CN105868921A - Method for hydropower station cluster stochastic programming model mode tree branch trimming under limited precision loss - Google Patents

Abstract

The invention discloses a method for hydropower station cluster stochastic programming model mode tree branch trimming under limited precision loss. The method comprises the steps that a hydropower station cluster optimized dispatching stochastic programming model is established; an indicator system representing solution precision is established; a plurality of runoff mode trees of different structures are generated, and the multiple sets of mode trees are input into the stochastic programming model; stochastic programming models corresponding to different sets of runoff mode trees are solved, the relation between model precision indicators and mode tree scales and the relation between calculation expenditures and model tree scales are recorded, and model precision corresponding to a complete mode tree serves as a reference; according to the relation of the model precision and model tree scales, precision threshold values with no obvious deviation from the model precision corresponding to the complete mode tree are extracted with the mean value hypothesis testing theory, and corresponding mode tree scales are determined; a trimmed model tree scale serves as a final result for guiding practical dispatching online. By means of the method, the reliability of the result of a dimension-reduced model is guaranteed, and the defect that the influence on the precision of a model is not considered in previous branch trimming dimension-reducing methods is overcome.

Description

Limit GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree under loss of significance and cut out branch method

Technical field

The invention belongs to hydrology resource and hydraulic engineering scheduling field, especially one utilize Hydropower Plant Reservoir group the most excellent Change model solves characteristic information under Different Diameter stream mode tree initial conditions to carry out scheme-tree cutting out branch, reduces model amount of calculation Dimension reduction method.

Background technology

In power station (group) Long-term Optimal Dispatch, scheduling decision person is often according to forecast footpath stream information, with reservoir operation benefit Maximize as optimization aim to formulate optimal scheduling strategy.At present, due to long-term (month by month, season by season) weather forecast precision still Relatively low, the precision of long-period runoff prediction is still difficult to ensure.Determine long-period runoff formed staple in, meteorological condition, under The pad feature such as planar condition and Vegetation condition often has at random, chaos, causes long-period runoff to be difficult to Accurate Prediction.Due to runoff Etc. the uncertainty of information, the substantially decision in the face of risk problem of Long-term Hydropower Station Scheduling.

Consider that the multi-stage stochastic programming revised in real time is the effective means solving decision in the face of risk problem.Model is often adopted With runoff model tree, uncertain water process is described.Runoff model tree comprises surveys, from the conception of history, the allusion quotation extracted Streamflow Data Type carrys out aqueous mode, characterizes the random water process of discretization with tree, is the initial conditions of Stochastic Programming Model.Tradition Runoff model tree generation method include empirical approach, optimization method and clustering method.Empirical approach directly utilize with The distribution function of machine variable generates sample, and supposes that sequence is single order Markov Chain, maintains the state transfer of runoff model tree Probability is consistent with former sequence transition probability.But, owing to not considering that crosscorrelation between stochastic variable is (such as footpath, GROUP OF HYDROPOWER STATIONS interval Correlation between the station of stream), the method is difficult to be applicable to the sampling of multiple random variable.Optimization method with match by moment method as representative, Often with optimized algorithm as means, seek runoff model tree and former sequence statistic square (average, variance, the coefficient of skew, fourth central away from And covariance) optimal coupling.Clustering procedure provides the approach of another kind of forming types tree.It is different from empirical method, this method Directly sample from history runoff observation series, and extract representational runoff model by cluster analysis.Clustering procedure excellent Gesture is that the pattern refined is the representative mode in various classification in DS, thus tends to the average of Assured Mode tree Consistent with the average of former DS.

With the increase of scheme-tree scale, Stochastic Programming Model will meet with " dimension calamity " problem and be difficult to solve.Due at random The calculating scale of plan model is the most relevant to the scale of scheme-tree, and the scale being reduced scheme-tree by cutting scheme-tree can be effective Reduce the computation complexity of model, therefore obtain extensive concern.But, characterizing former random series with small-scale scheme-tree will not The loss of random series of features information can be caused with avoiding so that cut out corresponding the cutting out of branch scheme-tree and dismember the office for former optimization problem Portion's optimal solution.On the one hand, policymaker wishes that the scale by reducing scheme-tree is to reduce computing cost as far as possible；Meanwhile, decision-making Person wishes to reduce as far as possible the difference of model result under conditions of reducing calculating scale.Owing to the scale of scheme-tree affects simultaneously The quality solved and computing cost, analytical model tree is cut out branch and the impact solving quality and computing cost determines that optimum sanction branch degree Key.

Traditional scheme-tree is cut out the many information according to tree self of branch method and is carried out cutting, the mould that such as cutting deletion is similar Formula, and do not consider that scheme-tree is cut out after branch the impact solved.In the research of Stochastic Programming Model is applied, cut out branch to model result Impact is only the emphasis that policymaker pays close attention to.Current branch research method of cutting out causes the differentia influence analysis existence of solution not to cutting out branch Foot, how under conditions of reducing loss of significance, farthest cutting scheme-tree, reduction model computing cost are urgently as far as possible The technical barrier solved.

Summary of the invention

The problem that it is an object of the invention to exist for prior art, it is provided that a kind of limit under loss of significance GROUP OF HYDROPOWER STATIONS with Machine plan model scheme-tree cuts out branch method, to can solve the problem that above-mentioned technical problem.

It is an object of the invention to be achieved through the following technical solutions: a kind of limit GROUP OF HYDROPOWER STATIONS under loss of significance and advise at random Draw pattern tree and cut out branch method, it is characterised in that comprise the steps:

Step 1, set up GROUP OF HYDROPOWER STATIONS Optimized Operation Stochastic Programming Model, preparation model related data；

Step 2, foundation characterize the index system solving precision；

Step 3, generate the runoff model tree of some different structures, be one group with the runoff model tree of identical scale, respectively Scheme-tree input Stochastic Programming Model will be organized more；

Step 4, solve the different corresponding Stochastic Programming Model of group runoff model tree, statistical model precision index and scheme-tree rule Mould, computing cost and the relation of scheme-tree scale, on the basis of the corresponding model accuracy of integrated pattern tree；

Step 5, foundation model accuracy and scheme-tree scale relation, use average hypothesis testing theory to extract and integrated pattern The corresponding model accuracy of tree, without the precision threshold of notable deviation, determines the scheme-tree scale of correspondence；

Step 6, using cut out whole after scheme-tree scale as final result, online direction actual schedule.

Preferably, described step 1 is further:

GROUP OF HYDROPOWER STATIONS natural two Phase flow series in collection research region, and corresponding reservoir engineering characteristic parameter；To Prestige Energy Maximization is object function, levies runoff with runoff model tree table uncertain, sets up Optimal operation of cascade hydropower stations Stochastic Programming Model.

Preferably, described step 1 is further:

Described object function is:

$\begin{array}{cc}\max & Es\left(\right\{{\mathrm{\ω}}_i\left\}\right)=\underset{m=1}{\overset{M}{\Σ}}{E}_{m,1}+\underset{i=1}{\overset{I}{\Σ}}P\left({\mathrm{\ω}}_i\right)\·\underset{m=1}{\overset{M}{\Σ}}\underset{t=2}{\overset{T}{\Σ}}{E}_{m,t}^i\end{array};$

This bound for objective function is:

Water balance retrains,

Upstream and downstream hydraulic connection retrains:

Generated energy retrains:

$H_{m,t}^i=f_1\left(\right(S_{m,t}^i+S_{m,t+1}^i)/2)-f_2(R_{m,t}^i+{\mathrm{SP}}_{m,t}^i);$

Storage capacity retrains:

Units limits:

Initial and boundary condition retrains:

In formula,For reservoir m generated energy under period t, runoff model i, m is the sequence number of reservoir, and M is reservoir number,Represent the reservoir group system expectation generated energy at future time period, i ∈ { 1,2,3 ... I}, P (ω_i) it is Runoff model ω_iProbability, Es ({ ω_i) it is runoff model tree { ω_iThe target function value of corresponding Stochastic Programming Model, currently The generated energy of periodFor deterministic unique value；Corresponding to runoff model ω_iUnder generated energy, i.e. reflection runoff with The machine impact on scheduling benefit；It is the time that t belongs to 2 to period of period T, T；

It is respectively reservoir m under runoff model i, at the beginning of the t period and the reservoir storage capacity of period Mo； AndIt is respectively reservoir m reservoir inflow, generating flow under period t, runoff model i and abandons discharge；For Reservoir m evaporation from water surface speed under period t, runoff model i；Δt_tTime segment length for period t；Rⁱ _m-1,tAnd SPⁱ _m-1,tPoint Wei reservoir m-1 generating flow under period t, runoff model i and abandon discharge；

ω_i,t,mFor reservoir m local inflow under period t, runoff model i, i.e. footpath flow vector ω_i,tM-th element；1 For the sequence number of most upstream reservoir, M is the sequence number of most downstream reservoir；

For reservoir m at runoff model i, the average gross head of period t；f₁And f₂It is respectively reservoir level and tailwater level Calculate function；For hydropower station efficiency；WithS _m,t+1It is respectively the reservoir m bound at t period end storage capacity；L _m,tWithIt is respectively lower limit and the upper limit of unit output；SB_mAnd SE_mIt is respectively initial storage and the end of term storage capacity of reservoir m.

Preferably, described step 2 is further:

The result of Stochastic Programming Model target function value and solution is directly affected by the scale of scheme-tree.For weighing scheme-tree Cutting out the branch impact on target function value, use two kinds of object function stability conditions that sample is relevant and sample is unrelated, foundation should Stability condition, builds sample and is correlated with the object function under sample don't-care condition as model accuracy evaluation index, enter respectively Row sample is relevant and the unrelated two kinds of numerical experiments of sample, detects under two kinds of experimental conditions target function value with runoff model tree scale Variation relation.

Preferably, described step 3 is further:

With the natural runoff observational data of reservoir group system for input, cluster algorithm is used to combine Monte Carlo sampling Method generates different scales, the runoff model tree of different structure, and carries out grouping and classifying by tree scale.

Preferably, described step 4 is further:

Input using the scheme-tree generated as Stochastic Optimization Model according to this, specifying constraint value and initial, perimeter strip Part value, uses Non-Linear Programming software LINGO to solve the model of correspondence, adds up not by the scale statistical packet of runoff model tree The characteristic parameter such as relevant, the average of target function value of the unrelated criterion of sample, variance with sample under scale, and adjust the mould of correspondence Type scale, average calculation times etc..

Preferably, described step 5 is further:

Due to computational accuracy, computing cost all with calculate scale correlation, reduce model by cutting out by the way of branch Computing cost will unavoidably cause loss of significance.For Real-time Decision, too low reduction precision reduces the calculating of expense Result tends not to be accepted, and answers definition mode tree to cut out the loss of significance threshold value that branch causes, damages in the acceptable precision of policymaker Model dimensionality reduction is carried out under mistake degree；

On the basis of the precision index of scheme-tree (completely tree) the corresponding model not cutting out branch, the inspection of average t is used to give Under the conditions of fixation reliability, different branch degree of cutting out produce the conspicuousness of loss of significance corresponding to reference precision, determine therefrom that precision is damaged The sanction branch degree of the maximum possible under the conditions of mistake is notable.

Preferably, described step 6 is further:

The maximum possible that output step 5 determines cuts out branch degree, according to foolscap branch part drag computing cost and sanction branch The variance analysis of front model computing cost is cut out branch and is reduced the degree of computing cost.

Preferably, described step 2 is further: when use different structure, identical scale scheme-tree as stochastic programming During mode input, if the target function value of its correspondence is close, then meet the object function stability condition that sample is relevant:

$Es\left(\right\{{\mathrm{\ω}}_{l_1}\left\}\right)\≈Es\left(\right\{{\mathrm{\ω}}_{l_2}\left\}\right),l_1=1,2...,I;l_2=1,2...,I$

WithIt is respectively two and there is different structure, the scheme-tree of identical scale.

The present invention has the following advantages compared to existing technology: the present invention proposes under consideration model calculation accuracy condition not show Write the dimensionality reduction criterion premised on reduction model accuracy, ensured the reliability of dimensionality reduction model result, compensate for cutting out a dimensionality reduction in the past Method does not considers the deficiency on model accuracy impact.

Accompanying drawing explanation

Fig. 1 is the flow chart of the inventive method.

Fig. 2 a to Fig. 2 d is the sanction branch runoff model tree construction signal of complete runoff model tree, different scales and sanction branch degree Figure；Wherein, the scale of Fig. 2 b is 27, and cutting out branch degree is 20%；The scale 17 of Fig. 2 c, cuts out branch degree 50%；

The scale 4 of Fig. 2 d, cuts out branch degree 90%.

The relevant two kind experiment criterion drag precision unrelated with sample of Fig. 3 a and Fig. 3 b respectively sample are put with the CPU time Change graph of a relation.

Fig. 4 a and Fig. 4 b is respectively difference under relevant two kinds of experiment criterions unrelated with sample of sample and cuts out branches to loss of significance shadow Ring conspicuousness (t inspection) result figure.

Detailed description of the invention

Existing research does not consider to cut out branch to model essence using the similitude of each pattern self information in tree as sanction branch foundation Degree impact, it may appear that precision produces notable loss, causes solving the problems such as reliability reduction.Therefore, and it is applicant's understanding that research Runoff model tree is cut out in branch algorithm, it is ensured that cut out the model accuracy loss after branch controlled most important.

For solving the problem that prior art exists, the present invention proposes GROUP OF HYDROPOWER STATIONS under a kind of restriction loss of significance and advises at random Drawing pattern tree and cut out branch method, build model accuracy evaluation index, the scheme-tree cutting out branch degree using difference as input and is built Vertical reference precision, farthest reduces computing cost on the premise of not significantly reducing model accuracy, obtains the pattern of correspondence Tree scale, is applied to instruct actual schedule.

Mainly include walking as follows as it is shown in figure 1, the present invention sets up GROUP OF HYDROPOWER STATIONS stochastic programming runoff model tree sanction branch method Rapid:

Step 1, sets up GROUP OF HYDROPOWER STATIONS Optimized Operation Stochastic Programming Model, preparation model related data；

I.e. with expectation Energy Maximization as object function, levy runoff with runoff model tree table uncertain, set up power station Group's Optimized Operation Stochastic Programming Model, preparation model related data.

Step 2, sets up and characterizes the index system solving precision；

Random process characteristic information will be caused to lose as it was previously stated, scheme-tree cuts out branch, cause sanction branch model result distortion.Logical Cross and cut out the precision also reducing solution while branch reduces model computing cost.It is said that in general, scheme-tree sanction branch degree is the highest, calculate Complexity is the lowest, cuts out branch model result deviation master mould result the most.Therefore, distinct model result and the relation pair of sanction branch degree Significant in the most optimal sanction branch proportion scheme.

When real-time reservoir operation, owing to calculating the restriction of time, policymaker is only capable of using the runoff model of limited quantity Represent the random runoff process of former continuous print.The result of Stochastic Programming Model target function value and solution is directly by the scale of scheme-tree Impact.Cut out the branch impact on target function value for weighing scheme-tree, use " sample is correlated with ", two kinds of target letters of " sample is unrelated " Number stability condition.

Research mode tree cuts out the branch impact on precision index (sample related objective function, sample independent object function), point Do not carry out " sample be correlated with ", " sample is unrelated " two kinds of numerical experiments, detect under two kinds of experimental conditions target function value with runoff mould The variation relation of formula tree scale.

Step 3, generates the runoff model tree of some different structures, is one group with the runoff model tree of identical scale, respectively Scheme-tree input Stochastic Programming Model will be organized more；

Generate different scales, the runoff model tree of different structure, and carry out grouping and classifying by tree scale: with multi-reservoir The natural runoff observational data of system is input, uses clustering method to generate reference model tree { ω_L, L=1...IF.In reference On the basis of scheme-tree, generating G group sanction branch runoff model tree, often group and comprise K tree in cutting out branch scheme-tree, its scale is respectively IR, (G-1)/G IR, (G-2)/G IR ..., 1/G IR, represent sanction branch in various degree respectively.

Step 4, solves the different corresponding Stochastic Programming Model of group runoff model tree, and statistical model precision index is advised with scheme-tree Mould, computing cost and the relation of scheme-tree scale, on the basis of the corresponding model accuracy of integrated pattern tree.

Input using the scheme-tree generated as Stochastic Optimization Model according to this, specifying constraint value and initial, perimeter strip Part value, uses Non-Linear Programming software LINGO to solve the model of correspondence, adds up not by the scale statistical packet of runoff model tree The characteristic parameter such as relevant, the average of target function value of the unrelated criterion of sample, variance with sample under scale, and adjust the mould of correspondence Type scale, average calculation times etc..

Step 5, according to model accuracy and scheme-tree scale relation, uses average hypothesis testing theory to extract and integrated pattern The corresponding model accuracy of tree, without the precision threshold of notable deviation, determines the scheme-tree scale of correspondence.

Due to computational accuracy, computing cost all with calculate scale correlation, reduce model by cutting out by the way of branch Computing cost will unavoidably cause loss of significance.For Real-time Decision, too low reduction precision reduces the calculating of expense Result tends not to be accepted, and answers definition mode tree to cut out the loss of significance threshold value that branch causes, damages in the acceptable precision of policymaker Model dimensionality reduction is carried out under mistake degree.

On the basis of the precision index of scale scheme-tree (completely tree) the corresponding model as IR, use the inspection of average t Under the conditions of given confidence level, different branch degree of cutting out produce the conspicuousness of loss of significance corresponding to reference precision, determine therefrom that precision The sanction branch degree of the maximum possible under the conditions of loss is not notable.

Step 6, using cut out whole after scheme-tree scale as final result, online direction actual schedule.

The maximum possible that output step 5 determines cuts out branch degree, according to foolscap branch part drag computing cost and sanction branch The variance analysis of front model computing cost is cut out branch and is reduced the degree of computing cost.

Below by embodiment, and combine accompanying drawing and realize process, technical scheme is further elaborated with.

As it is shown in figure 1, under restriction loss of significance, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, including following step Rapid:

Step 1, to expect that Energy Maximization, as object function, is levied runoff with runoff model tree table uncertain, set up ladder Level GROUP OF HYDROPOWER STATIONS Optimized Operation Stochastic Programming Model, preparation model related data；Model concrete structure is as follows:

Step 11. determines object function

With reservoir group system expectation Energy Maximization in schedule periods as target:

$\begin{array}{cc}\max & Es\left(\right\{{\mathrm{\ω}}_i\left\}\right)=\underset{m=1}{\overset{M}{\Σ}}{E}_{m,1}+\underset{i=1}{\overset{I}{\Σ}}P\left({\mathrm{\ω}}_i\right)\·\underset{m=1}{\overset{M}{\Σ}}\underset{t=2}{\overset{T}{\Σ}}{E}_{m,t}^i\end{array},$

For reservoir m generated energy under period t, runoff model i, M is reservoir number.Represent Reservoir group system is at the expectation generated energy of future time period (2 to period of period T), P (ω_i) it is runoff model ω_iProbability.Es ({ω_i) it is runoff model tree { ω_iThe target function value of corresponding Stochastic Programming Model.The generated energy E of present period_m,1For determining The unique value of property；Owing to the future time period strategy that discharges water has uncertainty, the generated energy of its correspondence also has randomness:Right Should be in runoff model ω_iUnder generated energy, i.e. reflection runoff randomness on scheduling benefit impact.Step 12. determines constraint bar Part

Described constraints includes water balance equation, upstream and downstream hydraulic connection, generated energy, and storage capacity limits, restriction of exerting oneself, Initial and boundary condition；

Wherein, water balance equation:

$S_{m,t+1}^i=S_{m,t}^i+(W_{m,t}^i-R_{m,t}^i-{\mathrm{SP}}_{m,t}^i-{\mathrm{EV}}_{m,t}^i)\·{\mathrm{\Δt}}_t,$

WithIt is respectively reservoir m under runoff model i, at the beginning of the t period and the reservoir storage capacity of period Mo, [m³]；AndIt is respectively reservoir m reservoir inflow, generating flow under period t, runoff model i and abandons discharge, [m³/s]；For reservoir m evaporation from water surface speed under period t, runoff model i, [m³/s]；Δt_tPeriod for period t Long, [s].

Upstream and downstream hydraulic connection:

$\begin{array}{c}{W}_{m,t}^i={\mathrm{\ω}}_{i,t,m}+R_{m-1,k}^i+{\mathrm{SP}}_{m-1,t}^i,m\≥2\\ W_{m,t}^i={\mathrm{\ω}}_{i,t,m},m=1\end{array},$

Make the serial number 1 of most upstream reservoir, most downstream reservoir serial number M.ω_i,t,mFor reservoir m at period t, runoff model i Under local inflow, i.e. footpath flow vector ω_i,tM-th element.

Generated energy:

$E_{m,t}^i=R_{m,t}^i\·\mathrm{\η}\left(H_{m,t}^i\right)\·{\mathrm{\Δt}}_t$

$H_{m,t}^i=f_1\left(\right(S_{m,t}^i+S_{m,t+1}^i)/2)-f_2(R_{m,t}^i+{\mathrm{SP}}_{m,t}^i),$

For reservoir m at runoff model i, the average gross head of period t, [m]；f₁And f₂It is respectively reservoir level and tail water The calculating function of position；For hydropower station efficiency [MWh/m³]。

Storage capacity limits:

$\underset{\‾}{S_{m,t+1}}\≤S_{m,t+1}^i\≤\stackrel{\‾}{S_{m,t+1}},$

WithS _m,t+1It is respectively the reservoir m bound at t period end storage capacity, [m³]。

Exert oneself restriction:

$\underset{\‾}{L_{m,t}}\≤E_{m,t}^i/{\mathrm{\Δt}}_t\≤\stackrel{\‾}{L_{m,t}},$

L _m,tWithIt is respectively lower limit and the upper limit, [MW] of unit output.

Initial and boundary condition:

$S_{m,1}^i={\mathrm{SB}}_m;S_{m,T+1}^i={\mathrm{SE}}_m,$

SB_mAnd SE_mIt is respectively initial storage and end of term storage capacity, [m of reservoir m³]。

Step 2, research mode tree cuts out the branch shadow to precision index (sample related objective function, sample independent object function) Ring, carry out " sample be correlated with ", " sample is unrelated " two kinds of numerical experiments respectively, detect under two kinds of experimental conditions target function value with footpath The variation relation of stream mode tree scale；

When using different structure, the scheme-tree of identical scale to input as Stochastic Programming Model, if the target of its correspondence Functional value is close, then meet the object function stability condition of " sample is correlated with ", it may be assumed that

$Es\left(\right\{{\mathrm{\ω}}_{l_1}\left\}\right)\≈Es\left(\right\{{\mathrm{\ω}}_{l_2}\left\}\right),l_1=1,2...,I;l_2=1,2...,I,$

WithIt is respectively two and there is different structure, the scheme-tree of identical scale.

The stability condition of " sample is correlated with " defines the stability of model objective function value, different, " sample Unrelated " stability condition describe the deviation impact on target function value of model solution.Specifically, the stablizing of " sample is unrelated " Property condition require to be updated to the solution tried to achieve under different structure, identical scale scheme-tree the Stochastic Programming Model of former continuous distributed In, corresponding target function value is close.Former continuous distributed Stochastic Programming Model represents that random factor uses continuity distribution correspondence Stochastic Programming Model, the theoretical optimal solution of the i.e. Stochastic Programming Model of its solution.Owing to being difficult to solve continuous distributed stochastic programming mould Type, in production practices, the general discrete distribution Stochastic Programming Model using its equivalence substitutes, i.e. sufficiently large by a scale Reference model tree represents the continuous distributed of stochastic variable.The stability condition requirement that sample is unrelated:

$Es\left(\right\{{\mathrm{\ω}}_L\};\arg \max Es(\left\{{\mathrm{\ω}}_{l_1}\right\}\left)\right)\≈Es\left(\right\{{\mathrm{\ω}}_L\};\arg \max Es(\left\{{\mathrm{\ω}}_{l_2}\right\}\left)\right),$

{ω_L, L=1...IF is reference model tree；IF is the scale (model number) of reference model tree.

Step 3, generates different scales, the runoff model tree of different structure, and carries out grouping and classifying by setting scale:

Runoff model tree generates with following steps.First, at reference model tree { ω_L, random on the basis of L=1...IF Removing partial mode (scale is IF-IR), the scale of obtaining is the tree construction of the runoff model tree of IR, uses in clustering algorithm Neural gas algorithm generation mode tree.Then, on the basis of the scheme-tree that scale is IR, remove the pattern of 1/G IR at random, And utilize Neural gas method to update the information such as numerical value cutting out the upper node of branch tree, obtain the runoff mould that scale is (G-1)/G IR Formula tree.By that analogy, remaining runoff model tree method the most according to this generates one by one.

Fig. 2 is complete runoff model tree, cuts out branch runoff model tree construction schematic diagram.

Step 4, inputs using the scheme-tree generated as Stochastic Optimization Model according to this, specifying constraint value and initial, Boundary condition value, uses Non-Linear Programming software LINGO to solve the model of correspondence, by the scale statistical packet of runoff model tree The characteristic parameter such as sample relevant, the average of target function value of the unrelated criterion of sample, variance under statistics different scales, and adjust right The scale of model answered, average calculation times etc..

Fig. 3 is " sample is correlated with ", " sample is unrelated " two kinds of experiment criterion drag precision and the displacement graph of a relation of CPU time.

Step 5, due to computational accuracy, computing cost all with calculate scale correlation, drop by cutting out by the way of branch Low model computing cost will unavoidably cause loss of significance.For Real-time Decision, too low reduction precision reduces expense Result of calculation tend not to be accepted, answer definition mode tree to cut out the loss of significance threshold value that causes of branch, acceptable policymaker Model dimensionality reduction is carried out under loss of significance degree.

On the basis of the precision index of scale scheme-tree (completely tree) the corresponding model as IR, use the inspection of average t Under the conditions of given confidence level, different branch degree of cutting out produce the conspicuousness of loss of significance corresponding to reference precision, determine therefrom that precision The sanction branch degree of the maximum possible under the conditions of loss is not notable.

When application Stochastic Programming Model instructs actual schedule, still need to determine optimal sanction branch degree, make runoff model tree be subject to Cutting out branch impact causes the deviation of object function in tolerance interval.Specifically, (variance does not wait bar to use the inspection of Welch average t Average t inspection under part) detect under certain confidence level, whether the target function value cutting out dismemberment corresponding has been significantly deviating from The target function value that whole solution (the corresponding solution to model of integrated pattern tree) is corresponding.Null hypothesis HP₀For: cut out the object function that dismemberment is corresponding It is worth target function value corresponding with global solution without significant difference:

${\mathrm{HP}}_0:\frac{1}{G}\underset{g=1}{\overset{G}{\&Sigma;}}Es\left(\right\{{\mathrm{\&omega;}}_{l_g}\left\}\right)=\frac{1}{G}\underset{g^{\&prime;}=1}{\overset{G}{\&Sigma;}}Es\left(\right\{{\mathrm{\&omega;}}_{l_{g^{\&prime;}}}\left\}\right),l_g=1,...,I;I<IR;l_{g^{\&prime;}}=1,...,IR$

Structure test statistics ttest₁:

${\mathrm{ttest}}_1=1/G\&CenterDot;\&lsqb;\underset{g=1}{\overset{G}{\&Sigma;}}Es\left(\right\{{\mathrm{\&omega;}}_{l_g}\left\}\right)-\underset{g=1}{\overset{G}{\&Sigma;}}Es\left(\right\{{\mathrm{\&omega;}}_{l_{g^{\&prime;}}}\left\}\right)\&rsqb;/\sqrt{{{\mathrm{\&sigma;}}_1}^2/G+{{\mathrm{\&sigma;}}_2}^2/G},$

In formula, σ₁ ²And σ₂ ²It is respectively and cuts out branch scheme-tree target function valueIntegrated pattern tree target function valueVariance, this statistical check amount ttest₁The obedience free degree is ν₁≈(σ₁ ²/G+σ₂ ²/G)²/{[σ₁ ⁴+σ₂ ⁴]/[G²(G- 1) t distribution] }.

Similarly, under the unrelated test model of sample, null hypothesis HP₀For: cut out dismemberment correspondence under the unrelated criterion of sample Target function value and global solution under corresponding criterion corresponding target function value without significant difference:

${\mathrm{HP}}_0:\frac{1}{G}\underset{g=1}{\overset{G}{\&Sigma;}}Es\left(\right\{{\mathrm{\&omega;}}_L\};\arg \max Es(\left\{{\mathrm{\&omega;}}_{l_g}\right\}\left)\right)=\frac{1}{G}\underset{g^{\&prime;}=1}{\overset{G}{\&Sigma;}}Es\left(\right\{{\mathrm{\&omega;}}_L\};\arg \max Es(\left\{{\mathrm{\&omega;}}_{l_{g^{\&prime;}}}\right\}\left)\right),$

l_g=1 ..., I；I<IF；l_g'=1 ..., IF；L=1 ..., IR

Statistical check amount ttest₂For: In formula, σ '₁ ²With σ '₂ ²It is respectively and cuts out branch scheme-tree target function value under the unrelated criterion of sample Integrated pattern tree is target function value under the unrelated criterion of sampleVariance, this statistical check Amount ttest₂The obedience free degree is ν₁≈(σ′₁ ²/G+σ′₂ ²/G)²/{[σ′₁ ⁴+σ′₂ ⁴]/[G²(G-1) t distribution] }.

Respectively the target function value result under " sample is correlated with " and " sample is unrelated " two kinds of test models is carried out t inspection Testing, confidence level is 95%.Specifically, in the result of calculation of " sample is correlated with ", the target under difference cuts out branch degree is compared Functional value and the difference of complete tree-model target function value average.If t test statistics is distributed under given confidence level than t Critical value wants height, then refuse null hypothesis, it is believed that both averages have significant difference；Otherwise, null hypothesis is accepted, it is believed that both of which Value is without significant difference.

Fig. 4 is " sample is correlated with ", " sample is unrelated " two groups of experiment condition differences cut out branch affects conspicuousness (t to loss of significance Inspection) result figure.In example, understand from the result of calculation of " sample is correlated with ", when cutting out branch degree higher than 40%, t test value It is distributed critical value more than t；In the result of calculation of " sample is unrelated ", when cutting out branch degree higher than 60%, t test value is distributed more than t Critical value.That is, the sanction branch of 40% will not significantly reduce model model accuracy under two kinds of experiment conditions.

Step 6, output maximum possible cuts out branch degree, according to model before foolscap branch part drag computing cost and sanction branch The variance analysis of computing cost is cut out branch and is reduced the degree of computing cost.

In a word, the present invention establishes Stochastic Programming Model model accuracy evaluation under different mode tree initial conditions and refers to Mark.Add the stochastic simulation analysis scheme-tree by Monte Carlo and cut out the former of the loss of significance result that is likely to result in of branch and correspondence Cause.The present invention is directed to tradition sanction branch method and model accuracy is considered that not enough shortcoming improves, propose not significantly reduce mould Sanction branch criterion premised on type precision so that model can finite accuracy lose under conditions of at utmost reduce computing cost and Calculating scale, improves model ageing.Although it should be noted that the part steps of the present invention is to use in the above-described embodiments Optimizing what software Lingo solved, the main idea of the present invention is to provide a kind of GROUP OF HYDROPOWER STATIONS Optimized Operation Stochastic Programming Model Dimension reduction method, Lingo be test this method technological means (one of), the process that realizes of software can be regarded as skill of the present invention A kind of implementation process of the materialization of art thought.The software that similar software or exploitation can certainly be used to be similar to realizes, Do not repeat them here.

Claims (9)

1. one kind limits GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree under loss of significance and cuts out branch method, it is characterised in that include as Lower step:

Step 1, set up GROUP OF HYDROPOWER STATIONS Optimized Operation Stochastic Programming Model, preparation model related data；

Step 2, foundation characterize the index system solving precision；

Step 3, generate the runoff model tree of some different structures, be one group with the runoff model tree of identical scale, will be many respectively Group scheme-tree input Stochastic Programming Model；

Step 4, solve the different corresponding Stochastic Programming Model of group runoff model tree, statistical model precision index and scheme-tree scale, Computing cost and the relation of scheme-tree scale, on the basis of the corresponding model accuracy of integrated pattern tree；

Step 5, foundation model accuracy and scheme-tree scale relation, use average hypothesis testing theory to extract right with integrated pattern tree Answer model accuracy without the precision threshold of notable deviation, determine the scheme-tree scale of correspondence；

Step 6, using cut out whole after scheme-tree scale as final result, online direction actual schedule.

2. under restriction loss of significance as claimed in claim 1, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levying and be, described step 1 is further:

GROUP OF HYDROPOWER STATIONS natural two Phase flow series in collection research region, and corresponding reservoir engineering characteristic parameter；Send out with expectation Electricity is object function to the maximum, levies runoff with runoff model tree table uncertain, sets up Optimal operation of cascade hydropower stations random Plan model.

3. under restriction loss of significance as claimed in claim 2, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levying and be, described step 1 is further:

Described object function is:

$\max Es\left(\right\{{\mathrm{\&omega;}}_i\left\}\right)=\underset{m=1}{\overset{M}{\&Sigma;}}{E}_{m,1}+\underset{i=1}{\overset{I}{\&Sigma;}}P\left({\mathrm{\&omega;}}_i\right)\&CenterDot;\underset{m=1}{\overset{M}{\&Sigma;}}\underset{t=2}{\overset{T}{\&Sigma;}}{E}_{m,t}^i;$

This bound for objective function is:

Water balance retrains,

Upstream and downstream hydraulic connection retrains:

Generated energy retrains:

$H_{m,t}^i=f_1\left(\right(S_{m,t}^i+S_{m,t+1}^i)/2)-f_2(R_{m,t}^i+{\mathrm{SP}}_{m,t}^i);$

Storage capacity retrains:

Units limits:

Initial and boundary condition retrains:

In formula,For reservoir m generated energy under period t, runoff model i, m is the sequence number of reservoir, and M is reservoir number,Represent the reservoir group system expectation generated energy at future time period, i ∈ { 1,2,3 ... I}, P (ω_i) it is Runoff model ω_iProbability, Es ({ ω_i) it is runoff model tree { ω_iThe target function value of corresponding Stochastic Programming Model, currently The generated energy E of period_m,1For deterministic unique value；Corresponding to runoff model ω_iUnder generated energy, i.e. reflection runoff random Property on scheduling benefit impact；It is the time that t belongs to 2 to period of period T, T；

It is respectively reservoir m under runoff model i, at the beginning of the t period and the reservoir storage capacity of period Mo； With AndIt is respectively reservoir m reservoir inflow, generating flow under period t, runoff model i and abandons discharge；For reservoir m Evaporation from water surface speed under period t, runoff model i；Δt_tTime segment length for period t；AndIt is respectively water Storehouse m-1 generating flow under period t, runoff model i and abandon discharge；

ω_i,t,mFor reservoir m local inflow under period t, runoff model i, i.e. footpath flow vector ω_i,tM-th element；1 is The sequence number of upper pond, M is the sequence number of most downstream reservoir；

For reservoir m at runoff model i, the average gross head of period t；f₁And f₂It is respectively reservoir level and the calculating letter of tailwater level Number；For hydropower station efficiency；WithS _m,t+1It is respectively the reservoir m bound at t period end storage capacity；L _m,tWith It is respectively lower limit and the upper limit of unit output；SB_mAnd SE_mIt is respectively initial storage and the end of term storage capacity of reservoir m.

4. under restriction loss of significance as claimed in claim 1, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levying and be, described step 2 is further:

The result of Stochastic Programming Model target function value and solution is directly affected by the scale of scheme-tree；Branch is cut out for weighing scheme-tree Impact on target function value, uses two kinds of object function stability conditions that sample is relevant and sample is unrelated, stable according to this Property condition, build that sample is relevant and object function under sample don't-care condition be as model accuracy evaluation index, carry out sample respectively These relevant and unrelated two kinds of numerical experiments of sample, detect under two kinds of experimental conditions target function value with the change of runoff model tree scale Change relation.

5. under restriction loss of significance as claimed in claim 1, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levying and be, described step 3 is further:

With the natural runoff observational data of reservoir group system for input, cluster algorithm is used to combine Monte Carlo sampling raw Become different scales, the runoff model tree of different structure, and carry out grouping and classifying by tree scale.

6. under restriction loss of significance as claimed in claim 1, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levying and be, described step 4 is further:

Inputting using the scheme-tree generated as Stochastic Optimization Model according to this, specifying constraint value and initial, boundary condition take Value, uses Non-Linear Programming software LINGO to solve the model of correspondence, adds up difference rule by the scale statistical packet of runoff model tree Under mould, sample is relevant, the average of the target function value of the unrelated criterion of sample and variance, and adjusts the scale of model of correspondence and average The calculating time.

7. under restriction loss of significance as claimed in claim 1, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levy and be, described step 5 is further:

Due to computational accuracy, computing cost all with calculate scale correlation, reduce model by the way of branch calculate by cutting out Expense will unavoidably cause loss of significance；For Real-time Decision, too low reduction precision reduces the result of calculation of expense Tend not to be accepted, answer definition mode tree to cut out the loss of significance threshold value that branch causes, in policymaker's acceptable loss of significance journey Model dimensionality reduction is carried out under degree；

On the basis of the precision index of the scheme-tree correspondence model not cutting out branch, the inspection of average t is used to give confidence level condition Under, different branch degree of cutting out produce the conspicuousness of loss of significance corresponding to reference precision, determine therefrom that the not notable condition of loss of significance Under the sanction branch degree of maximum possible.

8. under restriction loss of significance as claimed in claim 1, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levy and be, described step 6 is further:

The maximum possible that output step 5 determines cuts out branch degree, according to foolscap branch part drag computing cost and sanction branch front mould The variance analysis of type computing cost is cut out branch and is reduced the degree of computing cost.

9. under restriction loss of significance as claimed in claim 3, GROUP OF HYDROPOWER STATIONS Stochastic Programming Model scheme-tree cuts out branch method, and it is special Levying and be, described step 2 is further: when the scheme-tree of employing different structure, identical scale inputs as Stochastic Programming Model Time, if the target function value of its correspondence is close, then meet the object function stability condition that sample is relevant:

$Es\left(\right\{{\mathrm{\&omega;}}_{l_1}\left\}\right)\&ap;Es\left(\right\{{\mathrm{\&omega;}}_{l_2}\left\}\right),l_1=1,2...,I;l_2=1,2...,I$

WithIt is respectively two and there is different structure, the scheme-tree of identical scale.