CN106228276B - Water resource optimization configuration method for single pump station-single reservoir system for directly supplementing channels under insufficient irrigation condition - Google Patents

Water resource optimization configuration method for single pump station-single reservoir system for directly supplementing channels under insufficient irrigation condition Download PDF

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CN106228276B
CN106228276B CN201610669719.3A CN201610669719A CN106228276B CN 106228276 B CN106228276 B CN 106228276B CN 201610669719 A CN201610669719 A CN 201610669719A CN 106228276 B CN106228276 B CN 106228276B
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龚懿
程吉林
张礼华
陈兴
蒋晓红
袁承斌
周建康
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Yangzhou University
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Abstract

The invention relates to a method for scheduling the joint operation of a single water replenishing pump station and a single reservoir of a direct channel replenishment under the condition of insufficient irrigation, which is characterized in that the maximum annual yield of crops in a water receiving area is an objective function, the water supply quantity of the reservoir and the pump station in each growth stage of the crops is a decision variable, the annual available water supply quantity of the reservoir, the annual available water supply quantity of the water replenishing pump station without the pump station, the reservoir water balance of the direct channel replenishment of the reservoir, the reservoir capacity, the annual allowable water lifting total quantity of the water replenishing pump station and the like are taken as constraint conditions, a water resource optimization scheduling model of the single pump station-single reservoir system of the direct channel replenishment is established, and the dynamic programming successive approximation method is adopted to solve, so that the maximum annual yield of the. The method can realize the optimized scheduling of the water resource of the single-pump-station-single-reservoir system for directly supplementing the channel under the condition of insufficient irrigation, and has important practical significance for improving the channel supplementing water resource efficiency of the pump station and the irrigation guarantee rate of the irrigation district.

Description

Water resource optimization configuration method for single pump station-single reservoir system for directly supplementing channels under insufficient irrigation condition
Technical Field
The invention relates to a method for jointly operating and scheduling a single water replenishing pump station and a single reservoir under the condition of insufficient irrigation, belonging to the technical field of water resource optimization configuration of irrigation areas.
Background
At present, because the water resources are unevenly distributed in time and space, the economic and social development of regions is restricted, for regions which are not irrigated sufficiently, under the condition that the total quantity of available water resources is insufficient, the maximum comprehensive benefit of water is used as a target, the unified scheduling and management of regional water resources are enhanced, the hydraulic engineering of an irrigation system is used as a unified whole for application and regulation, and the established engineering (such as reservoir and pump station combined scheduling operation) is used for playing a greater role, so that the method is a main way for solving the problem of water shortage in the irrigation regions. The operation scheduling of a single pump station-single water reservoir system of a direct channel supplementing is a content of water resource management, and how to reasonably apply system water resource scheduling to enable a certain target system to have the best benefit is a common problem in the management and application of hydraulic engineering.
Disclosure of Invention
The invention aims at a single-pump station-single-reservoir system for directly supplementing channels under insufficient irrigation, considers the water shortage condition of reservoir areas under different water supply frequencies, and establishes an annual adjustment reservoir-pump station combined optimization scheduling mathematical model by the water shortage of a water supplementing pump station and a reservoir combined supplementing channel. Aiming at a specific direct canal-supplementing annual regulation single pump station-single reservoir combined operation scheduling system, under the condition constraints of the known number of stages of the crop whole growth period, the initial reservoir capacity of a reservoir, the dead reservoir capacity, the reservoir capacity corresponding to the flood control limit water level, the total annual available water supply, the water supply amount of each stage, the evaporation and leakage amount, the total annual allowable water lifting amount of a water-supplementing pump station, the available water supply amount of each stage, and the water demand amount and the maximum annual output of each stage under the condition of full irrigation of crops in a water receiving area, a dynamic planning successive approximation method is adopted to solve, so that the maximum annual output of the crops under the condition of insufficient irrigation, and the optimal water supply amount, the water abandonment amount and the water supplementing amount of the pump station of each corresponding stage can be obtained.
The scheme of the invention is as follows:
a water resource optimal allocation method for a single pump station-single reservoir system for directly supplementing channels under the condition of insufficient irrigation is characterized in that a water supplementing pump station and a reservoir jointly supply water to the channels, and the channels supplement water shortage in water receiving areas, and comprises the following steps:
firstly, model construction, comprising the following steps 1-2:
1. establishing the following objective function by taking the maximum annual yield of crops in the water receiving area as an objective:
Figure BDA0001077683500000011
in the formula:f is the maximum annual yield (kg) of crops in the water receiving area; y is the actual annual yield (kg) of crops in the water receiving area; n is the number of crop growing stages divided in the year; i is a stage number, i is 1,2, … …, N; y ismThe maximum annual yield (kg) of crops under full irrigation conditions, KiThe moisture sensitivity coefficient of the crop in the stage i of water shortage on yield influence; xi、YiWater supply of reservoir at stage i under insufficient irrigation condition (ten thousand meters)3) Water supply quantity of pump station3) Water supply X for reservoiriWater supply Y for pump stationi，YSiWater demand (ten thousand meters) for the i stage crops under full irrigation conditions3)。
2. Setting constraint conditions
The method comprises a total amount of available water supply of a reservoir per year constraint condition, a total amount of allowable water lifting of a water replenishing pump station per year constraint condition, a water supply amount available quantity constraint condition of a water replenishing pump station stage, a reservoir water balance constraint condition without a pump station and a reservoir capacity constraint condition of a reservoir direct channel replenishing channel.
Second, model solution
Firstly, data preparation is carried out, and the method specifically comprises the following steps: dividing the whole growth period of crops into N stages; according to the initial water level of the reservoir, searching a relation curve of the water level and the reservoir capacity, and determining the initial reservoir capacity V of the reservoir0(ii) a According to the actual operation condition of the reservoir, the total quantity SK of annual available water supply and the dead storage volume V are determinedminReservoir capacity V corresponding to flood control water level limitP(ii) a Determining the amount LS of water coming from each stage of the reservoir according to the local meteorological hydrological data of the reservoiriEvaporation and leakage EFi(ii) a According to the performance characteristics of the water pump and the actual working condition of the pump station, the annual allowable water lifting total amount BZ of the water replenishing pump station is determined, and the annual change of the water level of a water taking source is combined to determine the water supply amount JD of each stagei(ii) a Determining water demand YS of each stage of the catchment area according to crop varieties, planting scale and multiple cropping index of the catchment areaiMaximum annual crop yield Y under full irrigationm(ii) a Wherein i is 1,2, … …, N.
And secondly, performing dynamic programming successive approximation solving.
Further, the constraints include:
(1) the total annual available water supply of the reservoir is restricted:
X1+X2+…+XN≤SK (2)
in the formula: SK is total annual available water supply of reservoir (ten thousand meters)3)；
(2) And (3) restricting the annual allowable water lifting total amount of a water replenishing pump station:
Y1+Y2+…+YN≤BZ (3)
in the formula: BZ is the total allowable water lifting amount (ten thousand meters) of the water replenishing pump station3)。
(3) And (3) restricting the water supply amount in the stage of the water replenishing pump station:
Yi≤JDi(4)
in the formula: JDiFor the pumping station of the i-th stage, water supply (ten thousand meters)3)。
(4) The reservoir water balance constraint of the direct reservoir channel compensation without a pump station:
Vi＝Vi-1+LSi-PSi-EFi-Xi(5)
in the formula: vi、Vi-1The water storage capacity (ten thousand m) at the i-th stage and the i-1 th stage of the reservoir respectively3)；LSi、PSi、EFiThe water inflow amount, the water abandonment amount, the evaporation amount and the leakage amount (ten thousand meters) of the ith stage of the reservoir respectively3)。
(5) Reservoir capacity constraint:
Vmin≤Vi≤VP(6)
in the formula: vmin、VPThe reservoir capacity is respectively the reservoir capacity at the dead reservoir and the reservoir capacity corresponding to the flood control limit water level (ten thousand meters)3)；ViThe water storage capacity at the end of the ith stage of the reservoir (ten thousand meters)3)。
Further, the dynamic programming successive approximation solving specifically comprises the following steps:
(1) determining that the daily water supply amount of the reservoir and the water replenishing scale of the pump station meet the requirements of the formulas (2) to (3), and avoiding the situation that the reservoir capacity of the reservoir at a certain stage is lower than the dead reservoir capacity Vmin(ii) a Reservoir stage water supply amount X under insufficient irrigation condition of water receiving area1iAs an initial iteration value, it is substituted into the formula (1), thenThe formulas (1) to (6) are converted into water supplement amount Y of the pump station at each stageiFor decision variable, the total water replenishing amount lambda of the pump station in the first i stagesiA one-dimensional dynamic programming model for the state variables;
(2) obtaining a corresponding recursion equation according to a one-dimensional dynamic programming solution principle:
1) stage i ═ 1
Figure BDA0001077683500000031
Water supply X of reservoir at this stage11Given by an initial value, a state variable λ1Discretizing within the corresponding feasible domain: lambda [ alpha ]1＝0,W1,W2…, BZ; for each discrete lambda1Decision variable is the pump station water supplement amount Y11The discrete values are discrete in the corresponding feasible region, the minimum value of the discrete values is 0, and the maximum value is JD1(ii) a Will be given X11And each discrete Y11Correspondingly, the moisture sensitivity coefficient K is determined through the crop field test1(ii) a While also satisfying Y11≥λ1(ii) a Y to satisfy the requirement11Substituting formula (7) to obtain each discrete value lambda1Corresponding optimal water supplement amount Y of pump station11And g corresponding thereto1(λ1)。
Then, according to the formula (5), the 1 st stage end reservoir water storage quantity V1＝V0+LS1-EF1-X11At the moment, reservoir water abandon is not considered, the formula (6) is adopted for detection, and if the reservoir capacity V corresponding to the flood control limit water level is exceeded, the reservoir capacity V is detectedPThe excess part is used as the water abandoning quantity PS of the reservoir11At this time V1 *＝VP(ii) a Otherwise, if not, PS11When V is equal to 01 *＝V1。
2) Stage i-2, 3, … …, N-1
Figure BDA0001077683500000032
Water supply X of reservoir at this stage1iGiven by an initial value, a state variable λiAlso, the dispersion is performed separately: lambda [ alpha ]i＝0,W1,W2…, BZ; for each discrete lambdaiDecision variable is the pump station water supplement amount Y1iDispersing in the same step 1); likewise, X will be given1iAnd each discrete Y1iCorrespondingly, the moisture sensitivity coefficient K is respectively determined through crop field testsiAnd should satisfy:
Figure BDA0001077683500000033
the state transition equation: lambda [ alpha ]i-1＝λi-Y1i(9)
Each discrete Y1iValues being respectively substituted in formula (8)
Figure BDA0001077683500000034
From the state transition equation (9), find i-1 stage satisfied
Figure BDA0001077683500000041
Required gi-1(λi-1) Value, thereby obtaining a value satisfying λiRequired optimal water supplement amount Y of pump station1iAnd g corresponding theretoi(λi) (ii) a Also, according to the formula (5), the i-th stage end reservoir storage capacity Vi＝Vi-1+LSi-EFi-X1iAt the moment, reservoir water abandon is not considered, the formula (6) is adopted for checking, and if the reservoir capacity V corresponding to the flood control limit water level is exceeded, the reservoir capacity V is detectedPThe excess part is used as the water abandoning quantity PS of the reservoir1iAt this time Vi *＝VP(ii) a Otherwise, if not, PS1iWhen V is equal to 0i *＝Vi(ii) a Deriving from the water quantity of reservoir water abandon1iWherein i is 2,3, … …, N-1.
3) Stage i ═ N:
Figure BDA0001077683500000042
water supply X of reservoir at this stage1NGiven by an initial value, a state variable λNBZ; decision variable, namely pump station water supplement amount Y1NAlso discrete within the corresponding feasible domain; will be given X1NAnd each discrete Y1NCorrespondingly, the moisture sensitivity coefficient K is respectively determined through crop field testsNAnd should satisfy lambdaN-1＝λN-Y1N(ii) a Adopting the method in the step 2), finally obtaining the lambda satisfying the lambdaNRequired optimal water supplement amount Y of pump station1NAnd corresponding reservoir water abandon amount PS1NWherein i is 1,2 … …, N.
(3) Adding water Y into the pump station obtained in the step (2)1iWhen formula (1) is substituted as the initial set value, the formulas (1) to (6) are converted into the water supply amount X of the reservoir at each stageiAs decision variable, total reservoir water supply of the first i stages lambda'iFor the one-dimensional dynamic programming model of the state variable, referring to the step (2), solving by adopting a one-dimensional dynamic programming method to obtain the state variable satisfying the lambdaN' required optimum water supply X for reservoir2iAnd a corresponding reject water quantity PS2iWhere i is 1,2, … …, N.
(4) Supplying water X to the reservoir obtained in the step (3)2iSubstituting the formula (1) as an initial given value, repeating the steps (2) to (3), and repeating successive approximation solving until the error precision of the optimal value of the objective function of two adjacent times is less than 1%, and ending the model optimization; reservoir water supply X obtained by last optimizationeiWater supply Y of harmony pump stationeiAs a model optimal solution, simultaneously obtaining an optimal value of a target function and an optimal water abandon amount PS of the reservoireiAnd i is 1,2, … …, and N, e is a serial number of successive approximation times of the dynamic programming.
The method can realize the water resource optimization scheduling of a single-pump station-single reservoir system for directly supplementing channels under the condition of insufficient irrigation, has important practical significance for improving the channel supplementing water resource efficiency of the pump station and the irrigation guarantee rate of the irrigation areas, and has certain reference value for the water resource optimization scheduling of the irrigation areas of the reservoirs.
Drawings
FIG. 1 is a schematic diagram of a system for year-regulated single pumping station-single reservoir water resource generalization.
Detailed Description
A schematic diagram of a single pump station-single reservoir water resource generalization system is shown in fig. 1.
The method comprises the following steps of establishing a single-pump station-single-reservoir system water resource optimization scheduling model for directly supplementing channels by taking the maximum annual yield of crops in a water receiving area as a target function, the water supply of reservoirs and pump stations in each growth stage of the crops as decision variables and the annual available water supply total amount of the reservoirs and the pump stations, the scheduling criterion of the reservoirs, the water balance of the reservoirs, the dead storage capacity, the corresponding storage capacity of flood control limiting water levels, the available water supply in the pump stations as constraint conditions, and the like as follows:
first, model construction
1. Objective function
Adopting Blank models in the crop moisture production function models at different growth stages, establishing the following objective function by taking the annual yield of crops in a water receiving area as the maximum target:
Figure BDA0001077683500000051
in the formula: f is the maximum annual yield (kg) of crops in the water receiving area; y is the actual annual yield (kg) of crops in the water receiving area; n is the number of crop growing stages divided in the year; i is a stage number (i ═ 1,2, … …, N); y ism、ETi、ETm,iThe maximum annual yield (kg), the actual transpiration amount and the maximum transpiration amount (ten thousand meters) of the i stage under the condition of full irrigation of crops are respectively3)；
Figure BDA0001077683500000052
Namely the relative transpiration amount of the i-stage crops; kiThe water sensitivity coefficient of the crop with the influence of water shortage on the yield at the i stage.
In the above formula, Ym、ETm,iKnown to specific crops in a particular area, ETiThe sum of the water supply of stage reservoir and pump station under insufficient irrigation condition, i.e. ETi＝Xi+Yi，ETm,iNamely YS (water demand for crops) at each stage under the condition of full irrigationiAnd at given stages ETiIn case of K for a particular cropiIt can also be determined that the objective function can be converted into:
Figure BDA0001077683500000053
in the formula, Xi、YiWater supply amount of the i stage of the reservoir under insufficient irrigation condition (ten thousand meters) respectively3) Water supply amount of pumping station in stage i (ten thousand meters)3) Water supply X for reservoiriWater supply Y for pump stationi，YSiWater demand (ten thousand meters) for the i stage crops under full irrigation conditions3) The remaining variables have the same meanings as in formula (1-1).
2. Constraint conditions
(1) The total annual available water supply of the reservoir is restricted:
X1+X2+…+XN≤SK (2)
in the formula: SK is total annual available water supply of reservoir (ten thousand meters)3)；
(2) And (3) restricting the annual allowable water lifting total amount of a water replenishing pump station:
Y1+Y2+…+YN≤BZ (3)
in the formula: BZ is the total allowable water lifting amount (ten thousand meters) of the water replenishing pump station3)。
(3) And (3) restricting the water supply amount in the stage of the water replenishing pump station:
Yi≤JDi(4)
in the formula: JDiFor the pumping station of the i-th stage, water supply (ten thousand meters)3)。
(4) The reservoir water balance constraint of the direct reservoir channel compensation without a pump station:
Vi＝Vi-1+LSi-PSi-EFi-Xi(5)
in the formula: vi、Vi-1The water storage capacity (ten thousand m) at the i-th stage and the i-1 th stage of the reservoir respectively3)；LSi、PSi、EFiThe water inflow amount, the water abandonment amount, the evaporation amount and the leakage amount (ten thousand meters) of the ith stage of the reservoir respectively3)。
(5) Reservoir capacity constraint:
Vmin≤Vi≤VP(6)
in the formula: vmin、VPThe reservoir capacity is respectively the reservoir capacity at the dead reservoir and the reservoir capacity corresponding to the flood control limit water level (ten thousand meters)3)；ViThe water storage capacity at the end of the ith stage of the reservoir (ten thousand meters)3)。
Secondly, the characteristics of the model
(1) And considering the insufficient irrigation condition, adding a stage available water supply amount constraint of a water replenishing pumping station into the constraint condition of the model, namely an equation (4).
(2) And the water balance and the reservoir capacity constraint of the reservoir are considered in the constraint conditions, so that the optimal scheduling of water resources of a reservoir-pump station system of 'water replenishing of a free reservoir and combined water supply of a busy reservoir station' can be realized. In idle time, if the storage capacity of the final reservoir is lower than the dead storage capacity of the reservoir at the end of a certain stage, a water replenishing pump station is adopted to directly replenish water to the channel at the stage; and if the water storage capacity of the reservoir at the end of a certain stage exceeds the reservoir capacity corresponding to the flood control limit water level of the reservoir, water needs to be pumped and abandoned to ensure the dispatching requirement of the reservoir capacity of the reservoir. In busy hours, according to the water storage capacity of the reservoir, the reservoir and the pump station are considered to jointly supply water to the water receiving area, so as to meet the growth demand of crops as far as possible.
Third, model solution
The formulas (1-2) to (6) in the above model are a nonlinear mathematical model with one separable stage, and Y in the objective functionm、YSiGiven X at each stage, as is known for a particular crop in a particular regioni、YiIn case of K for a particular cropiIt can also be determined that the model actually takes the stage i (i is 1,2, … …, N) of reservoir water supply divided according to the growth stage of the crops as the stage variable, and the water supply X of the reservoir in each stageiWater supply Y for pump stationiThe stage of the decision variables can be divided into nonlinear models, and a dynamic programming successive approximation method is adopted for solving.
Initial reservoir capacity V of assumed year regulation reservoir0In the known mode, formulas (2) to (4) are dynamic planning coupling constraints, and formula (5) is a water balance constraint of each stage of reservoir scheduling; solving by adopting a dynamic programming successive approximation method, simultaneously detecting the storage capacity by utilizing the formula (6), correcting the storage capacity of the final reservoir at each stage, and finally obtaining the maximum annual yield of crops under the condition of insufficient irrigation,and corresponding optimal water supply X of the reservoir in each stageiPS water reject amountiWater supply Y of harmony pump stationiAnd (i is 1,2, … …, N), and provides a basis for optimizing and scheduling water resources in an irrigation area where a single pump station-single reservoir system adopting a direct channel supplement is located.
Firstly, data preparation is carried out, and the method specifically comprises the following steps:
aiming at a year-regulated single pump station-single water reservoir combined operation scheduling system of a certain specific direct channel under the condition of insufficient irrigation, dividing the whole growth period of crops into N stages; according to the initial water level of the reservoir, searching a relation curve of the water level and the reservoir capacity, and determining the initial reservoir capacity V of the reservoir0(ii) a According to the actual operation condition of the reservoir, the total quantity SK of annual available water supply and the dead storage volume V are determinedminReservoir capacity V corresponding to flood control water level limitP(ii) a Determining the amount LS of water coming from each stage of the reservoir according to the local meteorological hydrological data of the reservoiriEvaporation and leakage EFi(ii) a According to the performance characteristics of the water pump and the actual working condition of the pump station, the annual allowable water lifting total amount BZ of the water replenishing pump station is determined, and the annual change of the water level of a water taking source is combined to determine the water supply amount JD of each stagei(ii) a Calculating and determining water demand YS of each stage of the catchment area according to the crop varieties, planting scale, multiple cropping index and other data of the catchment areai(i-1, 2, … …, N) under intensive irrigation conditions for maximum annual yield Y of the cropm。
Secondly, performing dynamic programming successive approximation solving, which specifically comprises the following steps:
(1) developing research on water receiving area, collecting and counting daily water supply amount of reservoir and water replenishing scale of pump station, wherein the data satisfies the requirements of formulas (2) to (3), and the condition that the reservoir capacity at a certain stage of the reservoir is lower than the dead reservoir capacity V is avoidedmin. Reservoir stage water supply amount X under daily insufficient irrigation condition of specific water receiving area1i(i is 1,2, … …, N) as an initial iteration value, substituting the initial iteration value into the formula (1-2), and converting the formulas (1-2) to (6) in the original model into the water supplement amount Y of the pump station at each stageiFor decision variables, the total water supplement amount lambda of the pump station in the first i stagesiThe dynamic programming model is a one-dimensional dynamic programming model of the state variables, and can be solved by adopting a one-dimensional dynamic programming method.
(2) And (3) obtaining a corresponding recursion equation according to a one-dimensional dynamic programming solving principle:
1) stage i ═ 1
Figure BDA0001077683500000071
Water supply X of reservoir at this stage11Given by an initial value, a state variable λ1Discretizing within the corresponding feasible domain: lambda [ alpha ]1＝0,W1,W2…, BZ. For each discrete lambda1Decision variable (i.e. pump station water supply amount Y)11) Discrete within a corresponding feasible region, e.g. 0 km35 km/l310 km, 10315 km of3、…Y11,max(Y11,maxNamely the maximum water replenishing capacity JD of the pump station in the 1 st stage1). Will be given X11And each discrete Y11Correspondingly, the moisture sensitivity coefficient K of the water shortage state influencing the yield is respectively determined through crop field tests1. At the same time, the following requirements should be met: y is11≥λ1. Y to satisfy the requirement11Respectively substituting the formula (7) to respectively obtain each discrete value lambda1The optimal water supplement amount Y of the pumping station11And g corresponding thereto1(λ1)。
Then, according to the formula (5), the storage capacity V of the final reservoir at the 1 st stage1＝V0+LS1-EF1-X11At the moment, reservoir water abandon is not considered, the formula (6) is adopted for detection, and if the reservoir capacity V corresponding to the flood control limit water level is exceeded, the reservoir capacity V is detectedPThe excess part is used as the water abandoning quantity PS of the reservoir11At this time V1 *＝VP(ii) a Otherwise, if not, PS11When V is equal to 01 *＝V1。
2) Stage i-2, 3, … …, N-1
Figure BDA0001077683500000072
Water supply X of reservoir at this stage1iGiven by an initial value, a state variable λiAlso, the dispersion is performed separately: lambda [ alpha ]i＝0,W1,W2…, BZ. For each discrete lambdaiDecision variable (pump station water supply amount Y)1i) The dispersion is as above. Likewise, X will be given1iAnd each discrete Y1iCorrespondingly, the moisture sensitivity coefficient K of the water shortage state influencing the yield is respectively determined through crop field testsiAnd should satisfy:
Figure BDA0001077683500000081
the state transition equation: lambda [ alpha ]i-1＝λi-Y1i(9)
In the formula: i-2, 3, … …, N-1.
Each discrete Y1iValues being respectively substituted in formula (8)
Figure BDA0001077683500000082
From the state transition equation (9), find i-1 stage satisfied
Figure BDA0001077683500000083
Required gi-1(λi-1) Value, thereby obtaining a value satisfying λiRequired optimal water supplement amount Y of pump station1iAnd g corresponding theretoi(λi). Similarly, according to the formula (5), the storage capacity V of the i-th stage final reservoiri＝Vi-1+LSi-EFi-X1iAt the moment, reservoir water abandon is not considered, the formula (6) is adopted for checking, and if the reservoir capacity V corresponding to the flood control limit water level is exceeded, the reservoir capacity V is detectedPThe excess part is used as the water abandoning quantity PS of the reservoir1iAt this time Vi *＝VP(ii) a Otherwise, if not, PS1iWhen V is equal to 0i *＝Vi. Thereby deriving the corresponding water abandon amount PS of the reservoir1iWherein i is 2,3, … …, N-1.
3) Stage i ═ N:
Figure BDA0001077683500000084
water supply X of reservoir at this stage1NHas been given by an initial valueOf state variable lambdaNBZ; decision variable (pump station water supply Y)1N) Again discrete within the corresponding feasible domain. Will be given X1NAnd each discrete Y1NCorrespondingly, the moisture sensitivity coefficient K of the water shortage state influencing the yield is respectively determined through crop field testsNAnd should satisfy: lambda [ alpha ]N-1＝λN-Y1N。
Adopting the method in the step 2), finally obtaining the lambda satisfying the lambdaNRequired optimal water supplement amount Y of pump station1NAnd corresponding reservoir water reject amount PS1N(i＝1,…N)。
(3) Adding water Y into the pump station obtained in the step (2)1iSubstituting the formula (1-2) as an initial given value, converting the formula (1-2) to the formula (6) in the original model into the reservoir water supply amount X in each stageiAs decision variable, total reservoir water supply of the first i stages lambda'iFor the one-dimensional dynamic programming model of the state variable, referring to the step (2), solving by adopting a one-dimensional dynamic programming method to obtain the state variable satisfying the lambdaN' required optimum water supply X for reservoir2iAnd a corresponding reject water quantity PS2i(i＝1,2,……,N)。
(4) Supplying water X to the reservoir obtained in the step (3)2iAnd (3) substituting the formula (1-2) as an initial given value, repeating the steps (2) to (3), and repeating successive approximation solving until the error precision of the optimal value of the objective function of two adjacent times is less than 1%, so that the model optimization is finished. Reservoir water supply X obtained by last optimizationeiWater supply Y of harmony pump stationeiAs the optimal solution of the original model, the optimal value of the objective function and the optimal water abandon quantity PS of the reservoir can be obtainedei(i ═ 1,2, … …, N) (where e is the dynamic programming successive approximation order number).
The method is convenient to solve and reliable in precision, can be popularized and applied by large and medium irrigation district management units adopting a single pump station-single reservoir to supply water under the condition of insufficient irrigation, achieves the aim of optimizing and configuring water resources of the irrigation district, and improves economic, social and ecological benefits of the irrigation district.

Claims (1)

1. A water resource optimal allocation method for a single pump station-single reservoir system for directly supplementing channels under the condition of insufficient irrigation is characterized by comprising the following steps of:
firstly, model construction, comprising the following steps:
1. establishing the following objective function by taking the maximum annual yield of crops in the water receiving area as an objective:
Figure FDA0002444115360000011
in the formula: f is the maximum annual yield of crops in the water receiving area; y is the actual annual yield of crops in the water receiving area; n is the number of crop growing stages divided in the year; i is a stage number, i is 1,2, … …, N; y ismFor maximum annual crop yield under full irrigation conditions, KiThe moisture sensitivity coefficient of the crop in the stage i of water shortage on yield influence; xi、YiThe reservoir water supply quantity and the pump station water supply quantity in the i stage under the insufficient irrigation condition are respectively called reservoir water supply quantity X for shortiWater supply Y for pump stationi，YSiThe water demand of the crops in the stage i under the condition of sufficient irrigation;
2. setting constraint conditions specifically as follows:
(1) the total annual available water supply of the reservoir is restricted:
X1+X2+……+XN≤SK (2)
in the formula: SK is total annual available water supply of the reservoir;
(2) and (3) restricting the annual allowable water lifting total amount of a water replenishing pump station:
Y1+Y2+……+YN≤BZ (3)
in the formula: BZ is the total water lifting amount allowed by the water replenishing pump station in a year;
(3) and (3) restricting the water supply amount in the stage of the water replenishing pump station:
Yi≤JDi(4)
in the formula: JDiWater supply amount can be supplied to the pumping station in the i stage;
(4) the reservoir water balance constraint of the direct reservoir channel compensation without a pump station:
Vi＝Vi-1+LSi-PSi-EFi-Xi(5)
in the formula: vi、Vi-1The water storage capacity of the i stage and the i-1 stage of the reservoir respectively; LS (least squares)i、PSi、EFiThe water inflow amount, the water abandoning amount, the evaporation amount and the leakage amount of the ith stage of the reservoir are respectively;
(5) reservoir capacity constraint:
Vmin≤Vi≤VP(6)
in the formula: vmin、VPThe reservoir capacity is respectively the reservoir capacity corresponding to the reservoir dead reservoir capacity and the flood control limit water level; viThe water storage capacity at the end of the ith stage of the reservoir;
second, model solution
Utilizing reservoir capacity constraint: vmin≤Vi≤VPChecking the storage capacity, and correcting the storage capacity of the final reservoir at each stage;
firstly, data preparation is carried out, and the method specifically comprises the following steps: dividing the whole growth period of crops into N stages; according to the initial water level of the reservoir, searching a relation curve of the water level and the reservoir capacity, and determining the initial reservoir capacity V of the reservoir0(ii) a According to the actual operation condition of the reservoir, the total quantity SK of annual available water supply and the dead storage volume V are determinedminReservoir capacity V corresponding to flood control water level limitP(ii) a Determining the amount LS of water coming from each stage of the reservoir according to the local meteorological hydrological data of the reservoiriEvaporation and leakage EFi(ii) a According to the performance characteristics of the water pump and the actual working condition of the pump station, the annual allowable water lifting total amount BZ of the water replenishing pump station is determined, and the annual change of the water level of a water taking source is combined to determine the water supply amount JD of each stagei(ii) a Determining water demand YS of each stage of the catchment area according to crop varieties, planting scale and multiple cropping index of the catchment areaiMaximum annual crop yield Y under full irrigationm(ii) a Wherein i is 1,2, … …, N;
secondly, performing dynamic programming successive approximation solving, wherein the specific steps of the dynamic programming successive approximation solving are as follows:
(1) determining that the daily water supply amount of the reservoir and the water replenishing scale of the pump station meet the requirements of the formulas (2) to (3), and avoiding the situation that the reservoir capacity of the reservoir at a certain stage is lower than the dead reservoir capacity Vmin(ii) a Reservoir stage water supply amount X under insufficient irrigation condition of water receiving area1iAs the initial iteration value, substituting the initial iteration value into the formula (1), converting the formulas (1) to (6) into the water supplement amount Y of the pump station at each stageiFor decision variable, the total water replenishing amount lambda of the pump station in the first i stagesiA one-dimensional dynamic programming model for the state variables;
(2) obtaining a corresponding recursion equation according to a one-dimensional dynamic programming solution principle:
1) stage i ═ 1
Figure FDA0002444115360000021
Water supply X of reservoir at this stage11Given by an initial value, a state variable λ1Discretizing within the corresponding feasible domain: lambda [ alpha ]1＝0,W1,W2… …, BZ; for each discrete lambda1Decision variable is the pump station water supplement amount Y11The discrete values are discrete in the corresponding feasible region, the minimum value of the discrete values is 0, and the maximum value is JD1(ii) a Will be given X11And each discrete Y11Correspondingly, the moisture sensitivity coefficient K is determined through the crop field test1(ii) a While also satisfying Y11≥λ1(ii) a Y to satisfy the requirement11Substituting formula (7) to obtain each discrete value lambda1Corresponding optimal water supplement amount Y of pump station11And g corresponding thereto1(λ1)；
Then, according to the formula (5), the 1 st stage end reservoir water storage quantity V1＝V0+LS1-EF1-X11At the moment, reservoir water abandon is not considered, the formula (6) is adopted for detection, and if the reservoir capacity V corresponding to the flood control limit water level is exceeded, the reservoir capacity V is detectedPThe excess part is used as the water abandoning quantity PS of the reservoir11At this time V1 *＝VP(ii) a Otherwise, if not, PS11When V is equal to 01 *＝V1；
2) Stage i-2, 3, … …, N-1
Figure FDA0002444115360000031
Water supply X of reservoir at this stage1iGiven by an initial value, a state variable λiAlso, the dispersion is performed separately: lambda [ alpha ]i＝0,W1,W2… …, BZ; for each discrete lambdaiDecision variable is the pump station water supplement amount Y1iDispersing in the same step 1); likewise, X will be given1iAnd each discrete Y1iCorrespondingly, the moisture sensitivity coefficient K is respectively determined through crop field testsiAnd should satisfy:
Figure FDA0002444115360000032
the state transition equation: lambda [ alpha ]i-1＝λi-Y1i(9)
In the formula: 2,3, … …, N-1;
each discrete Y1iValues being respectively substituted in formula (8)
Figure FDA0002444115360000033
From the state transition equation (9), find i-1 stage satisfied
Figure FDA0002444115360000034
Required gi-1(λi-1) Value, thereby obtaining a value satisfying λiRequired optimal water supplement amount Y of pump station1iAnd g corresponding theretoi(λi) (ii) a Also, according to the formula (5), the i-th stage end reservoir storage capacity Vi＝Vi-1+LSi-EFi-X1iAt the moment, reservoir water abandon is not considered, the formula (6) is adopted for checking, and if the reservoir capacity V corresponding to the flood control limit water level is exceeded, the reservoir capacity V is detectedPThe excess part is used as the water abandoning quantity PS of the reservoir1iAt this time Vi *＝VP(ii) a Otherwise, if not, PS1iWhen V is equal to 0i *＝Vi(ii) a Deriving from the water quantity of reservoir water abandon1iWherein i ═ 2,3, … …, N-1;
3) stage i ═ N:
Figure FDA0002444115360000035
water supply X of reservoir at this stage1NGiven by an initial value, a state variable λNBZ; decision variable, namely pump station water supplement amount Y1NAlso discrete within the corresponding feasible domain; will be given X1NAnd each discrete Y1NCorrespondingly, the moisture sensitivity coefficient K is respectively determined through crop field testsNAnd should satisfy lambdaN-1＝λN-Y1N(ii) a Adopting the method in the step 2), finally obtaining the lambda satisfying the lambdaNRequired optimal water supplement amount Y of pump station1NAnd corresponding reservoir water abandon amount PS1NWherein i is 1,2 … …, N;
(3) adding water Y into the pump station obtained in the step (2)1iWhen formula (1) is substituted as the initial set value, the formulas (1) to (6) are converted into the water supply amount X of the reservoir at each stageiAs decision variable, total reservoir water supply of the first i stages lambda'iReferring to the step (2), solving by adopting a one-dimensional dynamic programming method to obtain a one-dimensional dynamic programming model of the state variables, wherein the model satisfies the lambda'NRequired optimum water supply X for reservoir2iAnd a corresponding reject water quantity PS2iWherein i ═ 1,2, … …, N;
(4) supplying water X to the reservoir obtained in the step (3)2iSubstituting the formula (1) as an initial given value, repeating the steps (2) to (3), and repeating successive approximation solving until the error precision of the optimal value of the objective function of two adjacent times is less than 1%, and ending the model optimization; reservoir water supply X obtained by last optimizationeiWater supply Y of harmony pump stationeiAs a model optimal solution, simultaneously obtaining an optimal value of a target function and an optimal water abandon amount PS of the reservoireiAnd i is 1,2, … …, and N, e is a serial number of successive approximation times of the dynamic programming.
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