CN109002932B - A kind of random optimization dispatching method towards Hydropower Plant Reservoir - Google Patents
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Abstract
The invention discloses a kind of random optimization dispatching method towards Hydropower Plant Reservoir, including establish runoff and its probabilistic quantitative model of forecast；It is proposed runoff and its probabilistic theoretical estimation method of forecast；Stochastic dynamic programming (SDP) model under different stream flow description modes is constructed, scheduling rule is extracted, to instruct Hydropower Plant Reservoir actual motion.The method of the present invention breaches Conventional wisdom estimation method when quantifying runoff uncertainty, it is limited by the defect of measuring runoff sample completely, avoids and generates artificial runoff sample, calculates easier, data space greatly reduces, and improves the benefit of random optimization scheduling.
Description
Technical field
The present invention relates to reservoir operation technical fields, dispatch more particularly to a kind of random optimization towards Hydropower Plant Reservoir
Method.
Background technique
Optimizing scheduling of reservoir research is risen in the 1960s, so far, theoretical and adjust in Optimized Operation
A series of plentiful and substantial research achievements are achieved in degree model construction and solution.However, these achievements are seldom applied to power station
In actual schedule.To find out its cause, mainly since reservoir operation is faced with the probabilistic problem of runoff.Optimal Operation Model is normal
Consider that runoff is uncertain using such two ways: 1. hidden random fashion assumes that following runoff track is history runoff
It recurs, the uncertain feature of the following runoff is reflected by history runoff scene.2. aobvious random fashion, i.e., based on uncertainty
Hydrological Time Series and its probability distribution description become a mandarin at random.Wherein, stochastic dynamic programming (SDP) be most widely used it is aobvious
Randomized optimization process.
SDP is uncertain come final quantization runoff by runoff state transition probability.Along with the development of bayesian theory
And application, state transition probability can constantly roll update according to Runoff Forecast information, it is pre- a large amount of consideration runoffs occur
Report probabilistic SDP model-Bayes SDP (Bayesian SDP, BSDP) model.However, current state transition probability master
Will be placed one's entire reliance upon actual measurement/manually generated runoff by the experience estimation method acquisition with frequency instead of probability, computational accuracy
Sample.When surveying Finite Samples or manually generated runoff sample cannot retain the feature of original sample, calculated result will be lost
Very, the benefit of random optimization scheduling can be reduced.Moreover, BSDP will not only consider as runoff uncertainty is taken into account in SDP
The metastatic rule of runoff itself also wants the transition probability of CALCULATING PREDICTION runoff and measuring runoff.At this point, working as measuring runoff sample not
When enough, it will become infeasible using the method that Stochastic Simulation Model enriches runoff sample, because generating artificial Fuzzy Period of Runoff Series simultaneously
Fuzzy Period of Runoff Series is forecast with it, and the complicated correlativity without changing original runoff characteristic and itself and Runoff Forecast series, is very
Difficult.
Summary of the invention
Goal of the invention: to solve the deficiencies in the prior art, the present invention provides a kind of random optimization towards Hydropower Plant Reservoir
Dispatching method.
Technical solution: for achieving the above object, using following technical scheme:
A kind of random optimization dispatching method towards Hydropower Plant Reservoir, comprising the following steps:
(1) runoff and its probabilistic quantitative model of forecast are established；
(2) runoff and its probabilistic theoretical estimation method of forecast are proposed；
(3) stochastic dynamic programming under different stream flow description modes is constructed, scheduling rule is extracted, to instruct power station
Practical reservoir operation.
Further, the step (1) the following steps are included:
(11) in order to describe runoff itself randomness, runoff prior state transition probability is established
Runoff is considered as a simple single order markoff process, and with runoff state transition probability Pt-1 ijTo describe diameter
Flow the randomness of itself, i.e. Pt-1 ij=P [qt∈j|qt-1∈ i], it indicates the runoff q of known period t-1t-1When for grade i, when
The runoff q of section ttFor the probability of grade j；
Due to runoff state transition probability Pt-1 ijIt is to be obtained on the basis of not obtaining any Runoff Forecast information, by it
Referred to as runoff prior state transition probability；
(12) according to Runoff Forecast uncertainty, the likelihood probability of diameter stream mode transfer is established, and further establishes runoff
Predictability probability
With likelihood probability Pt jkIndicate the uncertainty of Runoff Forecast, i.e. Pt jk=P [qf t∈k|qt∈ j], it indicates period t
Measured path flow valuve qtWhen in grade j, diameter flow valuve q is forecastf tProbability in grade k；
After obtaining runoff prior state transition probability and likelihood probability, using total probability formula obtain runoff can
Predictive probability Pt jl, i.e. Pt jl=P [qf t+1∈l|qt∈ j], when it indicates that the practical runoff of period t is in grade j, the t+1 period is pre-
Calibrate the probability that stream is in grade l；The predictability probability calculation formula of runoff are as follows:
(13) posterior probability of diameter stream mode transfer is obtained
The posterior probability of diameter stream mode transfer is derived using Bayes' theorem according to the new forecast information got；This
Sample is constantly modified runoff prior state transition probability, diameter stream mode as Runoff Forecast information constantly rolls update
The calculation formula of the posterior probability of transfer are as follows:
Further, the step (2) the following steps are included:
(21) using measuring runoff sample and forecast runoff sample as data basis, day part measuring runoff and pre- is established respectively
Report the edge distribution of runoff；
(22) using Copula function as tool, the Joint Distribution and forecast of same period diameter of adjacent time interval measuring runoff are established
The Joint Distribution of stream and measuring runoff；
Assuming that the edge distribution of stochastic variable X, Y are respectively as follows:
FX(x)=P (X≤x) (3)；
FY(y)=P (Y≤y) (4)；
The Joint Distribution of X, Y are as follows:
FX,Y(x, y)=P (X≤x, Y≤y) (5)；
According to Sklar theorem: enabling F is a bivariate distribution function, edge distribution u=FX(x), v=FY(y)；Then deposit
In a dimensional Co pula function C, so as to any x,Have:
FX,Y(x, y)=C (u, v)=C (FX(x),FY(y)) (6)；
Using two kinds of Archimedean Copula family common Copula functions, i.e. Gumbel-Hougaard
Copula Frank Copula is fitted stochastic variable X, the Joint Distribution of Y；
Gumbel-Hougaard Copula function formula are as follows:
Frank Copula function formula are as follows:
Wherein, θ is the structure relevant parameter of Copula function, can be straight with the relationship of Kendall rank correlation coefficient according to it
Connect calculating；
As stochastic variable X, Y is the measuring runoff of adjacent time interval, or measuring runoff and forecast runoff for the same period
When, using above-mentioned Copula function, the Joint Distribution and forecast of same period runoff of adjacent time interval measuring runoff are established respectively
With the Joint Distribution of measuring runoff；
(23) condition probability formula is used, the prior state transition probability and description diameter of description runoff itself randomness are calculated
Stream forecasts probabilistic likelihood probability
The Joint Distribution F of known stochastic variable X, YX,Y(x, y) gives x1<X≤x2, Y≤y2Condition probability formula are as follows:
In formula, C (*) is a kind of given Copula function；U=FX(x), v=FYIt (y) is the edge distribution of X, Y；ui=
FX(xi), vi=FY(yi), i=1,2；
At this point, given x1<X≤x2, y1<Y≤y2Conditional probability calculation formula are as follows:
P(Y∈(y1,y2]|X∈(x1,x2])=P (Y≤y2|x1<X≤x2)-P(Y≤y1|x1<X≤x2) (10)；
If the measuring runoff q that given stochastic variable X is period tt, and qt∈(x1,x2], stochastic variable Y is period t+1's
Measuring runoff qt+1, and qt+1∈(y1,y2], then the prior state transition probability of t+1 period runoff can be calculated by formula (10)；
If the measuring runoff q that given stochastic variable X is period tt, and qt∈(x1,x2], stochastic variable Y is the pre- of period t
Report runoff qf t, and qf t∈(y1,y2], then the likelihood probability of t period runoff can also be calculated by formula (10).
(24) total probability formula of the Bayes' theorem based on formula (2) and formula (1), the posteriority state for calculating runoff turn
Move probability and predictability probability.
Further, Hydropower Plant Reservoir random optimization is dispatched to consider the phase under runoff uncertainty in the step (3)
Generated energy is hoped to be up to target, objective function indicates are as follows:
Wherein, f is the greatest hope generated energy in schedule periods T；Bt(st-1,qt,st) go out for the power generation in the power station period t
Power；st-1And stRespectively period t reservoir just, last storage capacity；qtFor period t runoff；EqtFor expectation operator；△ t is scheduling slot；
Model need to meet the water balance constraint, storage capacity constraint, storage outflow constraint, generated output of Hydropower Station Reservoir Dispatching
Constraint, the constraint of reservoir indicatrix.
Further, in the step (3), when Runoff Forecast precision is very low, consider instead Runoff Forecast information can be missed
Scheduling decision is led, using without forecast SDP model extraction scheduling rule；When Runoff Forecast precision is higher, certainly using coupling runoff
Body randomness and the probabilistic Bayes SDP model extraction scheduling rule of forecast；In special circumstances, the runoff of present period is pre-
When breath entirely accurate of notifying, SDP model extraction scheduling rule is forecast using perfection；Three kinds of models are respectively as follows:
(a) without forecast SDP model
Prior state transition probability is calculated first with the probabilistic theoretical estimation method of runoff, then utilizes formula
(12) recurrence equation backward induction method shown in calculates, and obtains the scheduling rule that can instruct Hydropower Plant Reservoir actual motion；
Without forecast SDP model, the Runoff Forecast information of present period is not considered, only considers the random transferring rule of runoff itself
Rule；T period runoff by a upper period diameter stream mode qt-1It determines, reservoir operation decision is by measuring runoff qt-1And initial storage
st-1It codetermines；Recurrence equation without forecast SDP model are as follows:
Wherein, j is measuring runoff grading index；P(qt∈j|qt-1) be the t period runoff prior state transition probability；Bt
(st-1,qt∈j,st) be at the beginning of the t period, last storage capacity is respectively st-1And st, runoff qtImmediate effect when ∈ j；ft(st-1,qt-1) be
Given original state is st-1,qt-1In the case of, the greatest hope benefit of period t to T；
(b) BSDP model
Prior state transition probability, likelihood probability are calculated first with the probabilistic theoretical estimation method of runoff, and is led to
It crosses Bayes' theorem and total probability formula obtains the posteriority state transition probability and predictability probability of runoff, then utilize formula
(13) recurrence equation backward induction method shown in calculates, and obtains the scheduling rule that can instruct Hydropower Plant Reservoir actual motion；
BSDP model also utilizes Bayes' theorem by Runoff Forecast other than the random transferring rule for considering runoff itself
Uncertainty is in the form of likelihood probability in view of in recurrence equation；T period runoff is by previous period diameter stream mode qt-1With this when
The Runoff Forecast q of sectionf tCommon to determine, reservoir operation decision is by measuring runoff qt-1, forecast runoff qf tWith initial storage st-1Certainly
It is fixed；The recurrence equation of BSDP model at this time are as follows:
Wherein, j, k are respectively the grading index of measuring runoff and forecast runoff；qf tAnd qf t+1Respectively t period and when t+1
The Runoff Forecast value of section；P(qt∈j|qt-1,qf t) be t period runoff posteriority state transition probability；P(qf t+1∈k|qt∈ j) be
The predictability probability of the runoff of t+1 period；
(c) perfect forecast SDP model
Prior state transition probability is calculated first with the probabilistic theoretical estimation method of runoff, then utilizes formula
(14) recurrence equation backward induction method shown in calculates, and obtains the scheduling rule that can instruct Hydropower Plant Reservoir actual motion；
Perfection forecast SDP model assumption present period has accurate Runoff Forecast information, and the Runoff Forecast value of t period is equal to
Measured value, i.e. qf t=qt；The reservoir operation decision of t period is by measuring runoff qtWith initial storage st-1It codetermines；Perfection forecast
The recurrence equation of SDP model are as follows:
Wherein, j is measuring runoff grading index；P(qt+1∈j|qt) be the t+1 period runoff prior state transition probability；
Bt(st-1,qt,st) be at the beginning of the t period, last storage capacity is respectively st-1And st, runoff qtWhen immediate effect；ft(st-1,qt) be to
Determining original state is st-1,qtIn the case of, the greatest hope benefit of period t to T.
The utility model has the advantages that compared with prior art, the invention has the following advantages that
(1) Conventional wisdom estimation method is breached when quantifying runoff uncertainty, is limited by measuring runoff sample completely
Defect.The state transition probability of Conventional wisdom estimation method calculates the history runoff sample that places one's entire reliance upon, and uses with frequency generation
It is obtained for the experience estimation method of probability.Enable P (qt+1∈j|qt∈i)、P(qf t∈j|qt∈ i) respectively indicate t period measured path
When stream is grade i, the likelihood probability of t+1 period prior state transition probability and t period.Due to history runoff Finite Samples, pass
Often there are two disadvantages in system method: 1) the prior state transition probability when the t period being in grade i without history measuring runoff data
It will be unable to calculate with likelihood probability；2) grade j or the t period is in without history forecast diameter without history measuring runoff when the t+1 period
When stream is in grade j, it will appear a large amount of 0 value in prior state transition probability and likelihood probability matrix.Due to hydrology phenomenon
Randomness and ambiguity rely on 0 value of the state transition probability that history runoff sample calculates, sometimes and unreasonable.Theory estimation
Method realizes the interpolation and extension of runoff, overcomes conventional method by establishing measuring runoff and forecasting the edge distribution of runoff
The shortcomings that.
(2) it calculates easier.Theoretical estimation method only needs to calculate adjacent time interval measuring runoff and the same period is real
The Joint Distribution for surveying and forecasting runoff, can be obtained the display expression formula of prior state transition probability and likelihood probability.Then, base
In Bayes' theorem and total probability formula, the posteriority state transition probability and predictability probability of runoff can be calculated.The present invention pushes away
The Joint Distribution using Archimedean Copula Function Fitting runoff is recommended, a structure relevant parameter θ, and θ are contained only
It can directly be calculated according to the relationship of itself and Kendall rank correlation coefficient.Although and experience estimation method calculate thinking it is simple,
Calculation amount is larger.Especially when history runoff sample size is inadequate, it is also necessary to which Mr. increases calculating at artificial runoff sample
Amount.
(3) it avoids and generates artificial runoff sample.Theoretical estimation method can be realized pair by establishing the edge distribution of runoff
The interpolation and extension of runoff avoid and generate artificial runoff sample by other Runoff Simulations, reduce introduce runoff with
Machine simulation model bring is uncertain.Moreover, being considered as forecast is uncertain in sdp, will not only calculate runoff certainly
The state transition probability of period, also wants the state transition probability of CALCULATING PREDICTION runoff and measuring runoff before and after body.At this point, will be simultaneously
Generate artificial Fuzzy Period of Runoff Series and it forecast Fuzzy Period of Runoff Series, without change original runoff characteristic and its to forecast the related of Fuzzy Period of Runoff Series
Relationship characteristic, it is substantially impossible.
(4) data space greatly reduces.Experience estimation method needs to store the state transition probability of each period, institute
Need data space with the increase exponentially type growth of runoff grade and state variable.And theoretical estimation method only needs to deposit
The runoff edge distribution parameter and Joint Distribution parameter for storing up day part, i.e., calculate state transition probability using formula in real time.With
For edge distribution uses Archimedean Copula function using Pearson III distribution, Joint Distribution, theoretical estimation side
Each period of method need to only store three parameters (mean values, C of edge distributionv、Cs) it is related to a structure of Copula function ginseng
Number (θ), greatly saves data space.
(5) benefit of random optimization scheduling is improved.It is not true that theoretical estimation method overcomes experience estimation method quantization runoff
Qualitative defect reduces due to introducing Runoff model bring uncertainty, it is probabilistic that runoff can be improved
Quantified precision, and then improve random optimization and dispatch benefit.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart；
Fig. 2 is runoff analysis of uncertainty flow chart；
Fig. 3 is NF-SDP model recursive process figure；
Fig. 4 is BSDP model recursive process figure；
Fig. 5 is PF-SDP model recursive process figure.
Specific embodiment
Technical solution of the present invention is described in detail in the following with reference to the drawings and specific embodiments.
A kind of random optimization dispatching method towards Hydropower Plant Reservoir of the invention, as shown in Figure 1, having initially set up runoff
And its forecast uncertain quantitative model, then using Copula function as theoretical basis, proposes runoff and its forecast is uncertain
Property theoretical estimation method, finally consider practical Runoff Forecast level, establish the SDP model under different stream flow description modes,
To extract scheduling rule, the actual motion of Hydropower Plant Reservoir is instructed.Specifically:
(1) runoff and its forecast uncertainty description model are established
(11) in order to describe runoff itself randomness, runoff prior state transition probability is established
Runoff is considered as a simple single order markoff process by the present invention, and with runoff state transition probability Pt-1 ijCome
The randomness of runoff itself, i.e. P are describedt-1 ij=P [qt∈j|qt-1∈ i], it indicates the runoff q of known period t-1t-1For grade
When i, the runoff q of period ttFor the probability of grade j.
Due to runoff state transition probability Pt-1 ijIt is to be obtained on the basis of not obtaining any Runoff Forecast information, by it
Referred to as runoff prior state transition probability.
(12) according to Runoff Forecast uncertainty, the likelihood probability of diameter stream mode transfer is established, and further establishes runoff
Predictability probability；
Present invention likelihood probability Pt jkIndicate the uncertainty of Runoff Forecast, i.e. Pt jk=P [qf t∈k|qt∈ j], its table
Show period t measured path flow valuve qtWhen in grade j, diameter flow valuve q is forecastf tProbability in grade k.The size of likelihood probability and pre-
Report is horizontal closely bound up, when forecast precision is higher, forecasts that diameter flow valuve and measured path flow valuve take the probability of same levels higher.Cause
This, forecasts that the likelihood probability matrix of runoff and measuring runoff can reflect prediction error information.
After obtaining runoff prior state transition probability and likelihood probability, runoff is obtained using total probability formula
Predictability probability Pt jl, i.e. Pt jl=P [qf t+1∈l|qt∈ j], when it indicates that the practical runoff of period t is in grade j, the t+1 period
Prediction runoff is in the probability of grade l.The predictability probability calculation formula of runoff are as follows:
(13) posterior probability of diameter stream mode transfer is obtained
Due to runoff state transition probability Pt-1 ijIt is to be obtained on the basis of not obtaining any Runoff Forecast information, by it
Referred to as runoff prior state transition probability.Once getting new forecast information, using Bayes' theorem, runoff shape is derived
The posterior probability of state transfer.In this way, as Runoff Forecast information constantly rolls update, it can be constantly to prior state transition probability
It is modified, to improve stream flow description precision.The calculation formula of the posterior probability of diameter stream mode transfer are as follows:
(2) runoff and its probabilistic theoretical estimation method of forecast are proposed
The present invention initially sets up day part measuring runoff and forecasts the edge distribution of runoff；It is then based on Copula function,
Establish the Joint Distribution of adjacent time interval measuring runoff and the actual measurement of same period and forecast runoff；Then, straight according to the derivation of equation
It connects to obtain the calculation formula of state transition probability.Based on this, runoff and its forecast for proposing complete set are uncertain
Theoretical estimation method process.As shown in Fig. 2, mainly including following sub-step:
(21) using measuring runoff sample and forecast runoff sample as data basis, day part measuring runoff and pre- is established respectively
Report the edge distribution of runoff；
It is provided according to " Design of Water Resources and Hydroelectric Projects Calculation of Flood specification " (SL44-2006), the line style of frequency curve
III type of Pearson came (P-III type) curve is generally used, other line styles can be used in special circumstances after analytic demonstration.Therefore, this hair
The bright edge distribution for recommending to establish runoff using the distribution of P-III type, can also be used other distributions through demonstration in practice.
The probability density function of P-III type distribution are as follows:
In formula: Γ (α) is the gamma function of α；α,β,a0Respectively shape, scale and the location parameter of P-III type distribution,
α > 0, β > 0.Three statistical parameter mean values of these three parameters and population sampleCoefficient of variation Cv, coefficient of skew CsIt can be mutual
Inquire into, there is following relationship:
(22) using Copula function as tool, the Joint Distribution and forecast of same period diameter of adjacent time interval measuring runoff are established
The Joint Distribution of stream and measuring runoff
Assuming that the edge distribution of stochastic variable X, Y are respectively as follows:
FX(x)=P (X≤x) (5)；
FY(y)=P (Y≤y) (6)；
The Joint Distribution of X, Y are as follows:
FX,Y(x, y)=P (X≤x, Y≤y) (7)；
According to Sklar theorem: enabling F is a bivariate distribution function, edge distribution u=FX(x), v=FY(y)；Then deposit
In a dimensional Co pula function C, so as to any x,Have:
FX,Y(x, y)=C (u, v)=C (FX(x),FY(y)) (8)；
Archimedean Copula is a kind of important Copula function, and it is excellent that construction is convenient due to it, is easy to use etc.
Point is widely used in hydrology field.The present invention recommends to use two kinds of common Copula of Archimedean Copula family
Function, i.e. Gumbel-Hougaard Copula or Frank Copula are fitted stochastic variable X, the Joint Distribution of Y；
Gumbel-Hougaard Copula function formula are as follows:
Frank Copula function formula are as follows:
Wherein, θ is the structure relevant parameter of Copula function, can be straight with the relationship of Kendall rank correlation coefficient according to it
Connect calculating；
As stochastic variable X, Y is the measuring runoff of adjacent time interval, or measuring runoff and forecast runoff for the same period
When, using above-mentioned derivation process, the Joint Distribution and forecast of same period runoff of adjacent time interval measuring runoff are established respectively
With the Joint Distribution of measuring runoff.
(23) condition probability formula is used, the prior state transition probability and description diameter of description runoff itself randomness are calculated
Stream forecasts probabilistic likelihood probability
The Joint Distribution F of known stochastic variable X, YX,Y(x, y) gives x1<X≤x2, Y≤y2Condition probability formula are as follows:
In formula, C (*) is a kind of given Copula function；U=FX(x), v=FYIt (y) is the edge distribution of X, Y；ui=
FX(xi), vi=FY(yi), i=1,2；
At this point, given x1<X≤x2, y1<Y≤y2Conditional probability calculation formula are as follows:
P(Y∈(y1,y2]|X∈(x1,x2])=P (Y≤y2|x1<X≤x2)-P(Y≤y1|x1<X≤x2) (12)；
If the measuring runoff q that given stochastic variable X is period tt, and qt∈(x1,x2], stochastic variable Y is period t+1's
Measuring runoff qt+1, and qt+1∈(y1,y2], then the prior state transition probability of t+1 period runoff can be calculated by formula (12)；
If the measuring runoff q that given stochastic variable X is period tt, and qt∈(x1,x2], stochastic variable Y is the pre- of period t
Report runoff qf t, and qf t∈(y1,y2], then the likelihood probability of t period runoff can also be calculated by formula (12).
(24) total probability formula of the Bayes' theorem based on formula (2) and formula (1), the posteriority state for calculating runoff turn
Move probability and predictability probability.
(3) the SDP model under different stream flow description modes is constructed, scheduling rule is extracted, instructs the practical fortune of Hydropower Plant Reservoir
Row
The scheduling of Hydropower Plant Reservoir random optimization is up to target, mesh with the expectation generated energy considered under runoff uncertainty
Scalar functions indicate are as follows:
Wherein, f is the greatest hope generated energy in schedule periods T；Bt(st-1,qt,st) go out for the power generation in the power station period t
Power；st-1And stRespectively period t reservoir just, last storage capacity；qtFor period t runoff；EqtFor expectation operator；△ t is scheduling slot；
Model should meet following constraint condition:
Water balance constraint:
st=st-1+(qt-rt)△t (14)；
Storage capacity constraint:
st,min≤st≤st,max(15)；
Traffic constraints:
rt,min≤rt≤rt,max, qfd,t≤qfd,max(16)；
rt=qfd,t+qqs,t(17)；
Generated output constraint:
Nt=A*qfd,t*△Ht(18)；
Nt≤Nmax(19)；
Water level~storage-capacity curve constraint:
Zt=f (st), st=f-1(Zt) (20)；
Tailwater level~flow curve constraint:
Zdr,t=g (rt),rt=g-1(Zdr,t) (21)；
Wherein, rtIndicate the flow discharges of period t reservoir, m3/s；rt,max,rt,minRespectively indicate discharging water for period t reservoir
Flow upper and lower limit t, m3/s；st,max,st,minRespectively indicate the storage capacity upper and lower limit of period t reservoir, m3；qfd,t,qqs,tIt respectively indicates
The generating flow and abandoning water flow in period t power station, m3/s；qfd,maxIndicate the generating flow upper limit in the power station period t, m3/s；
Nt,NmaxRespectively indicate generated output and its installed capacity in period t power station, kW.h；A indicates power output coefficient of efficiency；△HtTable
Show period t productive head, m；Zt,Zdr,tRespectively indicate the water level and tailwater level of period t reservoir, m；F (*) indicates that water level-storage capacity closes
System's constraint；G (*) indicates tailwater level-discharge relation constraint.
According to whether considering that Runoff Forecast information and uncertainty, the present invention construct 3 kinds of SDP models.When runoff is pre-
When reporting precision very low, consider instead Runoff Forecast information can mislead scheduling decision, the present invention recommends to mention using without forecast SDP model
Take scheduling rule；When Runoff Forecast precision is higher, the present invention recommends uncertain using coupling runoff itself randomness and forecast
The BSDP model extraction scheduling rule of property.In special circumstances, when the Runoff Forecast information entirely accurate of present period, recommend to use
Perfection forecast SDP model extraction scheduling rule.It is horizontal according to practical Runoff Forecast, following three kinds of embodiments can be established respectively:
1) embodiment 1- is without forecast SDP model
Without forecast SDP (No Forecasting SDP, NF-SDP) model, the Runoff Forecast letter of present period is not considered
Breath only considers the random transferring rule of runoff itself.T period runoff by a upper period diameter stream mode qt-1It determines, reservoir operation
Decision is by measuring runoff qt-1With initial storage st-1It codetermines.The recurrence equation of NF-SDP model are as follows:
Wherein, j is measuring runoff grading index；P(qt∈j|qt-1) be the t period runoff prior state transition probability；Bt
(st-1,qt∈j,st) be at the beginning of the t period, last storage capacity is respectively st-1、st, runoff qtImmediate effect when ∈ j；ft(st-1,qt-1) be
Given original state is st-1,qt-1In the case of, the greatest hope benefit of period t to T.The recursive process of NF-SDP model is shown in attached drawing
3。
Embodiment 1 calculates prior state transfer first with the probabilistic theoretical estimation method of runoff proposed by the present invention
Probability, is then calculated using recurrence equation backward induction method shown in formula (22), and acquisition can instruct Hydropower Plant Reservoir actual motion
Scheduling rule.It is real using the measuring runoff grade of previous period and initial storage as scheduling discriminant criterion in actual schedule
When determine the last storage capacity state of this period.
2) embodiment 2-BSDP model
BSDP is not also true by Runoff Forecast using Bayes' theorem other than the random transferring rule for considering runoff itself
It is qualitative to be considered in recurrence equation in the form of likelihood probability.T period runoff is by previous period diameter stream mode qt-1With this period
Runoff Forecast qf tCommon to determine, reservoir operation decision is by measuring runoff qt-1, forecast runoff qf tWith initial storage st-1It determines.This
When BSDP model recurrence equation are as follows:
Wherein, j, k are respectively the grading index of measuring runoff and forecast runoff；qf tAnd qf t+1Respectively t period and when t+1
The Runoff Forecast value of section；P(qt∈j|qt-1,qf t) be t period runoff posteriority state transition probability；P(qf t+1∈k|qt∈ j) be
The predictability probability of the runoff of t+1 period.The recursive process of BSDP model is shown in attached drawing 4.
Embodiment 2 calculates prior state transfer first with the probabilistic theoretical estimation method of runoff proposed by the present invention
Probability, likelihood probability, and the posteriority state transition probability of runoff is obtained by Bayes' theorem and total probability formula and can be predicted
Property probability, then calculated using recurrence equation backward induction method shown in formula (23), acquisition can instruct the practical fortune of Hydropower Plant Reservoir
Capable scheduling rule.In actual schedule, using the measuring runoff grade of previous period, the forecast runoff grade of this period, and
Initial storage state determines the last storage capacity state of this period as scheduling discriminant criterion in real time.
3) SDP model is forecast in embodiment 3- perfection
Perfection forecast SDP (Perfect Forecasting SDP, PF-SDP) model assumption present period has accurate diameter
Flow forecast information.The Runoff Forecast value of t period is equal to measured value, i.e. qf t=qt.The reservoir operation decision of t period is by measuring runoff
qtWith initial storage st-1It codetermines.The recurrence equation of PF-SDP model are as follows:
Wherein, j is measuring runoff grading index；P(qt+1∈j|qt) be the t+1 period runoff prior state transition probability；
Bt(st-1,qt,st) be at the beginning of the t period, last storage capacity is respectively st-1And st, runoff qtWhen immediate effect；ft(st-1,qt) be to
Determining original state is st-1,qtIn the case of, the greatest hope benefit of period t to T.The recursive process of PF-SDP model is shown in attached drawing 5.
Embodiment 3 calculates prior state transfer first with the probabilistic theoretical estimation method of runoff proposed by the present invention
Probability, is then calculated using recurrence equation backward induction method shown in formula (24), and acquisition can instruct Hydropower Plant Reservoir actual motion
Scheduling rule.In actual schedule, using the measuring runoff grade of this period and initial storage state as scheduling discriminant criterion,
The last storage capacity state of this period is determined in real time.
Claims (1)
1. a kind of random optimization dispatching method towards Hydropower Plant Reservoir, which comprises the following steps:
(1) runoff and its probabilistic quantitative model of forecast are established；Specifically:
(11) in order to describe runoff itself randomness, runoff prior state transition probability is established；
Runoff is considered as a simple single order markoff process, and with runoff state transition probability Pt-1 ijTo describe runoff certainly
The randomness of body, i.e. Pt-1 ij=P [qt∈j|qt-1∈ i], it indicates the runoff q of known period t-1t-1When for grade i, period t
Runoff qtFor the probability of grade j；
Due to runoff state transition probability Pt-1 ijIt is to be obtained on the basis of not obtaining any Runoff Forecast information, is referred to as
For runoff prior state transition probability；
(12) according to Runoff Forecast uncertainty, establish the likelihood probability of diameter stream mode transfer, and further establish runoff can
Predictive probability；
With likelihood probability Pt jkIndicate the uncertainty of Runoff Forecast, i.e. Pt jk=P [qf t∈k|qt∈ j], it indicates period t actual measurement
Diameter flow valuve qtWhen in grade j, diameter flow valuve q is forecastf tProbability in grade k；
After obtaining runoff prior state transition probability and likelihood probability, the predictable of runoff is obtained using total probability formula
Property probability Pt jl, i.e. Pt jl=P [qf t+1∈l|qt∈ j], when it indicates that the practical runoff of period t is in grade j, the t+1 period calibrates in advance
Stream is in the probability of grade l；The predictability probability calculation formula of runoff are as follows:
(13) posterior probability of diameter stream mode transfer is obtained；
The posterior probability of diameter stream mode transfer is derived using Bayes' theorem according to the new forecast information got；In this way,
As Runoff Forecast information constantly rolls update, constantly runoff prior state transition probability is modified, diameter stream mode turns
The calculation formula of the posterior probability of shifting are as follows:
(2) runoff and its probabilistic theoretical estimation method of forecast are proposed；Specifically:
(21) using measuring runoff sample and forecast runoff sample as data basis, day part measuring runoff and forecast diameter are established respectively
The edge distribution of stream；
(22) using Copula function as tool, establish adjacent time interval measuring runoff Joint Distribution and the same period forecast runoff and
The Joint Distribution of measuring runoff；
Assuming that the edge distribution of stochastic variable X, Y are respectively as follows:
FX(x)=P (X≤x) (3)；
FY(y)=P (Y≤y) (4)；
The Joint Distribution of X, Y are as follows:
FX,Y(x, y)=P (X≤x, Y≤y) (5)；
According to Sklar theorem: enabling F is a bivariate distribution function, edge distribution u=FX(x), v=FY(y)；Then have one
A dimensional Co pula function C, so as to any x,Have:
FX,Y(x, y)=C (u, v)=C (FX(x),FY(y)) (6)；
Using two kinds of Archimedean Copula family common Copula functions, i.e. Gumbel-Hougaard Copula
Or Frank Copula, it is fitted stochastic variable X, the Joint Distribution of Y；
Gumbel-Hougaard Copula function formula are as follows:
Frank Copula function formula are as follows:
Wherein, θ is the structure relevant parameter of Copula function, can directly be counted according to the relationship of itself and Kendall rank correlation coefficient
It calculates；
When stochastic variable X, Y are the measuring runoff of adjacent time interval, or the measuring runoff for the same period is with forecast runoff, benefit
With above-mentioned Copula function, the Joint Distribution and same period for establishing adjacent time interval measuring runoff respectively forecast runoff and reality
Calibrate the Joint Distribution of stream；
(23) condition probability formula is used, prior state transition probability and the description runoff for calculating description runoff itself randomness are pre-
Report probabilistic likelihood probability；
The Joint Distribution F of known stochastic variable X, YX,Y(x, y) gives x1<X≤x2, Y≤y2Condition probability formula are as follows:
In formula, C (*) is a kind of given Copula function；U=FX(x), v=FYIt (y) is the edge distribution of X, Y；ui=FX
(xi), vi=FY(yi), i=1,2；
At this point, given x1<X≤x2, y1<Y≤y2Conditional probability calculation formula are as follows:
P(Y∈(y1,y2]|X∈(x1,x2])=P (Y≤y2|x1<X≤x2)-P(Y≤y1|x1<X≤x2) (10)；
If the measuring runoff q that given stochastic variable X is period tt, and qt∈(x1,x2], stochastic variable Y is the measured path of period t+1
Flow qt+1, and qt+1∈(y1,y2], then the prior state transition probability of t+1 period runoff can be calculated by formula (10)；
If the measuring runoff q that given stochastic variable X is period tt, and qt∈(x1,x2], stochastic variable Y is the forecast runoff of period t
qf t, and qf t∈(y1,y2], then the likelihood probability of t period runoff can also be calculated by formula (10)；
(24) total probability formula of the Bayes' theorem based on formula (2) and formula (1), the posteriority state transfer for calculating runoff are general
Rate and predictability probability；
(3) stochastic dynamic programming under different stream flow description modes is constructed, scheduling rule is extracted, to instruct Hydropower Plant Reservoir
Actual motion；
The scheduling of Hydropower Plant Reservoir random optimization is up to target, target letter with the expectation generated energy considered under runoff uncertainty
Number indicates are as follows:
Wherein, f is the greatest hope generated energy in schedule periods T；Bt(st-1,qt,st) be the power station period t generated output；st-1
And stRespectively period t reservoir just, last storage capacity；qtFor period t runoff；For expectation operator；△ t is scheduling slot；
Model need to meet Hydropower Station Reservoir Dispatching water balance constraint, storage capacity constraint, storage outflow constraint, generated output about
Beam, the constraint of reservoir indicatrix；
When Runoff Forecast precision is very low, consider Runoff Forecast information instead can mislead scheduling decision, using without forecast with motor-driven
State plan model extracts scheduling rule；When Runoff Forecast precision is higher, using coupling runoff itself randomness and forecast not true
Qualitative Bayes's stochastic dynamic programming extracts scheduling rule；In special circumstances, the Runoff Forecast information of present period is complete
When complete accurate, scheduling rule is extracted using perfection forecast stochastic dynamic programming；Three kinds of models are respectively as follows:
(a) without forecast stochastic dynamic programming；
Prior state transition probability is calculated first with the probabilistic theoretical estimation method of runoff, then utilizes formula (12) institute
The recurrence equation backward induction method shown calculates, and obtains the scheduling rule that can instruct Hydropower Plant Reservoir actual motion；
Without forecast stochastic dynamic programming, the Runoff Forecast information of present period is not considered, only considers the random of runoff itself
Metastatic rule；T period runoff by a upper period diameter stream mode qt-1It determines, reservoir operation decision is by measuring runoff qt- 1 and just
Beginning storage capacity st-1It codetermines；Recurrence equation without forecast stochastic dynamic programming are as follows:
Wherein, j is measuring runoff grading index；P(qt∈j|qt-1) be the t period runoff prior state transition probability；Bt(st-1,
qt∈j,st) be at the beginning of the t period, last storage capacity is respectively st-1And st, runoff qtImmediate effect when ∈ j；ft(st-1,qt-1) it is given
Original state is st-1,qt-1In the case of, the greatest hope benefit of period t to T；
(b) Bayes's stochastic dynamic programming；
Prior state transition probability, likelihood probability are calculated first with the probabilistic theoretical estimation method of runoff, and passes through shellfish
This theorem of leaf and total probability formula obtain the posteriority state transition probability and predictability probability of runoff, then utilize formula (13)
Shown in recurrence equation backward induction method calculate, the scheduling rule of Hydropower Plant Reservoir actual motion can be instructed by obtaining；
Bayes's stochastic dynamic programming also utilizes Bayes' theorem other than the random transferring rule for considering runoff itself
By Runoff Forecast uncertainty in view of in recurrence equation in the form of likelihood probability；T period runoff is by previous period runoff shape
State qt-1With the Runoff Forecast q of this periodf tCommon to determine, reservoir operation decision is by measuring runoff qt-1, forecast runoff qf tWith it is initial
Storage capacity st-1It determines；The recurrence equation of Bayes's stochastic dynamic programming at this time are as follows:
Wherein, j, k are respectively the grading index of measuring runoff and forecast runoff；qf tAnd qf t+1Respectively t period and t+1 period
Runoff Forecast value；P(qt∈j|qt-1,qf t) be t period runoff posteriority state transition probability；P(qf t+1∈k|qt∈ j) it is t+1
The predictability probability of the runoff of period；
(c) perfect forecast stochastic dynamic programming；
Prior state transition probability is calculated first with the probabilistic theoretical estimation method of runoff, then utilizes formula (14) institute
The recurrence equation backward induction method shown calculates, and obtains the scheduling rule that can instruct Hydropower Plant Reservoir actual motion；
Perfection forecast stochastic dynamic programming assumes that present period has accurate Runoff Forecast information, the Runoff Forecast of t period
Value is equal to measured value, i.e. qf t=qt；The reservoir operation decision of t period is by measuring runoff qtWith initial storage st-1It codetermines；It is complete
The recurrence equation of U.S. forecast stochastic dynamic programming are as follows:
Wherein, j is measuring runoff grading index；P(qt+1∈j|qt) be the t+1 period runoff prior state transition probability；Bt
(st-1,qt,st) be at the beginning of the t period, last storage capacity is respectively st-1And st, runoff qtWhen immediate effect；ft(st-1,qt) it is given
Original state is st-1,qtIn the case of, the greatest hope benefit of period t to T.
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