an optimal scheduling model is established with the minimum difference rate of benefits between the decision-making stage and the reserved stage and the minimum flood control risk rate as the optimization objectives. The weighted summation method is used to transform the beneficial flood season objective function and the flood season flood control objective function into a single-objective function to construct the optimal scheduling model, and the optimal solution of the reservoir scheduling in flood seasons is obtained by solving the reservoir scheduling model in flood seasons; for the reservoir scheduling in non-flood seasons, a reservoir scheduling model is constructed with the maximum economic benefits in the decision-making stage and the reserved stage as the objective. Based on the objective of the maximum economic benefits in the decision-making stage and the reserved stage, the corresponding non-flood season objective function is constructed, and the optimal solution of the reservoir scheduling in non-flood seasons is obtained by solving the theoretical optimal value and correcting the theoretical optimal value according to the constraint conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of agricultural water conservancy supply, and particularly relates to an adaptive scheduling method for an agricultural water supply system. Background Art

[0002] The research on reservoir optimal scheduling at home and abroad has a long history and has formed a relatively rich theoretical system, which can be mainly divided into mathematical programming and intelligent optimization.

[0003] The linear programming method has the characteristics of simple operation, high calculation efficiency, and good global convergence. Affected by the insufficient computing power in the early stage, linear programming was widely used to solve the reservoir optimal scheduling problem. In 1962, William Yeh used the linear programming method to solve the scheduling model and solved the optimal scheduling problem of a single reservoir with good results. Parikh et al. extended the application scope of reservoir linear programming by means of spatio-temporal decomposition, extending the single reservoir problem to multiple reservoirs. With the continuous development of computing power, scholars have conducted more in-depth research on reservoir scheduling models and gradually found that reservoir scheduling problems are usually non-linear. Therefore, linear programming has been ignored in non-linear reservoir scheduling problems and gradually faded out of people's vision. Later, it was re-valued due to its high efficiency advantage in the joint scheduling problem of large reservoir groups. Kang et al. used the linear programming method to achieve the efficient joint optimal scheduling of cascade reservoir groups. Non-linear programming can solve non-linear reservoir scheduling problems, and common methods include quadratic programming, successive gradient descent and other algorithms. However, since the reservoir scheduling model is usually a non-convex optimization problem, there is a situation of easily falling into local optimal solutions when using non-linear programming algorithms to solve it.

[0004] The dynamic programming (DP) algorithm can decompose complex optimization problems into sub-problems in multiple stages and then solve them step by step. This method was proposed by Bellman in the 1950s. It decomposes complex optimization problems into sub-problems in multiple stages and then solves them step by step. Since the DP algorithm has no restrictions on the objective function and constraint conditions of the scheduling model and can ensure global convergence within a certain discrete accuracy, it has been widely used in the solution of reservoir optimal scheduling problems after the development of computer technology. In 1981, Zhang Yongchuan et al. applied the dynamic programming method to optimal scheduling, formulated a scheduling diagram, and significantly improved the benefits of the Tuoxi cascade reservoir. However, due to the optimization principle of dynamic programming, when the number of reservoirs to be scheduled increases and the solution accuracy improves, the dimension of the state variables will increase, resulting in a sharp increase in the solution complexity, showing an exponential magnitude, thus presenting the phenomenon of "curse of dimensionality". To solve the "curse of dimensionality" problem, a large number of scholars have carried out extended development on DP, and a number of new improved algorithms have emerged, such as the discrete differential dynamic programming method with fast convergence and stable results, the progressive optimization algorithm applicable to multiple reservoirs with fast search speed and high accuracy, and the DPSA algorithm applicable to cascade reservoirs. At present, the planning effectiveness and improvement of the operating speed and efficiency of DP-based algorithms are still hot research topics.

[0005] The principle of intelligent algorithms is to search for the optimal solution by simulating intelligent behaviors in nature, such as evolution, swarm intelligence, immune systems, etc. With the continuous development of computer technology, the computing power has been significantly improved, and intelligent optimization algorithms applicable to complex non-linear reservoir optimal scheduling problems have also developed rapidly. The advantage of intelligent algorithms is that as the number of reservoirs participating in the operation increases, the computational complexity of intelligent algorithms only increases linearly, and the "curse of dimensionality" problem will not occur. Therefore, various new intelligent optimization algorithms have been applied to the field of reservoir optimal scheduling calculation. However, due to the generally poor global convergence of intelligent algorithms and the tendency to fall into local optimal solutions, they are rarely applied to the actual reservoir scheduling process at present. Boomgaard applied the genetic algorithm to the management of wastewater resource systems and proposed that the genetic algorithm has advantages in solving high-dimensional problems. Subsequently, domestic and foreign scholars have tried to apply the genetic algorithm to various reservoir optimal scheduling problems and made certain improvements to the genetic algorithm, improving the global convergence ability and optimization efficiency. In 1997, Storn et al. proposed the differential evolution algorithm. This method has good global convergence, strong search ability, and a simple algorithm structure that is easy to implement, and has been applied and promoted in the solution of reservoir optimal scheduling models. Regarding the spatio-temporal optimization efficiency of the algorithm, domestic and foreign scholars have improved it by adjusting the operation steps, adding other algorithms, etc. The emergence of intelligent algorithms has solved the defect of the "curse of dimensionality" of the DP algorithm. However, due to the generally poor convergence stability and the tendency to fall into local optimal solutions, it is still difficult to carry out in actual scheduling work at present.

[0006] Through the above reservoir optimal operation algorithm, the optimal reservoir operation process can be obtained under the condition of deterministic inflow. However, in the actual operation process of the reservoir, various uncertain factors brought by rainfall and runoff are often faced. The operation calculation results under the condition of deterministic inflow are difficult to be directly used to guide the actual operation of the reservoir. Moreover, due to the possible large differences between the representative annual inflow process and the actual situation, the traditional operation schemes designed according to the inflow information of different representative years are not reasonable enough, lacking consideration of current and future information, and having relatively insufficient response capabilities in the face of emergencies. At the same time, it will also result in inefficient and unreasonable utilization of water resources. Summary of the Invention

[0007] Aiming at the problem of reservoir optimal operation under uncertain inflow conditions, the present invention provides a real-time operation model for reservoirs in flood season and non-flood season, which optimizes the objective function during their respective observation periods and designs a solution algorithm according to the Karush-Kuhn-Tucker conditions, so as to realize the adaptive operation method of the agricultural water supply system.

[0008] The solution adopted by the present invention to solve its technical problems is: an adaptive operation method for an agricultural water supply system, which constructs a reservoir operation model for flood season and non-flood season, adaptively operates the reservoir decision according to different focuses in flood season and non-flood season, and the reservoir operation is divided into a decision-making stage and a reservation stage;

[0009] Among them, the decision-making stage of reservoir operation in flood season is used to determine the operation mode of the reservoir to achieve the beneficial operation goal of the reservoir. The reservation stage is used to verify whether the flood control requirements in the future can be met after the operation mode in the decision-making stage is adopted, so as to achieve the flood control goal of the reservoir operation; The reservoir operation in flood season establishes an optimal operation model with the minimum difference rate of benefits and the minimum flood control risk rate between the decision-making stage and the reservation stage as the optimization goals. The optimal operation model includes a beneficial operation objective function in flood season and a flood control objective function in flood season. The weighted summation method is used to transform the beneficial operation objective function in flood season and the flood control objective function in flood season into a single objective function to construct the optimal operation model. The optimal solution of reservoir operation in flood season is obtained by solving the reservoir operation model in flood season through three steps: iteration of the theoretical optimal solution, processing of simplified model constraints, and limitation of reservoir discharge.

[0010] The reservoir operation in non-flood season constructs a reservoir operation model with the maximum economic benefits in the decision-making stage and the reservation stage as the goal. Based on the goal of the maximum economic benefits in the decision-making stage and the reservation stage, and taking into account the influence of forecast error and rainfall, a corresponding non-flood season objective function is constructed. The optimal solution of reservoir operation in non-flood season is obtained by solving the theoretical optimal value and correcting the theoretical optimal value according to the constraint conditions.

[0011] Furthermore, the decision-making stage covers a relatively short time period, while the reserved stage covers a relatively long time period. Let the total number of time periods included in the two stages be T. Then, the time period length of the decision-making stage is set to be a Δt, and the time period length of the reserved stage is (T - 1)·Δt. The value of Δt is 12 h or 1 d.

[0012] Furthermore, the flood-season beneficial operation objective function takes the minimum ratio of the difference between the upper limit of pre-storage benefit and the actual regulation benefit as the optimization objective. The smaller its value, the greater the beneficial operation benefit. The benefit difference rate B - is calculated by the formula

[0013]

[0014] where W is the pre-storage water volume, W max is the upper limit of pre-storage water volume, m is the shape coefficient, and the larger its value, the more obvious the nonlinearity. When m > 1, the above formula is a convex function and has a minimum value;

[0015] The benefit difference rate in the decision-making stage and the benefit difference rate in the reserved stage are respectively

[0016]

[0017]

[0018] Since all the pre-storage water volume in the decision-making stage will be discharged in the reserved stage, so W2 = 0, then there is

[0019]

[0020] The flood-season flood control objective function takes the minimum flood control risk rate as the optimization objective. The calculation formulas for the risk rate R1 in the decision-making stage and the risk rate R2 in the reserved stage are

[0021] R1 = 0

[0022]

[0023] Set the weight of the beneficial operation objective to be ω, then the weight of the flood control objective is 1 - ω. Substitute R1 = 0, and obtain the objective functions of each stage respectively as:

[0024]

[0025] The comprehensive objective function combining the flood-season beneficial operation objective function and the flood-season flood control objective function is:

[0026]

[0027] Furthermore, the constraint conditions of the comprehensive objective function include water balance constraint

[0028]

[0029] Reservoir storage capacity constraint

[0030] 0 ≤ W1 ≤ W max

[0031] Discharge water volume constraint

[0032] Discharge water volume constraint in the decision-making stage: The incoming water in the decision-making stage is determined and controllable, so the constraint is D1 ≤ D 1,max It can always be satisfied. Considering the certain rainfall recharge in the irrigation area, the final lower limit constraint is determined as

[0033] D1 ≥ max(D 1,min -p1, 0)

[0034] In the formula, p1 is the water volume of rainfall recharge in the irrigation area during the decision-making stage

[0035] Discharge water volume constraint in the reservation stage:

[0036]

[0037] That is

[0038] δ ≥ δ min

[0039] Based on the above constraints, the dual-objective optimization model of flood control and beneficial use during the flood season of the reservoir is:

[0040] min G1(W1) + G2(δ)

[0041] s.t.

[0042]

[0043] 0 ≤ W1 ≤ W max

[0044] D1 ≥ max(D 1,min -p1, 0)

[0045] δ ≥ δ min .

[0046] Furthermore, the solution process of the dual-objective optimization model of flood control and beneficial use during the flood season is:

[0047] Substitute into to obtain

[0048]

[0049] Define as the remaining flood control capacity, denoted by RFCC, that is

[0050] W1 + δ = RFCC

[0051] RFCC is the maximum water volume that the reservoir is allowed to release during the reserved stage without considering the forecast error. When the remaining flood control capacity RFCC > 0, the reservoir stores more water during the decision-making stage to increase the beneficial utilization benefits during the decision-making stage; or stores less water during the decision-making stage to increase the error safety value δ during the reserved stage and reduce the flood control risk. Therefore, the competition relationship between the flood control and beneficial utilization objectives of the reservoir during the flood season is the allocation problem of the remaining flood control capacity RFCC between the pre-stored water volume W1 and the error safety value δ.

[0052] For the non-linear programming, the Karush-Kuhn-Tucker conditions are used to explain and analyze the optimal solution of the model. The KKT conditions are as follows:

[0053]

[0054] In the formula, and δ * are the optimal pre-stored water volume and the optimal error safety value respectively. and G′2(δ * ) are the marginal contributions of the pre-stored water volume W1 and the error safety value δ to the losses in the two stages respectively.

[0055]

[0056] In the formula, f1(W1) is the marginal benefit of water storage, representing the increased water storage benefit caused by the unit pre-stored water volume W1. Among them, G1(W1) is a convex function, and it can be obtained that f1(W1) is a decreasing function of W1, with the economic characteristic of diminishing marginal benefit. f2(δ) also has the economic characteristic of diminishing marginal benefit.

[0057] From the three formulas of the KKT conditions, the marginal benefit of water storage and the marginal flood control benefit f2(δ * ) at the optimal solution satisfy the relationship

[0058]

[0059] Some of the equality terms in the KKT conditions are as follows

[0060]

[0061] -μ δl (δ * -δ min ) = 0

[0062]

[0063] When the constraint conditions of the model are all satisfied and not at the boundary values, it can be known that the term in the brackets is not equal to 0, so there must be a Lagrange multiplier μ dl = μ δl = μ wl = μ wu = 0. The condition for the optimal model can be obtained as the marginal benefit of water storage being equal to the marginal flood control benefit f2(δ * ), that is

[0064]

[0065] Substitute into f2(δ * ), and we get Put in the same coordinate system. The transformed curve has undergone symmetry and translation transformations compared to the original graph. If there is an intersection point within the domain of (0, RFCC) for the two curves, then there exists a theoretical optimal solution. The distance from this intersection point to the line x = 0 is equal to and the distance from the line x = RFCC is equal to δ * ,

[0066] The scheduling model can be simplified to

[0067] min G1(W1)+G2(δ)

[0068] s.t.

[0069]

[0070] 0 ≤ W1 ≤ W max

[0071] δ ≥ δ min

[0072] Then becomes

[0073]

[0074] From the above formula, the theoretical optimal pre-storage water volume and the error safety value δ * are obtained. After being restricted by the constraint conditions of the simplified model, the optimal solution can be obtained. Then, considering the minimum downstream discharge constraint in the decision-making stage, the actual optimal pre-storage water volume The error safety value δ * and the downstream discharge are used as the decision for reservoir scheduling

[0075] The Newton iteration method with a relatively fast convergence rate is used to solve the theoretical optimal pre-storage water volume satisfying the equality of marginal benefits and the error safety value δ *, the specific process includes:

[0076] ① Determine whether the incoming water exceeds the limit

[0077] Based on the magnitude of the predicted incoming water in the second stage, judge whether when the reservoir does not pre-store water, discharging all the predicted incoming water can not exceed the limit of the maximum discharge: if not (i.e., RFCC ≤ δ min ), then no pre-storage is carried out in the reservoir decision-making stage, and let Calculate the error safety value δ * and the discharge Output the result; if it can (i.e., RFCC > δ min ), then go to step ②;

[0078] ② Set the initial value

[0079] Let the error safety value take the minimum error safety value, i.e., (δ0) = δ min , according to the competition relationship, the pre-stored water volume (W1)0 = RFCC - (δ)0;

[0080] ③ Judge whether the iteration ends

[0081] Calculate the difference between the current marginal benefit of water storage f1[(W1) j and the marginal benefit of flood control f2[(δ) j . If the difference is less than the initial threshold ε, the iteration ends, and the current variable value is the optimal solution, δ * = (δ) j ; otherwise, go to step ④;

[0082] ④ Correct the search step size

[0083] Judge whether j is equal to 0. If j ≠ 0, then calculate the product of the marginal differences of two iterations {[f1[W1) j - f2[δ) j} × {[f1[W1) j-1 - f2[(δ) j-1 . If its value is greater than 0, it means the search direction is correct, and the search step size is retained, Δδ = Δδ; otherwise, the optimal solution is between (δ) j and (δ) j-1 , and the search step size needs to be shortened. Let Δδ = Δδ / h (h is the step size adjustment coefficient, and h > 1), and then go to step ⑤;

[0084] ⑤ Determine the iteration direction

[0085] The marginal benefit functions of water conservation and flood control both have the property of monotonically decreasing, decreasing with the increase of the independent variable. When the marginal benefit of water storage f1[(W1) jGreater than the flood control marginal benefit f2[(δ)] j When it is, the error safety value δ is decreased, and the pre-stored water volume W1 increases accordingly, that is, (δ) j =(δ) j-1 -Δδ, (W1) j =RFCC-(δ) j , then the storage marginal benefit f1[(W1)] j decreases, and the flood control marginal benefit f2[(δ)] j increases, and the gap between the storage and flood control marginal benefits narrows; when the storage marginal benefit f1[(W1)] j is less than the flood control marginal benefit f2[(δ)] j , the error safety value δ is increased, and the pre-stored water volume W1 decreases accordingly, that is, (δ) j =(δ) j-1 +Δδ, (W1) j =RFCC-(δ) j , then the storage marginal benefit f1[(W1)] j increases, and the flood control marginal benefit f2[(δ)] j decreases, and the gap between the storage and flood control marginal benefits will still narrow. After determining the iteration direction, enter step ③ again to complete the loop,

[0086] When the difference between the storage marginal benefit f1[(W1)] j and the flood control marginal benefit f2[(δ)] j is less than the threshold ε, the Newton iteration method ends, and the theoretical optimal pre-stored water volume and the error safety value δ * are output, and then it is judged and δ * whether they meet the constraint conditions of the model,

[0087] Calculate the downstream discharge volume at the decision-making stage according to the water volume balance equation at the decision-making stage Judge whether it meets the constraint conditions. If it meets, the pre-stored water volume the error safety value δ * and the downstream discharge volume at the decision-making stage are the optimal solutions; if not, let take the boundary value, and adjust the pre-stored water volume the error safety value δ * value, and output the optimal solution.

[0088] Furthermore, the non-flood season reservoir operation model includes the objective function

[0089] max E[B1(x1 + p1)] + E[B2(x2 + p2)]

[0090] Wherein, x1 and x2 are the water supply volumes in the decision-making stage and the reserved stage respectively, p1 and p2 are the water volumes replenished by rainfall in the irrigation area in the decision-making stage and the reserved stage respectively, E[B1(·)] and E[B2(·)] are the mathematical expectations of the economic benefits in the decision-making stage and the reserved stage respectively.

[0091] Optimize the objective function based on the constraint conditions to obtain the optimized non-flood-season reservoir operation model.

[0092] max E[B1(x1 + p1)] + E[B2(x2 + p2)]

[0093] s.t.

[0094]

[0095] x1 ≥ max(x 1,min - p1, 0)

[0096] x2 ≥ max(x 2,min - p2, 0)

[0097] W1 ≤ W max

[0098] W1 ≥ 0

[0099] l1, l2 ≥ 0.

[0100] Furthermore, the constraint conditions include water volume balance constraint, water supply volume constraint, reservoir storage capacity constraint and non-negativity constraint;

[0101] Among them, the water volume balance constraint

[0102]

[0103] Wherein, W0 is the initial reservoir storage capacity, W1 is the end reservoir storage capacity in the decision-making stage, W2 is the end reservoir storage capacity in the reserved stage, and are the predicted incoming water volumes in the decision-making stage and the reserved stage respectively, ε1 and ε2 are the runoff prediction errors in the decision-making stage and the reserved stage respectively, and l1 and l2 are the water volumes discharged as waste in the decision-making stage and the reserved stage respectively;

[0104] Water supply volume constraint: The water supply volume of the reservoir should be greater than the gap existing after the rainfall replenishment in the irrigation area.

[0105] x1 ≥ max(x 1,min - p1, 0)

[0106] x2 ≥ max(x 2,min - p2, 0)

[0107] Wherein, x 1，min and x 2，minThey are the minimum water supply volumes for the decision-making stage and the reservation stage respectively.

[0108] Reservoir storage capacity constraint

[0109] 0 ≤ W1 ≤ W max

[0110] In the formula, W max is the beneficial storage capacity of the reservoir.

[0111] Non-negativity constraint

[0112] l1, l2 ≥ 0.

[0113] Furthermore, the solution method for the objective function of the reservoir operation model during the non-flood season includes the first step of solving the theoretical optimal value and the second step of correcting the theoretical optimal value according to the constraint conditions.

[0114] S1. Set the initial values

[0115] Let the initial water supply volumes in the decision-making stage and the reservation stage be equal to the predicted inflow, that is At this time, the water abandonment volumes l1 = 0, l2 = 0;

[0116] S2. Judge whether the iteration ends

[0117] Calculate the difference between the marginal benefit g1[(x1) i in the current decision-making stage and the marginal benefit g2[(x2) i in the reservation stage. If the difference is less than the initial threshold ε, the iteration ends, and the current variable values are the optimal solutions. Otherwise, go to step S3;

[0118] S3. Correct the search step size

[0119] Judge whether i is equal to 0. If i ≠ 0, then calculate the product of the marginal differences between two iterations {g1[(x1) i - g2[(x2) i} × {g1[(x1) i-1 - g2[(x2) i-1}. If its value is greater than 0, it means that the search direction is correct, and the search step size is retained, Δx i = Δx i-1 ; Otherwise, the optimal value range of the water supply volume in the decision-making stage is between (x1) i and (x1) i-1 , and it is necessary to shorten the search step size. Let Δx i = Δx i-1 / h; h is the step size adjustment coefficient, and h > 1, then go to step S4;

[0120] S4. Determine the iteration direction

[0121] The marginal benefit functions in the decision-making and reservation stages both have the property of monotonically decreasing, decreasing as the independent variable increases. When the marginal benefit g1[(x1) i in the decision-making stage is greater than the marginal benefit g2[(x2) i in the reservation stage, increasing the water supply volume x1 in the decision-making stage will cause the water supply volume x2 in the reservation stage to decrease, that is, (x1) i =(x1) i-1 +Δx, This step reduces g1[(x1) i and increases g2[(x2) i , narrowing the gap between the marginal benefits in the decision-making and reservation stages; when the marginal benefit g1[(x1) i in the decision-making stage is less than the marginal benefit g2[(x2) i in the reservation stage, decreasing the water supply volume x1 in the decision-making stage will cause the water supply volume x2 in the reservation stage to increase, that is, (x1) i =(x1) i-1 -△x, This step increases g1[(x1) i and decreases g2[(x2) i , and the gap between the marginal benefits in the two stages will still narrow. After determining the iteration direction, enter step S2 again to complete the loop;

[0122] Iteratively obtain the theoretical optimal value After that, judge whether its value meets the constraint conditions. The values that meet the constraint conditions are retained, and the boundary values are taken for those that do not. After two-step screening calculations, the optimal solution can finally be obtained

[0123] Advantages of the present invention: The present invention provides an adaptive scheduling method for an agricultural water supply system. This method constructs an adaptive scheduling model for an agricultural water supply system combined with a forecasting module, which includes two reservoir scheduling models, respectively applied to the flood season and the non-flood season. By combining real-time forecasting results with historical data to predict and simulate future situations, and quantifying the forecasting errors through methods such as normal distribution, Taylor formula, and mathematical expectation, it realizes reasonable planning of reservoir storage volume on the premise of ensuring flood control objectives during the flood season, improves the beneficial utilization benefits, and reasonably plans the regulation process based on the benefit curve during the non-flood season to improve the water supply benefits. The model constructed by the present invention includes a risk hedging strategy inside. When using the KKT conditions to derive the optimal solution equations, the marginal benefit values of the objective functions in the decision-making stage and the reservation stage are made equal, thereby reducing the overall risk. Through the above means, not only the adaptive ability of the reservoir in the face of extreme situations is realized, but also the regulation method of the reservoir becomes more scientific and reasonable.

[0124] The scheduling module can select different scheduling models according to the flood season division, with flood prevention emphasized during the flood season and water conservancy development emphasized during the non-flood season. The model can also adaptively adjust reservoir scheduling decisions based on the incoming water process within the forecast period. In the actual application process, different combinations of scheduling models can be adopted according to actual needs. When there is no flood threat in a place, the non-flood season model can be used alone for real-time scheduling. Description of the Drawings

[0125] Figure 1 It is a schematic diagram of the two-stage real-time rolling scheduling process.

[0126] Figure 2 It is a corresponding diagram of variable symbols in the present invention.

[0127] Figure 3 It is a schematic diagram of the solution process of the flood season scheduling model.

[0128] Figure 4 It is a schematic diagram of the solution process of the Newton iteration method.

[0129] Figure 5 It is a schematic diagram of the solution process of the non-flood season scheduling model. Detailed Implementation Modes

[0130] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be described in detail below.

[0131] Example 1: Since the incoming water process of the representative year may vary greatly from the actual situation, the traditional scheduling plan designed based on the incoming water information of different representative years is not reasonable enough, lacking consideration of current and future information and having relatively insufficient response capabilities in the face of emergencies. At the same time, it will also result in inefficient and unreasonable utilization of water resources. To address the above problems, the present invention constructs an adaptive scheduling model for the agricultural water supply system combined with a forecasting module, which includes two reservoir scheduling models, respectively applied to the flood season and the non-flood season. By combining real-time forecasting results with historical data to predict and simulate future situations, and quantifying the forecasting errors through methods such as normal distribution, Taylor formula, and mathematical expectation, it attempts to reasonably plan the reservoir storage volume on the premise of ensuring flood control objectives during the flood season, improve water conservancy development benefits, and reasonably plan the regulation process based on the benefit curve during the non-flood season to improve water supply benefits. The model internally includes a risk hedging strategy. When using the KKT conditions to derive the optimal solution equations, the marginal benefit values of the objective functions in the first stage and the second stage are made equal, thereby reducing the overall risk. Through the above means, not only is the adaptive ability of the reservoir in the face of extreme situations realized, but also the regulation method of the reservoir becomes more scientific and reasonable.

[0132] The scheduling module can select different scheduling models according to the flood season division, with flood control emphasized during the flood season and water conservancy development emphasized during the non-flood season. The model can also adaptively adjust the reservoir scheduling decision according to the incoming water process within the forecast period. In the actual application process, different combinations of scheduling models can be adopted according to actual needs. When there is no flood threat in a place, the non-flood season model can be used alone for real-time scheduling.

[0133] For a reservoir, generally speaking, the more water stored, the greater the water conservancy development benefit. However, during the flood season, it is generally impossible to determine whether floods will occur in the future. If a large amount of water is stored, it will increase the potential flood control risk, while maintaining less water storage will result in damage to the water conservancy development benefit. Therefore, there is a competitive relationship between the two goals of water conservancy development and flood control. The scheduling method for the reservoir during the flood season can be attributed to the coordinated control problem of the two goals of flood control and water conservancy development. To address this problem, the present invention constructs a two-stage reservoir scheduling model for the flood season considering the two goals of flood control and water conservancy development. According to the forecast information, it simulates the water storage and discharge scheduling method of the reservoir in the future time period, hoping to maximize the water conservancy development benefit of the reservoir through water level control on the premise of meeting future flood control requirements and achieve the adaptive regulation of the reservoir.

[0134] The present invention divides the reservoir scheduling process into two stages, as Figure 1 shown. The first stage is defined as the decision-making stage, which is used to determine the scheduling method of the reservoir, while the second stage is defined as the reservation stage, which is used to verify whether the future flood control requirements can be met after scheduling according to the decision-making method of the first stage. Since the uncertainty increases with the increase of the observation period, generally, the time covered by the decision-making stage is set to be relatively short, while the time covered by the reservation stage is relatively long. If the total number of time periods included in the two stages is T, the time period length included in the decision-making stage is set to be a Δt, and the time period length included in the reservation stage is (T - 1)·Δt. The value of Δt is 12h or 1d. The purpose of dividing the scheduling process into two stages is to explore what scheduling method can maximize the water conservancy development benefit of the first stage and ensure that the flood control requirements of the second stage are met under the existing forecast information and risk conditions. According to such rules, the model seeks the optimal scheduling method D t for the future decision-making stage according to the forecast information in the next two stages and moves along the time axis in steps of Δt to simulate the real-time scheduling process within one year.

[0135] As Figure 2 shown, the following is the corresponding information of the relevant key variables and corresponding symbols of the present invention.

[0136] Ideally, a portion of water is allowed to be pre-stored in the reservoir during the first phase. However, this pre-stored water must be safely released during the second phase without increasing flood control risks downstream. This means that the water level must be lowered to the flood control limit by the end of each phase to ensure the safety of downstream protected areas and the reservoir itself. However, due to forecast errors, while ensuring downstream safety, the water level may not fall back to the flood control limit before a flood arrives. In this case, if a design flood or verification flood occurs, the flood control safety of the reservoir or upstream and downstream planning and design cannot be guaranteed. Therefore, a quantitative analysis of these errors is necessary.

[0137] Because forecast uncertainty decreases with a shorter forecast horizon, the first-phase water inflow forecast has relatively high accuracy and small error. Therefore, the first-phase forecast can be considered a deterministic forecast with an error of zero. However, the second-phase water inflow forecast spans a relatively long timeframe, and its error is considered non-negligible. This paper uses a normal distribution to fit the second-phase forecast error, assuming that the error satisfies a normal distribution with a mean of μ² and a standard deviation of σ², to facilitate the quantification of risk below.

[0138] In the two-stage flood season scheduling model constructed by the present invention, there is no flood control risk in the first stage, but the forecast error in the second stage will bring certain flood control risks. The reservoir water level can be controlled, so the forecast error can be transferred entirely to the downstream flow. Under normal circumstances, the water level at the end of the control stage is maintained at the lower limit of the flood limit water level. When the forecast is too large, the actual amount of water discharged from the reservoir will be smaller than the calculated amount of water discharged, and the flood control risk of the downstream protection objects will be reduced; and when the forecast is too small, the actual amount of water discharged will be larger than the calculated amount of water discharged, which will increase the flood control risk of the downstream protection objects.

[0139] In order to quantify the flood control risk during the flood season, the flood control risk rate is defined as the probability that the actual discharge volume exceeds the maximum discharge volume. The flood control risk rate R i for

[0140] R i =P(D i >D i,max ) (1)

[0141] (1) Downstream flood control risk rate in the first phase

[0142] Since the first period is considered as a deterministic forecast, as long as the discharge volume does not exceed the limit, the planning and design requirements can be met, and there is no flood control risk caused by errors.

[0143] ε1=0,R1=P(D1>D 1,max )=0 (2)

[0144] Where D 1,maxis the maximum discharge of the reservoir in the first stage.

[0145] (2) Downstream flood control risk rate in the second stage

[0146] The forecast error in the second stage cannot be ignored. From the water balance equation, we can obtain

[0147]

[0148] Since the uncertainty of the forecasted incoming water increases with the increase of the forecast period, for the sake of safety, the water level at the end of the stage is maintained at the flood limit water level V d , so there is

[0149] V2 = V d (4)

[0150] It should be noted that the actual operation process is a process of rolling forward forecasting and decision-making hour by hour. The decision-making results of the first stage starting from that hour will be adopted in each hour, and a new round of simulation will be started in the next hour. Therefore, the simulation operation results of the second stage may not necessarily be used for the hours covered by this stage, and this stage is reserved for assisting flood control calculation.

[0151] Since the pre-stored water volume of the reservoir in the first stage will be fully discharged in the second stage, so there is

[0152] W1 = V1 - V d (5)

[0153] The uncertainty of the discharge D2 of the reservoir in the second stage is caused by the forecast error of the incoming water of the reservoir. From equations (3), (4) and (5), we can obtain

[0154]

[0155] Downstream flood control risk rate in the second stage

[0156]

[0157] By replacing D2 with ε2, we can obtain the calculation formula for the downstream flood control risk rate with the forecast error as the independent variable

[0158]

[0159] In the formula, h(D2) and h(ε2) are the probability density functions of the reservoir discharge D2 and the incoming water forecast error ε2 respectively. The replacement of the independent variable is conducive to further calculating the flood control risk rate.

[0160] (3) Error safety value

[0161] Define the difference between the maximum discharge of the reservoir in the second stage and the expected discharge as the error safety value, denoted by δ, then there is

[0162]

[0163] The error safety value δ is the safety margin reserved for the forecast uncertainty and is the safety index for flood prevention and control. The larger this value is, the greater the forecast error that the downstream can tolerate.

[0164] Substitute δ into the formula (8) Then the calculation formula for the downstream flood control risk rate in the second stage can be transformed into

[0165] R2 = P(ε2 > δ) = ∫ δ +∞ h(ε2)dε2 = H(+∞) - H(δ) = 1 - H(δ) (10)

[0166] δ = H -1 (1 - R2) = μ2 + σ2Φ -1 (1 - R2) (11)

[0167] Where H(·) is the distribution function of the error in the second stage, which satisfies the normal distribution with a mean of μ2 and a standard deviation of σ2, and H -1 (·) is the inverse function of the distribution function of the error, and Φ -1 (·) is the inverse function of the standard normal distribution function.

[0168] In this way, we obtain the relationship between the flood control risk rate and the forecast error.

[0169] (4) Quantification of additional risk of forecast error

[0170] For the scheduling process with a total flood season length of l days, a downstream flood control standard of P-year recurrence interval, and a time interval of n days, the flood control risk rate R max satisfies the calculation formula

[0171]

[0172] When R2 ≤ R max , it is considered to meet the flood control standard. That is, when R2 = R max , the error safety value reserved for the maximum error value planned can be calculated, that is, the minimum error safety value, denoted by δ min , which can quantify the flood control risk brought by the error. Substitute R2 = R max into formula (11), and we can get

[0173] δ min = H -1 (1 - R max ) = μ2 + σ2Φ -1 (1 - R max ) (13)

[0174] Through the above method, the quantification of error risk is realized, and the maximum error that the runoff forecast can withstand is obtained.

[0175] Construction of flood season reservoir operation model

[0176] An optimal operation model is established with the minimum two-stage benefit difference rate and the minimum flood control risk rate as the optimization objectives.

[0177] (1) Beneficial use objective function

[0178] When the pre-storage water volume reaches the upper limit W max the increase value of beneficial use benefit reaches the maximum. Therefore, the ratio of the difference between the upper limit of pre-storage benefit and the actual regulation benefit (abbreviated as benefit difference rate) can be minimized as the optimization objective. The smaller its value, the greater the beneficial use benefit. The calculation formula of the benefit difference rate is

[0179]

[0180] In the formula, m is the shape coefficient. The larger the value, the more obvious the nonlinearity. When m>1, the above formula is a convex function and has a minimum value.

[0181] From formula (14), the benefit difference rates of the first stage and the second stage can be obtained as

[0182]

[0183] Since all the pre-storage water volume in the first stage will be discharged in the second stage, so W2 = 0, then there is

[0184]

[0185] (2) Flood control objective function

[0186] In the flood control stage, the minimum flood control risk rate is taken as the optimization objective. According to the risk rate calculation formulas (2) and (10) derived for each stage, there is

[0187] R1 = 0 (18)

[0188] R2 = P(ε2 > δ) = ∫ δ +∞ h(ε2)dε2 (19)

[0189] (3) Total optimization objective function

[0190] The multi-objective function is transformed into a single objective by using the weighted summation method. The weight of the beneficial use objective is set as ω, then the weight of the flood control objective is 1 - ω. Substituting R1 = 0, the objective functions of each stage are obtained as:

[0191]

[0192]

[0193] As can be seen from the formula, the objective function in the first stage only varies with the pre-storage water volume W1, and the objective function in the second stage only varies with the error safety value δ, with the others being constants. In this way, the complex problem of coordinated control of flood prevention and water utilization during the flood season of the reservoir is transformed into a two-stage optimization problem of coordinated control between the water utilization objective in the first stage and the flood prevention objective in the second stage, thus reasonably simplifying the complex problem and well reflecting the superiority of two-stage optimization. The comprehensive objective function of the two stages is:

[0194]

[0195] (4) Constraint conditions

[0196] ① Water balance constraint

[0197]

[0198] ② Reservoir storage capacity constraint

[0199] 0 ≤ W1 ≤ W max (25)

[0200] ③ Discharge water volume constraint

[0201] Discharge water volume constraint in the first stage: The incoming water in the first stage is determined and controllable, so the constraint is D1 ≤ D 1，max Can always be satisfied. Considering that there is a certain rainfall recharge in the irrigation area, the final determined lower limit constraint is

[0202] D1 ≥ max(D 1，min - p1, 0) (26)

[0203] In the formula, p1 is the water volume of rainfall recharge in the irrigation area in the first stage

[0204] Discharge water volume constraint in the second stage:

[0205]

[0206] That is

[0207] δ ≥ δ min (28)

[0208] (5) Optimization model

[0209] Based on the above analysis, the two-stage optimization model for the dual objectives of water utilization and flood prevention during the flood season of the reservoir is:

[0210] min G1(W1) + G2(δ)

[0211] s.t.

[0212]

[0213] 0 ≤ W1 ≤ W max

[0214] D1 ≥ max(D 1,min -p1, 0)

[0215] δ ≥ δ min (29).

[0216] Solution of the reservoir operation model during the flood season

[0217] (1) Competitive relationship between beneficial utilization and flood control risk

[0218] Substitute into to obtain

[0219]

[0220] Define as the remaining flood control capacity, denoted by RFCC, i.e.,

[0221] W1 + δ = RFCC (3l)

[0222] RFCC can be interpreted as the maximum water volume that the reservoir is allowed to release in the second stage without considering the forecast error. When the remaining flood control capacity RFCC > 0, the reservoir can store more water in the first stage to increase the beneficial utilization in the first stage; or store less water in the first stage to increase the error safety value δ in the second stage and reduce the flood control risk. Therefore, the competitive relationship between the flood control and beneficial utilization objectives of the reservoir during the flood season is actually the distribution problem of the remaining flood control capacity RFCC between the pre-stored water volume W1 and the error safety value δ.

[0223] (2) Model solution method

[0224] For nonlinear programming problems, the Karush-Kuhn-Tucker (KKT) conditions are often used to explain and analyze the optimal solution of the model.

[0225] For an optimization model in the following form:

[0226] min f(x1,..., x n )

[0227] s.t.

[0228] g i (x1,..., x n ) ≤ 0, i = (1,..., m)

[0229] hj (x1,..., x n ) = 0, j = (1,..., l) (32)

[0230] In the formula, f(x1,..., x n ) is the objective function, g i (x1,..., x n ) is the inequality constraint, h i (x1,..., x n ) is the equality constraint. The KKT conditions for this formula are:

[0231]

[0232] In the formula, μ i is the Lagrange multiplier of the equality constraint, and λ j is the Lagrange multiplier of the inequality constraint. Generally speaking, the KKT conditions can only be used as the necessary conditions for the optimal solution of a non - linear programming problem. Only when the objective function is a convex function and the equality constraint is an affine function, the KKT conditions are the sufficient and necessary conditions for the optimal solution of the model.

[0233] The non - flood - season scheduling model constructed in the present invention belongs to a non - linear convex programming problem. Therefore, the KKT conditions are the sufficient and necessary conditions for the optimal solution. Its KKT conditions are:

[0234]

[0235] In the formula, and δ * are the optimal pre - storage water volume and the optimal error safety value respectively, and G′2(δ * ) are the marginal contributions of the pre - storage water volume W1 and the error safety value δ to the two - stage losses respectively.

[0236]

[0237] In the formula, f1(W1) is the marginal benefit of water storage, representing the increase in water storage benefit caused by a unit of pre - storage water volume W1. Since G1(W1) is a convex function, it can be obtained that f1(W1) is a decreasing function of W1, having the economic characteristic of diminishing marginal benefit. Similarly, f2(δ) also has the economic characteristic of diminishing marginal benefit.

[0238] From the three formulas of the KKT conditions, the relationship between the marginal benefit of water storage and the marginal flood - control benefit f2(δ * ) at the optimal solution is

[0239]

[0240] Some of the equality terms in the KKT conditions derived in Equation (34) are as follows

[0241]

[0242] -μ δl (δ * -δ min ) = 0

[0243]

[0244] When the constraint conditions of the model are all satisfied and not at the boundary values, it can be known that the term in the parentheses is not equal to 0, so there must be a Lagrange multiplier μ dl = μ δl = μ wl = μ wu = 0. The condition for the optimal model can be obtained as the marginal benefit of water storage equal to the marginal flood control benefit f2(δ * ), that is

[0245]

[0246] Substitute into f2(δ * ), and get Put in the same coordinate system. The transformed curve has undergone symmetry and translation transformations compared to the original graph. If there is an intersection point within the domain of (0, RFCC) for the two curves, there is a theoretical optimal solution. The distance from this intersection point to the line x = 0 is equal to and the distance from the line x = RFCC is equal to δ * .

[0247] (3) Model simplification

[0248] The first-stage discharge D1 has no direct relationship with the objective function and only affects the value of the pre-stored water volume. Therefore, the constraint condition of the minimum first-stage discharge can be temporarily not considered, and the constraint can be carried out after obtaining the theoretical optimal solution. Therefore, the scheduling model can be simplified to

[0249] min G1(W1)+G2(δ)

[0250] s.t.

[0251]

[0252] 0 ≤ W1 ≤ W max

[0253] δ ≥ δ min (40)

[0254] Then becomes

[0255]

[0256] The theoretical optimal pre-storage water volume is obtained from the above formula and the error safety value δ * After that, through the constraint conditions of the simplified model, the optimal solution can be obtained. Then, considering the minimum downstream discharge constraint in the first stage, the actual optimal pre-storage water volume can be finally obtained Error safety value δ * and the downstream discharge are used as the decision-making for reservoir operation

[0257] (4) Design of model solution algorithm

[0258] The solution algorithm mainly includes three steps: iteration of the theoretical optimal solution, processing of the constraint conditions of the simplified model, and limitation of the reservoir downstream discharge. The solution process is as Figure 3 shown

[0259] Among them, the most critical step is the iteration of the theoretical optimal solution. The present invention uses the Newton iteration method with a relatively fast convergence rate to solve the theoretical optimal pre-storage water volume satisfying the equality of marginal benefits and the error safety value δ * . The solution process of the Newton iteration method is as Figure 4 shown, and its specific process is as follows

[0260] ① Determine whether the incoming water exceeds the limit. According to the magnitude of the predicted incoming water in the second stage, judge whether when the reservoir does not pre-store water volume, discharging all the predicted incoming water can not exceed the limit of the maximum downstream discharge: if not (i.e., RFCC ≤ δ min ), then the reservoir does not pre-store water in the first stage, and let Calculate the error safety value δ * and the downstream discharge Output the result; if it can (i.e., RFCC > δ min ), then go to step ②

[0261] ② Set the initial value. Let the error safety value take the minimum error safety value, i.e., (δ0) = δ min , and according to the competition relationship, the pre-storage water volume (W1)0 = RFCC - (δ)0

[0262] ③ Judge whether the iteration ends. Calculate the difference between the current marginal benefit of water storage f1[(W1) j and the marginal benefit of flood control f2[(δ) j . If the difference is less than the initial threshold ε, the iteration ends, and the current variable value is the optimal solution δ * = (δ) j ; otherwise, go to step ④

[0263] ④ Modify the search step size. Determine whether j is equal to 0. If j ≠ 0, then calculate the product of the marginal differences between two iterations {[f1[(W1) j -f2[(δ) j}×{[f1[(W1) j-1 -f2[(δ) j-1}. If its value is greater than 0, it means the search direction is correct, and the search step size is retained, Δδ = Δδ; otherwise, the optimal solution is between (δ) j and (δ) j-1 , and the search step size needs to be shortened. Let Δδ = Δδ / h (h is the step size adjustment coefficient, and h > 1), and then enter step ⑤.

[0264] ⑤ Determine the iteration direction. The marginal benefit functions of water conservancy and flood control both have the property of monotonically decreasing, decreasing as the independent variable increases. When the marginal benefit of water storage f1(W1) j is greater than the marginal benefit of flood control f2[(δ) j , reduce the error safety value δ, and the pre-stored water volume W1 increases accordingly, that is, (δ) j =(δ) j-1 -Δδ, (W1) j =RFCC-(δ) j , then the marginal benefit of water storage f1[(W1) j decreases, and the marginal benefit of flood control f2[(δ) j increases, and the gap between the marginal benefits of water storage and flood control narrows; when the marginal benefit of water storage f1[(W1) j is less than the marginal benefit of flood control f2[(δ) j , increase the error safety value δ, and the pre-stored water volume W1 decreases accordingly, that is, (δ) j =(δ) j-1 +Δδ, (W1) j =RFCC-(δ) j , then the marginal benefit of water storage f1[(W1) j increases, and the marginal benefit of flood control f2[(δ) j decreases, and the gap between the marginal benefits of water storage and flood control still narrows. After determining the iteration direction, enter step ③ again to complete the loop.

[0265] When the difference between the marginal benefit of water storage f1[(W1) j and the marginal benefit of flood control f2[(δ) j is less than the threshold ε, the Newton iteration method ends, and the theoretical optimal pre-stored water volume and the error safety value δ * are output. Then it is necessary to judge and δ *Whether the constraints of the model are satisfied. If so, then and δ * are the optimal solutions. If not, then take the corresponding boundary values as the optimal solutions.

[0266] Finally, calculate the downstream discharge in the first stage according to the water balance equation of the first stage Judge whether it satisfies the constraint conditions. If so, then the pre-stored water volume error safety value δ * and the downstream discharge in the first stage are the optimal solutions; if not, then let take the boundary value and adjust the pre-stored water volume according to the water balance equation error safety value δ * value and output the optimal solution.

[0267] A two-stage risk hedging reservoir operation model aiming at the optimal economic benefit: During the non-flood season, the incoming water process is relatively gentle and the flood control pressure is small. Therefore, the main goal of the operation task becomes to make full use of the incoming water and the reservoir water volume to improve the beneficial use efficiency. For this purpose, the present invention constructs a two-stage reservoir operation model aiming at the maximum economic benefit, taking into account the incoming water situation and the reservoir storage capacity in two stages, finding the most suitable way of distributing the incoming water according to the water supply benefit curve, and formulating the water supply strategy with the highest benefit.

[0268] For water users, the more water is supplied, the greater the benefit brought, but the water supply benefit generally does not increase linearly. Usually, as the water supply volume increases, the increase in benefit will gradually decrease, and due to the different incoming water volumes every day, if the incoming water is more on a certain day and all is supplied to water users, the increase in water supply benefit may not be obvious, resulting in a certain waste of resources. Based on this phenomenon, the present invention constructs a two-stage reservoir operation model, which uses the regulating function of the reservoir, combines the forecast information with the water supply benefit curve, makes the water supply more balanced, so as to achieve the maximum sum of benefits in the next two stages.

[0269] The model makes local optimal decisions based on the forecast results. Suppose it is forecast that the incoming water is more in the first stage and less in the second stage, then the reservoir can store a part of the water volume for use in the second stage, so that the sum of the benefits in the two stages reaches the maximum; if it is forecast that the incoming water is more in the second stage and less in the first stage, then the reservoir storage water volume can be used more in the first stage, and the surplus water volume in the second stage can be used to supplement this part of the deficit water volume, while meeting the water use in this stage, so that the sum of the benefits in the two stages reaches the maximum. Based on this principle, the model rolls along the time axis, continuously updates the decision according to the forecast results, and gives the operation plan that meets the requirements.

[0270] Construction of the non-flood season reservoir operation model

[0271] (1) Objective function

[0272] To achieve the goal of maximizing the two - stage economic benefits and taking into account the influence of forecast error and rainfall simultaneously, the objective function is constructed as follows

[0273] max E[B1(x1 + p1)]+E[B2(x2 + p2)] (42)

[0274] Where x1 and x2 are the water supply volumes in the first stage and the second stage respectively, p1 and p2 are the water volumes of rainfall recharge in the irrigation area in the first stage and the second stage respectively, and E[B1(·)] and E[B2(·)] are the mathematical expectations of the economic benefits in the first stage and the second stage respectively.

[0275] (2) Constraints

[0276] ① Water volume balance constraint

[0277]

[0278] Where W0 is the initial reservoir storage, W1 is the end - of - period reservoir storage in the first stage, W2 is the end - of - period reservoir storage in the second stage, and are the forecast inflow volumes in the first stage and the second stage respectively, ε1 and ε2 are the runoff forecast errors in the first stage and the second stage respectively, and l1 and l2 are the water abandonment volumes in the first stage and the second stage respectively.

[0279] ② Water supply volume constraint

[0280] The reservoir water supply volume should be greater than the gap existing after rainfall recharge in the irrigation area.

[0281] x1≥max(x 1，min - p1, 0)

[0282] x2≥max(x 2，min - p2, 0) (44)

[0283] Where x 1，min and x 2，min are the minimum water supply volumes in the first stage and the second stage respectively.

[0284] ③ Reservoir storage capacity constraint

[0285] 0≤W1≤W max (45)

[0286] Where W max is the useful storage capacity of the reservoir.

[0287] ④ Non - negative constraint

[0288] l1, l2≥0 (46)

[0289] (3) Optimized Model

[0290] The two - stage reservoir operation model for the non - flood season with the goal of water utilization is as follows:

[0291] max E[B1(x1 + p1)]+E[B2(x2 + p2)]

[0292] s.t.

[0293]

[0294] x1≥max(x 1,min -p1, 0)

[0295] x2≥max(x 2,min -p2, 0)

[0296] W1≤W max

[0297] W1≥0

[0298] l1, l2≥0 (47).

[0299] Solution of the non - flood season reservoir operation model

[0300] (1) Model solution method

[0301] Since the uncertainty of the forecast decreases with the reduction of the forecast period, the accuracy of the inflow forecast in the first stage is relatively high and the error is small. The prediction result of the first stage can be regarded as a deterministic forecast, considering its error equal to 0. While the time span of the inflow forecast in the second stage is relatively long, its error cannot be ignored. The forecast error in the second stage is fitted with a normal distribution, considering that the error satisfies a normal distribution with a mean of 0 and a standard deviation of σ2. Then there are:

[0302] E[ε1]=0

[0303] E[ε2]=0

[0304]

[0305] Since the reservoir storage capacity can be controlled and regarded as a definite value, the forecast error is transmitted to x1 and x2. It is considered that the uncertainty of the reservoir water supply is caused by the forecast error of the reservoir inflow. Therefore, there are:

[0306]

[0307] Consistent with the flood season model, the non - flood season model also uses the KKT conditions for derivation. The necessary and sufficient conditions for the model to be optimal are as follows:

[0308]

[0309] In the formula, E[B′1(x1)] and E[B′2(x2)] are the expected marginal benefit functions in the first stage and the second stage respectively. Usually, as the water supply increases, the increasing rate of economic benefit will gradually slow down. Therefore, the marginal benefit is gradually decreasing. In the present invention, it is considered that the marginal benefit functions in both stages have the property of decreasing.

[0310] According to the Taylor series, we can get

[0311]

[0312] Ignoring the high-order terms, we have:

[0313]

[0314] Substituting Equation (48) into the above formula, we then have

[0315]

[0316] In the formula, and are respectively defined as the marginal benefit functions in the first stage and the second stage. Through the Taylor formula, the transformation of the prediction error uncertainty is completed.

[0317] From the first three equalities of Equation (50) and Equation (53), the conditions for satisfying the optimal solution are:

[0318]

[0319] When the solution of the model satisfies the constraint conditions and is not a boundary value, the inequality constraint terms are all non-zero. From Equation (50), it can be deduced that in this case, λ n1 = λ c = λ n2 = λ d = 0. Therefore, the conditions satisfied by the optimal solution become:

[0320]

[0321] Substituting Equation (53) into Equation (50), the sufficient and necessary conditions for deriving the optimality of the stochastic model from the KKT conditions can be finally obtained as follows:

[0322]

[0323] When Equation (55) is satisfied, that is, the model obtains the optimal solution.

[0324] (2) Competition relationship of water supply

[0325] There is a competitive relationship between the water supply amounts x1 and x2. When the reservoir is not full, there is no water abandonment amount, and both l1 and l2 are 0. After adding the two equations and eliminating s1, we can obtain:

[0326] x1 + x2 = Q1 + Q2 + W0 - W2 (57)

[0327] It is expected that the incoming water in the two stages can meet the water use demand after being regulated by the reservoir, and the reservoir water level remains unchanged. Therefore, in this invention, the initial and final reservoir capacities are set to be equal, that is, W0 = W2. Thus, we have:

[0328] x1 + x2 = Q1 + Q2 (58)

[0329] When the spare capacity or the remaining water amount of the reservoir is insufficient, the regulation capacity of the reservoir is restricted, and the water volume transfer between the two stages cannot be fully satisfied, resulting in x1 and x2 not being able to obtain the theoretical optimal values.

[0330] (3) Model Solving Algorithm Design

[0331] The solving process of the model mainly includes two steps. The first step is to solve the theoretical optimal value, and the second step is to correct the theoretical optimal value according to the constraint conditions. The specific process is as Figure 4 shown.

[0332] ① Set the initial values. Let the initial water supply amounts in the first stage and the second stage be equal to the predicted incoming water amounts, that is At this time, the water abandonment amounts l1 = 0 and l2 = 0.

[0333] ② Determine whether the iteration ends. Calculate the difference between the marginal benefit g1[(x1) i of the first stage and the marginal benefit g2[(x2) i of the second stage. If the difference is less than the initial threshold ε, the iteration ends, and the current variable values are the optimal solutions. Otherwise, go to step ③.

[0334] ③ Correct the search step size. Determine whether i is equal to 0. If i ≠ 0, then calculate the product of the marginal differences of two iterations {g1[x1) i - g2[(x2) i} × {g1[(x1) i-1 - g2[(x2) i-1}. If its value is greater than 0, it means the search direction is correct, and the search step size is retained, Δx i = Δx i-1 ; otherwise, the optimal value range of the water supply amount in the first stage is between (x1) i and (x1) i-1 , and it is necessary to shorten the search step size. Let Δx i = Δx i-1 / h (where h is the step adjustment coefficient and h > 1), and then proceed to step ④.

[0335] ④ Determine the iteration direction. The marginal benefit functions in both stages have the property of monotonically decreasing, decreasing as the independent variable increases. When the marginal benefit g1[(x1) i of the first stage is greater than the marginal benefit g2[(x2) i of the second stage, increase the water supply x1 in the first stage, and the water supply x2 in the second stage will decrease accordingly, that is, (x1) i = (x1) i-1 + △x, This step reduces g1[(x1) i and increases g2[(x2) i , narrowing the gap between the marginal benefits of the two stages; when the marginal benefit g1[(x1) i of the first stage is less than the marginal benefit g2[(x2) i of the second stage, decrease the water supply x1 in the first stage, and the water supply x2 in the second stage will increase accordingly, that is, (x1) i = (x1) i-1 - Δx, This step increases g1[(x1) i and decreases g2[(x2) i , and the gap between the marginal benefits of the two stages will still narrow. After determining the iteration direction, enter step ② again to complete the loop.

[0336] Iteratively obtain the theoretical optimal value After that, judge whether its value meets the constraint conditions. The values that meet the constraint conditions are retained, and the boundary values are taken for those that do not. After two-step screening calculations, the optimal solution can finally be obtained

[0337] The present invention mainly constructs two two-stage reservoir operation models for flood season and non-flood season respectively. The two models have different focuses in design. The flood season model transforms the problem of coordinated control of flood control and water utilization in the flood season of the reservoir into a competition problem between the water utilization target in the decision-making stage and the flood control target in the reserved stage. Aiming at the prediction error, an error safety value is introduced to quantify the flood control risk. With the maximum water storage benefit in the decision-making stage and the minimum flood control risk in the reserved stage as the optimization objectives, a two-stage optimization hedging model for the reservoir in the flood season is constructed. Subsequently, the KKT conditions are used to deduce that the condition for the model to obtain the optimal solution is that the marginal benefit of water storage is equal to the marginal benefit of flood control. Finally, combined with the function characteristic of the decreasing marginal benefit of the objective function, a solution algorithm for the flood season model is designed. The core problem of the non-flood season model lies in the allocation of incoming water. With the maximum two-stage expected economic benefit as the objective function, the uncertainty of the prediction error is transformed by the Taylor formula. Similarly, the KKT conditions are used for derivation. When the two-stage marginal benefits are equal, the model has the optimal solution. According to the function characteristic of the decreasing marginal benefit, a solution algorithm for the non-flood season model is designed.

[0338] Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other implementation manners obtained by those of ordinary skill in the art without creative efforts shall fall within the scope protected by the present invention.

Claims

1. An adaptive scheduling method for an agricultural water supply system, characterized in that, Under the condition of considering both the prediction error and the rainfall influence, a reservoir operation model for flood season and non-flood season is constructed, and the reservoir decision-making is adaptively adjusted according to different focuses in flood season and non-flood season. The reservoir operation is divided into a decision-making stage and a reservation stage. In the flood season, the relationship between the flood control risk rate and the prediction error in the reservation stage is obtained by integral method to quantify the prediction error; in the non-flood season, the Taylor formula and expectation are used to quantify the prediction error. Among them, the decision-making stage of the reservoir operation in the flood season is used to determine the operation mode of the reservoir to achieve the beneficial operation goal of the reservoir operation. The reservation stage is used to verify whether the flood control requirements in the future can be met after the decision-making mode in the decision-making stage is used for operation, so as to achieve the flood control goal of the reservoir operation. The reservoir operation in the flood season establishes an optimal operation model with the minimum difference rate of benefits and the minimum flood control risk rate between the decision-making stage and the reservation stage as the optimization goals. The optimal operation model includes the beneficial operation objective function in the flood season and the flood control objective function in the flood season. The weighted summation method is used to transform the beneficial operation objective function in the flood season and the flood control objective function in the flood season into a single-objective function to construct the optimal operation model. The optimal solution of the reservoir operation in the flood season is obtained by solving the reservoir operation model in the flood season through three steps: iteration of the theoretical optimal solution, processing of simplified model constraints, and limitation of the reservoir discharge. The non-flood season reservoir operation constructs a reservoir operation model with the maximum economic benefit between the decision-making stage and the reservation stage as the goal. Based on the goal of the maximum economic benefit between the decision-making stage and the reservation stage, the corresponding non-flood season objective function is constructed, and the optimal solution of the non-flood season reservoir operation is obtained by solving the theoretical optimal value and correcting the theoretical optimal value according to the constraint conditions. The non-flood season reservoir operation model includes an objective function max E[B1(x1 + p1)] + E[B2(x2 + p2)] where x1 and x2 are the water supply volumes in the decision-making stage and the reservation stage respectively, p1 and p2 are the water volumes replenished by rainfall in the irrigation area in the decision-making stage and the reservation stage respectively, and E[B1(·)] and E[B2(·)] are the mathematical expectations of the economic benefits in the decision-making stage and the reservation stage respectively. Based on the constraint conditions, the objective function is optimized to obtain the optimized non-flood season reservoir operation model max E[B1(x1 + p1)] + E[B2(x2 + p2)] s.t x1≥max(x 1，min -p1, 0) x2≥max(x 2，min -p2, 0) W1 ≤ W max W1≥0 l1，l2≥0； The constraint conditions of the non-flood season reservoir operation model include water balance constraint, water supply volume constraint, reservoir storage capacity constraint, and non-negativity constraint. Among them, the water balance constraint Wherein, W0 is the initial reservoir storage capacity, W1 is the final reservoir storage capacity at the decision-making stage, and W2 is the final reservoir storage capacity at the reserved stage. and are the predicted incoming water volumes at the decision-making stage and the reserved stage respectively, ε1 and ε2 are the runoff prediction errors at the decision-making stage and the reserved stage respectively, and l1 and l2 are the water abandonment volumes at the decision-making stage and the reserved stage respectively. Water supply volume constraint: The water supply volume of the reservoir should be greater than the gap existing after the rainfall replenishment in the irrigation area. x1≥max(x 1，min -p1, 0) x2≥max(x 2，min -p2, 0) where x 1，min and x 2，min are the minimum water supply amounts in the decision-making stage and the reservation stage, respectively; Reservoir storage capacity constraint 0 ≤ W1 ≤ W max Where, W max is the beneficial storage capacity of the reservoir; Non-negativity constraint l1，l2≥0。 2. The adaptive scheduling method for the agricultural water supply system according to claim 1, wherein The time covered by the decision-making stage is relatively short, while the time covered by the reservation stage is relatively long. Let the total number of time periods included in the two stages be T, then the time period length included in the decision-making stage is set to be a Δt, and the time period length included in the reservation stage is (T - 1)·Δt. The value of Δt is 12h or 1d.

3. The adaptive scheduling method for the agricultural water supply system according to claim 1, characterized in that The flood season benefit maximization objective function takes the minimum ratio of the difference between the upper limit of the pre-storage benefit and the actual regulation benefit as the optimization objective. The smaller the value, the greater the benefit. The benefit difference ratio B - is calculated as follows Among them, W is the pre-stored water volume, and W max is the upper limit of the pre-stored water volume, m is the shape coefficient, and the larger the value, the more obvious the non-linearity. When m > 1, the above formula is a convex function and has a minimum value; Benefit difference rate in the decision-making stage and benefit difference rate in the reservation stage are respectively Since all the pre-stored water volume in the decision-making stage will be discharged in the reservation stage, so W2 = 0, then there is The flood control objective function in the flood season takes the minimum flood control risk rate as the optimization goal. The calculation formulas for the risk rate R1 in the decision-making stage and the risk rate R2 in the reservation stage are R1＝0 Set the weight of the beneficial use target as ω, then the weight of the flood control target is 1 - ω. Substitute R1 = 0, and substitute it to obtain the objective functions for each stage as follows: The comprehensive objective function combining the beneficial operation objective function in the flood season and the flood control objective function in the flood season is:

4. The adaptive scheduling method for the agricultural water supply system according to claim 3, characterized in that The constraint conditions of the comprehensive objective function include water balance constraints reservoir storage capacity constraints 0 ≤ W1 ≤ W max downstream discharge constraints Downstream discharge constraint in the decision-making stage: The incoming water in the decision-making stage is determined and controllable, so the constraint is D1 ≤ D 1，max It can always be satisfied. Considering the certain rainfall recharge in the irrigation area, the final lower limit constraint is D1≥max(D 1，min -p1, 0) where p1 is the water volume replenished by rainfall in the irrigation area during the decision-making stage Downstream discharge constraint during the reservation stage: that is δ≥δ min Based on the above constraint conditions, the dual-objective optimization model for flood control and beneficial use during the flood season of the reservoir is: min G1(W1)+G2(δ) s.t. 0 ≤ W1 ≤ W max D1≥max(D 1，min -p1, 0) δ≥δ min 。 5. The adaptive scheduling method for the agricultural water supply system according to claim 4, wherein The solution process of the dual-objective optimization model for flood control and beneficial use during the flood season is as follows: Substitute into to obtain Definition is the remaining flood control capacity, denoted by RFCC, that is W1 + δ = RFCC RFCC is the maximum allowable downstream discharge of the reservoir during the reservation stage without considering the forecast error. When the remaining flood control capacity RFCC > 0, the reservoir stores more water during the decision-making stage to increase the beneficial use benefit during the decision-making stage; or stores less water during the decision-making stage to increase the error safety value δ during the reservation stage and reduce the flood control risk. Therefore, the competition relationship between the flood control and beneficial use objectives of the reservoir during the flood season is the allocation problem of the remaining flood control capacity RFCC between the pre-stored water volume W1 and the error safety value δ For nonlinear programming, the Karush-Kuhn-Tucker conditions are used to explain and analyze the optimal solution of the model. The KKT conditions are: In the formula, and δ * are the optimal pre-storage water volume and the optimal error safety value respectively, and G′2(δ * ) are the marginal contributions of the pre-storage water volume W1 and the error safety value δ to the two-stage losses respectively, where f1(W1) is the marginal benefit of water storage, representing the increased water storage benefit caused by a unit of pre-stored water volume W1. Since G1(W1) is a convex function, f1(W1) is a decreasing function of W1 and has the economic characteristic of diminishing marginal benefit. f2(δ) also has the economic characteristic of diminishing marginal benefit The marginal benefit of water storage at the optimal solution can be obtained from the three formulas of the KKT conditions and the marginal benefit of flood control f2(δ * ) is as follows Some equality terms in the KKT conditions are as follows -μ δl (δ * -δ min ) = 0 When the constraint conditions of the model are all satisfied and not boundary values, it can be known that the term in the brackets is not equal to 0, then there must be a Lagrange multiplier μ dl = μ δl = μ wl = μ wu = 0. The condition for obtaining the optimal model is that the marginal benefit of water storage is equal to the marginal benefit of flood control , that is Substitute into f2(δ * ), we get and are placed in the same coordinate system. The transformed curve has undergone symmetry and translation transformations compared to the original graph. If there is an intersection point between the two curves within the domain of (0, RFCC), then there exists a theoretical optimal solution. The distance from this intersection point to the line x = 0 is equal to and the distance from the line x = RFCC is equal to δ * , The scheduling model can be simplified to min G1(W1)+G2(δ) s.t. 0 ≤ W1 ≤ W max δ≥δ min Then becomes The theoretical optimal pre-storage water volume is obtained from the above formula and the error safety value δ * After that, the optimal solution can be obtained by restricting the constraint conditions of the simplified model, and then considering the minimum downstream discharge constraint in the decision-making stage, the actual optimal pre-storage water volume can finally be obtained Error safety value δ * and the downstream discharge are used as the decisions for reservoir operation Use the Newton iteration method with a relatively fast convergence rate to solve the theoretical optimal pre-storage water volume that satisfies equal marginal benefits and the error safety value δ * , and the specific process includes: ① Determine whether the incoming water exceeds the limit According to the size of the predicted incoming water in the reserved stage, it is judged whether when the reservoir does not pre-store water, discharging all the predicted incoming water can not exceed the limit of the maximum discharging water volume: If not (i.e., RFCC ≤ δ min ), then no pre-storage is carried out in the reservoir decision-making stage, and let Calculate the error safety value δ * and the discharging water volume Output the result; if it can (i.e., RFCC > δ min ), then go to step ②; ② Set the initial value Let the error safety value be the minimum error safety value, i.e., (δ0) = δ min , according to the competition relationship, the pre-stored water volume (W1)0 = RFCC - (δ)0; ③ Judge whether the iteration ends Calculate the difference between the current marginal benefit of water storage f1[(W1) j and the marginal benefit of flood control f2[(δ) j . If the difference is less than the initial threshold ε, the iteration ends, and the current variable value is the optimal solution. δ * =(δ) j ; Otherwise, go to step ④; ④ Correct the search step size Determine whether j is equal to 0. If j ≠ 0, calculate the product of the marginal differences of two iterations {[f1[(W1) j -f2[(δ) j}×{[f1[(W1) j-1 -f2[(δ) j-1}. If its value is greater than 0, it means that the search direction is correct and the search step size is retained, Δδ = Δδ; otherwise, the optimal solution is between (δ) j and (δ) j-1 . It is necessary to shorten the search step size. Let Δδ = Δδ / h (h is the step size adjustment coefficient and h > 1), and then enter step ⑤; ⑤ Determine the iteration direction The marginal benefit functions of water conservancy and flood control both have the property of monotonically decreasing, decreasing as the independent variable increases. When the marginal benefit of water storage f1[(W1) j is greater than the marginal benefit of flood control f2[(δ) j , reducing the error safety value δ will increase the pre-stored water volume W1, that is, (δ) j =(δ) j-1 -Δδ, (W1) j =RFCC-(δ) j , then the marginal benefit of water storage f1[(W1) j will decrease, and the marginal benefit of flood control f2[(δ) j will increase, narrowing the gap between the marginal benefits of water storage and flood control; when the marginal benefit of water storage f1[(W1) j is less than the marginal benefit of flood control f2[(δ) j , increasing the error safety value δ will decrease the pre-stored water volume W1, that is, (δ) j =(δ) j-1 +Δδ, (W1) j =RFCC-(δ) j , then the marginal benefit of water storage f1[(W1) j will increase, and the marginal benefit of flood control f2[(δ) j will decrease, and the gap between the marginal benefits of water storage and flood control will still narrow. After determining the iteration direction, enter step ③ again to complete the loop. When the difference between the marginal benefit of water storage f1[(W1) j and the marginal benefit of flood control f2[(δ) j is less than the threshold value, the Newton iteration method ends, and the theoretical optimal pre-storage water volume and the error safety value δ * are output, and then it is judged and δ * whether they meet the constraint conditions of the model Calculate the downstream discharge volume at the decision stage according to the water balance equation at the decision stage Judge whether it meets the constraint conditions. If it meets, then store water in advance Error safety value δ * and the downstream discharge volume at the decision stage are the optimal solutions; if it does not meet, then let Take the boundary value and adjust the water stored in advance according to the water balance equation Error safety value δ * value and output the optimal solution.

6. The adaptive scheduling method of the agricultural water supply system according to claim 1, characterized in that The solution method for the objective function of the reservoir scheduling model during the non-flood season includes solving the theoretical optimal value in the first step and correcting the theoretical optimal value according to the constraint conditions in the second step; S1. Set the initial value Let the initial water supply in the decision-making stage and the reservation stage be equal to the predicted inflow, that is At this time, the water discharge to be abandoned is l1 = 0 and l2 = 0; S2. Judge whether the iteration ends Calculate the difference between the marginal benefit g1[(x1) i and the marginal benefit g2[(x2) i in the reservation stage. If the difference is less than the initial threshold ε, the iteration ends, and the current variable value is the optimal solution. Otherwise, go to step S3; S3. Correct the search step size Judge whether i is equal to 0. If i ≠ 0, then calculate the product of the marginal differences of two iterations {g1[(x1) i -g2[(x2) i}, × {g1[(x1) i-1 -g2[(x2) i-1}. If its value is greater than 0, it means that the search direction is correct, and the search step size is retained, Δx i = Δx i-1 [[ID= 12]]; Otherwise, the optimal value range of the water supply volume in the decision-making stage is between (x1) i and (x1) i-1 . It is necessary to shorten the search step size. Let Δx i = Δx i-1 / h; h is the step size adjustment coefficient, and h > 1. Then enter step S4; S4. Determine the iteration direction The marginal benefit functions in both the decision-making and reservation stages have the property of monotonically decreasing, decreasing as the independent variable increases. When the marginal benefit g1[(x1) i in the decision-making stage is greater than the marginal benefit g2[(x2) i in the reservation stage, increasing the water supply x1 in the decision-making stage causes the water supply x2 in the reservation stage to decrease, that is, (x1) i =(x1) i-1 +Δx, This step reduces g1[(x1) i and increases g2[(x2) i , narrowing the gap in marginal benefits between the decision-making and reservation stages; When the marginal benefit g1[(x1) i in the decision-making stage is less than the marginal benefit g2[(x2) i in the reservation stage, the water supply volume x1 in the decision-making stage is decreased, and the water supply volume x2 in the reservation stage increases accordingly, that is, (x1) i =(x1) i-1 -Δx, This step increases g1[(x1) i and decreases g2[(x2) i , and the gap between the marginal benefits of the two stages will still narrow. After determining the iteration direction, enter step S2 again to complete the loop; Iteratively obtain the theoretical optimal value After that, judge whether its value meets the constraint conditions. Keep the values that meet the constraint conditions and take the boundary values for those that do not. After two-step screening calculations, the optimal solution can finally be obtained

Images