CN106327065A - Water resource optimization configuration method for single pumping station - single reservoir system for direct canal supplement under full irrigation condition - Google Patents

Abstract

The invention relates to a combined operation dispatching method of a single supplementary water pumping station and a single reservoir for directly replenishing canals under sufficient irrigation conditions. The sum of the water supply of the reservoir and the single supplementary water pumping station in each period of the year and the water demand of the water receiving area are adjusted in a single year. The goal is to minimize the sum of the squares of the difference, and the water supply volume of the reservoir and the water replenishment volume of the pumping station are the decision variables at each time period. The flood control limit water level corresponds to the storage capacity, etc., and establishes a single pumping station-single reservoir system water resource optimization dispatching model that directly supplements the canal, and uses the dynamic programming successive approximation method to solve the problem, which can obtain the minimum water shortage in the water receiving area within a certain period of time, and Corresponding reservoir optimal water supply, discarded water and pumping station replenishment process. The invention can realize the optimal dispatch of water resources in a single pumping station-single reservoir system under the condition of full irrigation, and has important practical significance for improving the water resource efficiency of pumping station replenishing canals and the irrigation guarantee rate of irrigation areas.

Description

Water resource optimization of a single pumping station-single reservoir system with direct replenishment of canals under sufficient irrigation conditions configuration method

technical field

The invention relates to a method for joint operation scheduling of a single supplementary water pumping station and a single reservoir under sufficient irrigation conditions, and belongs to the technical field of optimal allocation of water resources in irrigation areas.

Background technique

At present, due to the uneven distribution of water resources in time and space, the economic and social development of many areas has been restricted. For irrigation areas with sufficient irrigation conditions, under the limited total amount of water resources and the scale of water source projects, the goal of maximizing the comprehensive benefits of water use is to strengthen regional The unified scheduling and management of water resources, the use and adjustment of water conservancy projects in the irrigation system as a unified whole, and the use of existing projects (such as joint scheduling and operation of reservoirs and pumping stations) to make them play a greater role are the key to solving the problem of water shortage in irrigation areas. the main way. The operation scheduling of the single pumping station-single reservoir system for direct replenishment of canals is a content of water resources management. How to rationally use the system water resources scheduling to achieve a certain goal and optimize the system benefits is a relatively common problem in the management and application of water conservancy projects.

Contents of the invention

The present invention aims at the single pumping station and single reservoir system that directly supplements the canal under sufficient irrigation conditions, considers the water shortage in the water receiving area under different water inflow frequencies, considers for the first time that the water shortage in the canal is directly supplemented by the water pumping station, and establishes an annual regulating reservoir -Mathematical model for combined optimal scheduling of pumping stations. Adjust the single pumping station-single reservoir joint operation dispatching system for a specific year of direct replenishment of canals. Knowing the number of time periods for reservoir water supply, initial storage capacity, dead storage capacity, storage capacity corresponding to flood control limit water level, annual total water supply, and each time period In the process of water inflow, evaporation and leakage, the total annual allowable water lift of the water supply pump station, and the process of crop water demand in the water receiving area in each period, the dynamic programming successive approximation method is used to solve the problem, and the water receiving area in a certain period of time can be obtained The minimum water shortage, and the corresponding process of optimal water supply, discarded water and pumping station water replenishment.

The present invention scheme is as follows:

A method for optimal configuration of water resources in a single pumping station-single reservoir system that directly replenishes canals under sufficient irrigation conditions, wherein water shortages in canals are directly supplemented by water-lifting pumping stations, including the following steps:

1. Model construction, including the following steps 1 to 2:

1. Taking the minimum sum of the squares of the difference between the sum of the water supply of a single annual regulating reservoir and a single supplementary pumping station at each time period of the year and the water demand in the receiving area as the goal, the following objective function is established:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; YS</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula: F is the minimum sum of squares of the difference between water supply and demand in each period of the year of the research object; Z is the sum of squares of the difference between water supply and demand in each period of the year of the research object; N is the number of periods divided in the year; i is the period number (i= 1, 2,...N); Xi and Yi are the water supply and replenishment of the reservoir and the pumping station in the _i -th period (10,000 m ³ ); YS _i is the water demand in the _i -th period of the water receiving area (10,000 m ³ ); the objective function is expressed by the sum of squares in order to accelerate the reduction of the deviation between the water supply of the system and the water demand of the water receiving area.

2. Set constraints

Including the constraints on the total annual water supply of reservoirs and water replenishment pumping stations, the constraints on the water balance of reservoirs without direct replenishment by pumping stations, and the constraints on reservoir capacity.

2. Model solution

Firstly, data preparation is carried out, specifically including: dividing a year into N periods; according to the initial water level of the reservoir, find the water level-storage capacity relationship curve to determine the initial storage capacity V ₀ of the reservoir; refer to the reservoir operation management regulations to determine the annual total water supply SK, The dead storage capacity V _min and the storage capacity V _P corresponding to the flood control limit water level; according to the local meteorological and hydrological data of the reservoir, calculate and determine the water inflow LS _i , evaporation and seepage EF _i of the reservoir in each period; determine the supplementary pumping station according to the working system of the pumping station The total amount of water allowed to be lifted in a year BZ; according to the crop species, planting scale, multiple cropping index and other data in the water receiving area, calculate and determine the water demand YS _i of the crops in the water receiving area in each period; where, i=1,2,...,N;

Secondly, the dynamic programming successive approximation is used to solve the problem.

Further, the constraints include:

(1) Constraints on the total annual water supply of reservoirs and supplementary pumping stations: the amount of water that may be provided by water supply projects in consideration of water demand requirements under the conditions of different guaranteed rates in different years.

X ₁ +X ₂ +…+X _N ≤SK (2)

Y ₁ +Y ₂ +…+Y _N ≤ BZ (3)

In the formula: SK is the total annual water supply of the reservoir (10,000 m ³ ); BZ is the total annual water supply allowed by the supplementary pumping station (10,000 m ³ ).

(2) Reservoir water balance constraints without pumping station direct replenishment:

V _i =V _i-1 +LS _i -PS _i -EF _i -X _i , (i=1,2,...,N) (4)

In the formula: V _i , _{V i-1} are the storage capacity of the reservoir at the end of period _i and _i -1 respectively (10,000 m ³ ); ³ ), discarded water (10,000 m ³ ), evaporation and seepage (10,000 m ³ ).

(3) Reservoir capacity constraint: The storage capacity of the reservoir at the end of each period should be between the dead storage capacity of the reservoir and the storage capacity corresponding to the flood control limit water level, that is:

V _min ≤ V _i ≤ V _P , (i=1,2,···,N) (5)

In the formula: V _min and V _P are the dead storage capacity of the reservoir and the storage capacity corresponding to the flood control limit water level (10,000 m ³ ).

Further, the specific steps of the dynamic programming successive approximation solution are as follows:

(1) Carry out research in the study area, collect statistics on the daily water supply of the reservoir and the water replenishment scale of the pumping station, the data should have met the requirements of formulas (2) to (3), and the storage capacity of the reservoir at a certain stage should not be lower than the dead storage capacity V _min . Taking the reservoir stage water supply X _1i that actually satisfies the sufficient irrigation conditions of the specific water receiving area as the initial iterative value, and substituting it into formula (1), the original models (1)-(5) are converted into The water quantity Y _i is the decision variable, and the total amount of pumping water in the first i stages λ _i is the one-dimensional dynamic programming model of the state variable, which is solved by one-dimensional dynamic programming method; where, i=1,2,...N.

(2) Referring to the solution principle of one-dimensional dynamic programming, the corresponding recurrence equation is:

1) Phase i=1:

g ₁ (λ ₁ )=min(X ₁₁ +Y ₁₁ -YS ₁ ) ² (6)

The water supply quantity X ₁₁ of the reservoir during this period has been given by the initial value, and the state variable λ ₁ can be discretized in the corresponding feasible region: λ ₁ =0, W ₁ , W ₂ ,...,BZ. For each discrete λ ₁ , the decision variable (pumping station replenishment volume Y ₁₁ ) can be discrete within the corresponding feasible domain, such as 00,000 m ³ , 50,000 m ³ , 100,000 m ³ , 150,000 m ³ , ... Y _{11, max} , etc. (Y _{11, max} is the maximum water replenishment capacity of the pumping station in the first stage), which should satisfy: Y ₁₁ ≥λ ₁ . Substitute Y ₁₁ that meets the requirements into formula (6) to obtain the optimal Y ₁₁ and its corresponding g ₁ (λ ₁ ) for each discrete value of λ ₁ .

Then, according to formula (4), the storage capacity of the reservoir at the end of the first stage is V ₁ =V ₀ +LS ₁ -EF ₁ -X ₁₁ . At this time, the water abandonment of the reservoir has not been considered, and the formula (5) is used to test. For the corresponding storage capacity V _p , the excess part is regarded as the discarded water volume PS ₁₁ of the reservoir, at this time V ₁ ^* = V _P ; otherwise, if it is not exceeded, then PS ₁₁ = 0, and V ₁ ^* = V ₁ at this time.

2) Phase i=2, 3, ... N-1:

g _i (λ _i )=min[(X _1i +Y _1i -YS _i ) ² +g _i-1 (λ _i-1 )] (7)

The reservoir water supply X _1i during this period has been given by the initial value, and the state variable λ _i is also discretized: λ _i = 0, W ₁ , W ₂ ,..., BZ. For each discrete λ _i , the decision variable (pumping station replenishment water Y _1i ) is discrete as above, and should satisfy:

State transition equation: λ _i-1 ＝λ _i -Y _1i (8)

In the formula: i=2, 3, ..., N-1.

Substituting each discrete value of Y _1i into (X _1i +Y _1i -YS _i ) ² in equation (7) respectively, from state transition equation (8), find stage i-1 that satisfies The required value of g _i-1 (λ _i-1 ), thus obtaining the optimal Y _1i process and its corresponding g _i (λ _i ) meeting the requirement of λ _i . Similarly, according to formula (4), the storage capacity of the reservoir at the end of the i-th period is V _i =V _i-1 +LS _i -EF _i -X _1i . At this time, the water abandonment of the reservoir has not been considered, and the test is carried out using formula (5). For the storage capacity V _P corresponding to the limit water level, the excess part is regarded as the discarded water volume PS _1i of the reservoir, at this time V _i ^* = V _P ; otherwise, if it is not exceeded, then PS _1i = 0, and at this time V _i ^* = V _i . Deduced from this, the corresponding process PS _1i of water discarded by the reservoir can be obtained. Among them, i=1,...i.

3) Phase N:

The water supply volume X _1N of the reservoir during this period has been given by the initial value, and the state variable λ _N = BZ; the decision variable (water replenishment volume Y _1N of the pumping station) is also discrete in the corresponding feasible region, which should satisfy: λ _N-1 = λ _N -Y _1N .

By adopting the method described in step 2), the optimal water replenishment process Y _1i of the pumping station meeting the requirement of λ _N and the corresponding process PS _1i of water discarded in the reservoir are finally obtained, where i=1,...N.

(3) Taking the process Y _1i of pumping station supplementary channel water obtained in step (2) as the initial given value, and substituting it into formula (1), the original models (1)-(5) are transformed into the reservoir water supply in each stage X _i is the decision variable, and the total water supply of the reservoir in the previous i stages λ _i ' is a one-dimensional dynamic programming model of the state variable. Referring to step (2), the one-dimensional dynamic programming method is used to solve the problem, and the optimal reservoir that satisfies the requirement of λ _N ' is obtained A water supply process X _2i (i=1,...N), and a corresponding discarded water process PS _2i , where i=1,...N.

(4) Use the reservoir water supply process X _2i obtained in step (3) as the initial given value, substitute it into formula (1), repeat steps (2) to (3), and repeatedly approximate the solution until two adjacent objective functions If the error accuracy of the optimal value is less than 1%, the model optimization ends. The reservoir water supply process X _mi and the pumping station replenishment water process Y _mi obtained from the last optimization are used as the optimal solution of the original model. At the same time, the optimal value of the objective function and the optimal water abandonment process PS _mi of the reservoir can be obtained. Among them, i=1,...N, m is the serial number of successive approximation iterations of dynamic programming.

The invention is convenient to solve and has reliable accuracy, and can be popularized and applied to large and medium-sized irrigation area management units that use a single pump station and a single reservoir for water supply under sufficient irrigation conditions, so as to achieve the purpose of optimal allocation of water resources in the irrigation area and improve the economic, social and ecological benefits of the irrigation area.

Description of drawings

Figure 1 is a schematic diagram of the water resources generalization system for direct supplementary canal single pumping station-single reservoir.

detailed description

The schematic diagram of the single pumping station-single reservoir water resources generalization system is shown in Figure 1.

The goal is to minimize the square sum of the difference between the sum of the water supply of a single annual regulating reservoir and a single supplementary pumping station in each period of the year and the water demand in the water receiving area. The total annual water supply of reservoirs and pumping stations, reservoir scheduling criteria, water balance criteria, dead storage capacity, flood control limit water level corresponding storage capacity, etc. are constrained conditions, and a single pumping station-single reservoir system water resource optimization scheduling model for direct replenishment of canals is established. Specifically as follows:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; YS</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula: F is the minimum sum of squares of the difference between water supply and demand in each period of the year of the research object; Z is the sum of squares of the difference between water supply and demand in each period of the year of the research object; N is the number of periods divided in the year; i is the period number (i= 1, 2,...N); Xi and Yi are the water supply and replenishment of the reservoir and the pumping station in the _i -th period (10,000 m ³ ); YS _i is the water demand in the _i -th period of the water receiving area (10,000 m ³ ); the objective function is expressed by the sum of squares in order to accelerate the reduction of the deviation between the water supply of the system and the water demand of the water receiving area.

3.1.2 Constraints

(1) Constraints on the total annual water supply: the amount of water that may be provided by the water supply project in consideration of the water demand requirements under the circumstances of different guarantee rates in different years.

X ₁ +X ₂ +…+X _N ≤SK (2)

Y ₁ +Y ₂ +…+Y _N ≤ BZ (3)

In the formula: SK is the total annual water supply of the reservoir (10,000 m ³ ); BZ is the total annual water supply allowed by the supplementary pumping station (10,000 m ³ ).

(2) Reservoir water balance constraints without pumping station direct replenishment:

V _i =V _i-1 +LS _i -PS _i -EF _i -X _i , (i=1,2,...,N) (4)

In the formula: V _i , _{V i-1} are the storage capacity of the reservoir at the end of period _i and _i -1 respectively (10,000 m ³ ); ³ ), discarded water (10,000 m ³ ), evaporation and seepage (10,000 m ³ ).

(3) Reservoir capacity constraint: The storage capacity of the reservoir at the end of each period should be between the dead storage capacity of the reservoir and the storage capacity corresponding to the flood control limit water level, that is:

V _min ≤ V _i ≤ V _P , (i=1,2,···,N) (5)

In the formula: V _min and V _P are the dead storage capacity of the reservoir and the storage capacity corresponding to the flood control limit water level (10,000 m ³ )

3.2 Model Features

(1) Considering that the total amount of water consumption should be strictly controlled in the development and utilization of water resources, the constraints of the total annual water supply of the reservoir and the total amount of water allowed to be lifted by the pumping station are added to the constraints of the model, that is, formula (2)～( 3).

(2) Considering the reservoir water balance and storage capacity constraints in the constraint conditions, the reservoir-pumping station system water resource optimization scheduling mode of "reservoir replenishment in idle hours and combined water supply with reservoir stations in busy hours" can be realized. If the storage capacity of the reservoir at the end of a certain period of time is lower than the dead storage capacity of the reservoir during idle time, consider using a water supply pump station to replenish water directly to the channel during this period; To ensure the dispatching demand of reservoir capacity. According to the water storage capacity of the reservoir during busy hours, it is considered to jointly supply water to the water receiving area by the reservoir and the pumping station, in order to meet the water demand of the water users as much as possible.

3.3 Model solution

The above models (1)-(5) are one-stage separable nonlinear mathematical models. In the objective function, the water demand YS _i in each stage of the water receiving area is known, and the model is the period i divided by the water supply period of the reservoir (i= 1, 2, ..., N) are stage variables, reservoir water supply X _i and pumping station replenishment water Y _i are decision variables at each stage, and are solved by dynamic programming successive approximation method.

Assuming that the initial reservoir capacity V ₀ of the annual regulation reservoir is known, the equations (2)-(3) in the model are the dynamic programming coupling constraints, and the equation (4) is the water balance criterion for each period of the reservoir operation; it is solved by the dynamic programming successive approximation method, and at the same time Use Equation (5) to test the storage capacity, correct the reservoir storage capacity at the end of each stage, and finally obtain the minimum water shortage in the water receiving area within a certain period of time, as well as the corresponding reservoir optimal water supply X _i , discarded water PS _i and pumping station replenishment The measurement process Y _i (i=1, 2, ..., N) provides a basis for the optimal scheduling of water resources in the irrigation area where the single pumping station-single reservoir system is located under the condition of sufficient irrigation.

Divide one year into N periods; find the water level-storage capacity relationship curve according to the initial water level of the reservoir, and determine the initial reservoir capacity V ₀ ; refer to the reservoir operation management regulations to determine the annual total water supply SK, dead storage capacity V _min , and flood control limits The storage capacity V _P corresponding to the water level; according to the local meteorological and hydrological data of the reservoir, calculate and determine the water inflow LS _i , evaporation and leakage EF _i of the reservoir in each period; determine the annual allowable total water lifting BZ of the supplementary pumping station according to the working system of the pumping station; According to the crop species, planting scale, multiple cropping index and other data in the water receiving area, calculate and determine the crop water demand YS _i (i=1,2,...N) in each water receiving area.

The dynamic programming successive approximation solution process is as follows:

(1) Carry out research in the study area, collect statistics on the daily water supply of the reservoir and the water replenishment scale of the pumping station, the data should have met the requirements of formulas (2) to (3), and the storage capacity of the reservoir at a certain stage should not be lower than the dead storage capacity V _min . Taking the stage water supply X _1i (i=1,2,…N) of the reservoir stage that actually meets the sufficient irrigation conditions of the specific water receiving area as the initial iterative value, and substituting it into formula (1), the original model (1)～( 5) It is transformed into a one-dimensional dynamic programming model with the amount of water Y _i replenished by pumping stations at each stage as the decision variable, and the total amount of water replenished by pumping stations in the previous i stages λ _i as the state variable, and is solved by one-dimensional dynamic programming.

(2) Referring to the solution principle of one-dimensional dynamic programming, the corresponding recurrence equation is:

1) Phase i=1:

g ₁ (λ ₁ )=min(X ₁₁ +Y ₁₁ -YS ₁ ) ² (6)

The water supply quantity X ₁₁ of the reservoir during this period has been given by the initial value, and the state variable λ ₁ can be discretized in the corresponding feasible region: λ ₁ =0, W ₁ , W ₂ ,...,BZ. For each discrete λ ₁ , the decision variable (pumping station replenishment volume Y ₁₁ ) can be discrete within the corresponding feasible domain, such as 00,000 m ³ , 50,000 m ³ , 100,000 m ³ , 150,000 m ³ , ... Y _{11, max} , etc. (Y _{11, max} is the maximum water replenishment capacity of the pumping station in the first stage), which should satisfy: Y ₁₁ ≥λ ₁ . Substitute Y ₁₁ that meets the requirements into formula (6) to obtain the optimal Y ₁₁ and its corresponding g ₁ (λ ₁ ) for each discrete value of λ ₁ .

Then, according to formula (4), the storage capacity of the reservoir at the end of the first stage is V ₁ =V ₀ +LS ₁ -EF ₁ -X ₁₁ . At this time, the water abandonment of the reservoir has not been considered, and the formula (5) is used to test. For the corresponding storage capacity V _P , the excess part is regarded as the discarded water volume PS ₁₁ of the reservoir, at this time V ₁ ^* = V _P ; otherwise, if it is not exceeded, then PS ₁₁ = 0, and V ₁ ^* = V ₁ at this time.

2) Stage i=2, 3, ... N-1:

g _i (λ _i )=min[(X _1i +Y _1i -YS _i ) ² +g _i-1 (λ _i-1 )] (7)

The reservoir water supply X _1i during this period has been given by the initial value, and the state variable λ _i is also discretized: λ _i = 0, W ₁ , W ₂ ,..., BZ. For each discrete λ _i , the decision variable (pumping station replenishment water Y _1i ) is discrete as above, and should satisfy:

State transition equation: λ _i-1 ＝λ _i -Y _1i (8)

In the formula: i=2, 3, ..., N-1.

Substituting each discrete value of Y _1i into (X _1i +Y _1i -YS _i ) ² in equation (7) respectively, from state transition equation (8), find stage i-1 that satisfies The required g _i-1 (λ _i-1 ) value, thereby obtaining the optimal Y _1i process (i=1,...i) and its corresponding g _i (λ _i ) meeting the requirement of this λ _i . Similarly, according to formula (4), the storage capacity of the reservoir at the end of the i-th period is V _i =V _i-1 +LS _i -EF _i -X _1i . At this time, the water abandonment of the reservoir has not been considered, and the test is carried out using formula (5). For the storage capacity V _P corresponding to the limit water level, the excess part is regarded as the discarded water volume PS _1i of the reservoir, at this time V _i ^* = V _P ; otherwise, if it is not exceeded, then PS _1i = 0, and at this time V _i ^* = V _i . Deduced from this, the corresponding process PS _1i (i=1, .

3) Phase N:

g _N (λ _N )=min[(X _1N +Y _1N -YS _N ) ² +g _N-1 (λ _N-1 )] (9)

The water supply volume X _1N of the reservoir during this period has been given by the initial value, and the state variable λ _N = BZ; the decision variable (water replenishment volume Y _1N of the pumping station) is also discrete in the corresponding feasible region, which should satisfy: λ _N-1 = λ _N -Y _1N .

Using the method described in step 2), finally obtain the optimal water replenishment process Y _1i (i=1,...N) of the pumping station that meets the requirements of the λ _N , and the corresponding process PS _1i (i=1,...N) of the water discarded in the reservoir .

(3) Taking the process Y _1i of pumping station supplementary channel water obtained in step (2) as the initial given value, and substituting it into formula (1), the original models (1)-(5) are transformed into the reservoir water supply in each stage X _i is the decision variable, and the total water supply of the reservoir in the previous i stages λ _i ' is a one-dimensional dynamic programming model of the state variable. Referring to step (2), the one-dimensional dynamic programming method is used to solve the problem, and the optimal reservoir that satisfies the requirement of λ _N ' is obtained The water supply process X _2i (i=1,...N), and the corresponding discarded water process PS _2i (i=1,...N).

(4) Use the reservoir water supply process X _2i obtained in step (3) as the initial given value, substitute it into formula (1), repeat steps (2) to (3), and repeatedly approximate the solution until two adjacent objective functions If the error accuracy of the optimal value is less than 1%, the model optimization ends. The reservoir water supply process _Xmi obtained in the last optimization and the pumping station water supply process _Ymi are used as the optimal solution of the original model. At the same time, the optimal value of the objective function and the optimal water abandonment process _PSmi of the reservoir can be obtained (i= 1,...N). Among them, m is the number of successive approximation iterations of dynamic programming.

The above invention is convenient to solve and has reliable accuracy, and can be popularized and applied by large and medium-sized irrigation area management units that use a single pump station-single reservoir for water supply under sufficient irrigation conditions, so as to achieve the purpose of optimal allocation of water resources in the irrigation area and improve the economic, social and ecological benefits of the irrigation area.

Claims (3)

1. A single pumping station-single reservoir system water resource optimization method for directly supplementing canals under sufficient irrigation conditions, directly replenishing water shortages in canals by the pumping station, is characterized in that, specifically comprises the following steps: 1. Model construction, including the following steps: 1. Taking the minimum of the square sum of the difference between the sum of the water supply of a single annual regulating reservoir and a single supplementary pump station at each time period of the year and the water demand of the receiving area as the goal, the following objective function is established: $\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; YS</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ In the formula: F is the minimum sum of squares of the difference between water supply and demand in each period of the year of the research object; Z is the sum of squares of the difference between water supply and demand in each period of the year of the research object; N is the number of periods divided in the year; i is the period number (i= 1, 2,...N); Xi and Yi are the water supply and replenishment of the reservoir and the pumping station in the _i -th period (10,000 m ³ ); YS _i is the water demand in the _i -th period of the water receiving area (10,000 m ³ ); the objective function adopts the sum of squares expression in order to accelerate the reduction of the deviation between the system water supply and the water demand of the water receiving area; 2. Set constraints, including constraints on the total annual water supply of reservoirs and pumping stations, water balance constraints and reservoir capacity constraints for reservoirs without direct replenishment by pumping stations. 2. Model solution Firstly, data preparation is carried out, specifically including: dividing a year into N periods; according to the initial water level of the reservoir, find the water level-storage capacity relationship curve to determine the initial storage capacity V ₀ of the reservoir; refer to the reservoir operation management regulations to determine the annual total water supply SK, The dead storage capacity V _min and the storage capacity V _P corresponding to the flood control limit water level; according to the local meteorological and hydrological data of the reservoir, calculate and determine the water inflow LS _i , evaporation and seepage EF _i of the reservoir in each period; determine the supplementary pumping station according to the working system of the pumping station The annual allowable total water withdrawal BZ; according to the crop varieties, planting scale, multiple cropping index and other data in the water receiving area, calculate and determine the water demand YS _i of the crops in the water receiving area in each period; where, i=1,2,...,N. Secondly, the dynamic programming successive approximation is used to solve the problem. 2. The method according to claim 1, wherein the constraints set are as follows: (1) Constraints on the total annual water supply of reservoirs and supplementary pumping stations: the amount of water that may be provided by water supply projects in consideration of water demand requirements under the conditions of different guarantee rates in different years. X ₁ +X ₂ +…+X _N ≤SK (2) Y ₁ +Y ₂ +…+Y _N ≤ BZ (3) In the formula: SK is the total annual water supply of the reservoir (10,000 m ³ ); BZ is the total annual water supply allowed by the supplementary pumping station (10,000 m ³ ). (2) Reservoir water balance constraints without pumping station direct replenishment: V _i =V _i-1 +LS _i -PS _i -EF _i -X _i , (i=1,2,...,N) (4) In the formula: V _i , _{V i-1} are the storage capacity of the reservoir at the end of period _i and _i -1 respectively (10,000 m ³ ); ³ ), discarded water (10,000 m ³ ), evaporation and seepage (10,000 m ³ ). (3) Reservoir capacity constraint: The storage capacity of the reservoir at the end of each period should be between the dead storage capacity of the reservoir and the storage capacity corresponding to the flood control limit water level, that is: V _min ≤ V _i ≤ V _P , (i=1,2,...,N) (5) In the formula: V _min and V _P are the dead storage capacity of the reservoir and the storage capacity corresponding to the flood control limit water level (10,000 m ³ ). 3. method according to claim 2, is characterized in that, the concrete steps of dynamic programming successive approximation solution are as follows: (1) Carry out research in the study area, collect statistics on the daily water supply of the reservoir and the water replenishment scale of the pumping station, the data should have met the requirements of formulas (2) to (3), and the storage capacity of the reservoir at a certain stage should not be lower than the dead storage capacity V _min . Taking the reservoir stage water supply X _1i that actually satisfies the sufficient irrigation conditions of the specific water receiving area as the initial iterative value, and substituting it into formula (1), the original models (1)-(5) are converted into The water quantity Y _i is the decision variable, and the total amount of pumping water in the first i stages λ _i is the one-dimensional dynamic programming model of the state variable, which is solved by one-dimensional dynamic programming method; where, i=1,2,...N. (2) Referring to the solution principle of one-dimensional dynamic programming, the corresponding recurrence equation is: 1) Phase i=1: g ₁ (λ ₁ )=min(X ₁₁ +Y ₁₁ -YS ₁ ) ² (6) The water supply quantity X ₁₁ of the reservoir during this period has been given by the initial value, and the state variable λ ₁ can be discretized in the corresponding feasible region: λ ₁ =0, W ₁ , W ₂ ,...,BZ. For each discrete λ ₁ , the decision variable Y ₁₁ is discrete in the corresponding feasible region, which should satisfy: Y ₁₁ ≥λ ₁ . Substitute Y ₁₁ that meets the requirements into formula (6) to obtain the optimal Y ₁₁ and its corresponding g ₁ (λ ₁ ) for each discrete value of λ ₁ . Then, according to formula (4), the storage capacity of the reservoir at the end of the first stage is V ₁ =V ₀ +LS ₁ -EF ₁ -X ₁₁ . At this time, the water abandonment of the reservoir has not been considered, and the formula (5) is used to test. For the corresponding storage capacity V _p , the excess part is regarded as the discarded water volume PS ₁₁ of the reservoir, at this time V ₁ ^* = V _P ; otherwise, if it is not exceeded, then PS ₁₁ = 0, and V ₁ ^* = V ₁ at this time. 2) Stage i=2, 3, ... N-1: g _i (λ _i )=min[(X _1i +Y _1i -YS _i ) ² +g _i-1 (λ _i-1 )] (7) The reservoir water supply X _1i during this period has been given by the initial value, and the state variable λ _i is also discretized: λ _i = 0, W ₁ , W ₂ ,..., BZ. For each discrete λ _i , the decision variable Y _1i is discrete as above, and should satisfy: State transition equation: λ _i-1 ＝λ _i -Y _1i (8) In the formula: i=2, 3, ..., N-1. Substituting each discrete value of Y _1i into (X _1i +Y _1i -YS _i ) ² in equation (7) respectively, from state transition equation (8), find stage i-1 that satisfies The required value of g _i-1 (λ _i-1 ), thus obtaining the optimal Y _1i process and its corresponding g _i (λ _i ) meeting the requirement of λ _i . Similarly, according to formula (4), the storage capacity of the reservoir at the end of the i-th period is V _i =V _i-1 +LS _i -EF _i -X _1i . At this time, the water abandonment of the reservoir has not been considered, and the test is carried out using formula (5). For the storage capacity V _p corresponding to the limited water level, the excess part is regarded as the discarded water volume PS _1i of the reservoir, at this time V _i ^* = V _P ; otherwise, if it is not exceeded, then PS _1i = 0, and at this time V _i ^* = V _i . Deduced from this, the corresponding process PS _1i of water discarded by the reservoir can be obtained. Among them, i=1,...i. 3) Stage N: g _N (λ _N )=min[(X _1N +Y _1N -YS _N ) ² +g _N-1 (λ _N-1 )] (9) The water supply X _1N of the reservoir during this period has been given by the initial value, and the state variable λ _N = BZ; the decision variable Y _1N is also discrete in the corresponding feasible region, which should satisfy: λ _N-1 = λ _N -Y _1N . By adopting the method described in step 2), the optimal water replenishment process Y _1i of the pumping station meeting the requirement of λ _N and the corresponding process PS _1i of water discarded in the reservoir are finally obtained, where i=1,...N. (3) Taking the process Y _1i of pumping station supplementary channel water obtained in step (2) as the initial given value, and substituting it into formula (1), the original models (1)-(5) are transformed into the reservoir water supply in each stage X _i is the decision variable, and the total water supply of the reservoir in the previous i stages λ _i ' is a one-dimensional dynamic programming model of the state variable. Referring to step (2), the one-dimensional dynamic programming method is used to solve the problem, and the optimal reservoir that satisfies the requirement of λ _N ' is obtained A water supply process X _2i (i=1,...N), and a corresponding discarded water process PS _2i , where i=1,...N. (4) Use the reservoir water supply process X _2i obtained in step (3) as the initial given value, substitute it into formula (1), repeat steps (2) to (3), and repeatedly approximate the solution until two adjacent objective functions If the error accuracy of the optimal value is less than 1%, the model optimization ends. The reservoir water supply process X _mi and the pumping station replenishment water process Y _mi obtained from the last optimization are used as the optimal solution of the original model. At the same time, the optimal value of the objective function and the optimal water abandonment process PS _mi of the reservoir can be obtained. Among them, i=1,...N, m is the serial number of successive approximation iterations of dynamic programming.