CN107798471B - More libraries-multiple station systems water resource optimal allocation method of canal is directly mended under a kind of abundant irrigation conditions - Google Patents

Abstract

The invention discloses a kind of more libraries-multiple station systems water resource optimal allocation methods that canal is directly mended under abundant irrigation conditions, the method for solving of " Dan Ku-multistation " subsystem backward Dynamic Programming Approach by inchmeal optimization-" mending canal Group of Pumping Station " second level subsystem decomposition-Dynamic Programming polymerization of canal is directly mended using " more library-multistations " large system decomposition-, it can get all intake area minimum water deficits in certain delivery period, corresponding each reservoir day part optimal water supply, abandon water, outer water diversion volume, and each benefit canal pumping plant rate of water make-up process.The present invention distributes with most important theories meaning and practical application value Wall in Plain Reservoir Water Resources Irrigation rationally.

Description

More libraries-multiple station systems water resource optimization of canal is directly mended under a kind of abundant irrigation conditions Configuration method

Technical field

The present invention relates to abundant irrigation conditions lower step multi-reservoir and it is multiple benefit canal Group of Pumping Station combined operatings scheduling methods, Belong to Water Resources Irrigation and distributes technical field rationally.

Background technique

Currently since water resource spatial and temporal distributions are uneven, the socio-economic development in many areas is restricted, for sufficiently irrigating For the irrigated area of condition, under limited water resources total amount and water source project scale, to be up to target with water comprehensive benefit, reinforce The United Dispatching of regional water resources and management as unified entirety use the hydraulic engineering of irrigation system and adjust, use Built engineering (such as multiple multi-reservoirs and the operation of multiple Group of Pumping Station combined dispatchings) makes it play bigger effect, is to solve irrigated area to lack The main path of water problems.How reasonably more more pumping station system traffic controls of reservoir-are as one content of water resources management, Reaching some target with system water scheduling of resource keeps system benefit best, is problem relatively conventional in water project management.

For directly mending more libraries-multiple station systems water resource optimal allocation of canal, supply water from multiple benefit canal pumping plants to single reservoir Canal water supply forms the single library-multiple station systems for directly mending canal, then is made of directly multiple concatenated single library-multiple station systems More library-the multiple station systems for mending canal are connect, combines and supplies water to multiple intake areas.Although water condition is abundant, due to being related to multiple water Library group, in running, in addition to final stage list library-multiple station systems only supply water to intake area, remaining single library-multistation at different levels System assigns next stage list library-multiple station systems water supply outside also adding；And for each single library-multiple station systems, again Comprising multiple benefit canal Group of Pumping Station, how under the conditions of guaranteeing that intake area is supplied water adequately, reduces benefit canal Group of Pumping Station system and run energy Consumption saves engineering operation cost, is very important major issue.

Summary of the invention

The present invention dispatches system for the more pumping plant combined operatings of more reservoirs-are adjusted specific year, supplies water and draws in known reservoir Point when number of segment, reservoir quantity, the initial storage of each reservoir, minimum capacity of a reservoir, utilizable capacity, the corresponding storage capacity of flood control, Year comes process water, evaporation and leakage process for water inventory, day part, and each reservoir mends canal pumping plant quantity, each benefit canal pumping plant Year allows under water lift total amount and each intake area water requirement process condition of day part, using " more library-multistations " big system point Solution-directly mends " Dan Ku-multistation " subsystem backward Dynamic Programming Approach by inchmeal optimization-" mending canal Group of Pumping Station " second level of canal System decomposition-Dynamic Programming polymerization method for solving, can get minimum water deficit in intake area in certain delivery period, corresponding each water Day part optimal water supply, abandoning water, outer water diversion volume in the delivery period of library, and each benefit canal pumping plant day part rate of water make-up process.

The present invention program is as follows:

More libraries-multiple station systems water resource optimal allocation that canal is directly mended under a kind of abundant irrigation conditions is pumped by multiple benefit canals Feeder channel where to single reservoir of standing supplies water, and forms the single library-multiple station systems for directly mending canal, then by multiple concatenated lists Library-multiple station systems constitute the more library-multiple station systems for directly mending canal, combine and supply water to multiple intake areas.Its water resource optimization is matched Set method the following steps are included:

One, model construction includes the following steps 1~step 2:

1. with directly mend each reservoir yield Yu intake area water requirement of more libraries-of canal day part in multiple station systems year it The minimum target of quadratic sum of difference, establishes following objective function:

In formula: F be research object year in day part the difference for water requirement least square and；Z is in research object year The quadratic sum of the difference for water requirement of day part；R is reservoir quantity, unit: seat；H is reservoir number, h=1,2 ... ... R；N is The when number of segment divided in year；Segment number when i is, i=1,2 ... ... N；G_h,i、YS_h,iThe confession of respectively h the i-th periods of reservoir The water requirement of i-th period of water and corresponding intake area, unit: ten thousand m³；YB_h,k,iFor feeder channel kth seat where h reservoirs Mend the i-th period of canal pumping plant water supply, unit: ten thousand m³；Objective function is to accelerate to reduce reservoir and supply water using quadratic sum expression Deviation between amount and intake area water requirement.

2. constraint condition is arranged

Including mending single library-multiple station systems year of canal directly for water inventory constraint condition, consider that higher level's reservoir is called in and oneself Single reservoir water equilibrium constraint that the outer water diversion volume of body requires, single reservoir capacity constraint condition, and mend the operation of canal Group of Pumping Station Energy consumption least commitment condition.

Two, model solution

1. data preparation specifically includes: being divided into N number of period for 1 year, and determine day part length；At the beginning of measuring each reservoir Beginning storage capacity V_h,0；Determine each reservoir year for water inventory SK_h, minimum capacity of a reservoir V_h,min, the corresponding storage capacity V of flood control_h,PAnd Utilizable capacity V_h,min+△_h,1；It measures and calculates each reservoir day part and carry out water LS_h,i, evaporation with leakage EF_h,i, h=1,2 ... R；Determine that each benefit canal pumping plant year allows water lift total amount BZ_h,k, k=1,2 ... M；Measure different periods lift H_h,k,iLower operation mentions Water flow Q_h,k,iAnd corresponding pump efficiency η_z,h,k,i, electric efficiency η_mot,h,k, transmission efficiency η_int,h,k；Determine day part respectively by The water demand of crop YS in pool_h,i, h=1,2 ... ... R；I=1,2 ..., N.

2. direct " more library-multistations " large-scale system model for mending canal is decomposed into single library-multistation water that R are directly mended canal to provide Source optimization configures mathematical model, objective function are as follows:

3. single library-multistation water resource optimal allocation mathematical model of pair directly benefit canal optimizes, from final stage without outer water transfer Single library-multiple station systems that amount requires set out, and successively carry out single library-multiple station systems water resource optimal allocation, specifically include:

(1) single seat reservoir-multiple station systems water resource optimal allocation submodel is solved using Dynamic Programming Approach by inchmeal, The reservoir yield process G of acquisition_h,iCanal total Water process Y is mended with Group of Pumping Station_h,iAs master mould optimal solution, while also obtaining mesh Scalar functions optimal value, the optimal abandoning process water PS of reservoir_h,iAnd upper level reservoir is to its benefit library process water BK_h,i, In, h=1 ... R；I=1 ... N.

(2) it is solved using decomposition-Dynamic Programming polymerization to group's Group of Pumping Station second level subsystem model is mended, obtains and meet the I period pumping plant multiple targets water lift total amount Y_h,iL_h,iValue and the optimal rate of water make-up of corresponding each pumping plant combine YB_h,k,i ^*K=1, 2,…M。

4. obtaining each reservoir day part water supply G in more more pumping station systems of reservoir-_h,i, outer water diversion volume WD_h,i, abandon water PS_h,i, the optimal benefit library water BK of upper level reservoir_h,iAnd corresponding each benefit canal pumping plant rate of water make-up YB_h,k,iProcess, h=1, 2 ..., R.

Further, the constraint condition in step (1) includes:

(1) single library-multiple station systems year of canal is mended directly for water inventory constraint condition: except final stage reservoir is only needed to place Outside intake area is supplied water, remaining reservoir at different levels also needs to undertake outer water transfer task, supplies next stage reservoir, it may be assumed that

To the 1st~the R-1 reservoirs:

Wherein, h=1,2 ... ... R-1.

To Building R reservoir:

In formula: WD_h,iFor the water supply for assigning next stage reservoir outside h the i-th periods of reservoir, unit: ten thousand m³；SK_hFor h The year of seat reservoir is for water inventory, unit: ten thousand m³；Benefit canal pumping plant quantity of the M for feeder channel where h reservoirs, unit: Seat；K is to mend canal pumping plant number, k=1,2 ... ... M；BZ_h,kCanal pumping plant year is mended for the kth seat of feeder channel where h reservoirs Allow water lift total amount, unit: ten thousand m³。

(2) consider that higher level's reservoir calls in single reservoir water equilibrium constraint with itself outer water diversion volume requirement: for appointing Meaning pumping plant more than h-th directly mends single library-multiple station systems of canal, considers that higher level's reservoir calls in the outer water diversion volume of water and reservoir itself It is required that, comprising: to the 1st reservoir, only outer water diversion volume requirement；To 2~R-1 reservoirs, benefit of the existing higher level's reservoir to it Library water, and have itself outer water diversion volume requirement；To Building R reservoir, only higher level's reservoir mends the requirement of library water, i.e., flat according to water Weigh equation:

To the 1st reservoir:

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-WD_1,i (6)

To the 2nd~the R-1 reservoirs:

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-WD_h,i (7)

Wherein, h=2,3 ..., R-1.

To Building R reservoir:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (8)

On this basis, reservoir operation criterion is as follows:

1. when the i-th period end pondage is lower than reservoir minimum capacity of a reservoir V_h,minWhen, then the i-th period should by upper level reservoir into Row moisturizing, moisturizing to utilizable capacity, it may be assumed that

V_h,i<V_h,minWhen: BK_h,i=V_h,min-V_h,i+Δ_h,1, (9)

This period reservoir abandons water PS_h,i=0；H=2,3 ... R.

2. when meeting with flood, the i-th period end pondage is greater than pondage V corresponding to flood control_h,P When, then the i-th period should carry out abandoning water to reservoir, abandon water to flood control by reservoir regulation limiting water level, it may be assumed that

V_h,i>V_h,PWhen: PS_h,i=V_h,i-V_h,P (10)

This period is not necessarily to upper level Reservoir Regulation, i.e. BK_h,i=0.

3. when the i-th period end pondage is between minimum capacity of a reservoir V_h,minWith pondage corresponding to flood control V_h,PBetween, then the i-th period reservoir does not need to abandon water, does not need upper level Reservoir Regulation, it may be assumed that

V_h,min≤V_h,i≤V_h,PWhen: PS_h,i=BK_h,i=0 (11)

In formula: V_h,i、V_h,i-1Respectively h reservoirs i-th, the reservoir storage of i-1 period Mo, unit: ten thousand m³；LS_h,i、 PS_h,i、 EF_h,iRespectively h the i-th periods of reservoir carry out water, abandon water, evaporation and leakage, unit: ten thousand m³；BK_h,iFor The benefit library water that h the i-th periods of reservoir are provided by upper level, i.e. h-1 reservoirs, unit: ten thousand m³。

(3) single reservoir capacity constraint condition: the pondage of day part should be between reservoir minimum capacity of a reservoir and flood control limitation water Between the corresponding storage capacity in position, it may be assumed that

V_h,min≤V_h,i≤V_h,P, i=1,2, N (12)

(4) canal Group of Pumping Station combined operating energy consumption least commitment condition is mended: to the benefit of feeder channel where any h reservoirs Canal Group of Pumping Station, the combined operating within each water supply period are considered as energy consumption minimum, it may be assumed that

In formula, L_h,iCanal Group of Pumping Station combined operation system energy consumption is mended for the i-th period of feeder channel where h reservoirs, it is single Position: kWh；l_h,k,iFor kth seat the i-th period of pumping plant operation energy consumption of feeder channel where h reservoirs, unit: kWh；M For the benefit canal pumping plant quantity of feeder channel where h reservoirs, unit: seat；ρ is water density, unit: kg/m³, g adds for gravity Speed, unit: m/s²；Q_h,k,i、H_h,k,i、△T_h,k,i、η_z,h,k,iThe kth seat pumping plant of feeder channel respectively where h reservoirs Flow (the m of i-th period³/ s), when equal lift (m), Period Length (h) and pump efficiency；η_mot,h,k、η_int,h,kRespectively h The motor efficiency and transmission efficiency of the kth seat pumping plant of feeder channel where reservoir.

Further, in step (2), single library-multistation water resource optimal allocation mathematical model of canal is individually directly mended Constraint condition is as follows:

(1) single library-multiple station systems year of canal is mended directly for water inventory constraint:

1. in addition to supplying water to intake area, there are also assign the water supply of junior's reservoir to want outside for the 1st~the R-1 reservoirs It asks, therefore:

In formula, h=1,2 ... ... R-1.

2. it only supplies water to intake area for Building R reservoir, without the water supply requirement for assigning junior's reservoir outside, therefore:

(2) consider that higher level's reservoir calls in single reservoir water equilibrium constraint with itself outer water diversion volume requirement:

1. to the 1st reservoir:

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-WD_1,i (19)

2. to the 2nd~the R-1 reservoirs:

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-WD_h,i (20)

Wherein, h=2,3 ..., R-1.

3. to Building R reservoir:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (21)

The same formula of reservoir operation criterion (9)~(11) on this basis.

(3) single reservoir capacity constraint condition: same to formula (12).

(4) canal Group of Pumping Station combined operating energy consumption least commitment condition: same to formula (13) is mended.

Further, specific step is as follows for the step 3 of step (2):

(1) Building R Dan Ku-multiple station systems water resource optimal allocation submodel solves

1) submodel is converted

For submodel (14)~(21), (9)~(13), takeThen submodel is converted to each with reservoir Stage water supply G_R,i, mend each stage moisturizing total amount Y of canal Group of Pumping Station_R,iFor the two-dimension non linearity mathematical model of decision variable, it may be assumed that

Objective function:

Dan Ku-multiple station systems year is for water inventory constraint condition:

Reservoir water equilibrium constraint:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (25)

On this basis, reservoir operation criterion condition are as follows:

1. when the i-th period end pondage is lower than reservoir minimum capacity of a reservoir V_R,minWhen, then the i-th period should by upper level reservoir into Row moisturizing, moisturizing to utilizable capacity, it may be assumed that

V_R,i<V_R,minWhen: BK_R,i=V_R,min-V_R,i+Δ_R,1 (26)

This period reservoir abandons water PS_R,i=0.

2. when meeting with flood, the i-th period end pondage is greater than pondage V corresponding to flood control_R,P When, then the i-th period should carry out abandoning water to reservoir, abandon water to flood control by reservoir regulation limiting water level, it may be assumed that

V_R,i>V_R,PWhen: PS_R,i=V_R,i-V_R,P (27)

This period is not necessarily to upper level Reservoir Regulation, i.e. BK_R,i=0.

3. when the i-th period end pondage is between minimum capacity of a reservoir V_R,minWith pondage corresponding to flood control V_R,PBetween, then the i-th period reservoir does not need to abandon water, does not need upper level Reservoir Regulation, it may be assumed that

V_R,min≤V_R,i≤V_R,PWhen: PS_R,i=BK_R,i=0 (28)

The same formula of its corestriction (12)~(13).

2) submodel Dynamic Programming Approach by inchmeal solves

For transformation model (22)~(28), (12)~(13), specific step is as follows for the solution of Dynamic Programming Approach by inchmeal:

1. with conventional reservoir stage water supply process G_R,i,1As primary iteration value, formula (22) are substituted into, then submodel (22)~(28), (12)~(13), which are converted into, mends canal total Water Y with each stage Group of Pumping Station_R,iFor decision variable, preceding i stage pump Group's moisturizing total amount of standing λ_iFor the one-dimensional dynamic programming model of state variable, solved using one-dimensional dynamic programming；Wherein, i=1, 2,……N。

2. obtaining corresponding recurrence equation referring to one-dimensional dynamic programming evaluation principle are as follows:

I) stage i=1:

g₁(λ₁)=min (G_R,1,1+Y_R,1,1-YS_R,1)² (29)

Period reservoir yield G_R,1,1It is given by initial value, state variable λ₁, it is discrete in corresponding feasible zone:To each discrete λ₁, Group of Pumping Station moisturizing total amount Y_R,1,1It is discrete in corresponding feasible zone, it answers Meet: Y_R,1,1≥λ₁.The Y that will be met the requirements_R,1,1Formula (29) are substituted into respectively, are respectively obtained corresponding to each discrete λ₁When value, most Excellent Y_R,1,1And its corresponding period minimum water deficit quadratic sum g₁(λ₁)。

Then, according to formula (25), the 1st stage end reservoir capacity V_R,1=V_R,0+LS_R,1-EF_R,1-G_R,1,1, not yet consider at this time The moisturizing of upper level reservoir and reservoir abandon water, are examined using formula (26)~(28):

A, work as V_R,1<V_R,min, then consider to mend library water BK to its moisturizing by upper level reservoir_R,1,1=V_R,min-V_R,1+ Δ_R,1, storage capacity V is corrected at this time_R,1 ^*=V_R,min+△_R,1。

B, work as V_R,1>V_R,P, then need to abandon dispatching requirement of the water to guarantee reservoir capacity, PS_R,1,1=V_R,1-V_R,P, repair at this time Positive storage capacity V_R,1 ^*=V_R,P。

C, work as V_R,min≤V_R,1≤V_R,P, then BK_R,1,1=PS_R,1,1=0, storage capacity V is corrected at this time_R,1 ^*=V_R,1。

By step a~c, corrects and determine the 1st stage end reservoir capacity V_R,1 ^*, while can get corresponding reservoir and abandoning water Measure PS_R,1,1Or upper level reservoir mends library water BK_R,1,1。

II) stage i=2,3 ... N-1:

g_i(λ_i)=min [(G_R,i,1+Y_R,i,1-YS_R,i)²+g_i-1(λ_i-1)] (30)

Period reservoir yield G_R,i,1It is given by initial value, state variable λ_iIt equally carries out respectively discrete:To each discrete λ_i, Group of Pumping Station moisturizing total amount Y_R,i,1It is discrete to meet:

State transition equation: λ_i-1=λ_i-(YS_R,i-G_R,i,1) (31)

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

To each discrete λ_i, by each discrete Y_R,i,1Value substitutes into the (G in formula (30) respectively_R,i,1+Y_R,i,1-YS_R,i)², by State transition equation formula (31), lookup i-1 stage meetIt is required that g_i-1(λ_i-1) value, thus to obtain the λ is met_i It is required that optimal Y_R,i,1Process and its corresponding preceding i period subsystem minimum water deficit quadratic sum g_i(λ_i).Equally, according to formula (25), the i-th period end reservoir capacity V_R,i=V_R,i-1+LS_R,i-EF_R,i-G_R,i,1, at this time not yet consider the moisturizing of upper level reservoir and Reservoir is abandoned water and is tested also according to formula (26)~(28) using above-mentioned steps a~c, is corrected and is determined the i-th stage end water Kuku holds V_R,i ^*, while can get corresponding reservoir and abandoning water PS_R,i,1Or upper level reservoir mends library water BK_R,i,1, wherein i= 1,2 ..., i.

III) stage N:

g_N(λ_N)=min [(G_R,N,1+Y_R,N,1-YS_R,N)²+g_N-1(λ_N-1)] (32)

Period reservoir yield G_R,N,1It is given by initial value, state variableDecision becomes Measure Group of Pumping Station moisturizing total amount Y_R,N,1It is equally discrete in corresponding feasible zone, it should meet: λ_N-1=λ_N-(YS_R,N-G_R,N,1)。

Using step II) the method, it finally obtains and meets the λ_NIt is required that the optimal moisturizing total amount process Y of Group of Pumping Station_R,i,1, Corresponding reservoir abandons process water PS_R,i,1And upper level reservoir is to its benefit library process water BK_R,i,1, wherein i=1 ... N。

3. 2. Group of Pumping Station that step is obtained mends canal total Water process Y_R,i,1As initial given value, substitute into formula (22), then Submodel (22)~(28), (12)~(13) are converted into again with each stage reservoir yield G_R,iFor decision variable, preceding i stage Reservoir is for water inventory λ_i' 2. referring to step asked using one-dimensional dynamic programming for the one-dimensional dynamic programming model of state variable Solution, acquisition meet the λ_N' require the optimal water supply process G of reservoir_R,i,2(i=1 ... N), corresponding reservoir abandon process water PS_R,i,2And upper level reservoir is to its benefit library process water BK_R,i,2, wherein i=1 ... N.

4. 3. reservoir yield process G that step is obtained_R,i,2It as initial given value, substitutes into formula (22), repeats step 2.~3., Approach by inchmeal solves repeatedly, until the adjacent optimal value error precision of objective function twice is less than desired iteration control Precision ε, then submodel optimization terminate.Optimize the reservoir yield process G obtained with last time_R,i,mCanal total Water is mended with pumping plant Process Y_R,i,mAs master mould optimal solution, while it also can get objective function optimal value, the optimal abandoning process water PS of reservoir_R,i,m, And upper level reservoir is to its benefit library process water BK_R,i,m.Wherein, i=1 ... N；M is Dynamic Programming Approach by inchmeal iteration time Number number.

3) " benefit canal Group of Pumping Station " second level subsystem model decomposition-Dynamic Programming polymerization solves

1. mending the building of canal Group of Pumping Station subsystem economical operation mathematical model

Consider moisturizing Group of Pumping Station combined operating energy consumption minimum criteria constraint condition, is established by formula (13) and mend canal Group of Pumping Station economy Run mathematical model:

Objective function:

The constraint of period water supply:

Power constraint:

In formula, N_R,k,0The kth seat of feeder channel mends the electric drilling match power (kW) of canal pumping plant where the reservoir of Building R.

2. " mending canal Group of Pumping Station " subsystem decomposition-Dynamic Programming polymerization solves

I) decomposition of second level subsystem:

Above-mentioned subsystem model (33)~(35) are further decomposed, M single station economical operation three-level submodel can be obtained:

Objective function:

Power constraint:

In formula, l_R,iFor the i-th period minimum operation energy consumption of single station of Building R reservoir, unit: kWh.

II) determination of three-level submodel energy consumption:

For model above (36)~(37), segment length △ T when the i-th period_R,iIt is known that simultaneously can be true by pumping plant water levels of upstream and downstream Determine water lift lift H_R,iAnd its corresponding Q_R,i、η_z,R,i、η_mot,RAnd η_int,R, and the period maximum rate of water make-up is YB_R,i,max= 3600Q_R,i△T_R,i/ 10000, by the discrete period maximum water lift amount YB of a fixed step size_R,i,max, can get each water lift amount YB_R,i,m Place an order the operation energy consumption l that stands_R,i,m, m=1,2 ... max.

To other pumping plants of the reservoir, using same method, thus to obtain each pumping plant difference water lift amount YB_R,k,i,mUnder, it is single Stand operation energy consumption l_R,k,i,m, k=1,2 ... M, m=1,2 ... max.

III) original second level subsystem Dynamic Programming polymerization:

It is solved by the above three-level subsystem, canal pumping plant is mended to each, can get a series of single station water lift energy consumptions l_R,k,i,mMend water in a canal amount YB in~mono- station_R,k,i,mIt is former to construct following polymerization model substitution by relationship, k=1,2 ... M, m=1,2 ... max Second level submodel (33)~(35):

Objective function:

Period water quantity restraint:

Polymerization model (38)~(39) are similarly one-dimensional dynamic programming model, and stage variable is confession where the reservoir of Building R Benefit canal pumping plant number k, k=1,2 ... the M in water channel road；Decision variable is each i-th period of pumping plant water lift amount YB_R,k,i, discrete model Target water discrete range YB when enclosing as single station optimization_R,k,i,m, k=1,2 ... M, m=1,2 ... max；It can by formula (39) The discrete value for knowing each pumping plant water lift total amount is state variable (λ)；The model is solved using one-dimensional dynamic programming, is met I-th period pumping plant target water lift total amount Y_R,iL_R,iValue and the optimal rate of water make-up of corresponding each pumping plant combine YB_R,k,i ^*, k=1, 2,…M。

4) Building R Dan Ku-multiple station systems submodel optimal solution is determined

The optimal moisturizing total amount Y of canal Group of Pumping Station is mended by the day part that step 2) obtains_R,i, after i=1,2 ... ... N；To each The Y that period determines_R,i, it is both needed to calculate via a step 3), altogether n times step 3), by day part Y_R,iOptimization is distributed to M and is mended Canal pumping plant obtains each optimal rate of water make-up YB of benefit canal pumping plant day part_R,k,i ^*；Thus final to obtain R grades of single library-multiple station systems years The least square and F of the difference for water requirement of interior day part_R, corresponding reservoir day part optimal water supply G_R,i, abandon water process PS_R,i, upper level reservoir is to its benefit library water BK_R,i, and each benefit optimal rate of water make-up process YB of canal pumping plant day part_R,k,i ^*, i =1,2 ... ... N, k=1,2 ... M.

(2) R-1, R-2 ..., 1 single library-multiple station systems water resource optimal allocation submodel solve

For R-1, R-2 ..., 1 directly mend canal single library-multiple station systems, equally using submodel (14)~ (21), (9)~(13) are with reservoir day part water supply G_R,i, feeder channel where the reservoir respectively mend canal pumping plant day part benefit Water YB_R,k,iNonlinear model is tieed up for the M+1 of decision variable, referring to step (1), is takenThen the submodel turns It is changed to each stage water supply G of reservoir_h,i, mend each stage moisturizing total amount Y of canal Group of Pumping Station_h,iFor the two-dimension non linearity number of decision variable Model is learned, is still solved using Dynamic Programming successive approximation method.Difference is only that:

1) single library-multiple station systems year of canal is mended directly for water inventory constraint condition:

Dan Ku-multiple station systems year should use formula (15)~(16) for water inventory constraint, it may be assumed thatAndDue to using hysterology, outer water diversion volume WD_h,iIt is i.e. next The benefit library water BK of the single library-multiple station systems of grade_h+1,i, by the reservoir tune in preceding primary single library-multiple station systems optimization process Criterion is spent to determine, it may be assumed that

WD_h,i=BK_h+1,i (40)

Then formula (15) can be converted into such as following formula (41), to obtain reservoir yield restriction range.

2) meet outer water diversion volume and higher level's reservoir mend single reservoir operation criterion constraint that library water requires:

The outer water diversion volume WD of this reservoir is considered as to each stage water balance equation_h,iAnd upper level reservoir is to its benefit library Water BK_h,iTwo aspect factors, should consider respectively: to the 1st reservoir, Ying Caiyong formula (19), it may be assumed that V_1,i=V_1,i-1+LS_1,i- PS_1,i-EF_1,i-G_1,i-WD_1,i；To the 2nd~the R-1 reservoirs, Ying Caiyong formula (20), it may be assumed that V_h,i=V_h,i-1+LS_h,i+BK_h,i- PS_h,i-EF_h,i-G_h,i-WD_h,i。

Similarly, by formula (40), formula (19)~(20) can be converted following form:

1. to the 1st reservoir,

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-BK_2,i (42)

2. to the 2nd~the R-1 reservoirs,

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-BK_h+1,i (43)

On this basis, still each stage storage capacity is modified using formula (9)~(11).

The water resource optimization tune for the more pumping station systems of more reservoirs-that canal is directly mended under abundant irrigation conditions can be achieved in the invention Degree, method precision is reliable, and accuracy reduces up to 95% or more and mends 20% or more canal pumping station operation energy consumption, reaches irrigated area water money The purpose of source optimization configuration, improves irrigated area, society and ecological benefits.

Detailed description of the invention

Fig. 1 generally changes system schematic directly to mend more libraries-multistation water resource of canal under abundant irrigation conditions.

Specific embodiment

As shown in Figure 1, directly to mend more libraries-of canal each reservoir yield of day part and intake area in multiple station systems year The minimum target of the quadratic sum of the difference of water requirement, the day part reservoir yield divided in year, each canal pumping plant water lift amount of mending are certainly Plan variable, with the reservoir of every level-one list library-multiple station systems, it is each mend canal pumping plant year for water inventory, consider higher level's reservoir call in Single reservoir operation criterion, Dan Shuiku water balance, benefit canal Group of Pumping Station combined operating energy consumption minimum that itself outer water diversion volume requires etc. For constraint condition, establishes under abundant irrigation conditions and directly mend " more library-multistations " system water resources optimal operation model of canal.

One, model construction

1. objective function

In formula: F be research object year in day part the difference for water requirement least square and；Z is in research object year The quadratic sum of the difference for water requirement of day part；R is reservoir quantity (seat)；H is reservoir number (h=1,2 ... R)；N is year The when number of segment of interior division；Segment number when i is (i=1,2 ... N)；G_h,i、YS_h,iThe water supply of respectively h the i-th periods of reservoir Measure (ten thousand m³) and the i-th period of corresponding intake area water requirement (ten thousand m³)；YB_h,k,iFor feeder channel kth seat where h reservoirs Mend the i-th period of canal pumping plant water supply (ten thousand m³).Objective function using quadratic sum expression be in order to accelerate reduce system water supply amount with Deviation between the water requirement of intake area.

2. constraint condition

Including mending single library-multiple station systems year of canal directly for water inventory constraint condition, consider that higher level's reservoir is called in and oneself Single reservoir water Constraints of Equilibrium that the outer water diversion volume of body requires, single reservoir capacity constraint condition, and mend canal Group of Pumping Station operation energy consumption Least commitment condition.Specifically it is described below:

(1) single library-multiple station systems year of canal is mended directly for water inventory constraint: in different level year difference fraction feelings Under condition, consideration needs water requirement, the water that water supply project may provide.Wherein, except final stage reservoir only needs to supply water to place intake area Outside, remaining reservoir at different levels also needs to undertake outer water transfer task, supplies next stage reservoir, it may be assumed that

To the 1st~the R-1 reservoirs:

Wherein, h=1,2 ... ... R-1.

To Building R reservoir:

In formula: WD_h,iFor water supply (ten thousand m for assigning next stage (i.e. h+1 grades) reservoir outside h the i-th periods of reservoir³)； SK_hFor h reservoirs year for water inventory (ten thousand m³)；M is the benefit canal pumping plant quantity (seat) of feeder channel where h reservoirs； K is to mend canal pumping plant number (k=1,2 ... M)；BZ_h,kTo permit in the kth seat benefit canal pumping plant year of feeder channel where h reservoirs Perhaps water lift total amount (ten thousand m³)；Remaining variables meaning is same as above.

(2) consider that higher level's reservoir calls in single reservoir water Constraints of Equilibrium with itself outer water diversion volume requirement: for any h A more pumping plants directly mend single library-multiple station systems of canal, consider that higher level's reservoir calls in the outer water diversion volume requirement of water and reservoir itself, It include: to the 1st reservoir, only outer water diversion volume requirement；To 2~R-1 reservoirs, benefit library water of the existing higher level's reservoir to it Amount, and have itself outer water diversion volume requirement；To Building R reservoir, only higher level's reservoir mends the requirement of library water.I.e. according to water balance side Journey:

To the 1st reservoir:

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-WD_1,i (6)

To the 2nd~the R-1 reservoirs:

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-WD_h,i (7)

Wherein, h=2,3 ..., R-1.

To Building R reservoir:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (8)

On this basis, reservoir operation criterion is as follows:

1. when the i-th period end pondage is lower than reservoir minimum capacity of a reservoir V_h,minWhen, then the i-th period should by upper level reservoir into Row moisturizing, moisturizing to utilizable capacity (Δ more than reservoir minimum capacity of a reservoir_h,1), it may be assumed that

V_h,i<V_h,minWhen: BK_h,i=V_h,min-V_h,i+Δ_h,1, (9)

This period reservoir abandons water PS_h,i=0；H=2,3 ... R.

2. when meeting with flood, the i-th period end pondage is greater than pondage V corresponding to flood control_h,P When, then the i-th period should carry out abandoning water to reservoir, abandon water to flood control by reservoir regulation limiting water level, it may be assumed that

V_h,i>V_h,PWhen: PS_h,i=V_h,i-V_h,P (10)

This period is not necessarily to upper level Reservoir Regulation, i.e. BK_h,i=0.

3. when the i-th period end pondage is between minimum capacity of a reservoir V_h,minWith pondage corresponding to flood control V_h,PBetween, then the i-th period reservoir does not need to abandon water, does not need upper level Reservoir Regulation, it may be assumed that

V_h,min≤V_h,i≤V_h,PWhen: PS_h,i=BK_h,i=0 (11)

In formula: V_h,i、V_h,i-1Respectively h reservoirs i-th, the reservoir storage of i-1 period Mo (ten thousand m³)；LS_h,i、PS_h,i、 EF_h,iRespectively h the i-th periods of reservoir carry out water (ten thousand m³), abandon water (ten thousand m³), evaporation with leakage (ten thousand m³)；BK_h,i Benefit library water (ten thousand m provided for h the i-th periods of reservoir by upper level (i.e. h-1) reservoir³)。

(3) single reservoir capacity constraint: the pondage of day part should be between reservoir minimum capacity of a reservoir and flood control pair It answers between storage capacity, it may be assumed that

V_h,min≤V_h,i≤V_h,P, (i=1,2, N) (12)

(4) it mends the constraint of canal Group of Pumping Station combined operating energy consumption minimum criteria: further, meeting the constraint of reservoir operation criterion On the basis of, to guarantee the abundant irrigation conditions in intake area, to the benefit canal Group of Pumping Station of any h reservoirs place feeder channel, Each combined operating to supply water in the period is considered as energy consumption minimum, it may be assumed that

In formula, L_h,iCanal Group of Pumping Station combined operation system energy consumption (kW is mended for the i-th period of feeder channel where h reservoirs h)；l_h,k,iFor kth seat the i-th period of pumping plant operation energy consumption (kWh) of feeder channel where h reservoirs；M is h reservoirs The benefit canal pumping plant quantity (seat) of place feeder channel；ρ is water density (kg/m³), g is acceleration of gravity (m/s²)；Q_h,k,i、 H_h,k,i、△T_h,k,i、η_z,h,k,iFlow (the m of kth seat the i-th period of pumping plant of feeder channel respectively where h reservoirs³/s)、 When equal lift (m), Period Length (h) and pump efficiency；η_mot,h,k、η_int,h,kThe of feeder channel where respectively h reservoirs The motor efficiency and transmission efficiency of k pumping plants.

Two, model feature

(1) in view of should strictly carry out water total amount control in water resources development and utilization, therefore in model constraint condition It is added and mends single library-multiple station systems year of canal directly for water inventory constraint, i.e. formula (2)~(5).

(2) the single reservoir operation criterion for meeting outer water diversion volume and the benefit library water requirement of higher level's reservoir is considered in constraint condition Constraint, i.e. formula (6)~(8), water diversion volume outside reservoirs at different levels is mutually connected with higher level's reservoir rate of water make-up, to use backward Dynamic Programming Approach by inchmeal optimization provides feasibility；At the same time it can also realize more libraries-of lift pumping station group " idle mends library, busy supplies water " Multiple station systems water resources optimal operation mode.If idle pondage is lower than reservoir minimum capacity of a reservoir, consider by upper level reservoir Moisturizing is carried out to this reservoir, mends library water BK_h,iFor the difference of reservoir minimum capacity of a reservoir and the i-th period end pondage, dead library is added Hold the above Δ_h,1, i.e. BK_h,i=V_h,min-V_h,i+Δ_h,1；If reservoir capacity is more than reservoir storage corresponding to flood control by reservoir regulation limiting water level When, then need to abandon dispatching requirement of the water to guarantee reservoir capacity, reservoir abandons water PS_h,iFor the i-th period end pondage and water The difference of reservoir storage corresponding to the flood control of library, i.e. PS_h,i=V_h,i-V_h,P.Busy then considers according to pondage situation Combined from reservoir, benefit canal Group of Pumping Station to intake area and supplied water, to meet the water demand of water user as far as possible.

(3) combine for mending canal pumping plant from Building M to when certain level-one list reservoir place feeder channel water supply, it is contemplated that each pumping plant Unit performance property difference between standing under different lifts, joined the minimum constraint condition of Group of Pumping Station combined operating energy consumption, i.e. formula (13). It, will by establishing Group of Pumping Station second level subsystem combined optimization operation mathematical model and being solved using decomposition-Dynamic Programming polymerization The determining day part Group of Pumping Station moisturizing total amount Y of level-one subsystem model optimization_h,iDistribution is advanced optimized to each benefit canal pumping plant YB_h,k,i(k=1,2 ... M) reduce the operation of Group of Pumping Station subsystem by energy consumption as far as possible.

(4) complex nonlinear mathematical model is tieed up in form for M+1 in model (1)~(13), but big using " more library-multistations " System decomposition-directly mends " Dan Ku-multistation " subsystem backward Dynamic Programming Approach by inchmeal optimization-" mending canal Group of Pumping Station " of canal Second level subsystem decomposition-Dynamic Programming polymerization method for solving, not only can get the optimizing decision variable in objective function Value --- each stage each reservoir yield G_h,i, each mend canal pumping plant rate of water make-up YB_h,k,i；And consideration higher level's reservoir is called in and itself Single reservoir operation criterion constraint that outer water diversion volume requires is tested amendment to storage capacity by using formula (9)~(11), can also be obtained Obtain the optimal abandoning water PS of day part reservoir_h,i, outer water diversion volume WD_h,iWith upper level reservoir rate of water make-up process BK_h,i, actually solve (M+4) R-2 decision variable value is obtained, such complex nonlinear model solution method is enriched.

Three, model solution

1, data preparation is carried out

It specifically includes: being divided into N number of period for 1 year, and determine day part length；Measure each reservoir initial storage V_h,0；Really Fixed each reservoir year is for water inventory SK_h, minimum capacity of a reservoir V_h,min, the corresponding storage capacity V of flood control_h,PAnd utilizable capacity V_h,min+△_h,1；It measures and calculates each reservoir day part and carry out water LS_h,i, evaporation with leakage EF_h,i(h=1,2 ... R)；It determines Each mend allows water lift total amount BZ in canal pumping plant year_h,k(k=1,2 ... M)；Measure different lift H_h,k,iThe water lift flow of lower operation Q_h,k,iAnd corresponding pump efficiency η_z,h,k,i, electric efficiency η_mot,h,k, transmission efficiency η_int,h,k；Determine each intake area of day part Water demand of crop YS_h,i(h=1,2 ... R；I=1,2 ..., N).

2, " more library-multistations " large-scale system model for directly mending canal decomposes

Model above (1)~(13) are with each reservoir day part water supply G_h,i, feeder channel where each reservoir each benefit canal Pumping plant day part rate of water make-up YB_h,k,i(h=1,2 ... R；K=1,2 ... M) be decision variable R (M+1) dimension it is complicated non-thread Property mathematical model, consider that each reservoir supplies water to respective intake area respectively, can be the lists of R directly benefit canal by model decomposition Library-multistation water resource optimal allocation mathematical model.

(1) objective function:

(2) single library-multiple station systems year of canal is mended directly for water inventory constraint:

1. in addition to supplying water to intake area, there are also assign the water supply of junior's reservoir to want outside for the 1st~the R-1 reservoirs It asks, therefore:

In formula, h=1,2 ... ... R-1.

2. it only supplies water to intake area for Building R reservoir, without the water supply requirement for assigning junior's reservoir outside, therefore:

(3) consider that higher level's reservoir calls in single reservoir water Constraints of Equilibrium with itself outer water diversion volume requirement:

1. to the 1st reservoir:

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-WD_1,i (19)

2. to the 2nd~the R-1 reservoirs:

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-WD_h,i (20)

Wherein, h=2,3 ..., R-1.

3. to Building R reservoir:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (21)

The same formula of reservoir operation criterion (9)~(11) on this basis.

(4) single reservoir capacity constraint: same to formula (12).

(5) canal Group of Pumping Station combined operating energy consumption minimum criteria constraint: same to formula (13) is mended.

3, single library-multistation subsystem optimization of canal is directly mended

For the 1st~the R-1 reservoirs, the outer water supply WD for assigning next stage reservoir_h,i, practical is junior's reservoir Mend library water BK_h+1,i, it may be assumed that WD_h,i=BK_h+1,i, and BK_h+1,iIt need to be according to water user's water demand of contributing region where junior's reservoir Depending on.Therefore it is considered as hysterology, the single library-multiple station systems required from final stage without outer water transfer successively carry out single library- Multiple station systems water resource optimal allocation.

(1) Building R Dan Ku-multiple station systems water resource optimal allocation submodel solves

1) submodel is converted

It is with reservoir day part water supply G for submodel (14)~(21), (9)~(13)_R,i, supply where the reservoir Respectively mend canal pumping plant day part rate of water make-up YB in water channel road_R,k,iNonlinear model is tieed up for the M+1 of decision variable, therefore considers to takeThen the submodel is converted to each stage water supply G of reservoir_R,i, mend each stage moisturizing total amount of canal Group of Pumping Station Y_R,iFor the two-dimension non linearity mathematical model of decision variable, it may be assumed that

Objective function:

Dan Ku-multiple station systems year is for water inventory constraint:

Reservoir water Constraints of Equilibrium:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (25)

On this basis, reservoir operation criterion are as follows:

1. when the i-th period end pondage is lower than reservoir minimum capacity of a reservoir V_R,minWhen, then the i-th period should by upper level reservoir into Row moisturizing, moisturizing to utilizable capacity (Δ more than reservoir minimum capacity of a reservoir_R,1), it may be assumed that

V_R,i<V_R,minWhen: BK_R,i=V_R,min-V_R,i+Δ_R,1 (26)

This period reservoir abandons water PS_R,i=0.

2. when meeting with flood, the i-th period end pondage is greater than pondage V corresponding to flood control_R,P When, then the i-th period should carry out abandoning water to reservoir, abandon water to flood control by reservoir regulation limiting water level, it may be assumed that

V_R,i>V_R,PWhen: PS_R,i=V_R,i-V_R,P (27)

This period is not necessarily to upper level Reservoir Regulation, i.e. BK_R,i=0.

3. when the i-th period end pondage is between minimum capacity of a reservoir V_R,minWith pondage corresponding to flood control V_R,PBetween, then the i-th period reservoir does not need to abandon water, does not need upper level Reservoir Regulation, it may be assumed that

V_R,min≤V_R,i≤V_R,PWhen: PS_R,i=BK_R,i=0 (28)

The same formula of its corestriction (12)~(13).

2) submodel Dynamic Programming Approach by inchmeal solves

Further, for the above transformation model (22)~(28), (12)~(13), Dynamic Programming Approach by inchmeal solves tool Steps are as follows for body:

1. with conventional reservoir stage water supply process G_R,i,1As primary iteration value, formula (22) are substituted into, then submodel (22)~(28), (12)~(13), which are converted into, mends canal total Water Y with each stage Group of Pumping Station_R,iFor decision variable, preceding i stage pump Group's moisturizing total amount of standing λ_iFor the one-dimensional dynamic programming model of state variable, solved using one-dimensional dynamic programming；Wherein, i=1, 2,……N。

2. obtaining corresponding recurrence equation referring to one-dimensional dynamic programming evaluation principle are as follows:

I) stage i=1:

g₁(λ₁)=min (G_R,1,1+Y_R,1,1-YS_R,1)² (29)

Period reservoir yield G_R,1,1It is given by initial value, state variable λ₁, it can be discrete in corresponding feasible zone:To each discrete λ₁, decision variable (Group of Pumping Station moisturizing total amount Y_R,1,1) can be feasible in correspondence It is discrete in domain, such as 00,000 m³, 50,000 m³, 100,000 m³, 150,000 m³、…Y_R,1,1,maxDeng (Y_R,1,1,maxFor the 1st stage Group of Pumping Station maximum benefit Outlet capacity), it should meet: Y_R,1,1≥λ₁.The Y that will be met the requirements_R,1,1Formula (29) are substituted into respectively, are respectively obtained corresponding to each discrete λ₁When value, optimal Y_R,1,1And its corresponding period minimum water deficit quadratic sum g₁(λ₁)。

Then, according to formula (25), the 1st stage end reservoir capacity V_R,1=V_R,0+LS_R,1-EF_R,1-G_R,1,1, not yet consider at this time The moisturizing of upper level reservoir and reservoir abandon water, are examined using formula (26)~(28):

A, work as V_R,1<V_R,min, then consider to mend library water BK to its moisturizing by upper level reservoir_R,1,1=V_R,min-V_R,1+ Δ_R,1, storage capacity V is corrected at this time_R,1 ^*=V_R,min+△_R,1。

B, work as V_R,1>V_R,P, then need to abandon dispatching requirement of the water to guarantee reservoir capacity, PS_R,1,1=V_R,1-V_R,P, repair at this time Positive storage capacity V_R,1 ^*=V_R,P。

C, work as V_R,min≤V_R,1≤V_R,P, then BK_R,1,1=PS_R,1,1=0, storage capacity V is corrected at this time_R,1 ^*=V_R,1。

By step a~c, corrects and determine the 1st stage end reservoir capacity V_R,1 ^*, while can get corresponding reservoir and abandoning water Measure PS_R,1,1Or upper level reservoir mends library water BK_R,1,1。

II) stage i=2,3 ... N-1:

g_i(λ_i)=min [(G_R,i,1+Y_R,i,1-YS_R,i)²+g_i-1(λ_i-1)] (30)

Period reservoir yield G_R,i,1It is given by initial value, state variable λ_iIt equally carries out respectively discrete:To each discrete λ_i, decision variable (Group of Pumping Station moisturizing total amount Y_R,i,1) it is discrete ibid, and It should meet:

State transition equation: λ_i-1=λ_i-(YS_R,i-G_R,i,1) (31)

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

To each discrete λ_i, by each discrete Y_R,i,1Value substitutes into the (G in formula (30) respectively_R,i,1+Y_R,i,1-YS_R,i)², by State transition equation formula (31), lookup i-1 stage meetIt is required that g_i-1(λ_i-1) value, thus to obtain the λ is met_i It is required that optimal Y_R,i,1Process and its corresponding preceding i period subsystem minimum water deficit quadratic sum g_i(λ_i).Equally, according to formula (25), the i-th period end reservoir capacity V_R,i=V_R,i-1+LS_R,i-EF_R,i-G_R,i,1, at this time not yet consider the moisturizing of upper level reservoir and Reservoir is abandoned water and is tested also according to formula (26)~(28) using above-mentioned steps a~c, is corrected and is determined the i-th stage end water Kuku holds V_R,i ^*, while can get corresponding reservoir and abandoning water PS_R,i,1Or upper level reservoir mends library water BK_R,i,1, wherein i= 1,2 ..., i.

III) stage N:

g_N(λ_N)=min [(G_R,N,1+Y_R,N,1-YS_R,N)²+g_N-1(λ_N-1)] (32)

Period reservoir yield G_R,N,1It is given by initial value, state variableDecision becomes Measure (Group of Pumping Station moisturizing total amount Y_R,N,1) equally discrete in corresponding feasible zone, it should meet: λ_N-1=λ_N-(YS_R,N-G_R,N,1)。

Using step II) the method, it finally obtains and meets the λ_NIt is required that the optimal moisturizing total amount process Y of Group of Pumping Station_R,i,1, Corresponding reservoir abandons process water PS_R,i,1And upper level reservoir is to its benefit library process water BK_R,i,1, wherein i=1 ... N。

3. 2. Group of Pumping Station that step is obtained mends canal total Water process Y_R,i,1As initial given value, substitute into formula (22), then Submodel (22)~(28), (12)~(13) are converted into again with each stage reservoir yield G_R,iFor decision variable, preceding i stage Reservoir is for water inventory λ_i' 2. referring to step asked using one-dimensional dynamic programming for the one-dimensional dynamic programming model of state variable Solution, acquisition meet the λ_N' require the optimal water supply process G of reservoir_R,i,2(i=1 ... N), corresponding reservoir abandon process water PS_R,i,2And upper level reservoir is to its benefit library process water BK_R,i,2, wherein i=1 ... N.

4. 3. reservoir yield process G that step is obtained_R,i,2It as initial given value, substitutes into formula (22), repeats step 2.~3., Approach by inchmeal solves repeatedly, until the adjacent optimal value error precision of objective function twice is less than desired iteration control Precision ε, then submodel optimization terminate.Optimize the reservoir yield process G obtained with last time_R,i,mCanal total Water is mended with pumping plant Process Y_R,i,mAs master mould optimal solution, while it also can get objective function optimal value, the optimal abandoning process water PS of reservoir_R,i,m, And upper level reservoir is to its benefit library process water BK_R,i,m.Wherein, i=1 ... N；M is Dynamic Programming Approach by inchmeal iteration time Number number.

3) " benefit canal Group of Pumping Station " second level subsystem model decomposition-Dynamic Programming polymerization solves

After above Building R " the more pumping plants of the Dan Shuiku-" subsystem is using the optimization of Dynamic Programming Approach by inchmeal, except having determined that R The least square and F of the difference for water requirement of day part in contributing region year where seat reservoir_R, reservoir day part optimal water supply G_R,i, abandon water process PS_R,iWith upper level reservoir to its benefit library water BK_R,iOutside, to canal Group of Pumping Station is mended, day part has only been determined Optimal moisturizing total amount Y_R,iProcess not yet considers specific each rate of water make-up YB for mending canal pumping plant and being assigned to_R,k,i(k=1,2 ... M), by It is had differences in each benefit canal pumping plant unit installation performance, along with day part water lift lift is different, causes pumping station operation energy consumption each It is not identical, canal Group of Pumping Station operation energy consumption is mended to reduce, it need to be by Y_R,iDistribution is advanced optimized to each benefit canal pumping plant, specifies day part Each canal pumping plant of mending optimizes rate of water make-up YB_R,k,i, to be really achieved single library-multiple station systems water resource optimal allocation purpose.

1. mending the building of canal Group of Pumping Station subsystem economical operation mathematical model

Consider the constraint of moisturizing Group of Pumping Station combined operating energy consumption minimum criteria, is established by formula (13) and mend the economical operation of canal Group of Pumping Station Mathematical model:

Objective function:

The constraint of period water supply:

Power constraint:

In formula, N_R,k,0The kth seat of feeder channel mends the electric drilling match power (kW) of canal pumping plant where the reservoir of Building R；Its Remaining variable meaning is same as above.

2. " mending canal Group of Pumping Station " subsystem decomposition-Dynamic Programming polymerization solves

I) decomposition of second level subsystem:

Above-mentioned subsystem model (33)~(35) are further decomposed, M single station economical operation three-level submodel can be obtained:

Objective function:

Power constraint:

In formula, l_R,iFor the i-th period minimum operation energy consumption of single station of Building R reservoir, unit: kWh.

II) determination of three-level submodel energy consumption:

For model above (36)~(37), segment length △ T when the i-th period_R,iIt is known that simultaneously can be true by pumping plant water levels of upstream and downstream Determine water lift lift H_R,iAnd its corresponding Q_R,i、η_z,R,i、η_mot,RAnd η_int,R, and the period maximum rate of water make-up is YB_R,i,max= 3600Q_R,i△T_R,i/ 10000, by the discrete period maximum water lift amount YB of a fixed step size_R,i,max(i.e. to period duration △ T_R,i Carry out discrete), it can get each water lift amount YB_R,i,mPlace an order the operation energy consumption l that stands_R,i,m(m=1,2 ... max).

To other pumping plants of the reservoir, above method is used, equally thus to obtain each pumping plant difference water lift amount YB_R,k,i,m Under, single operation energy consumption l that stands_R,k,i,m(k=1,2 ... M, m=1,2 ... max).

III) original second level subsystem Dynamic Programming polymerization:

It is solved by the above three-level subsystem, canal pumping plant is mended to each, can get a series of single station water lift energy consumptions l_R,k,i,mMend water in a canal amount YB in~mono- station_R,k,i,mRelationship (k=1,2 ... M, m=1,2 ... max) thus can construct following polymerization mould Type substitutes former second level submodel (33)~(35):

Objective function:

Period water quantity restraint:

Polymerization model (38)~(39) are similarly one-dimensional dynamic programming model, and stage variable is confession where the reservoir of Building R The benefit canal pumping plant number k (k=1,2 ... M) in water channel road；Decision variable is each i-th period of pumping plant water lift amount YB_R,k,i, discrete model Target water discrete range YB when enclosing as single station optimization_R,k,i,m(k=1,2 ... M, m=1,2 ... max)；It can by formula (39) The discrete value for knowing each pumping plant water lift total amount is state variable (λ).The model is solved referring to the above one-dimensional dynamic programming, is obtained Meet the i-th period pumping plant target water lift total amount Y_R,iL_R,iValue and the optimal rate of water make-up of corresponding each pumping plant combine YB_R,k,i ^*(k =1,2 ... M).

4) Building R Dan Ku-multiple station systems submodel optimal solution is determined

The optimal moisturizing total amount Y of canal Group of Pumping Station is mended by the day part that step 2) obtains_R,i(i=1,2 ... N) after；To every The Y that a period determines_R,i, it is both needed to calculate via a step 3), altogether n times step 3), it can be further by day part Y_R,iOptimization Distribution obtains each optimal rate of water make-up YB of benefit canal pumping plant day part to M benefit canal pumping plant_R,k,i ^*；Thus final to obtain R grades of lists The least square and F of library-difference for water requirement of day part in multiple station systems year_R, corresponding reservoir day part optimal water supply G_R,i, abandon water process PS_R,i, upper level reservoir is to its benefit library water BK_R,i, and each benefit optimal rate of water make-up of canal pumping plant day part Process YB_R,k,i ^*(i=1,2 ... ... N, k=1,2 ... M).

(2) R-1, R-2 ..., 1 single library-multiple station systems water resource optimal allocation submodel solve

For R-1, R-2 ..., 1 directly mend canal single library-multiple station systems, equally using submodel (14)~ (21), (9)~(13) are with reservoir day part water supply G_R,i, feeder channel where the reservoir respectively mend canal pumping plant day part benefit Water YB_R,k,iNonlinear model is tieed up for the M+1 of decision variable, referring to step (1), is takenThen the submodel turns It is changed to each stage water supply G of reservoir_h,i, mend each stage moisturizing total amount Y of canal Group of Pumping Station_h,iFor the two-dimension non linearity number of decision variable Model is learned, is still solved using Dynamic Programming successive approximation method.Difference is only that:

1) single library-multiple station systems year of canal is mended directly for water inventory constraint:

Reservoir, which supplies water, should supply the water supply G of intake area_h,i, it is also contemplated that assigning the water supply of next stage reservoir outside WD_h,iFactor, then Dan Ku-multiple station systems year should use formula (15)~(16) for water inventory constraint, it may be assumed thatAndDue to using hysterology, outer water diversion volume WD_h,iIt is i.e. next The benefit library water BK of the single library-multiple station systems of grade_h+1,i, by the reservoir tune in preceding primary single library-multiple station systems optimization process Criterion is spent to determine, it may be assumed that

WD_h,i=BK_h+1,i (40)

Then formula (15) can be converted into such as following formula (41), to obtain reservoir yield restriction range.

2) meet outer water diversion volume and higher level's reservoir mend single reservoir operation criterion constraint that library water requires:

The outer water diversion volume WD of this reservoir is considered as to each stage water balance equation_h,iAnd upper level reservoir is to its benefit library Water BK_h,iTwo aspect factors, should consider respectively: to the 1st reservoir, Ying Caiyong formula (19), it may be assumed that V_1,i=V_1,i-1+LS_1,i- PS_1,i-EF_1,i-G_1,i-WD_1,i；To the 2nd~the R-1 reservoirs, Ying Caiyong formula (20), it may be assumed that V_h,i=V_h,i-1+LS_h,i+BK_h,i- PS_h,i-EF_h,i-G_h,i-WD_h,i。

Similarly, by formula (40), formula (19)~(20) can be converted following form:

1. to the 1st reservoir,

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-BK_2,i (42)

2. to the 2nd~the R-1 reservoirs,

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-BK_h+1,i (43)

On this basis, still each stage storage capacity is modified using formula (9)~(11).

4, master mould optimal solution is determined

As a result, to each single library-multistation subsystem model for directly mending canal, single library-multiple station systems submodel is respectively adopted Dynamic Programming Approach by inchmeal solves, mends canal Group of Pumping Station second level subsystem model decomposition-Dynamic Programming polymerization solution, determines respectively Dan Ku-multiple station systems submodel optimal solution finally obtains the optimal reservoir day part water supply G of each subsystem_h,i, outer water diversion volume WD_h,i, abandon water PS_h,i, the optimal benefit library water BK of upper level reservoir_h,iAnd corresponding each benefit canal pumping plant rate of water make-up YB_h,k,iIt crosses Journey (h=1,2 ..., R).

Claims (3)

1. more libraries-multiple station systems water resource optimal allocation method of canal is directly mended under a kind of abundant irrigation conditions, by multiple benefit canals Feeder channel supplies water where pumping plant to single reservoir, forms the single library-multiple station systems for directly mending canal, then by multiple concatenated Dan Ku-multiple station systems constitute the more library-multiple station systems for directly mending canal, combine and supply water to multiple intake areas, which is characterized in that water Resource optimization configuration method the following steps are included:

One, model construction includes the following steps 1~step 2:

1. directly to mend more libraries-of canal difference of each reservoir yield and intake area water requirement of day part in multiple station systems year The minimum target of quadratic sum, establishes following objective function:

In formula: F be research object year in day part the difference for water requirement least square and；When Z is each in research object year The quadratic sum of the difference for water requirement of section；R is reservoir quantity, unit: seat；H is reservoir number, h=1,2 ... ... R；N is in year The when number of segment of division；Segment number when i is, i=1,2 ... ... N；G_h,i、YS_h,iThe water supply of respectively h the i-th periods of reservoir With the water requirement of corresponding i-th period of intake area, unit: ten thousand m³；YB_h,k,iCanal is mended for feeder channel kth seat where h reservoirs I-th period of pumping plant water supply, unit: ten thousand m³；Objective function using quadratic sum expression be in order to accelerate reduce reservoir yield with Deviation between the water requirement of intake area；

2. constraint condition is arranged

Including mending single library-multiple station systems year of canal directly for water inventory constraint condition, consider higher level's reservoir call in outside itself Single reservoir water equilibrium constraint that water diversion volume requires, single reservoir capacity constraint condition, and mend canal Group of Pumping Station operation energy consumption Least commitment condition；

Two, model solution

1. data preparation specifically includes: being divided into N number of period for 1 year, and determine day part length；Measure the initial library of each reservoir Hold V_h,0；Determine each reservoir year for water inventory SK_h, minimum capacity of a reservoir V_h,min, the corresponding storage capacity V of flood control_h,PAnd Xing Li Storage capacity V_h,min+△_h,1；It measures and calculates each reservoir day part and carry out water LS_h,i, evaporation with leakage EF_h,i, h=1,2 ... R；Really Fixed each benefit canal pumping plant year allows water lift total amount BZ_h,k, k=1,2 ... M；Measure different periods lift H_h,k,iThe water lift stream of lower operation Measure Q_h,k,iAnd corresponding η_z,h,k,i、η_mot,h,k、η_int,h,k；Determine the water demand of crop YS of each intake area of day part_h,i, h=1, 2,……R；I=1,2 ..., N；

2. it is excellent that direct " more library-multistations " large-scale system model for mending canal is decomposed into single library-multistation water resource that R are directly mended canal Change configuration mathematical model, objective function are as follows:

3. single library-multistation water resource optimal allocation mathematical model of pair directly benefit canal optimizes, wanted from final stage without outer water diversion volume Single library-the multiple station systems asked set out, and successively carry out single library-multiple station systems water resource optimal allocation, specifically include:

(1) single seat reservoir-multiple station systems water resource optimal allocation submodel is solved using Dynamic Programming Approach by inchmeal, is obtained Reservoir yield process G_h,iCanal total Water process Y is mended with Group of Pumping Station_h,iAs master mould optimal solution, while also obtaining target letter Number optimal value, the optimal abandoning process water PS of reservoir_h,iAnd upper level reservoir is to its benefit library process water BK_h,i, wherein h= 1,…R；I=1 ... N；

(2) it is solved using decomposition-Dynamic Programming polymerization to group's Group of Pumping Station second level subsystem model is mended, when obtaining satisfaction i-th Section pumping plant multiple targets water lift total amount Y_h,iL_h,iValue and the optimal rate of water make-up of corresponding each pumping plant combine YB_h,k,i ^*K=1,2 ... M；

4. obtaining each reservoir day part water supply G in more more pumping station systems of reservoir-_h,i, outer water diversion volume WD_h,i, abandon water PS_h,i、 The optimal benefit library water BK of upper level reservoir_h,iAnd corresponding each benefit canal pumping plant rate of water make-up YB_h,k,iProcess, h=1,2 ..., R；

Constraint condition in step (1) includes:

(1) single library-multiple station systems year of canal is mended directly for water inventory constraint condition: except final stage reservoir is only needed to place by water Outside area supplies water, remaining reservoir at different levels also needs to undertake outer water transfer task, supplies next stage reservoir, it may be assumed that

To the 1st~the R-1 reservoirs:

Wherein, h=1,2 ... ... R-1；

To Building R reservoir:

In formula: WD_h,iFor the water supply for assigning next stage reservoir outside h the i-th periods of reservoir, unit: ten thousand m³；SK_hFor h water The year in library is for water inventory, unit: ten thousand m³；M is the benefit canal pumping plant quantity of feeder channel where h reservoirs, unit: seat；K is Mend canal pumping plant number, k=1,2 ... ... M；BZ_h,kCanal pumping plant year allow to mention for the kth seat benefit of feeder channel where h reservoirs Water inventory, unit: ten thousand m³；

(2) consider that higher level's reservoir calls in single reservoir water equilibrium constraint with itself outer water diversion volume requirement: for any h A more pumping plants directly mend single library-multiple station systems of canal, consider that higher level's reservoir calls in the outer water diversion volume requirement of water and reservoir itself, It include: to the 1st reservoir, only outer water diversion volume requirement；To 2~R-1 reservoirs, benefit library water of the existing higher level's reservoir to it Amount, and have itself outer water diversion volume requirement；To Building R reservoir, only higher level's reservoir mends the requirement of library water, i.e., according to water balance side Journey:

To the 1st reservoir:

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-WD_1,i (6)

To the 2nd~the R-1 reservoirs:

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-WD_h,i (7)

Wherein, h=2,3 ..., R-1；

To Building R reservoir:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (8)

On this basis, reservoir operation criterion is as follows:

1. when the i-th period end pondage is lower than reservoir minimum capacity of a reservoir V_h,minWhen, then the i-th period should be mended by upper level reservoir Water, moisturizing to utilizable capacity, it may be assumed that

V_h,i<V_h,minWhen: BK_{H, i}=V_{H, min}-V_{H, i}+Δ_{H, 1} (9)

This period reservoir abandons water PS_h,i=0；H=2,3 ... R；

2. when meeting with flood, the i-th period end pondage is greater than pondage V corresponding to flood control_h,PWhen, then I-th period should carry out abandoning water to reservoir, abandon water to flood control by reservoir regulation limiting water level, it may be assumed that

V_h,i>V_h,PWhen: PS_{H, i}=V_{H, i}-V_{H, P} (10)

This period is not necessarily to upper level Reservoir Regulation, i.e. BK_h,i=0；

3. when the i-th period end pondage is between minimum capacity of a reservoir V_h,minWith pondage V corresponding to flood control_h,PIt Between, then the i-th period reservoir does not need to abandon water, does not need upper level Reservoir Regulation, it may be assumed that

V_h,min≤V_h,i≤V_h,PWhen: PS_h,i=BK_h,i=0 (11)

In formula: V_h,i、V_h,i-1Respectively h reservoirs i-th, the reservoir storage of i-1 period Mo, unit: ten thousand m³；LS_h,i、PS_h,i、 EF_h,iRespectively h the i-th periods of reservoir carry out water, abandon water, evaporation and leakage, unit: ten thousand m³；BK_h,iIt is h The benefit library water that i-th period of reservoir is provided by upper level, i.e. h-1 reservoirs, unit: ten thousand m³；

(3) single reservoir capacity constraint condition: the pondage of day part should be between reservoir minimum capacity of a reservoir and flood control pair It answers between storage capacity, it may be assumed that

V_h,min≤V_h,i≤V_h,P, i=1,2, N (12)

(4) it mends canal Group of Pumping Station combined operating energy consumption least commitment condition: the benefit canal of feeder channel where any h reservoirs is pumped Stand group, and the combined operating within each water supply period is considered as energy consumption minimum, it may be assumed that

In formula, L_h,iCanal Group of Pumping Station combined operation system energy consumption is mended for the i-th period of feeder channel where h reservoirs, unit: kW·h；l_h,k,iFor kth seat the i-th period of pumping plant operation energy consumption of feeder channel where h reservoirs, unit: kWh；M is h The benefit canal pumping plant quantity of feeder channel, unit: seat where seat reservoir；ρ is water density, unit: kg/m³, g is acceleration of gravity, Unit: m/s²；Q_h,k,i、H_h,k,i、△T_h,k,i、η_z,h,k,iRespectively where h reservoirs when the kth seat pumping plant the i-th of feeder channel Flow (the m of section³/ s), when equal lift (m), Period Length (h) and pump efficiency；η_mot,h,k、η_int,h,kRespectively h reservoirs The motor efficiency and transmission efficiency of the kth seat pumping plant of place feeder channel.

2. the method according to claim 1, wherein individually directly mending single library-multistation of canal in step (2) The constraint condition of water resource optimal allocation mathematical model is as follows:

(1) single library-multiple station systems year of canal is mended directly for water inventory constraint:

1. in addition to supplying water to intake area, the water supply requirement of junior's reservoir is also assigned outside for the 1st~the R-1 reservoirs, because This:

In formula, h=1,2 ... ... R-1；

2. it only supplies water to intake area for Building R reservoir, without the water supply requirement for assigning junior's reservoir outside, therefore:

(2) consider that higher level's reservoir calls in single reservoir water equilibrium constraint with itself outer water diversion volume requirement:

1. to the 1st reservoir:

V_{1, i}=V_{1, i-1}+LS_{1, i}-PS_{1, i}-EF_{1, i}-G_{1, i}-WD_{1, i} (19)

2. to the 2nd~the R-1 reservoirs:

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-WD_h,i (20)

Wherein, h=2,3 ..., R-1；

3. to Building R reservoir:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (21)

The same formula of reservoir operation criterion (9)~(11) on this basis；

(3) single reservoir capacity constraint condition: same to formula (12)；

(4) canal Group of Pumping Station combined operating energy consumption least commitment condition: same to formula (13) is mended.

3. according to the method described in claim 2, it is characterized in that, the step 3 of step (2) specific step is as follows: (1) Building R Dan Ku-multiple station systems water resource optimal allocation submodel solves

1) submodel is converted

For submodel (14)~(21), (9)~(13), takeThen submodel was converted to reservoir each stage Water supply G_R,i, mend each stage moisturizing total amount Y of canal Group of Pumping Station_R,iFor the two-dimension non linearity mathematical model of decision variable, it may be assumed that

Objective function:

Dan Ku-multiple station systems year is for water inventory constraint condition:

Reservoir water equilibrium constraint:

V_R,i=V_R,i-1+LS_R,i+BK_R,i-PS_R,i-EF_R,i-G_R,i (25)

On this basis, reservoir operation criterion condition are as follows:

1. when the i-th period end pondage is lower than reservoir minimum capacity of a reservoir V_R,minWhen, then the i-th period should be mended by upper level reservoir Water, moisturizing to utilizable capacity, it may be assumed that

V_R,i<V_R,minWhen: BK_{R, i}=V_{R, min}-V_{R, i}+Δ_{R, 1} (26)

This period reservoir abandons water PS_R,i=0；

2. when meeting with flood, the i-th period end pondage is greater than pondage V corresponding to flood control_R,PWhen, then I-th period should carry out abandoning water to reservoir, abandon water to flood control by reservoir regulation limiting water level, it may be assumed that

V_R,i>V_R,PWhen: PS_R,i=V_R,i-V_R,P (27)

This period is not necessarily to upper level Reservoir Regulation, i.e. BK_R,i=0；

3. when the i-th period end pondage is between minimum capacity of a reservoir V_R,minWith pondage V corresponding to flood control_R,PIt Between, then the i-th period reservoir does not need to abandon water, does not need upper level Reservoir Regulation, it may be assumed that

V_R,min≤V_R,i≤V_R,PWhen: PS_R,i=BK_R,i=0 (28)

The same formula of its corestriction (12)~(13)；

2) submodel Dynamic Programming Approach by inchmeal solves

For transformation model (22)~(28), (12)~(13), specific step is as follows for the solution of Dynamic Programming Approach by inchmeal:

1. with conventional reservoir stage water supply process G_R,i,1As primary iteration value, formula (22) are substituted into, then submodel (22) ~(28), (12)~(13), which are converted into, mends canal total Water Y with each stage Group of Pumping Station_R,iFor decision variable, preceding i stage Group of Pumping Station Moisturizing total amount λ_iFor the one-dimensional dynamic programming model of state variable, solved using one-dimensional dynamic programming；Wherein, i=1, 2,……N；

2. obtaining corresponding recurrence equation referring to one-dimensional dynamic programming evaluation principle are as follows:

I) stage i=1:

g₁(λ₁)=min (G_R,1,1+Y_R,1,1-YS_R,1)² (29)

Period reservoir yield G_R,1,1It is given by initial value, state variable λ₁, it is discrete in corresponding feasible zone:To each discrete λ₁, Group of Pumping Station moisturizing total amount Y_R,1,1It is discrete in corresponding feasible zone, it answers Meet: Y_R,1,1≥λ₁, the Y that will meet the requirements_R,1,1Formula (29) are substituted into respectively, are respectively obtained corresponding to each discrete λ₁When value, most It is excellent_YR,1,1And its corresponding period minimum water deficit quadratic sum g₁(λ₁)；

Then, according to formula (25), the 1st stage end reservoir capacity V_R,1=V_R,0+LS_R,1-EF_R,1-G_R,1,1, upper one is not yet considered at this time Grade reservoir moisturizing and reservoir abandon water, are examined using formula (26)~(28):

A, work as V_R,1<V_R,min, then consider to mend library water BK to its moisturizing by upper level reservoir_R,1,1=V_R,min-V_R,1+Δ_R,1, this Shi Xiuzheng storage capacity V_R,1 ^*=V_R,min+△_R,1；

B, work as V_R,1>V_R,P, then need to abandon dispatching requirement of the water to guarantee reservoir capacity, PS_R,1,1=V_R,1-V_R,P, library is corrected at this time Hold V_R,1 ^*=V_R,P；

C, work as V_R,min≤V_R,1≤V_R,P, then BK_R,1,1=PS_R,1,1=0, storage capacity V is corrected at this time_R,1 ^*=V_R,1；

By step a~c, corrects and determine the 1st stage end reservoir capacity V_R,1 ^*, while can get corresponding reservoir and abandoning water PS_R,1,1Or upper level reservoir mends library water BK_R,1,1；

II) stage i=2,3 ... N-1:

g_i(λ_i)=min [(G_R,i,1+Y_R,i,1-YS_R,i)²+g_i-1(λ_i-1)] (30)

Period reservoir yield G_R,i,1It is given by initial value, state variable λ_iIt equally carries out respectively discrete:To each discrete λ_i, Group of Pumping Station moisturizing total amount Y_R,i,1It is discrete to meet:

State transition equation: λ_i-1=λ_i-(YS_R,i-G_R,i,1) (31)

In formula: i=2,3 ..., N-1；

To each discrete λ_i, by each discrete Y_R,i,1Value substitutes into the (G in formula (30) respectively_R,i,1+Y_R,i,1-YS_R,i)², by state Equation of transfer formula (31), lookup i-1 stage meetIt is required that g_i-1(λ_i-1) value, thus to obtain the λ is met_iIt is required that Optimal Y_R,i,1Process and its corresponding preceding i period subsystem minimum water deficit quadratic sum g_i(λ_i), equally, according to formula (25), the i-th period end reservoir capacity V_R,i=V_R,i-1+LS_R,i-EF_R,i-G_R,i,1, at this time not yet consider the moisturizing of upper level reservoir and Reservoir is abandoned water and is tested also according to formula (26)~(28) using above-mentioned steps a~c, is corrected and is determined the i-th stage end water Kuku holds V_R,i ^*, while can get corresponding reservoir and abandoning water PS_R,i,1Or upper level reservoir mends library water BK_R,i,1, wherein i= 1,2 ..., i；

III) stage N:

g_N(λ_N)=min [(G_R,N,1+Y_R,N,1-YS_R,N)²+g_N-1(λ_N-1)] (32)

Period reservoir yield G_R,N,1It is given by initial value, state variableDecision variable pump Group's moisturizing total amount of standing Y_R,N,1It is equally discrete in corresponding feasible zone, it should meet: λ_N-1=λ_N-(YS_R,N-G_R,N,1)；

Using step II) the method, it finally obtains and meets the λ_NIt is required that the optimal moisturizing total amount process Y of Group of Pumping Station_R,i,1, corresponding Reservoir abandon process water PS_R,i,1And upper level reservoir is to its benefit library process water BK_R,i,1, wherein i=1 ... N；

3. 2. Group of Pumping Station that step is obtained mends canal total Water process Y_R,i,1As initial given value, substitute into formula (22), then submodule Type (22)~(28), (12)~(13) are converted into again with each stage reservoir yield G_R,iFor decision variable, preceding i stage reservoir For water inventory λ_i' 2. referring to step solved, obtained using one-dimensional dynamic programming for the one-dimensional dynamic programming model of state variable The λ must be met_N' require the optimal water supply process G of reservoir_R,i,2(i=1 ... N), corresponding reservoir abandon process water PS_R,i,2, with And upper level reservoir is to its benefit library process water BK_R,i,2, wherein i=1 ... N；

4. 3. reservoir yield process G that step is obtained_R,i,2As initial given value, substitute into formula (22), repeat step 2.~ 3. Approach by inchmeal solves repeatedly, until the adjacent optimal value error precision of objective function twice is less than desired iteration control precision ε, then submodel optimization terminate, and optimize the reservoir yield process G obtained with last time_R,i,mCanal total Water process is mended with pumping plant Y_R,i,mAs master mould optimal solution, while it also can get objective function optimal value, the optimal abandoning process water PS of reservoir_R,i,m, and Benefit library process water BK of the upper level reservoir to it_R,i,m, wherein i=1 ... N；M is Dynamic Programming Approach by inchmeal the number of iterations volume Number；

3) " benefit canal Group of Pumping Station " second level subsystem model decomposition-Dynamic Programming polymerization solves

1. mending the building of canal Group of Pumping Station subsystem economical operation mathematical model

Consider moisturizing Group of Pumping Station combined operating energy consumption minimum criteria constraint condition, is established by formula (13) and mend the economical operation of canal Group of Pumping Station Mathematical model:

Objective function:

The constraint of period water supply:

Power constraint:

In formula, N_R,k,0The kth seat of feeder channel mends the electric drilling match power (kW) of canal pumping plant where the reservoir of Building R；

2. " mending canal Group of Pumping Station " subsystem decomposition-Dynamic Programming polymerization solves

I) decomposition of second level subsystem:

Above-mentioned subsystem model (33)~(35) are further decomposed, M single station economical operation three-level submodel can be obtained:

Objective function:

Power constraint:

In formula, l_R,iFor the i-th period minimum operation energy consumption of single station of Building R reservoir, unit: kWh；

II) determination of three-level submodel energy consumption:

For model above (36)~(37), segment length △ T when the i-th period_R,iIt is mentioned it is known that can simultaneously be determined by pumping plant water levels of upstream and downstream Bigcatkin willow journey H_R,iAnd its corresponding Q_R,i、η_z,R,i、η_mot,RAnd η_int,R, and the period maximum rate of water make-up is YB_R,i,max=3600Q_R,i △T_R,i/ 10000, by the discrete period maximum water lift amount YB of a fixed step size_R,i,max, can get each water lift amount YB_R,i,mPlace an order station fortune Row energy consumption l_R,i,m, m=1,2 ... max；

To other pumping plants of the reservoir, using same method, thus to obtain each pumping plant difference water lift amount YB_R,k,i,mUnder, single station operation Energy consumption l_R,k,i,m, k=1,2 ... M, m=1,2 ... max；

III) original second level subsystem Dynamic Programming polymerization:

It is solved by the above three-level subsystem, canal pumping plant is mended to each, can get a series of single station water lift energy consumption l_R,k,i,m~mono- It stands and mends water in a canal amount YB_R,k,i,mRelationship, k=1,2 ... M, m=1,2 ... max construct following polymerization model and substitute former second level submodule Type (33)~(35):

Objective function:

Period water quantity restraint:

Polymerization model (38)~(39) are similarly one-dimensional dynamic programming model, and stage variable is supply canal where the reservoir of Building R Benefit canal pumping plant number k, k=1,2 ... the M in road；Decision variable is each i-th period of pumping plant water lift amount YB_R,k,i, discrete range is Target water discrete range YB when optimizing for single station_R,k,i,m, k=1,2 ... M, m=1,2 ... max；It is each known to formula (39) The discrete value of pumping plant water lift total amount is state variable (λ)；The model is solved using one-dimensional dynamic programming, obtains and meets i-th Period pumping plant target water lift total amount Y_R,iL_R,iValue and the optimal rate of water make-up of corresponding each pumping plant combine YB_R,k,i ^*, k=1,2 ... M；

4) Building R Dan Ku-multiple station systems submodel optimal solution is determined

The optimal moisturizing total amount Y of canal Group of Pumping Station is mended by the day part that step 2) obtains_R,i, after i=1,2 ... ... N；To each period Determining Y_R,i, it is both needed to calculate via a step 3), altogether n times step 3), by day part Y_R,iOptimization distribution to M benefit canal pumps It stands, obtains each optimal rate of water make-up YB of benefit canal pumping plant day part_R,k,i ^*；Thus R grades of final acquisition single libraries-are each in multiple station systems year The least square and F of the difference for water requirement of period_R, corresponding reservoir day part optimal water supply G_R,i, abandon water process PS_R,i、 Benefit library water BK of the upper level reservoir to it_R,i, and each benefit optimal rate of water make-up process YB of canal pumping plant day part_R,k,i ^*, i=1, 2 ... ... N, k=1,2 ... M；

(2) R-1, R-2 ..., 1 single library-multiple station systems water resource optimal allocation submodel solve

Single library-multiple station systems that R-1, R-2 ..., 1 are directly mended with canal, equally use submodel (14)~(21), (9) ~(13) are with reservoir day part water supply G_R,i, feeder channel where the reservoir respectively mend canal pumping plant day part rate of water make-up YB_R,k,i Nonlinear model is tieed up for the M+1 of decision variable, referring to step (1), is takenThen the submodel is converted to reservoir Each stage water supply G_h,i, mend each stage moisturizing total amount Y of canal Group of Pumping Station_h,iFor the two-dimension non linearity mathematical model of decision variable, still It is solved using Dynamic Programming successive approximation method, difference is only that:

1) single library-multiple station systems year of canal is mended directly for water inventory constraint condition:

Dan Ku-multiple station systems year should use formula (15)~(16) for water inventory constraint, it may be assumed thatWith AndDue to using hysterology, outer water diversion volume WD_h,iThat is next stage list library-multiple station systems benefit Library water BK_h+1,i, determined by the reservoir operation criterion in preceding primary single library-multiple station systems optimization process, it may be assumed that

WD_h,i=BK_h+1,i (40)

Then formula (15) can be converted into such as following formula (41), to obtain reservoir yield restriction range；

2) meet outer water diversion volume and higher level's reservoir mend single reservoir operation criterion constraint that library water requires:

The outer water diversion volume WD of this reservoir is considered as to each stage water balance equation_h,iAnd upper level reservoir is to its benefit library water BK_h,iTwo aspect factors, should consider respectively: to the 1st reservoir, Ying Caiyong formula (19), it may be assumed that V_1,i=V_1,i-1+LS_1,i-PS_1,i- EF_1,i-G_1,i-WD_1,i；To the 2nd~the R-1 reservoirs, Ying Caiyong formula (20), it may be assumed that V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i- EF_h,i-G_h,i-WD_h,i；

Similarly, by formula (40), formula (19)~(20) can be converted following form:

1. to the 1st reservoir,

V_1,i=V_1,i-1+LS_1,i-PS_1,i-EF_1,i-G_1,i-BK_2,i (42)

2. to the 2nd~the R-1 reservoirs,

V_h,i=V_h,i-1+LS_h,i+BK_h,i-PS_h,i-EF_h,i-G_h,i-BK_h+1,i (43)

On this basis, still each stage storage capacity is modified using formula (9)~(11).