CN103761583A - Reservoir sediment ejection power generation multi-target optimized dispatching method - Google Patents

Abstract

A reservoir sediment ejection power generation multi-target optimized dispatching method includes the following steps of firstly, setting up a target function with system generating capacity maximization serving as a target, and setting up a target function with reservoir sediment runoff maximization serving as a target; secondly, generating a plurality of sequences with the discharged volume serving as a decision variable, solving the decision variable through a genetic algorithm, and obtaining the optimal discharged volume through the steps. When the decision variable is solved, restraint conditions introduced into reservoir system running include a reservoir water level restraint, a reservoir discharged volume restraint and a volume daily amplitude restraint. By means of the reservoir sediment ejection power generation multi-target optimized dispatching method, the target function for the sediment ejection efficiency optimization and the target function for the power generation efficiency optimization are taken into comprehensive consideration, multi-target expression of reservoir group long-term running comprehensive benefit maximization is achieved, and the Pareto optimal solution set for reservoir dispatching is given through the multi-target optimization genetic algorithm.

Description

A kind of reservoir sand discharge generating Multiobjective Optimal Operation method

Technical field

The invention belongs to the waterpower scheduling field of field of water conservancy, particularly a kind of reservoir sand discharge generating Multiobjective Optimal Operation method.

Background technology

After reservoir is built in river, because water level raises, discharge area is strengthened, flow velocity slows down, thereby sediment transport capacity is reduced, cause depositing in reservoir.And the high power of sediment carrying capacity and flow velocity is proportional, a little change of water-carrying section, often can cause that sediment carrying capacity significantly reduces, and causes very adverse influence to the performance of reservoir comprehensive benefit.Main manifestations is:

1, reservoir usable storage constantly reduces, and has reduced the serviceable life of reservoir, affects the tune ability of reservoir.Emerging sharp benefit declines year by year, and the emerging sharp benefits such as flood control by reservoir regulation, generating, irrigation and water supply are had a greatly reduced quality.

2, be subject to the impact of reservoir filling, current enter behind reservoir area, and the silt in current can be at the backwater end of reservoir, and develops into gradually upstream, " wing tail " phenomenon that reservoir area tailwater level is produced.Bed elevation and the reservoir underground water table around of raising upstream, this not only can reduce the Benefit of Flood Preventation of upper river, navigation condition is worsened, and can cause adverse effect to two sides resident living, threatens local agricultural production security.

3, silt can cause hydraulic and the wearing and tearing of earial drainage facility, affects mechanical efficiency, shortens the hydraulic life-span, increases spillage of material and servicing time, accelerates the aged deterioration of engineering.

4, the husky condition of the original water of downstream river course changes.In non-flood season, under clear water, let out, wash away downstream river course; Reservoir entered after flood season, and silt is let out under concentrating, and can make again downstream reflux and deposit, and made dam downstream river course that very large change occur, and river realignment and two sides diversion work are caused to adverse effect.

Therefore, the management and running of reservoir not only need regulated flow, hold to be full of and fill a vacancy, and meet the requirement of the each side such as Xing Li, flood control, also will regulate silt, reduce usable storage trip and damage, and make reservoir long-term, effectively, and the performance benefit of safety.It is a multi-objective optimization question with Complex Constraints condition in essence.The Multipurpose Optimal Method existing at present is mainly divided into two large classes: traditional Multipurpose Optimal Method and Multiobjective Intelligent optimization method.

Tradition Multipurpose Optimal Method be take leash law, analytical hierarchy process, linear weighted function method, ideal point method as main processing means, according to decision maker's subjective factor, multi-objective optimization question is converted into single-object problem and solves.It in essence or single-object problem.

The difficult point essence of multi-objective optimization question is incommensurability and the paradox between target.So-called incommensurability refers to that each target does not have unified module, thereby is difficult to compare.For example: in the multiobjectives decision of water and sediment in reservoir uniting and adjustment, the unit of generated energy is degree, and carrying unit of force is kg/m ³, cannot compare.Paradox between target refers to if adopt a certain scheme to go to improve a certain desired value, may make another order target value improve or degenerate.The husky uniting and adjustment of the water of also take are example, and reservoir keeps peak level as far as possible, reduces earial drainage, can increase the generated energy of unit of water body, but earial drainage reduction will make reservoir sediment accumulation increase the weight of.Additional issue electric weight and minimizing alluvial are the operational objectives of conflict.

Due to the paradox between a plurality of targets and incommensurability, can not simply a plurality of targets be classified as to single target, and use the method for single goal decision problem to remove to solve decision-making problem of multi-objective.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of reservoir sand discharge generating Multiobjective Optimal Operation method, can realize the maximized scheduling of reservoir long-time running comprehensive benefit.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of reservoir sand discharge generating Multiobjective Optimal Operation method, comprises the following steps:

One, with system generated energy, be target to the maximum and set up objective function;

With reservoir sedimentary loading, be target to the maximum and set up objective function;

Two, using letdown flow as decision variable, produce a plurality of sequences based on above-mentioned objective function, utilize the multi-objective genetic algorithm based on non-domination solution to solve decision variable;

By above-mentioned steps, obtain optimum letdown flow.

When solving decision variable, introduce the constraint condition of water reservoir system operation, comprise reservoir level constraint, the constraint of reservoir letdown flow and the constraint of flow daily amplitude.

Preferably, in step 2, produce at random n chromosome, produce the sequence of n reservoir letdown flow (Q), form initial population P ₀, population scale=n;

Preferably, take a time period is the criteria for classifying, and corresponding each chromosome has the gene of a plurality of generating reference stream secondary elements and a plurality of flood discharge flow elements, these genomic constitution arrays.

Preferably,, there are 12 generating reference stream secondary elements and 4 flood discharge flow elements totally 16 genes in Yi Yuewei unit on each chromosome, form the array of 16 * n.

Further preferred, in n chromosome, choose a preferably chromosomal m value and carry out cross and variation calculating, generate new population P ₁;

Calculate target function value corresponding to chromosome in new population, enter next iteration.

Further preferred, any two pairs of chromosomes in traversal population, relatively two chromosomal fitness function values, select preferably chromosome;

A current chromosomal m value is entered to cross and variation;

If m=0, regenerates initial population; If m > 0, enters cross and variation;

According to the crossover probability of setting, if intersect, occur, from m value, select arbitrarily two chromosomes, generate at random a nonzero integer in a gene number interval, the gene location that is greater than this number exchanges;

According to the variation probability of setting, if variation occurs, for above-mentioned chromosome, generate at random a nonzero integer in a gene number interval, in this locational gene mutation, become in m chromosome any number between maximal value and minimum value on this position;

Newly-generated n chromosome after cross and variation, forms new population P together with the preferably chromosome obtaining with last iteration ₁, population scale is m+n;

Calculate new population P ₁the target function value of middle correspondence, enters next iteration.

Keep paradox and incommensurability in reservoir operation multiple goal, but not incorporate into, solve for single goal; Gained optimized operation strategy is one group of optimal solution set, wherein between each optimum solution, can not mutually compare, and while comparing between any two solutions in this optimal solution set, if one of target of certain solution is better than another, separates, and two of its target must be inferior to another solution.

System generated energy maximum target function is:

$\mathrm{MaxE}={\mathrm{\Σ}}_{t=1}^T{E}_t={\mathrm{\Σ}}_{t=1}^T{\mathrm{\Σ}}_{i=1}^5\stackrel{\‾}{N_i^t}\×n_i\×\mathrm{\Δt};$

Wherein, E is a year generating total amount;

it is unit average output; Δ t is for calculating duration; I is each machine group # in power station; n _inumber of units for each unit; Segment length when t represents.

Reservoir sedimentary loading maximum target function is:

$\mathrm{MaxS}={\mathrm{\Σ}}_{t=1}^T({\mathrm{QF}}^t\×\stackrel{\‾}{S_v^t}\×\mathrm{\Δt});$

Wherein, S is the sedimentary loading of reservoir, and unit is kg; QF is flood discharge flow, and unit is m ³/ s,

for the average percent sand of floodwater releasing port, unit is kg/m ³.

The average percent sand of floodwater releasing port is calculated by following formula:

$\stackrel{\‾}{S_v}={\∫}_n^{h+H}{S}_{\mathrm{va}}\×{\left(\frac{(h-y)\×a}{y\×(h-a)}\right)}^Z/\mathrm{Hdy};$

In formula, n is floodwater releasing port number, and y is current elevation, and h is floodwater releasing port Bottom Altitude, and L is floodwater releasing port width, and H is that floodwater releasing port is high.

Flood discharge flow is calculated by following formula:

$\mathrm{QF}=\stackrel{\‾}{U}\×H\×L\×n;$

In formula, n is floodwater releasing port number, and L is floodwater releasing port width, and H is that floodwater releasing port is high,

for floodwater releasing port mean flow rate.

Inventor finds that the optimum solution that multi-objective problem is corresponding is not certain single optimum solution, but the concept of a set is one group of Pareto optimum solution.

The research discovery of inventor to multi-objective optimization algorithm, evolution algorithm is applicable to solving this class multi-objective optimization question very much.Evolution algorithm is the element of volume one by one in colony using each possible solution, by operations such as simple intersection, variations, colony is evolved, and the chance of existence and breeding is left for to the individuality that adaptability is stronger.It comprises genetic algorithm, ant group algorithm, particle cluster algorithm etc.Evolution algorithm, compares with other intelligent computation method, is more suitable for the complicated optimum problem that can not solve by classic method for the treatment of those.Along with the development of intelligent computation, the evolution algorithm with parallel characteristics embodies and has great advantage to solving multi-objective optimization question tool.

A kind of reservoir sand discharge generating Multiobjective Optimal Operation method provided by the invention, by considering optimum these two objective functions of sand discharge efficiency optimization and power benefit, realization is expressed the maximized multiple goal of multi-reservoir long-time running comprehensive benefit, and adopt multi-objective Optimization Genetic Algorithm, provided the Pareto optimal solution set of reservoir operation.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described:

Fig. 1 be in the present invention before dam flood season suspended load silt content vertical line distribution curve.

Fig. 2 be in the present invention before dam flood season flow velocity vertical line distribution curve.

Fig. 3 be in the present invention after iteration non-domination separate corresponding objective function curve, in figure, to change amplitude be 50m to daily average water discharge ³/ s.

Fig. 4 be in the present invention after iteration non-domination separate corresponding objective function curve, in figure, to change amplitude be 150m to daily average water discharge ³/ s.

Fig. 5 be in the present invention after iteration non-domination separate corresponding objective function curve, in figure, to change amplitude be 1000m to daily average water discharge ³/ s.

Fig. 6 be in the present invention after iteration non-domination separate corresponding objective function curve, in figure, to change amplitude be 5000m to daily average water discharge ³/ s.

Embodiment

Embodiment 1:

A reservoir sand discharge generating Multiobjective Optimal Operation method, comprises the following steps:

One, with system generated energy, be target to the maximum and set up objective function;

With reservoir sedimentary loading, be target to the maximum and set up objective function;

Two, using letdown flow as decision variable, produce a plurality of sequences based on above-mentioned objective function, utilize the multi-objective genetic algorithm based on non-domination solution to solve decision variable;

By above-mentioned steps, obtain optimum letdown flow.

When solving decision variable, introduce the constraint condition of water reservoir system operation, comprise reservoir level constraint, the constraint of reservoir letdown flow and the constraint of flow daily amplitude.

Preferably, in step 2, produce at random n chromosome, produce the sequence of n reservoir letdown flow (Q), form initial population P ₀, population scale=n;

Preferably, take a time period is the criteria for classifying, and for example month or week, corresponding each chromosome has the gene of a plurality of generating reference stream secondary elements and a plurality of flood discharge flow elements, these genomic constitution arrays.

Preferably,, there are 12 generating reference stream secondary elements and 4 flood discharge flow elements totally 16 genes in Yi Yuewei unit on each chromosome, form the array of 16 * n.

Further preferred, in n chromosome, choose a preferably chromosomal m value and carry out cross and variation calculating, generate new population P ₁;

Calculate target function value corresponding to chromosome in new population, enter next iteration.

Further preferred, any two pairs of chromosomes in traversal population, relatively two chromosomal fitness function values, select preferably chromosome;

A current chromosomal m value is entered to cross and variation;

If m=0, regenerates initial population; If m > 0, enters cross and variation;

According to the crossover probability of setting, if intersect, occur, from m value, select arbitrarily two chromosomes, generate at random a nonzero integer in a gene number interval, the gene location that is greater than this number exchanges;

According to the variation probability of setting, if variation occurs, for above-mentioned chromosome, generate at random a nonzero integer in a gene number interval, in this locational gene mutation, become in m chromosome any number between maximal value and minimum value on this position;

Newly-generated n chromosome after cross and variation, forms new population P together with the preferably chromosome obtaining with last iteration ₁, population scale is m+n;

Calculate new population P ₁the target function value of middle correspondence, enters next iteration.

Preferably, described crossover probability is 0.6～0.8;

Described variation probability is 0.01～0.03.

Keep paradox and incommensurability in reservoir operation multiple goal, but not incorporate into, solve for single goal; Gained optimized operation strategy is one group of optimal solution set, wherein between each optimum solution, can not mutually compare, and while comparing between any two solutions in this optimal solution set, if one of target of certain solution is better than another, separates, and two of its target must be inferior to another solution.

System generated energy maximum target function is:

$\mathrm{MaxE}={\mathrm{\Σ}}_{t=1}^T{E}_t={\mathrm{\Σ}}_{t=1}^T{\mathrm{\Σ}}_{i=1}^5\stackrel{\‾}{N_i^t}\×n_i\×\mathrm{\Δt};$

Wherein, E is a year generating total amount;

it is unit average output; Δ t is for calculating duration; I is each machine group # in power station; n _inumber of units for each unit; Segment length when t represents.

Reservoir sedimentary loading maximum target function is:

$\mathrm{MaxS}={\mathrm{\Σ}}_{t=1}^T({\mathrm{QF}}^t\×\stackrel{\‾}{S_v^t}\×\mathrm{\Δt});$

Wherein, S is the sedimentary loading of reservoir, and unit is kg; QF is flood discharge flow, and unit is m ³/ s,

for the average percent sand of floodwater releasing port, unit is kg/m ³.

The average percent sand of floodwater releasing port is calculated by following formula:

$\stackrel{\‾}{S_v}={\∫}_n^{h+H}{S}_{\mathrm{va}}\×{\left(\frac{(h-y)\×a}{y\×(h-a)}\right)}^Z/\mathrm{Hdy};$

In formula, n is floodwater releasing port number, and y is current elevation, and h is floodwater releasing port Bottom Altitude, and L is floodwater releasing port width, and H is that floodwater releasing port is high.

Flood discharge flow is calculated by following formula:

$\mathrm{QF}=\stackrel{\‾}{U}\×H\×L\×n;$

In formula, n is floodwater releasing port number, and L is floodwater releasing port width, and H is that floodwater releasing port is high,

for floodwater releasing port mean flow rate.

Embodiment 2:

1..1 suspended load silt content is calculated

Sediment Transport major part in heavily silt-carrying river is to carry out with the form of suspense matter motion.The sand grain of suspended motion has thinner particle diameter, can follow turbulent fluctuation random motion in water body of current.On vertical, the motion of sand grain can be regarded the stack of two kinds of motions as, i.e. random motion under subsiding movement under segregation drive and flow turbulence driving.When the quantity of particle is very large, will form macroscopical mobile equilibrium of silt catenary motion, now sediment concentration has a stable distribution on vertical.

1) vertical line of suspended load silt content distributes

The gravity settling of silt makes along vertical line, to form muddy CONCENTRATION DISTRIBUTION under supernatant in silt carrying flow.In turbulent flow along the turbulent fluctuation exchange that has water body between each layer, place of depth of water differing heights water body, cause the exchange of silt between each water layer simultaneously, but the sand amount that the water body that under supernatant, muddy CONCENTRATION DISTRIBUTION makes to move upward is carried under one's arms is greater than the sand amount that countryside motion water body is carried under one's arms, so the result of turbulent fluctuation exchange is to form a silt flux q who moves upward _s1.On the other hand, because silt is than water weight, down sedimentation form a silt net flux q who moves downward _s2.If there is stable time equal sediment concentration and distribute, q is described in sediment concentration _s1with q _s2reached dynamic equilibrium state.Now, the turbulent fluctuation diffusion process of silt is even, constant, and two-dimensional diffusion equation becomes:

$\frac{d}{\mathrm{dy}}\left({\mathrm{\ϵ}}_y\frac{\∂S_v}{\∂y}\right)+\mathrm{\ω}\frac{d{S}_v}{\mathrm{dy}}=0---\left(1\right)$

To y integration once, make constant is zero to formula (1), obtains

${\mathrm{\ϵ}}_y\frac{{\mathrm{dS}}_v}{\mathrm{dy}}+{\mathrm{\ωS}}_v=0---\left(2\right)$

Subject matter while solving formula (2) is first to know ε _ydistribution along vertical line.As suppose ε _yfor constant (meaning that turbulent fluctuation is uniform on vertical line), the solution of above formula is

$\frac{S_V}{S_{\mathrm{va}}}=e^{-\mathrm{\ω}(y-a)/{\mathrm{\ϵ}}_y}---\left(3\right);$

Wherein, S _vafor suspended sediment is being the volume ratio sediment concentration at a place apart from bed surface.

Research shows, the coefficient of diffusion ε of silt _ybe not constant but the function of locus, but existing theory can't provide ε _ythe regularity of distribution along vertical line.The most frequently used method is supposition sediment diffusion coefficient ε _ywith momentum exchange coefficient ε _mequate.Shearing the shear stress between adjacent fluid layer in turbulent flow, is mainly that the exchange of momentum between the adjacent fluid layer causing due to fluid pulsation is caused, can copy the expression way of molecular viscosity stress to provide its expression formula:

$\mathrm{\τ}={\mathrm{\ρ\ϵ}}_m\frac{\mathrm{du}}{\mathrm{dy}}$ Or ${\mathrm{\ϵ}}_m=\frac{\mathrm{\τ}}{\mathrm{\ρ}\frac{\mathrm{du}}{\mathrm{dy}}}$

In Open Channel Steady Flow, shearing force is along the linear distribution of vertical line

distribute with the logarithmic of longitudinal flow velocity along vertical line

(τ wherein ₀=γ hJ, h is the depth of water), can obtain:

${\mathrm{\ϵ}}_y={\mathrm{\ϵ}}_m=\mathrm{kU}*y\frac{h-y}{h}---\left(4\right);$

Wherein, k=0.4 is Karman constant.

Formula (4) substitution formula (2) is obtained:

$\mathrm{kU}*y\frac{h-y}{h}\frac{{\mathrm{dS}}_v}{\mathrm{dy}}+{\mathrm{\ωS}}_v=0---\left(5\right);$

Formula (5) can be write as again:

$\frac{{\mathrm{dS}}_v}{S_v}=-\frac{\mathrm{\ω}}{\mathrm{kU}*}(\frac{1}{y}+\frac{1}{h-y})\mathrm{dy}---\left(6\right);$

Above formula integration is obtained:

${\ln S}_v=\ln {\left(\frac{h-y}{h}\right)}^Z+\ln C---\left(7\right);$

Making y=a is reference point, and this sediment concentration is designated as S _va, finally can obtain:

$\frac{S_v}{S_{\mathrm{va}}}={(\frac{h-y}{y}+\frac{a}{h-a})}^Z---\left(8\right)$

Wherein, the expression formula of index Z is:

$Z=\frac{\mathrm{\ω}}{\mathrm{kU}*}---\left(9\right);$

Z is called again Suspension index.In formula (8), the size of Suspension index Z has determined the degree of uniformity that silt distributes on vertical line.Z value is less, and suspended load distributes more even.

2) reservoir suspended load silt content vertical line distribution curve

The present invention is based on the vertical line distribution formula (8) of suspended load silt content, utilize Matlab software, develop the interactive mode of a set of suspended load discharge and calculate (SSDC, Suspended Sediment Discharge Calculation) software, and utilize this software, in conjunction with the vertical line distributed data of actual measurement silt content, calculate the vertical line distribution curve of reservoir suspended load silt content.The main thought of Software for Design of the present invention is: n data point of input actual measurement silt content vertical line distribution, bathymetric data h is set, and utilize silt content vertical line distribution function (8) matching said n measured data point, obtain the parameter value S in distribution function _va,a and Z.The non-linear curve fitting algorithm of employing based on least square method realized the matching to data point.

The measured data of front section, certain reservoir major flood season dam in 2011 main flow vertical line silt content of take is example, as shown in table 1.Owing to being major flood season, upstream comes flow larger, and upstream water level is low, and reservoir shows as river feature, and sediment concentration obviously increases, and main flow vertical line table, middle and bottom layers silt content have lamination, and near-bottom and bottom silt content are larger.

Vertical line silt content measured value before certain reservoir dam of table 1 (on August 6th, 2011,7 days measure)

Determine silt content vertical line distribution eyeball number n, bathymetric data h, and select silt content vertical line fitting of distribution function, input in SSDC software, then input successively n measured data point, the fitting parameter that actual measurement silt content data distribute along vertical line is presented on the interactive interface of software, and is stored in program backstage as sharing data, for other program modules, transfers.Silt content vertical line fitting of distribution curve as shown in Figure 1.This program module has realized the function that obtains continuous silt content vertical line distribution curve from some discrete measuring point datas.

1..2 before dam, flow velocity vertical line distributes

The vertical line that the present invention adopts turbulent cross-sectional flow distribution formula to calculate the front flow velocity of reservoir dam distributes, as the formula (10):

$u=\frac{v^{*}}{k}\ln y+c---\left(10\right);$

This formula is the logarithmic formula that turbulent cross-sectional flow distributes.Although it is to derive according near condition wall, experimental study shows, this formula is applicable to the whole flow section except viscous sublayer.

Above because mixing length theory has obtained equal shearing stress expression formula and the flow velocity logarithm regularity of distribution when turbulent.But this theoretical basic assumption is rigorous not, as thought, fluid particle is after mixing length, just disposablely carry out momentum-exchange with particle around, yet because fluid is continuous medium, particle constantly carries out momentum-exchange with particle around in transverse movement process.The constant k in formula and for example, C need to be determined by experiment.However, because this theory is from turbulent essential characteristic, derive simple, notional result is more consistent with experiment simultaneously, therefore it is theoretical to be still so far the turbulence resistance of being used widely in engineering.

This research adopts the logarithmic velocity distribution formulas in formula (10), in SSDC software, set up flow velocity vertical line distribution computing module, utilize actual measurement flow speed data, matching draws the parameter in formula (10), and and then obtains flow velocity vertical line distribution curve before reservoir dam.

$U=5.75\×U^{\′}\×\lg \left(\frac{30.2\×y}{k_s}\right)---\left(11\right);$

Front section, certain reservoir major flood season dam in 2011 main flow flow velocity measured data is as shown in table 2.Owing to being major flood season, upstream comes flow larger, and upstream water level is low, and reservoir shows as river feature, and flow rate of water flow all obviously increases, and main flow top layer, front section, dam flow rate of water flow is greater than other layers.

Vertical velocity measured value before table 2 reservoir dam (on August 6th, 2011,7 days measure)

N data point of input actual measurement flow velocity vertical line distribution, utilizes flow velocity vertical line distribution function (11) matching said n measured data point, obtains parameter value U ' and k in distribution function _s.The non-linear curve fitting algorithm of employing based on least square method realized the matching to data point.

Determine containing flow velocity vertical line distribution eyeball number n, and in SSDC, input successively n measured data point, the fitting parameter that actual measurement flow speed data distributes along vertical line is presented on the interactive interface of software, and is stored in program backstage as sharing data, for other program modules, transfers.Flow velocity vertical line fitting of distribution curve as shown in Figure 2.This program module has realized the function that obtains continuous flow velocity vertical line distribution curve from some discrete measuring point datas.

1..3 reservoir silt discharge calculates

1) single wide silt discharge

According to the theoretical method of introducing, can obtain suspended load silt content S above _vand flow velocity U is along the distribution of vertical line.Can calculate accordingly in the unit interval, the Suspended amount of passing through on elevation y place's unit interval, unit cross-sectional area in river course water-carrying section is US _v, it can be drawn to the wide silt discharge of suspended load list in the full depth of water along vertical line integration.

In analysis before, only drawn the relative distribution of suspended load along vertical line, when inquiring into suspended load discharge, must draw by means of other approach the silt content S at reference altitude a place _va, just can obtain the silt content of each point on vertical line.While quadraturing in addition,, first also must determine the upper lower limit value of integration.The simplest method is to be integrated to the water surface from bed surface.But in existing theoretical formula, when y=0, flow velocity and silt content will be tending towards respectively positive and negative infinity.On the other hand, from the physical process of sediment transport, direct integral is also irrational to bed surface, because the silt in near-bed motion, its weight supported by bed surface, rather than supported by the turbulent energy of current, so the silt of this one deck motion belongs to the category of traction load.

The wide silt discharge of list in the interior river course of depth of water scope [h, h+H] is the vertical line distribution of the suspended load silt content within the scope of this and the integration of the product of turbulent logarithmic velocity flow profile in this depth range.Vertical line distribution formula (8) based on suspended load silt content and turbulent logarithmic velocity distribution formulas (11) are calculated single wide silt discharge q _sw, as the formula (12):

$q_{\mathrm{sw}}={\∫}_h^{h+H}{S}_{\mathrm{va}}\×{\left(\frac{(h-y)\×a}{y\×(h-a)}\right)}^Z\×5.75\×U^{\′}\×{\log }_{10}\left(\frac{30.2\×y}{k_s}\right)\mathrm{dy}---\left(12\right);$

2) reservoir silt discharge calculates

Reservoir major flood season upstream comes flow larger, upstream water level is low, reservoir shows as river feature, sediment concentration, flow velocity all obviously increase, but the distribution characteristics of flow rate of water flow and silt content inconsistent, main flow top layer, front section, dam flow rate of water flow is greater than other layers, main flow vertical line table, middle and bottom layers silt content have lamination, near-bottom or bottom silt content are larger, the main period that major flood season is sand discharge, and mainly rely on floodwater releasing port sand discharge.

Take certain reservoir as example, calculate respectively the wide silt discharge q of list under reservoir spillway mouth full-gear _sw, silt discharge Q _sw, floodwater releasing port mean flow rate

the average percent sand of floodwater releasing port

flood discharge flow QF, shown in (13)～formula (16).

Silt discharge calculates:

Q _sw=n×L×q _sw (13);

Floodwater releasing port mean flow rate:

$\stackrel{\‾}{U}={\∫}_h^{h+H}5.75\×U^{\′}\×{\log }_{10}\left(\frac{30.2\×y}{k_s}\right)/\mathrm{Hdy}---\left(14\right);$

The average percent sand of floodwater releasing port:

${\stackrel{\‾}{S}}_v={\∫}_h^{h+H}{S}_{\mathrm{va}}\×{\left(\frac{(h-y)\×a}{y\×(h-a)}\right)}^Z/\mathrm{Hdy}---\left(15\right);$

Flood discharge flow:

$\mathrm{QF}=\stackrel{\‾}{U}\×H\×L\×n---\left(16\right);$

In various above, n is floodwater releasing port number, and h is floodwater releasing port Bottom Altitude, and L is floodwater releasing port width, and H is that floodwater releasing port is high.

This reservoir has n=23 floodwater releasing port, floodwater releasing port Bottom Altitude h=90m, the wide L=7m of floodwater releasing port, the high H=9m of floodwater releasing port.

SSDC program will be calculated this Flood Season of Reservoir floodwater releasing port mean flow rate, the average percent sand of floodwater releasing port, flood discharge flow, single wide silt discharge and floodwater releasing port total sediment discharge.In program, variable dimension is unified, and this example is used system international.

1.4 reservoir sand discharge generating Model for Multi-Objective Optimization

Sediment Siltation and reservoir impoundment power generation are the operating a pair of very outstanding contradiction of reservoir.If reduce alluvial and effective sand discharge, need reduce reservoir level and strengthen earial drainage, this can affect power benefit; If improve the power benefit of reservoir, need the water storage level and the minimizing that improve reservoir to abandon water, this can cause the development of Sediment Siltation again.Contradictory relation for Sediment Siltation and power benefit in coordination reservoir utilization process, this research is elementary object to the maximum with sand discharge efficiency maximum and power benefit, set up water and sediment in reservoir electricity Multiobjective Optimal Operation model, with the operating scheme of reasonable arrangement reservoir, thus the comprehensive benefit of raising hinge.

1) objective function

Objective function one: system generated energy is maximum;

Using generated energy maximum in schedule periods as a target, object is to utilize the regulating power in power station as far as possible, increasing generating average water head reduces simultaneously abandons water, especially make full use of hydraulic connection and the contact of the electric power between basin of step hydropower station, realization, the in the situation that of taking into account system power load, farthest utilizes hydraulic power potentials.Objective function can be written as:

$\mathrm{MaxE}={\mathrm{\Σ}}_{t=1}^T{E}_t={\mathrm{\Σ}}_{t=1}^T{\mathrm{\Σ}}_{i=1}^5\stackrel{\‾}{N_i^t}\×n_i\×\mathrm{\Δt}----\left(17\right);$

Wherein, E is a year generating total amount;

it is unit average output; Δ t is for calculating duration; I is each machine group # in power station; n _inumber of units for each unit; Segment length when t represents.

Objective function two: reservoir sedimentary loading is maximum;

Using reservoir sedimentary loading maximum as another target, sediment transport when object is to strengthen flood discharge.The warehouse-in silt of reservoir mainly comes from flood season, therefore according to the silt discharge computing formula of reservoir, increases the sand discharge amount of Flood Season of Reservoir.Objective function can be written as:

$\mathrm{MaxS}={\mathrm{\Σ}}_{t=1}^T({\mathrm{QF}}^t\×\stackrel{\‾}{S_v^t}\×\mathrm{\Δt})---\left(18\right);$

Wherein, S is the sedimentary loading of reservoir, and unit is kg; QF is flood discharge flow, by formula (16), be can be calculated, and unit is m ³/ s,

for the average percent sand of floodwater releasing port, by formula (15), calculate and obtain, unit is kg/m ³.

2) decision variable

From front analysis, the influence factor that vent flow had both been exerted oneself for power station, is again the determinative of reservoir sedimentary loading.Therefore, the vent flow of choosing reservoir is decision variable, meanwhile, generating is quoted to flow and flood discharge traffic differentiation comes.The vent flow that is reservoir at the decision variable in non-flood season, i.e. flow Q is quoted in generating; Flow Q and flood discharge flow QF are quoted in the generating that is reservoir at the decision variable in flood season.

Take certain reservoir as example, and because flood season of this reservoir is 4 totally months June to September, getting month is period step-length, and decision variable u can be expressed as follows:

u={Q ¹，Q ²，...，Q ¹²，QF ¹，QF ²，QF ³，QF ⁴} （19）；

While applying genetic algorithm, each chromosome has 16 genes.

3) constraint condition

The constraint condition of water reservoir system operation is divided into following several:

Reservoir level constraint

In order to guarantee dam safety and protection Lower Reaches, reservoir must reserve certain storage capacity in flood season, water level is dropped to flood and restrict water supply below position.In non-flood season, also must follow schedule regulation.The safe operation of reservoir realizes by the control to reservoir level:

$L_{\min }^t\≤L^t\≤L_{\max }^t---\left(20\right);$

Wherein,

with be respectively the minimum and peak level that the t period allows.

The constraint of reservoir letdown flow

The lower limit of outbound flow is in order to guarantee downstream navigation and to meet the ecological needs that operate, its maximum vent flow that allows in upper limit water intaking storehouse.Therefore, optimization need to optimizing on a large scale.This can produce a large amount of infeasible solutions, causes the extreme result on the unrestrained top of reservoir emptying or dam, is flooded with invalid individuality in the population of genetic algorithm.

For the efficiency of improved genetic algorithms method, according to reservoir inflow and actual schedule process, set the bound of outbound flow, its variation range is:

$\min (I_{\min }^t,Q_{\mathrm{actual},\min }^t)\≤Q^t\≤\max (I_{\max }^t,Q_{\mathrm{actual},\max }^t)---\left(21\right);$

Wherein,

with

minimum and the maximal value when monthly inflow; with

minimum and the maximal value of the actual outbound flow in this month.

The constraint of flow daily amplitude

As the river of Largest In China, important shipping task is being born in the Changjiang river, and this not only requires the water level in river course to reach certain height, also requires the SEA LEVEL VARIATION can not be too violent.

All constraint condition realizes by two kinds of modes: or automatically meet when producing initial population and new population, or whether be satisfied in the rear check of calculating, infeasible solution is disallowable, does not participate in evolving.

4) state equation

State equation refers to hydraulic power condition and contact in computation process, mainly contains following a few class:

Reservoir water yield balance equation:

V ^t=V ^t-1+I _t×Δt-(Q ^t+QF ^t)×Δt (22);

Wherein, V is storage capacity, and I is upstream reservoir inflow; Q is that hydropower station is quoted flow; QF is flood discharge flow; (Q+QF) be the total vent flow of reservoir, comprising generates electricity quotes flow and flood discharge flow.

Water level storage-capacity curve

Adopt piecewise linear interpolation function f (x) to express the water level storage capacity relation of reservoir:

V ^t=f(L ^t)

L ^t=f ^-1(V ^t) （23）；

Wherein, L is Reservoir water level.

Reservoir tailwater level--outbound discharge relation curve

To reservoir tailwater level-outbound discharge relation curve, adopt equally piecewise linear function interpolating function g (x) to express:

T ^t=g(Q ^t+QF ^t) （24）；

Wherein, T is downstream tailwater elevation; (Q+QF) be the total vent flow of reservoir.

Unit output family curve

Power station unit output curve adopts the total differential mode of binary function to carry out linearization, and when head one timing, unit output can be expressed as the linear function that unit is quoted flow:

N=C ₁(H)×q+C ₂(H) （25）；

Wherein, C ₁and C (H) ₂(H) be the linear coefficient under a certain head.

Flow velocity vertical line distribution curve

This research adopts logarithmic velocity distribution formulas, utilizes actual measurement flow speed data, and matching obtains the front flow velocity vertical line distribution curve of reservoir dam, and flow velocity U can be expressed as relative depth d _rfunction:

U=h(d _r) (26)；

Suspended load silt content vertical line distribution curve

This research adopts the suspended load silt content vertical line distribution formula based on diffusion theory in formula (8), utilizes actual measurement flow speed data, and matching obtains reservoir suspended load silt content vertical line distribution curve, sediment concentration S _vcan be expressed as relative depth d _vfunction:

S _v=k(d _r) (27)；

1..5 reservoir sand discharge generating multiple-objection optimization flow process

1) chromosome coding

Produce at random n chromosome, produce the sequence of n reservoir letdown flow Q, form initial population P ₀(population scale=n); , there are 12 generating reference stream secondary elements and 4 flood discharge flow elements totally 16 genes in Yi Yuewei unit on each chromosome.Wherein, i chromosomal coding is as the formula (28):

Q _i={QN _i[1]，QN _i[2]，...，QN _i[t]，...，QN _i[12]，

QF _i[1+5]，QF _i[2+5],QF _i[3+5],QF _i[4+5]} （28）；

Wherein, QN quotes flow for generating, for calculating power station, exerts oneself:

N (N=KQNH); QF is flood discharge flow;

Be used for calculating reservoir sand discharge amount:

S (S=QFQS), QT _i(QT _i[t]=QN _i[t]+QF _i[t]) be total vent flow, for water balance equation, calculate next parameter such as storage capacity water level constantly.

It should be noted that, due in general, can there is reservoir spillway in four months in 6-9 month in flood season only, therefore, flood discharge flow QF four variablees of only having encoded, and quote flow QN at once with total vent flow QT and generating, need to consider the mistiming of 5 months time.

In order to reduce search volume, improve optimization efficiency, adopting actual earial drainage sequence is benchmark, the certain flow that fluctuates up and down in certain scope forms search volume.First obtained then that the monthly vent flow obtaining is detected at station, mausoleum, Huang Ling and flow (flood season, the difference of the two was flood discharge flow) is quoted in monthly total generating of being obtained by power station, then set daily average water discharge fluctuation range value Q _dr, at [Q _dr, Q _dr] the interior random undulating quantity that produces of scope, this undulating quantity is added with the daily average water discharge value that detects acquisition the daily average water discharge value that the program that is generates.By above algorithm, produce the initial population that population scale is n, be stored in the array of 16 * n.

2) target function value calculates

Calculating target function value, comprise power station year gross capability and reservoir year total sand discharge amount.

Year gross capability calculating

Write the function Calculate_Obj_E that solves first aim function (power station year gross capability).Algorithm is as follows:

● calculate storage capacity (utilizing water balance equation):

V _i[t]=V _i[t-1]+L _i[t]×0.0264-QN _i[t]×0.0264-QF _i|[t]×0.0264

（29）；

Wherein 0.0264 is unit conversion coefficient 0.0264=30.5 * 24 * 3600/10 ⁸, guarantee that the unit of storage capacity is billion cubic meter.Initial storage value is set to V _i[0]=393 billion cubic meters.

● calculate upper pond level

● write interpolate value function L _i[t]=f ^-1(V _i[t]), water level-storage capacity relation data is determined the waterlevel data under any given storage capacity value by inner interpolation method.

● calculate level of tail water T _i[t] (tailwater level Tailwater Level);

The level of tail water is relevant with letdown flow, T _i[t]=g (QN _i[t]+QF _{| i}[r]);

● calculate monthly exerting oneself, shilling K[t]=const;

N _i[t]=K[t]×QN _i[t]×(L _i[t]-T _i[t]) （30）；

● calculating power station year gross capability, is i the first aim functional value that chromosome is corresponding, i.e. fitness fitness1.

Obj1 _i=N _i=N _i[1]+N _i[2]+...+N _i[t]+...+N _i[12] （31）；

Reservoir year total sand discharge amount Si

Write the function Calculate_Obj_S that solves second target function (total sand discharge amount of reservoir year).Algorithm is as follows:

● determine silt content

Flood season, floodwater releasing port silt content was obtained at floodwater releasing port altitude range integration by vertical line silt content distribution curve.Spend machine silt content and non-flood season flood season and cross machine silt content and obtained by measured data.Crossing machine silt content flood season represents by the monthly average value in flood season.

● calculate a month sand discharge amount

Calculate the t sand discharge amount of individual month on i chromosome:

s _i[t]=QF _i[t]×QS _i[t]×0.0264 （32）；

Wherein 0.0264 is unit conversion coefficient.

● calculate a year sand discharge amount

Calculate i reservoir year total sand discharge amount S that chromosome is corresponding _i, be i the second target functional value that chromosome is corresponding, i.e. fitness fitness2.

Dbj2 _i=S _i=S _i[1]+S _i[2]+...+S _i[t]+...+S _i[12] （33）；

3) Multi-objective genetic algorithm optimization

In n chromosome, choose preferably m value and carry out cross and variation calculating, generate new population P ₁:

● determine non-dominated solutions, i.e. non-domination solution:

Any two pairs of chromosomes in traversal population, the fitness function value Obj1 and the Obj2 that compare two chromosome i and j, if (Obj1i>Obj1j & & Obj2i>Obj2j), deletes chromosome j.

● current m non-dominated solutions entered to cross and variation

If m=0, regenerates initial population; If m>0, enters cross and variation.

Intersect: it is 0.75 that crossover probability is set.If intersect, occur, from m non-dominated solutions, choose arbitrarily two chromosomes, produce at random an integer between [1,16], the gene location that is greater than this number exchanges.

Variation: it is 0.02 that variation probability is set.If variation occurs, for above-mentioned chromosome, produce at random an integer between [1,16], in this locational gene mutation, be the Arbitrary Digit between maximal value and minimum value on this position in m chromosome.

● a newly-generated n chromosome after cross and variation, form new population P1 together with the non-domination solution obtaining with last iteration, population scale is (m+n).

● calculate target function value corresponding to chromosome in new population, enter next iteration.

Embodiment 3;

Take certain reservoir as example, adopt the reservoir sand discharge generating Multipurpose Optimal Method that the inventive method is set up to carry out example calculation, parameter arranges as follows: initial population scale is: 100, iterative steps: 100 steps, flood season floodwater releasing port silt content: 0.066738kg/m ³, cross machine silt content: 0.026722kg/m flood season ³, cross machine silt content: 0.009015kg/m non-flood season ³.Crossover probability: 0.75, variation probability: 0.02, daily average water discharge changes amplitude Q _drfrom 50m ³/ s changes to 5000m ³/ s.

In following Fig. 3 to Fig. 6, loose point represents objective function corresponding to initial population; After set of data points chain from lower-left to upper right represents respectively the N time iteration, corresponding objective function is separated in non-domination, i.e. Prato front curve; In figure, shown respectively that the non-domination after 1 iteration, 5 iteration, 10 iteration, 25 iteration, 100 iteration separates corresponding objective function, objective function thus, decision maker is the multiple-objection optimization result of the maximum and reservoir sedimentary loading maximum of selective system generated energy easily, for example, from figure, in the data point in the close upper right corner, select.

In Fig. 3 to Fig. 6, the longitudinal axis represents a year sand discharge amount, unit be hundred million tons/annual, transverse axis represents annual electricity generating capacity, unit is ten thousand kilowatts.In Fig. 3 to Fig. 6, daily average water discharge changes amplitude Q _drfor being followed successively by 50m ³/ s, 150m ³/ s, 1000m ³/ s, 5000m ³/ s.

Claims (11)

1. a reservoir sand discharge generating Multiobjective Optimal Operation method, is characterized in that comprising the following steps:

One, with system generated energy, be target to the maximum and set up objective function;

With reservoir sedimentary loading, be target to the maximum and set up objective function;

Two, using letdown flow as decision variable, produce a plurality of sequences based on above-mentioned objective function, utilize the multi-objective genetic algorithm based on non-domination solution to solve decision variable;

By above-mentioned steps, obtain optimum letdown flow.

2. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 1, it is characterized in that: when solving decision variable, introduce the constraint condition of water reservoir system operation, comprise reservoir level constraint, the constraint of reservoir letdown flow and the constraint of flow daily amplitude.

3. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 1, is characterized in that: in step 2, produce at random n chromosome, produce the sequence of n reservoir letdown flow (Q), form initial population P ₀, population scale=n;

Take a time period is the criteria for classifying, and corresponding each chromosome has the gene of a plurality of generating reference stream secondary elements and a plurality of flood discharge flow elements, these genomic constitution arrays.

4. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 3, is characterized in that: Yi Yuewei unit, on each chromosome, there are 12 generating reference stream secondary elements and 4 flood discharge flow elements totally 16 genes, and form the array of 16 * n.

5. according to a kind of reservoir sand discharge generating Multiobjective Optimal Operation method described in claim 3 or 4, it is characterized in that: in n chromosome, choose a preferably chromosomal m value and carry out cross and variation calculating, generate new population P ₁;

Calculate target function value corresponding to chromosome in new population, enter next iteration.

6. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 5, is characterized in that: travel through any two pairs of chromosomes in population, relatively two chromosomal fitness function values, select preferably chromosome;

A current chromosomal m value is entered to cross and variation;

If m=0, regenerates initial population; If m > 0, enters cross and variation;

According to the crossover probability of setting, if intersect, occur, from m value, select arbitrarily two chromosomes, generate at random a nonzero integer in a gene number interval, the gene location that is greater than this number exchanges;

According to the variation probability of setting, if variation occurs, for above-mentioned chromosome, generate at random a nonzero integer in a gene number interval, in this locational gene mutation, become in m chromosome any number between maximal value and minimum value on this position;

Newly-generated n chromosome after cross and variation, forms new population P together with the preferably chromosome obtaining with last iteration ₁, population scale is m+n;

Calculate new population P ₁the target function value of middle correspondence, enters next iteration.

7. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 1, is characterized in that:

Keep paradox and incommensurability in reservoir operation multiple goal, but not incorporate into, solve for single goal; Gained optimized operation strategy is one group of optimal solution set, wherein between each optimum solution, can not mutually compare, and while comparing between any two solutions in this optimal solution set, if one of target of certain solution is better than another, separates, and two of its target must be inferior to another solution.

8. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 1, is characterized in that system generated energy maximum target function is:

$\mathrm{MaxE}={\mathrm{\Σ}}_{t=1}^T{E}_t={\mathrm{\Σ}}_{t=1}^T{\mathrm{\Σ}}_{i=1}^5\stackrel{\‾}{N_i^t}\×n_i\×\mathrm{\Δt};$

Wherein, E is a year generating total amount;

it is unit average output; Δ t is for calculating duration; T is each machine group # in power station; n _inumber of units for each unit; Segment length when t represents.

9. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 1, is characterized in that reservoir sedimentary loading maximum target function is:

$\mathrm{MaxS}={\mathrm{\Σ}}_{t=1}^T({\mathrm{QF}}^t\×\stackrel{\‾}{S_v^t}\×\mathrm{\Δt});$

Wherein, S is the sedimentary loading of reservoir, and unit is kg; QF is flood discharge flow, and unit is m ³/ s,

for the average percent sand of floodwater releasing port, unit is kg/m ³.

10. a kind of reservoir sand discharge generating Multiobjective Optimal Operation method according to claim 9, is characterized in that the average percent sand of floodwater releasing port is calculated by following formula:

$\stackrel{\‾}{S_v}={\∫}_n^{h+H}{S}_{\mathrm{va}}\×{\left(\frac{(h-y)\×a}{y\×(h-a)}\right)}^Z/\mathrm{Hdy};$

In formula, n is floodwater releasing port number, and y is current elevation, and h is floodwater releasing port Bottom Altitude, and L is floodwater releasing port width, and H is that floodwater releasing port is high.

11. a kind of reservoir sand discharge generating Multiobjective Optimal Operation methods according to claim 9, is characterized in that flood discharge flow is calculated by following formula:

$\mathrm{QF}=\stackrel{\‾}{U}\×H\×L\×n;$

In formula, n is floodwater releasing port number, and L is floodwater releasing port width, and H is that floodwater releasing port is high,

for floodwater releasing port mean flow rate.

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