Adaptive scheduling method for agricultural water supply system

Abstract

The invention provides a self-adaptive scheduling method for an agricultural water supply system, and the method comprises the steps: constructing a reservoir scheduling model for a flood season and a non-flood season, and carrying out the self-adaptive scheduling of a reservoir decision according to different emphasis points of the flood season and the non-flood season; according to flood season reservoir scheduling, an optimal scheduling model is established by taking the minimum benefit difference rate and the minimum flood control risk rate of a decision-making stage and a reservation stage as optimization objectives, and a weighted summation method is adopted to convert a Xingli flood season objective function and a flood season flood control objective function into single objective functions to construct the optimal scheduling model. Solving the flood season reservoir scheduling model to obtain a flood season reservoir scheduling optimal solution; according to the non-flood season reservoir dispatching, a reservoir dispatching model is constructed with the maximum economic benefits of a decision-making stage and a reservation stage as the target, a corresponding non-flood season target function is constructed based on the maximum economic benefits of the decision-making stage and the reservation stage, and a theoretical optimal value is corrected by solving the theoretical optimal value and according to constraint conditions, so that the reservoir dispatching efficiency is improved. And obtaining a non-flood season reservoir scheduling optimal solution.

Description

Technical Field

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

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

[0003] Linear programming has the characteristics of simple operation, high computational efficiency and good global convergence. Influenced by the lack of computing power in the early days, linear programming has been widely used to solve the problem of optimal scheduling of reservoirs. In 1962, William Yeh used linear programming to solve the scheduling model and solved the problem of optimal scheduling of a single reservoir with good results. Parikh et al. expanded the scope of application of reservoir linear programming by using time-space decomposition, and expanded the problem of single reservoir to multiple reservoirs. With the continuous development of computing power, scholars have deepened their research on reservoir scheduling models and gradually found that reservoir scheduling problems are usually nonlinear. Therefore, linear programming has been neglected in nonlinear reservoir scheduling problems and gradually faded out of people's field of vision. Later, it was once again valued because of its high efficiency advantage in the joint scheduling of large-scale reservoir groups. Kang et al. used linear programming methods to achieve efficient joint optimization scheduling of cascade reservoir groups. Nonlinear programming can solve nonlinear reservoir scheduling problems. Common methods include quadratic programming, successive gradient descent and other algorithms. However, since reservoir operation models are usually non-convex optimization problems, it is easy to fall into local optimal solutions when using nonlinear programming algorithms to solve them.

[0004] The dynamic programming (DP) algorithm can decompose complex optimization problems into sub-problems of 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 of multiple stages and then solves them step by step. Since the DP algorithm has no restrictions on the objective function and constraints of the scheduling model and can ensure global convergence within a certain discrete accuracy, it has been widely used in solving reservoir optimization scheduling problems after the development of computer technology. In 1981, Zhang Yongchuan and others applied the dynamic programming method to optimization scheduling and developed a scheduling chart, which significantly improved the benefits of the Tuoxi cascade reservoirs. However, due to the optimization principle of dynamic programming, when the number of scheduled reservoirs increases and the accuracy of the solution is improved, the dimension of the state variable will increase, resulting in a sharp increase in the complexity of the solution, exponentially, and thus the "curse of dimensionality" phenomenon. In order to solve the "curse of dimensionality" problem, a large number of scholars have expanded and developed 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 step-by-step optimization algorithm suitable for multiple reservoirs with fast search speed and high accuracy, and the DPSA algorithm suitable for cascade reservoirs. At present, the improvement of planning effectiveness and running speed efficiency of DP algorithms is still a hot research topic.

[0005] The principle of intelligent algorithms is to search for optimal solutions by simulating intelligent behaviors in nature, such as evolution, swarm intelligence, and immune systems. With the continuous development of computer technology, computing power has been significantly improved, and intelligent optimization algorithms suitable for complex nonlinear reservoir optimization and scheduling problems have also developed rapidly. The advantage of intelligent algorithms is that with the increase in the number of reservoirs involved in the operation, the computational complexity of intelligent algorithms only increases linearly, and there will be no "dimensionality curse" problem. Therefore, various new intelligent optimization algorithms are applied to the field of reservoir optimization and scheduling calculations. However, since intelligent algorithms generally have poor global convergence and are prone to fall into local optimal solutions, they are rarely used in actual reservoir scheduling processes. Boomgaard applied genetic algorithms to wastewater resource system management and proposed that genetic algorithms have advantages in solving high-dimensional problems. Subsequently, domestic and foreign scholars tried to apply genetic algorithms to various reservoir optimization and scheduling problems, and made certain improvements to genetic algorithms, improving global convergence ability and optimization efficiency. In 1997, Storn et al. proposed a differential evolution algorithm, which has good global convergence, strong search ability, simple algorithm structure and easy implementation. It has been applied and promoted in solving reservoir optimization and scheduling models. In order to improve the time-space optimization efficiency of the algorithm, domestic and foreign scholars have improved it by adjusting the operation steps and adding other algorithms. The emergence of intelligent algorithms has solved the defect of the DP algorithm's "curse of dimensionality", but due to its common problems of poor convergence stability and easy to fall into local optimal solutions, it is still difficult to carry out in actual scheduling work.

[0006] Through the above-mentioned reservoir optimization scheduling algorithm, the optimal reservoir scheduling process can be obtained under deterministic water inflow conditions. However, the actual scheduling and operation of the reservoir often faces various uncertainties brought about by rainfall and runoff. The scheduling calculation results under deterministic water inflow conditions are difficult to be directly used to guide the actual scheduling and operation of the reservoir. Moreover, since the water inflow process in representative years may be quite different from the actual situation, the traditional scheduling scheme designed based on the water inflow information in different representative years is not reasonable enough, and the current and future information are not considered enough. The response ability in the face of emergencies is relatively insufficient, and it will also cause the use of water resources to be inefficient and unreasonable. Summary of the invention

[0007] In order to solve the problem of reservoir optimization scheduling under uncertain water inflow conditions, the present invention provides a real-time reservoir scheduling model in flood season and non-flood season, which allows the objective function to be optimized during the respective observation periods, and designs a solution algorithm based on the Karush-Kuhn-Tucker condition, thereby realizing an adaptive scheduling method for agricultural water supply systems.

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

[0009] The decision-making stage of flood season reservoir dispatching is used to determine the dispatching mode of the reservoir and achieve the benefit-benefiting target of reservoir dispatching. The reservation stage is used to verify whether the decision-making mode in the decision stage can meet the future flood control requirements and achieve the flood control target of reservoir dispatching after dispatching. The flood season reservoir dispatching takes the minimum benefit difference rate and the minimum flood control risk rate in the decision stage and the reservation stage as the optimization target to establish an optimization dispatching model. The optimization dispatching model includes the flood season benefit-benefiting target function and the flood season flood control target function. The weighted summation method is used to transform the flood season benefit-benefiting target function and the flood season flood control target function into a single target function to construct the optimization dispatching model. The flood season reservoir dispatching model is solved through three steps of theoretical optimal solution iteration, simplified model constraint condition processing, and reservoir discharge volume restriction to obtain the optimal solution for flood season reservoir dispatching.

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

[0011] Furthermore, the time covered by the decision stage is shorter, while the time covered by the reservation stage is relatively longer. Assuming that the total number of time periods included in the two stages is T, the time period length included in the decision stage is set to Δt, and the time period length included in the reservation stage is set to (T-1)·Δt. The value of Δt is 12h or 1d.

[0012] Furthermore, the flood season benefit 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 target. The smaller the value, the greater the benefit. The benefit difference rate B - The calculation formula is

[0013]

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

[0015] Benefit difference rate in decision-making stage and the benefit difference rate of the reserved stage They are

[0016]

[0017] Since the reserved water volume in the decision-making stage will be fully discharged in the reservation stage, W2 = 0, then

[0018]

[0019] The flood control objective function in the flood season takes the minimum flood control risk rate as the optimization target, and the risk rate in the decision-making stage and the reserve phase risk rate The calculation formula is

[0020] R1=0

[0021] R2=P(ε2>δ)=∫ δ -∞ h(ε2)dε2

[0022] If the weight of the benefit-promoting goal is set to ω, then the weight of the flood control goal is 1-ω, and R1=0. Substituting in, the objective functions of each stage are obtained as follows:

[0023]

[0024] The comprehensive objective function combining the flood season benefit objective function and the flood season flood control objective function is:

[0025]

[0026] Furthermore, the constraints of the comprehensive objective function include water balance constraints

[0027]

[0028] Reservoir capacity constraints

[0029] 0≤W1≤W max

[0030] Discharge volume constraints

[0031] Constraints on water discharge at the decision-making stage: The water inflow at the decision-making stage is certain and controllable, so the constraint D1≤D 1，max It can always be satisfied. Considering that there is a certain amount of rainfall replenishment in the irrigation area, the lower limit constraint is finally determined as

[0032] D1≥maxx(D 1，min -p1,0)

[0033] Where p1 is the amount of water supplied by rainfall in the irrigation area during the decision-making stage.

[0034] Constraints on water discharge during the reserved stage:

[0035]

[0036] Right now

[0037] δ ≥ δ min

[0038] Based on the above constraints, the dual-objective optimization model of reservoir flood season benefit and flood control is as follows:

[0039] min G1(W1)+G2(δ)

[0040] st

[0041]

[0042] 0≤W1≤W max

[0043] D1≥max(D 1,min -p1,0)

[0044] δ ≥ δ min .

[0045] Furthermore, the solution process of the dual-objective optimization model of flood prevention and benefit creation during flood season is as follows:

[0046] Will Substitution Available

[0047]

[0048] definition is the remaining flood control capacity, expressed as RFCC, that is,

[0049] W1+δ=RFCC

[0050] RFCC is the maximum amount of water that the reservoir is allowed to discharge in the reservation stage without considering the forecast error. When the remaining flood control capacity RFCC is greater than 0, the reservoir stores more water in the decision-making stage to increase the benefits of the decision-making stage; or stores less water in the decision-making stage to increase the error safety value δ in the reservation stage and reduce the flood control risk. Therefore, the competitive relationship between the flood control and benefit goals 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.

[0051] For nonlinear programming, the Karush-Kuhn-Tucker condition is used to explain and analyze the optimal solution of the model. The KKT condition is:

[0052]

[0053] 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,

[0054]

[0055] In the formula, f1(W1) is the marginal benefit of water storage, which represents the added value of water storage benefit caused by the unit pre-storage water volume W1. Among them, G1(W1) is a convex function, and f1(W1) is a decreasing function of W1, which has the economic characteristics of diminishing marginal benefits. f2(δ) also has the economic characteristics of diminishing marginal benefits.

[0056] The marginal benefit of water storage when the optimal solution is achieved can be obtained from the three formulas of KKT conditions: and the marginal benefit of flood control f2(δ * ) is

[0057]

[0058] Some of the equations in the KKT condition are as follows

[0059]

[0060] -μ δl (δ * -δ min )=0

[0061]

[0062] When the constraints of the model are satisfied and are not boundary values, it can be seen 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 optimal condition for the model is the marginal benefit of water storage and the marginal benefit of flood control f2(δ * ) are equal, that is

[0063]

[0064] Will Substitute f2(δ * ),get and Placed in the same coordinate system, the transformed curve has undergone symmetric and translation transformation compared to the original image. If the two curves have an intersection in the domain of (0, RFCC), then there is a theoretical optimal solution, and the distance between the intersection and the straight line x = 0 is equal to The distance from the line x = RFCC is equal to δ * ,

[0065] The scheduling model can be simplified as

[0066] min G1(W1)+G2(δ)

[0067] st

[0068]

[0069] 0≤W1≤W max

[0070] δ ≥ δ min

[0071] but becomes

[0072]

[0073] The theoretical optimal pre-storage water volume can be obtained from the above formula: and error safety value δ * After that, the optimal solution can be obtained by simplifying the constraints of the model, and then the minimum water discharge constraint in the decision-making stage is considered, and finally the actual optimal pre-storage water volume can be obtained. Error safety value δ * and the amount of water discharged As a decision-making tool for reservoir operation,

[0074] The Newton iteration method with faster convergence speed is used to solve the theoretical optimal pre-storage water volume that satisfies equal marginal benefits. and error safety value δ* The specific process includes:

[0075] ① Determine whether the incoming water exceeds the limit

[0076] Based on the size of the second-stage forecast water flow, determine whether the total forecast water flow can be discharged without exceeding the maximum discharge limit when the reservoir does not store water in advance: If not (i.e. RFCC≤δ min ), then no pre-storage is performed in the reservoir decision-making stage. Calculation error safety value δ * and the amount of water discharged Output result; if it is possible (i.e. RFCC>δ min ), then go to step ②;

[0077] ②Set the initial value

[0078] Let the error safety value take the minimum error safety value, that is, (δ0) = δ min , according to the competition relationship, the pre-storage water volume (W1)0 = RFCC-(δ)0;

[0079] ③Determine whether the iteration is over

[0080] Calculate 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;

[0081] ④Fix the search step length

[0082] Determine whether j is equal to 0. If j≠0, calculate the product of the marginal differences of the 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 (δ) j and (δ) j-1 The search step length needs to be shortened, and Δδ=Δδ / h (h is the step length adjustment coefficient, and h>1), and then go to step ⑤;

[0083] ⑤Determine the iteration direction

[0084] The marginal benefit functions of flood control and water conservation have the property of monotonically decreasing, which decreases with the increase of independent variables. j] is greater than the marginal benefit of flood control f2[(δ) j ], the error safety value δ is reduced, and the pre-storage 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 ] is reduced, and the marginal benefit of flood control f2[(δ) j ] increases, the gap in 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 ], the error safety value δ is increased, and the pre-storage 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, the marginal benefit of flood control f2[(δ) j ] is reduced, the gap in the marginal benefits of water storage and flood control will still be narrowed. After determining the iteration direction, enter step ③ again to complete the cycle.

[0085] When 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-storage water volume is output and error safety value δ * , then judge and δ * Whether the constraints of the model are met,

[0086] Calculate the water discharge volume in the decision-making stage according to the water balance equation in the decision-making stage Determine whether it meets the constraints. If so, the pre-storage water volume Error safety value δ * and the amount of water released during the decision-making stage is the optimal solution; if it is not satisfied, then Take the boundary value and adjust the pre-storage volume according to the water balance equation Error safety value δ * output the optimal solution.

[0087] Furthermore, the non-flood season reservoir operation model includes the objective function

[0088] max E[B1(x1+p1)]+E[B2(x2+p2)]

[0089] In the formula, x1 and x2 are the water supply in the decision-making stage and the reservation stage, p1 and p2 are the water replenishment of the irrigation area during the decision-making stage and the reservation stage, E[B1(·)] and E[B2(·)] are the mathematical expectations of the economic benefits in the decision-making stage and the reservation stage, respectively.

[0090] The objective function is optimized based on the constraints to obtain the optimized non-flood season reservoir operation model.

[0091] max E[B1(x1+p1)]+E[B2(x2+p2)]

[0092] st

[0093]

[0094] x1≥max(x 1，min -p1,0)

[0095] x2≥max(x 2，min -p2,0)

[0096] W1≤W max

[0097] W1≥0

[0098] l1,l2≥0.

[0099] Furthermore, the constraints include water balance constraints, water supply constraints, reservoir capacity constraints and non-negative constraints;

[0100] The water balance constraint

[0101]

[0102] Where W0 is the initial storage capacity of the reservoir, W1 is the final storage capacity of the reservoir in the decision-making stage, and W2 is the final storage capacity of the reservoir in the reservation stage. and are the forecast water inflow in the decision-making stage and the reservation stage, ε1 and ε2 are the runoff forecast errors in the decision-making stage and the reservation stage, l1 and l2 are the abandoned water in the decision-making stage and the reservation stage, respectively;

[0103] Water supply constraint: The water supply of the reservoir should be greater than the gap after the irrigation area is replenished by rainfall.

[0104] x1≥max(x 1，min -p1,0)

[0105] x2≥max(x 2，min -p2,0)

[0106] In the formula, x 1，min and x 2，minare the minimum water supply in the decision-making stage and the reservation stage, respectively;

[0107] Reservoir capacity constraints

[0108] 0≤W1≤W max

[0109] Where W max To improve the storage capacity of the reservoir;

[0110] Non-negative constraints

[0111] l1,l2≥0.

[0112] Furthermore, the method for solving the objective function of the reservoir operation model in 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;

[0113] S1. Set initial value

[0114] Let the initial water supply in the decision-making stage and the reservation stage be equal to the predicted water supply, that is, At this time, the amount of discarded water l1 = 0, l2 = 0;

[0115] S2. Determine whether the iteration is finished

[0116] Calculate the marginal benefit g1[(x1) i ] and the marginal benefit g2[(x2) i ], if the difference is less than the initial threshold ε, the iteration ends and the current variable value is the optimal solution. Otherwise, proceed to step S3;

[0117] S3. Correct the search step length

[0118] Determine whether i is equal to 0. If i≠0, calculate the product of the marginal differences of the 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, the search step size is retained, Δx i =Δx i-1 ; Otherwise, the optimal range of water supply in the decision-making stage is (x1) i and (x1) i-1 We need to shorten the search step length, let Δx i =Δx i-1 / h; h is the step length adjustment coefficient, and h>1, then enter step S4;

[0119] S4. Determine the iteration direction

[0120] The marginal benefit functions in the decision-making and reservation stages have a monotonically decreasing property, which decreases with the increase of the independent variable. When the marginal benefit g1(x1) in the decision-making stage is i ] is greater than the marginal benefit g2(x2) in the reservation stage i ], the water supply x1 in the decision-making stage is increased, and the water supply x2 in the reservation stage is reduced accordingly, that is, (x1) i =(x1) i-1 +Δx, This step makes g1[(x1) i ] decreases, g2[(x2) i ] increases, the marginal benefit gap between the decision-making and reservation stages narrows; when the marginal benefit g1[(x1) i ] is less than the marginal benefit g2[(x2) i ], the water supply x1 in the decision-making stage is reduced, and the water supply x2 in the reservation stage is increased accordingly, that is, (x1) i =(x1) i-1 -Δx This step makes g1[(x1) i ] increases, g2[(x2) i ] decreases, the marginal benefit gap between the two stages will still narrow. After determining the iteration direction, enter step S2 again to complete the cycle;

[0121] Iteration to obtain the theoretical optimal value Finally, determine whether its value meets the constraints. The value that meets the constraints is retained, and the value that does not meet the constraints is taken as the boundary value. After two steps of screening and calculation, the optimal solution can be obtained.

[0122] Beneficial effects of the present invention: The present invention provides an adaptive scheduling method for an agricultural water supply system. The method constructs an adaptive scheduling model for an agricultural water supply system combined with a forecast module, and includes two reservoir scheduling models, which are respectively applied to the flood season and the non-flood season. The future situation is simulated by combining the real-time forecast results with historical data predictions, and the prediction error is quantified by normal distribution, Taylor formula, mathematical expectation, etc., so as to achieve reasonable planning of reservoir water storage capacity and improve the benefits of benefits under the premise of ensuring flood control goals during the flood season. In the non-flood season, the regulation and storage process is reasonably planned based on the benefit curve to improve the water supply benefits. The model constructed by the present invention includes a risk hedging strategy. When the KKT condition is used to deduce the optimal solution to the equation group, the marginal benefit values ​​of the objective functions of the decision-making stage and the reservation stage are 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 achieved, but also the regulation and storage method of the reservoir is made more scientific and reasonable.

[0123] The dispatch module can select different dispatch models according to the flood season division, so that the flood season focuses on flood prevention and the non-flood season focuses on benefits. The model can also adaptively adjust the reservoir dispatch decision according to the water inflow process in the forecast period. In the actual application process, different dispatch model combinations can be used 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 dispatch. BRIEF DESCRIPTION OF THE DRAWINGS

[0124] Figure 1 It is a schematic diagram of the two-stage real-time rolling scheduling process.

[0125] Figure 2 It is a diagram corresponding to the symbols of variables in the present invention.

[0126] Figure 3 It is a schematic diagram of the solution process of the flood season scheduling model.

[0127] Figure 4 This is a schematic diagram of the solution process of Newton's iteration method.

[0128] Figure 5 This is a schematic diagram of the solution process of the non-flood season scheduling model. DETAILED DESCRIPTION

[0129] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described in detail below.

[0130] Embodiment 1: Since the water flow process in the representative year may be quite different from the actual situation, the traditional scheduling scheme designed according to the water flow information of different representative years is not reasonable enough, the current and future information is not considered enough, and the response ability in the face of emergencies is relatively insufficient, and the utilization of water resources is not efficient and reasonable. In view of the above problems, the present invention constructs an adaptive scheduling model of an agricultural water supply system combined with a forecast module, which includes two reservoir scheduling models, which are respectively applied to the flood season and the non-flood season. The future situation is simulated by combining the real-time forecast results with historical data prediction, and the prediction error is quantified by normal distribution, Taylor formula, mathematical expectation and other methods, in an effort to achieve the premise of ensuring the flood control target in the flood season, reasonably plan the reservoir water storage capacity, improve the benefits, and reasonably plan the regulation and storage process based on the benefit curve in the non-flood season to improve the water supply benefits. The model contains a risk hedging strategy. When the KKT condition is used to deduce the optimal solution of the equation group, the marginal benefit values ​​of the objective functions of the first stage and the second stage are 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 and storage method of the reservoir is made more scientific and reasonable.

[0131] The dispatch module can select different dispatch models according to the flood season division, so that the flood season focuses on flood prevention and the non-flood season focuses on benefits. The model can also adaptively adjust the reservoir dispatch decision according to the water inflow process in the forecast period. In the actual application process, different dispatch model combinations can be used 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 dispatch.

[0132] For a reservoir, generally speaking, the more water it stores, the greater its benefits. However, during the flood season, it is generally uncertain whether a flood will occur in the future. If more water is stored, the potential risk of flood control will increase, while maintaining less water storage will damage the benefits. Therefore, there is a competitive relationship between the two goals of benefit and flood control, and the scheduling and processing method of the reservoir during the flood season can be attributed to the problem of coordinated control of the dual goals of flood control and benefit. In response to this problem, the present invention constructs a two-stage reservoir scheduling model for the flood season that takes into account the dual goals of flood control and benefit. According to the forecast information, the water storage and discharge scheduling method of the reservoir in the future period is simulated. It is expected that under the premise of meeting the future flood control requirements, the benefits of the reservoir can be maximized by controlling the water level and realizing adaptive regulation of the reservoir.

[0133] The present invention divides the reservoir dispatching process into two stages: Figure 1 As shown in the figure, 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 scheduling according to the decision-making method of the first stage can meet the future flood control requirements. Since uncertainty increases with the increase of the observation period, the time covered by the decision stage is generally set to be shorter, and the time covered by the reservation stage is relatively longer. If the total number of time periods included in the two stages is T, the time period length included in the decision stage is set to Δt, and the time period length included in the reservation stage is (T-1)·Δt, and the value of Δt is 12h or 1d. The purpose of dividing the scheduling process into two stages is to explore what kind of scheduling method can be adopted under the existing forecast information and risk conditions to maximize the benefits of the first stage and ensure that the flood control requirements of the second stage are met. According to this rule, the model seeks the optimal scheduling method D for the future decision stage based on the forecast information in the next two stages. t , and moves along the time axis with a step size of Δt to simulate the real-time scheduling process within a year under real conditions.

[0134] like Figure 2 Shown is the corresponding information of the key variables and corresponding symbols related to the present invention.

[0135] Under ideal conditions, a portion of water is allowed to be stored in the reservoir in advance in the first stage, but it is necessary to ensure that the pre-stored water can be safely discharged in the second stage without increasing the flood control risk downstream of the reservoir, that is, the water level must be reduced to the flood limit water level at the end of the stage, so as to ensure the safety of the downstream protection objects and the reservoir itself. However, due to the existence of forecast errors, the water level may not fall back to the flood limit water level before the flood arrives, while ensuring the safety of the downstream. At this time, if a design flood or a check flood occurs, the flood control safety of the reservoir or the upstream and downstream planning and design cannot be guaranteed. Therefore, it is necessary to conduct a quantitative analysis of the error.

[0136] Since the uncertainty of the forecast decreases as the forecast period shortens, the water inflow forecast accuracy in the first stage is relatively high and the error is small. The forecast results in the first stage can be regarded as deterministic forecasts, and its error is considered to be equal to 0. The time span of the water inflow forecast in the second stage is relatively long, and its error is considered to be non-negligible. The present invention uses normal distribution to fit the forecast error in the second stage, and it is considered that the error satisfies the normal distribution with a mean of μ2 and a standard deviation of σ2, so as to facilitate the quantification of risks below.

[0137] 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. Normally, 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 object 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 object.

[0138] 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

[0139] R i =P(D i >D i,max ) (1)

[0140] (1) Downstream flood control risk rate in the first stage

[0141] Since the first period is regarded 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.

[0142] ε1=0,R1=P(D1>D 1,max )=0 (2)

[0143] Where D 1,maxIt is the maximum discharge volume of the reservoir in the first stage.

[0144] (2) Downstream flood control risk rate in the second stage

[0145] The forecast error in the second stage cannot be ignored. According to the water balance equation, we can get

[0146]

[0147] As the forecast period increases, the uncertainty of the water inflow forecast will increase. For the sake of safety, the water level at the end of the stage is kept at the flood limit water level V d , so there is

[0148] V2=V d (4)

[0149] It should be pointed out that the actual scheduling process is a process of rolling forecast and decision-making from time to time. Each time period will adopt the decision results of the first stage starting from that time period, and a new round of simulation will start in the next time period. Therefore, the simulation scheduling results of the second stage may not necessarily be used for the time period covered by this stage. This stage is reserved to assist flood control calculations.

[0150] Since the pre-storage water in the reservoir in the first stage will be fully discharged in the second stage, there is

[0151] W1=V1-V d (5)

[0152] The uncertainty of the reservoir discharge volume D2 in the second stage is caused by the forecast error of the reservoir water inflow. From equations (3), (4) and (5), we can get

[0153]

[0154] Downstream flood risk rate in the second phase

[0155]

[0156] Replacing D2 with ε2 can obtain the downstream flood control risk rate calculation formula with forecast error as the independent variable:

[0157]

[0158] In the formula, h(D2) and h(ε2) are the probability density functions of the reservoir discharge D2 and the inflow forecast error ε2, respectively. The replacement of independent variables is conducive to the further calculation of the flood control risk rate.

[0159] (3) Error safety value

[0160] Define the difference between the maximum discharge volume of the reservoir in the second stage and the expected discharge volume as the error safety value, represented by δ, then we have

[0161]

[0162] The error safety value δ is the safety space reserved for forecast uncertainty and is a safety indicator for flood prevention and control. The larger the value, the greater the forecast error that the downstream can withstand.

[0163] Replace δ in equation (8) The calculation formula of downstream flood control risk rate in the second stage can be formulated as

[0164] R2=P(ε2>δ)=∫ δ +∞ h(ε2)d ε2 =H(+∞)-H(δ)=1-H(δ) (10)

[0165] δ=H -1 (1-R2)=μ2+σ2Φ -1 (1-R2) (11)

[0166] Where H(·) is the distribution function of the second-stage error, which satisfies the normal distribution with mean μ2 and standard deviation σ2. -1 (·) is the inverse function of the error distribution function, Φ -1 (·) is the inverse function of the standard normal distribution function.

[0167] In this way, we obtain the relationship between the flood risk rate and the forecast error.

[0168] (4) Quantification of the additional risk of forecast error

[0169] For a flood season with a total length of l days, a downstream flood control standard of once in P years, and a scheduling process with a period length of n days, the flood control risk rate R that meets the planning design max The calculation formula is

[0170]

[0171] When R2≤R max When R2=R max When , the error safety value reserved for the planned maximum error value can be calculated, that is, the minimum error safety value, using δ min This value can quantify the flood risk caused by the error. max Substituting into formula (11), we can get

[0172] δ min =H -1 (1-R max )=μ2+σ2Φ -1 (1-R max) (13)

[0173] Through the above method, the error risk is quantified and the maximum error that the runoff forecast can tolerate is obtained.

[0174] Construction of reservoir operation model during flood season

[0175] An optimization scheduling model is established with the minimum two-stage benefit difference rate and the minimum flood control risk rate as the optimization objectives.

[0176] (1) Profit-making objective function

[0177] When the pre-storage water volume reaches the upper limit W max When , the added value of the benefit reaches the maximum, so the ratio of the difference between the upper limit of the pre-stored benefit and the actual regulation benefit (hereinafter referred to as the benefit difference rate) can be minimized as the optimization target. The smaller the value, the greater the benefit. The calculation formula of the benefit difference rate is

[0178]

[0179] Where m is the shape coefficient. The larger the value, the more obvious the nonlinearity. When m>1, the above formula is a convex function with a minimum value.

[0180] From formula (14), we can get the benefit difference rates of the first stage and the second stage respectively:

[0181]

[0182] Since the second stage will release all the pre-stored water in the first stage, W2 = 0, then

[0183]

[0184] (2) Flood control objective function

[0185] In the flood prevention stage, the minimum flood prevention risk rate is taken as the optimization goal. According to the risk rate calculation formulas (2) and (10) that have been derived for each stage, we have

[0186] R1=0 (18)

[0187] R2=P(ε2>δ)=∫ δ +∞ h(ε2)dε2 (19)

[0188] (3) Overall optimization objective function

[0189] The weighted summation method is used to transform the multi-objective function into a single objective. The weight of the benefit objective is set to ω, and the weight of the flood control objective is 1-ω. R1 = 0, Substituting in, the objective functions of each stage are obtained as follows:

[0190]

[0191] It can be seen from the formula that the objective function of the first stage only changes with the pre-storage water volume W1, and the objective function of the second stage only changes with the error safety value δ, and the others are constants. In this way, the complex problem of coordinated control of flood control and benefit development during the reservoir flood season is transformed into a two-stage optimization problem of coordinated control between the benefit development goal in the first stage and the flood control goal in the second stage, thereby reasonably simplifying the complex problem and well reflecting the superiority of the two-stage optimization. The comprehensive objective function of the two stages is:

[0192]

[0193] (4) Constraints

[0194] ① Water balance constraints

[0195]

[0196] ②Reservoir capacity constraints

[0197] 0≤W1≤W max (25)

[0198] ③ Constraints on the amount of water discharged

[0199] The first stage of water discharge constraint: The water inflow in the first stage is certain and controllable, so the constraint D1≤D 1，max It can always be satisfied. Considering that there is a certain amount of rainfall replenishment in the irrigation area, the lower limit constraint is finally determined as

[0200] D1≥max(D 1，min -p1,0) (26)

[0201] Where p1 is the amount of water supplied by rainfall in the irrigation area in the first stage.

[0202] Second stage water discharge constraints:

[0203]

[0204] Right now

[0205] δ ≥ δ min (28)

[0206] (5) Optimization model

[0207] Based on the above analysis, the two-stage optimization model of the dual objectives of benefit and flood control during the reservoir flood season is as follows:

[0208] min G1(W1)+G2(δ)

[0209] st

[0210]

[0211] 0≤W1≤W max

[0212] D1≥max(D 1,min -p1,0)

[0213] δ ≥ δ min (29).

[0214] Solution of reservoir operation model during flood season

[0215] (1) The competitive relationship between benefits and flood control risks

[0216] Will Substitution Available

[0217]

[0218] definition is the remaining flood control capacity, expressed as RFCC, that is,

[0219] W1+δ=RFCC (31)

[0220] RFCC can be interpreted as the maximum amount of water allowed to be discharged from the reservoir in the second stage without considering the forecast error. When the residual flood control capacity RFCC>0, the reservoir can store more water in the first stage to increase the benefits of 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 flood control and benefit goals of reservoirs during the flood season is actually the allocation problem of the residual flood control capacity RFCC between the pre-stored water volume W1 and the error safety value δ.

[0221] (2) Model solution method

[0222] For nonlinear programming problems, Karush-Kuhn-Tucker (KKT) conditions are often used to explain and analyze the optimal solution of the model.

[0223] For the following optimization models:

[0224] min f(x1, ..., x n )

[0225] st

[0226] g i (x1, ..., x n )≤0,i=(1,...,m)

[0227] h j (x1, ..., x n)=0,j=(1,...,l) (32)

[0228] In the formula, f(x1,...,x n ) is the objective function, g i (x1, ..., x n ) is an inequality constraint, h i (x1, ..., x n ) is an equality constraint. The KKT condition of this formula is:

[0229]

[0230] In the formula, μ i is the Lagrange multiplier of the equality constraint, λ j is the Lagrange multiplier of the inequality constraint. Generally speaking, the KKT condition can only be used as a necessary condition for the optimal solution of a nonlinear programming problem. Only when the objective function is a convex function and the equality constraint is an affine function, the KKT condition is a necessary and sufficient condition for the optimal solution of the model.

[0231] The non-flood season dispatching model constructed by the present invention belongs to a nonlinear convex programming problem, so the KKT condition is a necessary and sufficient condition for the optimal solution. The KKT condition is:

[0232]

[0233] 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.

[0234]

[0235] In the formula, f1(W1) is the marginal benefit of water storage, which represents the added value of water storage benefit caused by the unit pre-storage volume W1. Since G1(W1) is a convex function, f1(W1) is a decreasing function of W1, which has the economic characteristics of diminishing marginal benefits. Similarly, f2(δ) also has the economic characteristics of diminishing marginal benefits.

[0236] The marginal benefit of water storage when the optimal solution is achieved can be obtained from the three formulas of KKT conditions: and the marginal benefit of flood control f2(δ * ) is

[0237]

[0238] Some of the equations in the KKT condition derived from equation (34) are as follows:

[0239]

[0240] μ δl (δ * -δ min )=0

[0241]

[0242] When the constraints of the model are satisfied and are not boundary values, it can be seen 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 optimal condition for the model is the marginal benefit of water storage and the marginal benefit of flood control f2(δ * ) are equal, that is

[0243]

[0244] Will Substitute f2(δ * ),get and Placed in the same coordinate system, the transformed curve has undergone symmetric and translation transformation compared to the original image. If the two curves have an intersection in the domain of (0, RFCC), then there is a theoretical optimal solution, and the distance between the intersection and the straight line x = 0 is equal to The distance from the line x = RFCC is equal to δ * .

[0245] (3) Model simplification

[0246] The first stage discharge volume D1 has no direct relationship with the objective function and only affects the value of the pre-storage volume. Therefore, the constraint condition of the minimum discharge volume in the first stage can be temporarily ignored and the constraint can be imposed after the theoretical optimal solution is obtained. Therefore, the scheduling model can be simplified as

[0247] min G1(W1)+G2(δ)

[0248] st

[0249]

[0250] 0≤W1≤W max

[0251] δ ≥ δ min (40)

[0252] but becomes

[0253]

[0254] The theoretical optimal pre-storage water volume can be obtained from the above formula: and error safety value δ * After that, the optimal solution can be obtained by simplifying the constraints of the model, and then considering the minimum water discharge constraint in the first stage, the actual optimal pre-storage water volume can be obtained. Error safety value δ * and the amount of water discharged As a decision on reservoir operation.

[0255] (4) Model solving algorithm design

[0256] The solution algorithm mainly includes three steps: theoretical optimal solution iteration, simplified model constraint processing, and reservoir discharge volume restriction. The solution process is as follows: Figure 3 shown.

[0257] Among them, the most critical step is the iteration of the theoretical optimal solution. The present invention uses the Newton iteration method with a fast convergence speed to solve the marginal benefit equality. Theoretical optimal pre-storage water and error safety value δ * , the solution process of Newton iteration method is as follows Figure 4 As shown, the specific process is:

[0258] ① Determine whether the water inflow exceeds the limit. Based on the size of the second-stage forecast water inflow, determine whether the total forecast water inflow can be discharged without exceeding the maximum discharge limit when the reservoir does not store water in advance: If not (i.e. PFCC≤δ min ), the reservoir will not be pre-stored in the first stage, Calculation error safety value δ * and the amount of water discharged Output result; if it is possible (i.e. RFCC>δ min ), then go to step ②.

[0259] ② Set the initial value. Let the error safety value take the minimum error safety value, that is, (δ0) = δ min , according to the competition relationship, the pre-storage water volume (W1)0 = RFCC-(δ)0.

[0260] ③ Determine whether the iteration is finished. Calculate 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.

[0261] ④Fix the search step size. Determine whether j is equal to 0. If j≠0, calculate the product of the marginal differences of the 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 (δ) j and (δ) j-1 It is necessary to shorten the search step length, set Δδ=Δδ / h (h is the step length adjustment coefficient, and h>1), and then go to step ⑤.

[0262] ⑤ Determine the iteration direction. The marginal benefit functions of both water conservation and flood control have a monotonically decreasing nature, which decreases with the increase of the independent variable. When the marginal benefit of water storage f1[(W1) j ] is greater than the marginal benefit of flood control f2[(δ) j ], the error safety value δ is reduced, and the pre-storage 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 ] is reduced, and the marginal benefit of flood control f2[(δ) j ] increases, the gap in 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 ], the error safety value δ is increased, and the pre-storage 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, the marginal benefit of flood control f2[(δ) j ] decreases, the gap in marginal benefits of water storage and flood control will still narrow. After determining the iteration direction, enter step ③ again to complete the cycle.

[0263] When 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-storage water volume is output and error safety value δ * Then we need to judge and δ * Whether the constraints of the model are met, if so, and δ * That is the optimal solution. If it is not satisfied, the corresponding boundary value is taken as the optimal solution.

[0264] Finally, the first stage water discharge volume is calculated according to the first stage water balance equation Determine whether it meets the constraints. If so, the pre-storage water volume Error safety value δ * and the first stage of water discharge is the optimal solution; if it is not satisfied, then Take the boundary value and adjust the pre-storage volume according to the water balance equation Error safety value δ * output the optimal solution.

[0265] A two-stage risk hedging reservoir scheduling model in the non-flood season with the goal of optimizing economic benefits: In the non-flood season, the water inflow process is relatively slow and the flood control pressure is relatively small. Therefore, the most important goal of the scheduling task becomes to make full use of the water inflow and reservoir capacity to improve the benefits. To this end, the present invention constructs a two-stage reservoir scheduling model with the goal of maximizing economic benefits. Based on the overall consideration of the reservoir water inflow situation and reservoir water storage capacity in the two stages, the most suitable water inflow distribution method is found according to the water supply benefit curve, and the most efficient water supply strategy is formulated.

[0266] For water users, the more water is supplied, the greater the benefits it brings, but the benefits of water supply generally do not increase linearly. Usually, as the water supply increases, the increase in benefits will gradually decrease. Moreover, due to the different daily water inflows, if there is more water on a certain day and all of it is supplied to water users, the increase in water supply benefits may not be obvious, resulting in a certain waste of resources. Based on this phenomenon, the present invention constructs a two-stage reservoir scheduling model, which utilizes the reservoir's regulation and storage function, combines forecast information with the water supply benefit curve, and makes the water supply more balanced, so as to achieve the purpose of maximizing the sum of the benefits of the next two stages.

[0267] The model makes local optimal decisions based on the forecast results. If the forecast predicts more water inflow in the first stage and less water in the second stage, the reservoir can store part of the water for use in the second stage, so that the sum of the benefits of the two stages is maximized; if the forecast predicts more water in the second stage and less water in the first stage, the reservoir can use more water in the first stage, and use the excess water in the second stage to supplement the water deficit, while meeting the water demand in this stage, so that the sum of the benefits of the two stages is maximized. Based on this principle, the model rolls along the time axis, continuously updates decisions based on forecast results, and gives a dispatching plan that meets the requirements.

[0268] Construction of reservoir operation model in non-flood season

[0269] (1) Objective function

[0270] In order to achieve the goal of maximizing the economic benefits in the two stages, while taking into account the impact of forecast error and rainfall, the objective function is constructed as follows

[0271] max E[B1(x1+p1)]+E[B2(x2+p2)] (42)

[0272] Where x1 and x2 are the water supply in the first and second stages, respectively; p1 and p2 are the water replenishment of the irrigation area due to rainfall in the first and second stages, respectively; and E[B1(·)] and E[B2(·)] are the mathematical expectations of the economic benefits in the first and second stages, respectively.

[0273] (2) Constraints

[0274] ① Water balance constraints

[0275]

[0276] In the formula, W0 is the initial storage capacity of the reservoir, W1 is the final storage capacity of the reservoir in the first stage, and W2 is the final storage capacity of the reservoir in the second stage. and are the predicted water inflow in the first and second stages, ε1 and ε2 are the runoff forecast errors in the first and second stages, l1 and l2 are the abandoned water in the first and second stages, respectively.

[0277] ② Water supply constraints

[0278] The water supply of the reservoir should be greater than the existing gap after rainfall recharge in the irrigation area.

[0279] x1≥max(x 1,min -p1,0)

[0280] x2≥max(x 2，min -p2,0) (44)

[0281] In the formula, x 1，min and x 2，min are the minimum water supply for the first and second stages respectively.

[0282] ③Reservoir capacity constraints

[0283] 0≤W1≤W max (45)

[0284] Where W max To improve the storage capacity of the reservoir.

[0285] ④Non-negative constraints

[0286] l1, l2 ≥ 0 (46)

[0287] (3) Optimization model

[0288] The two-stage reservoir operation model in the non-flood season with the goal of benefiting the people is as follows:

[0289] max E[B1(x1+p1)]+E[B2(x2+p2)]

[0290] st

[0291]

[0292] x1≥max(x 1，min -p1,0)

[0293] x2≥max(x 2,min -p2,0)

[0294] W1≤W max

[0295] W1≥0

[0296] l1,l2≥0 (47).

[0297] Solution of reservoir operation model in non-flood season

[0298] (1) Model solution method

[0299] Since the uncertainty of the forecast decreases with the reduction of the forecast period, the accuracy of the water inflow forecast in the first stage is relatively high and the error is small. The forecast results of the first stage can be regarded as deterministic forecasts, and its error is considered to be equal to 0. However, the time span of the water inflow forecast in the second stage is relatively long, and its error is considered to be non-negligible. The normal distribution is used to fit the forecast error of the second stage, and it is considered that the error satisfies the normal distribution with a mean of 0 and a standard deviation of σ2, then:

[0300] E[ε1]=0

[0301] E[ε2]=0

[0302]

[0303] Since the reservoir capacity can be controlled, it can be regarded as a fixed value. The forecast error is passed to x1 and x2. It is considered that the uncertainty of the reservoir water supply is caused by the forecast error of the reservoir water inflow, so:

[0304]

[0305] Consistent with the flood season model, the non-flood season model is also derived using the KKT condition. The necessary and sufficient conditions for the model to meet the optimality are as follows:

[0306]

[0307] Wherein, E[B′1(x1)] and E[B′2(x2)] are the expected marginal benefit functions of the first stage and the second stage, respectively. Usually, with the increase of water supply, the rate of increase of economic benefits will gradually slow down, so the marginal benefit will gradually decrease. In the present invention, it is considered that the marginal benefit functions of the two stages have a decreasing property.

[0308] From the Taylor series we can get

[0309]

[0310] Ignoring higher-order terms, we have:

[0311]

[0312] Substituting equation (48) into the above equation, we have

[0313]

[0314] In the formula, and They are defined as the marginal benefit functions of the first and second stages respectively. The transformation of forecast error uncertainty is completed through Taylor formula.

[0315] From the first three equations of formula (50) and formula (53), the conditions for satisfying the optimal solution are:

[0316]

[0317] When the solution of the model satisfies the constraint conditions and is not a boundary value, the inequality constraint terms are not 0. From equation (50), we can deduce that in this case λ n1 =λ c =λ n2 =λ d =0, so the condition satisfied by the optimal solution becomes:

[0318]

[0319] Substituting equation (53) into equation (50), we can finally obtain the necessary and sufficient conditions for the optimality of the random model derived from the KKT condition as follows:

[0320]

[0321] When equation (55) is satisfied, When , the model obtains the optimal solution.

[0322] (2) Competition for water supply

[0323] There is a competitive relationship between the water supply x1 and x2. When the reservoir is not full, there is no water abandonment, l1 and l2 are both 0. After adding the two equations and eliminating s1, we can get:

[0324] x1+x2=Q1+Q2+W0-W2 (57)

[0325] It is expected that the water in the two stages can meet the water demand after being regulated by the reservoir, and the water level of the reservoir remains unchanged. Therefore, the present invention sets the initial and final storage capacities of the reservoir to be equal, that is, W0=W2, so:

[0326] x1+x2=Q1+Q2 (58)

[0327] When the reservoir's spare capacity or residual water is insufficient, the reservoir's storage capacity is limited, and the water transfer between the two stages cannot be fully satisfied, resulting in x1 and x2 failing to achieve the theoretical optimal values.

[0328] (3) Model solving algorithm design

[0329] The model solution process mainly includes two steps. The first step is to solve the theoretical optimal value, and the second step is to modify the theoretical optimal value according to the constraints. The specific process is as follows Figure 4 shown.

[0330] ① Set the initial value. Set the initial water supply in the first and second stages to be equal to the predicted water supply, that is,

[0331] At this time, the amount of discarded water l1=0, l2=0.

[0332] ② Determine whether the iteration is over. Calculate the marginal benefit g1[(x1) i ]The marginal benefit of the second stage g2[(x2) i ], 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 ③.

[0333] ③Fix the search step size. Determine whether i is equal to 0. If i≠0, calculate the product of the marginal differences of the 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, the search step size is retained, Δx i =Δx i-1 ; Otherwise, the optimal range of water supply in the first stage is (x1) i and (x1) i-1 We need to shorten the search step length, let Δx i=Δx i-1 / h (h is the step size adjustment coefficient, and h>1), and then enter step ④.

[0334] ④ Determine the iteration direction. The marginal benefit functions of the two stages have a monotonically decreasing property, which decreases as the independent variable increases. When the marginal benefit g1[(x1) i ] is greater than the marginal benefit g2[(x2) i ], the water supply x1 in the first stage is increased, and the water supply x2 in the second stage is reduced accordingly, that is, (x1) i =(x1) i-1 +Δx This step makes g1[(x1) i ] decreases, g2[(x2) i ] increases, the marginal benefit gap between the two stages narrows; when the marginal benefit g1[(x1) i ] is less than the marginal benefit g2[(x2) i ], the water supply x1 in the first stage is reduced, and the water supply x2 in the second stage is increased accordingly, that is, (x1) i =(x1) i-1 -Δx, This step makes g1[(x1) i ] increases, g2[(x2) i ] decreases, the marginal benefit gap between the two stages will still narrow. After determining the iteration direction, enter step ② again to complete the cycle.

[0335] Iteration to obtain the theoretical optimal value After that, we determine whether its value satisfies the constraint conditions. The value that satisfies the constraint conditions is retained, and the value that does not satisfy the constraint conditions is taken as the boundary value. After two steps of screening and calculation, we can finally get the optimal solution.

[0336] The present invention mainly constructs two two-stage reservoir dispatching models for flood season and non-flood season, respectively. The two models have different focuses when they are designed. The flood season model transforms the problem of coordinated control of flood control and benefit development in the flood season of the reservoir into a competition problem between the benefit development target in the decision-making stage and the flood control target in the reservation stage. In view of the forecast error, an error safety value is introduced to quantify the flood control risk. The optimization target is to maximize the water storage benefit in the decision-making stage and minimize the flood control risk in the reservation stage. A two-stage optimization hedging model for the flood season of the reservoir is constructed. Then, the KKT condition is used to derive the condition for the model to take the optimal solution, which is that the marginal benefit of water storage is equal to the marginal benefit of flood control. Finally, the solution algorithm of the flood season model is designed in combination with the function characteristic of the diminishing marginal benefit of the objective function. The core problem of the non-flood season model is the distribution of incoming water. The maximum expected economic benefit in the two stages is used as the objective function. The uncertainty of the forecast error is transformed by the Taylor formula. The KKT condition is also used to derive. When the marginal benefits of the two stages are equal, the model has the optimal solution. According to the function characteristic of the diminishing marginal benefit, the solution algorithm of the non-flood season model is designed.

[0337] Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Claims

1. An adaptive scheduling method for an agricultural water supply system, characterized in that: Taking into account the impact of forecast error and rainfall, a reservoir operation model for flood season and non-flood season is constructed. The reservoir operation decision is adaptively made according to the different focuses of 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 forecast error in the reservation stage is obtained by integration, so as to quantify the forecast error. In the non-flood season, the Taylor formula and expectation are used to quantify the forecast error. The decision-making stage of flood season reservoir dispatching is used to determine the dispatching mode of the reservoir and achieve the benefit-benefiting target of reservoir dispatching. The reservation stage is used to verify whether the decision-making mode in the decision stage can meet the future flood control requirements and achieve the flood control target of reservoir dispatching after dispatching. The flood season reservoir dispatching takes the minimum benefit difference rate and the minimum flood control risk rate in the decision stage and the reservation stage as the optimization target to establish an optimization dispatching model. The optimization dispatching model includes the flood season benefit-benefiting target function and the flood season flood control target function. The weighted summation method is used to transform the flood season benefit-benefiting target function and the flood season flood control target function into a single target function to construct the optimization dispatching model. The flood season reservoir dispatching model is solved through three steps of theoretical optimal solution iteration, simplified model constraint condition processing, and reservoir discharge volume restriction to obtain the optimal solution for flood season reservoir dispatching. The non-flood season reservoir operation constructs a reservoir operation model with the goal of maximizing the economic benefits in the decision-making stage and the reservation stage. Based on the goal of maximizing the economic benefits in the decision-making stage and the reservation stage, a corresponding non-flood season objective function is constructed, and the optimal solution for non-flood season reservoir operation is obtained by solving the theoretical optimal value and correcting the theoretical optimal value according to the constraint conditions.

2. The method for adaptively scheduling an agricultural water supply system according to claim 1, characterized in that: The time covered by the decision stage is shorter, while the time covered by the reservation stage is relatively longer. Suppose the total number of time periods included in the two stages is T, then the time period included in the decision stage is set to Δt, and the time period included in the reservation stage is set to (T-1)·Δt. The value of Δt is 12h or 1d.

3. The method for adaptively scheduling an agricultural water supply system according to claim 1, characterized in that: The flood season benefit 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 target. The smaller the value, the greater the benefit. The calculation formula of the benefit difference rate B- is: Among them, W is the pre-storage water volume, W max is the upper limit of pre-storage water volume, m is the shape coefficient, the larger the value is, the more obvious the nonlinearity is. When m>1, the above formula is a convex function with a minimum value; Benefit difference rate in decision-making stage and the benefit difference rate of the reserved stage They are Since the reserved water volume in the decision-making stage will be fully discharged in the reservation stage, W2 = 0, then The flood control objective function in the flood season takes the minimum flood control risk rate as the optimization target, and the risk rate in the decision-making stage and the reserve phase risk rate The calculation formula is R1＝0 If the weight of the benefit-promoting goal is set to ω, then the weight of the flood control goal is 1-ω, and R1=0. Substituting in, the objective functions of each stage are obtained as follows: The comprehensive objective function combining the flood season benefit objective function and the flood season flood control objective function is:

4. The method for adaptively scheduling an agricultural water supply system according to claim 3, characterized in that: The constraints of the comprehensive objective function include water balance constraints Reservoir capacity constraints 0≤W1≤W max Discharge volume constraints Discharge constraints at the decision-making stage: The water inflow at the decision-making stage is certain and controllable, so the constraint D1≤D 1，max It can always be satisfied. Considering that there is a certain amount of rainfall replenishment in the irrigation area, the lower limit constraint is finally determined as D1≥max(D 1，min -p1,0) Where p1 is the amount of water supplied by rainfall in the irrigation area during the decision-making stage. Constraints on water discharge during the reserved stage: Right now δ≥δ min Based on the above constraints, the dual-objective optimization model of reservoir flood season benefit and flood control is as follows: min G1(W1)+G2(δ) st 0≤W2≤W max D1≥max(D 1，min -p1,0) δ≥δ min 。 5. The method for adaptively scheduling an agricultural water supply system according to claim 4, characterized in that: The solution process of the dual-objective optimization model for flood prevention and benefit generation during flood season is as follows: Will Substitution Available definition is the remaining flood control capacity, expressed as RFCC, that is, W1+δ=RFCC RFCC is the maximum amount of water that the reservoir is allowed to discharge in the reservation stage without considering the forecast error. When the remaining flood control capacity RFCC>0, the reservoir stores more water in the decision-making stage to increase the benefits of the decision-making stage; or stores less water in the decision-making stage to increase the error safety value δ in the reservation stage and reduce the flood control risk. Therefore, the competitive relationship between the flood control and benefit goals 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 condition is used to explain and analyze the optimal solution of the model. The KKT condition is: 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, In the formula, f1(W1) is the marginal benefit of water storage, which represents the added value of water storage benefit caused by the unit pre-storage water volume W1. Among them, G1(W1) is a convex function, and f1(W1) is a decreasing function of W1, which has the economic characteristics of diminishing marginal benefits. f2(δ) also has the economic characteristics of diminishing marginal benefits. The marginal benefit of water storage when the optimal solution is achieved can be obtained from the three formulas of KKT conditions: and the marginal benefit of flood control f2(δ * ) is Some of the equations in the KKT condition are as follows -m δI (d * -d min )=0 When the constraints of the model are satisfied and are not boundary values, it can be seen 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 optimal condition for the model is the marginal benefit of water storage and the marginal benefit of flood control f2(δ * ) are equal, that is Will Substitute f2(δ * ),get and Placed in the same coordinate system, the transformed curve has undergone symmetric and translation transformation compared to the original image. If the two curves have an intersection in the domain of (0, RFCC), then there is a theoretical optimal solution, and the distance between the intersection and the straight line x = 0 is equal to The distance from the line x = RFCC is equal to δ * , The scheduling model can be simplified as min G1(W1)+G2(δ) st 0≤W1≤W max δ≥δ min but becomes The theoretical optimal pre-storage water volume can be obtained from the above formula: and error safety value δ * After that, the optimal solution can be obtained by simplifying the constraints of the model, and then the minimum water discharge constraint in the decision-making stage is considered, and finally the actual optimal pre-storage water volume can be obtained. Error safety value δ * and the amount of water discharged As a decision-making tool for reservoir operation, The Newton iteration method with faster convergence speed is used to solve the theoretical optimal pre-storage water volume that satisfies equal marginal benefits. and error safety value δ * The specific process includes: ① Determine whether the incoming water exceeds the limit Based on the amount of water forecasted in the reservation phase, determine whether the total amount of water forecasted for discharge will not exceed the maximum amount of water discharged when the reservoir does not store water in advance: If not (i.e. RFCC≤δ min ), then no pre-storage is performed in the reservoir decision-making stage. Calculation error safety value δ * and the amount of water discharged Output result; if it is possible (i.e. RFCC>δ min ), then go to step ②; ②Set the initial value Let the error safety value take the minimum error safety value, that is, (δ0) = δ min , according to the competition relationship, the pre-storage water volume (W1)0 = RFCC-(δ)0; ③Determine whether the iteration is over Calculate 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; ④Fix the search step length Determine whether j is equal to 0. If j≠0, calculate the product of the marginal differences of the 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 (δ) j and (δ) j-1 The search step length needs to be shortened, and Δδ=Δδ / h (h is the step length adjustment coefficient, and h>1), and then go to step ⑤; ⑤Determine the iteration direction The marginal benefit functions of flood control and water conservation have the property of monotonically decreasing, which decreases with the increase of independent variables. j ] is greater than the marginal benefit of flood control f2[(δ) j ], the error safety value δ is reduced, and the pre-storage 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 ] is reduced, and the marginal benefit of flood control f2[(δ) j ] increases, the gap in 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 ], the error safety value δ is increased, and the pre-storage 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, the marginal benefit of flood control f2[(δ) j ] is reduced, the gap in the marginal benefits of water storage and flood control will still be narrowed. After determining the iteration direction, enter step ③ again to complete the cycle. When 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-storage water volume is output and error safety value δ * , then judge and δ * Whether the constraints of the model are met, Calculate the water discharge volume in the decision-making stage according to the water balance equation in the decision-making stage Determine whether it meets the constraints. If so, the pre-storage water volume Error safety value δ * and the amount of water released during the decision-making stage is the optimal solution; if it is not satisfied, then Take the boundary value and adjust the pre-storage volume according to the water balance equation Error safety value δ * output the optimal solution.

6. The method for adaptively scheduling an agricultural water supply system according to claim 1, characterized in that: The non-flood season reservoir operation model includes the objective function max E[B1(x1+p1)]+E[B2(x2+p2)] In the formula, x1 and x2 are the water supply in the decision-making stage and the reservation stage, p1 and p2 are the water replenishment of the irrigation area during the decision-making stage and the reservation stage, E[B1(·)] and E[B2(·)] are the mathematical expectations of the economic benefits in the decision-making stage and the reservation stage, respectively. The objective function is optimized based on the constraints to obtain the optimized non-flood season reservoir operation model. maxE[B1(x1+p1)]+E[B2(x2+p2)] st x1≥max(x 1，min -p1,0) x2≥max(x 2，min -p2,0) W1≤W max W1≥0 l1，l2≥0。 7. The method for adaptively scheduling an agricultural water supply system according to claim 6, characterized in that: The constraints of the non-flood season reservoir operation model include water balance constraints, water supply constraints, reservoir capacity constraints and non-negative constraints. The water balance constraint Where W0 is the initial storage capacity of the reservoir, W1 is the final storage capacity of the reservoir in the decision-making stage, and W2 is the final storage capacity of the reservoir in the reservation stage. and are the forecast water inflow in the decision-making stage and the reservation stage, ε1 and ε2 are the runoff forecast errors in the decision-making stage and the reservation stage, l1 and l2 are the abandoned water in the decision-making stage and the reservation stage, respectively; Water supply constraint: The water supply of the reservoir should be greater than the gap after the irrigation area is replenished by rainfall. x1≥max(x 1，min -p1,0) x2≥max(x 2，min -p2,0) In the formula, x 1，min and x 2，min are the minimum water supply in the decision-making stage and the reservation stage, respectively; Reservoir capacity constraints 0≤W1≤W max Where W max To improve the storage capacity of the reservoir; Non-negative constraints l1，l2≥0。 8. The method for adaptively scheduling an agricultural water supply system according to claim 6, characterized in that: The method for solving the objective function of the reservoir operation model in 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; S1. Set initial value Let the initial water supply in the decision-making stage and the reservation stage be equal to the predicted water supply, that is, At this time, the amount of discarded water l1 = 0, l2 = 0; S2. Determine whether the iteration is finished Calculate the marginal benefit g1[(x1) i ] and the marginal benefit g2[(x2) i ], if the difference is less than the initial threshold ε, the iteration ends and the current variable value is the optimal solution. Otherwise, proceed to step S3; S3. Correct the search step length Determine whether i is equal to 0. If i≠0, calculate the product of the marginal differences of the 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, the search step size is retained, Δx i =Δx i-1 ; Otherwise, the optimal range of water supply in the decision-making stage is (x1) i and (x1) i-1 We need to shorten the search step length, let Δx i =Δx i-1 / h; h is the step length adjustment coefficient, and h>1, then go to step S4; S4. Determine the iteration direction The marginal benefit functions in the decision-making and reservation stages have a monotonically decreasing property, which decreases with the increase of the independent variable. When the marginal benefit g1[(x1) i ] is greater than the marginal benefit g2[(x2) i ], the water supply x1 in the decision-making stage is increased, and the water supply x2 in the reservation stage is reduced accordingly, that is, (x1) i =(x1) i-1 +Δx, This step makes g1[(x1) i ] decreases, g2[(x2) i ] increases, and the marginal benefit gap between the decision-making and reservation stages narrows; When the marginal benefit g1[(x1) i ] is less than the marginal benefit g2[(x2) i ], the water supply x1 in the decision-making stage is reduced, and the water supply x2 in the reservation stage is increased accordingly, that is, (x1) i =(x1) i-1 -Δx, This step makes g1[(x1) i ] increases, g2[(x2) i ] decreases, the marginal benefit gap between the two stages will still narrow. After determining the iteration direction, enter step S2 again to complete the cycle; Iteration to obtain the theoretical optimal value Finally, determine whether its value meets the constraints. The value that meets the constraints is retained, and the value that does not meet the constraints is taken as the boundary value. After two steps of screening and calculation, the optimal solution can be obtained.

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