CN113869646A - Reservoir flood control risk scheduling method under design flood comprehensive uncertainty - Google Patents

Reservoir flood control risk scheduling method under design flood comprehensive uncertainty Download PDF

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CN113869646A
CN113869646A CN202111006745.5A CN202111006745A CN113869646A CN 113869646 A CN113869646 A CN 113869646A CN 202111006745 A CN202111006745 A CN 202111006745A CN 113869646 A CN113869646 A CN 113869646A
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flood
reservoir
risk
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郭爱军
王义民
杨笛
畅建霞
吴彬
赵月欣
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Xian University of Technology
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Abstract

The invention discloses a reservoir flood control risk scheduling method under the design flood comprehensive uncertainty, which comprises the steps of estimating a parameter vector of a joint distribution function by using a maximum likelihood method; extracting a two-dimensional sample with the length equal to the length of the actually measured data from the sample by using a Monte Carlo method; estimating parameters of each group of simulation samples to obtain N groups of joint distribution function parameter vectors; calculating two-dimensional joint design values under different recurrence period types; calculating the design flood under the multidimensional uncertainty; and establishing a reservoir flood control optimal scheduling model based on CVaR risk measurement indexes to realize flood control risk scheduling. According to the reservoir flood control optimal scheduling method based on the CVaR risk measurement indexes, the CVaR risk measurement indexes are established, and risk measurement is carried out on the reservoir flood control optimal scheduling model, so that support is provided for making an actual flood control scheduling decision.

Description

Reservoir flood control risk scheduling method under design flood comprehensive uncertainty
Technical Field
The invention belongs to the technical field of hydraulic engineering planning, and relates to a reservoir flood control risk scheduling method under the condition of flood comprehensive uncertainty.
Background
Designing flood is an important basis for planning design and operation management of hydraulic engineering. The determination of reservoir engineering scale, the preparation of flood control dispatching rules and the like are obtained by calculation on the premise of deterministic design flood, but the calculation of the design flood is influenced by multiple uncertain factors, such as sample uncertainty, uncertainty of a typical flood process and the like. The method for calculating reservoir flood control dispatching rules under the uncertainty of flood design is a necessary way for ensuring the robustness of the flood control dispatching rules in practical application.
So far, many achievements have been formed in domestic and foreign research on uncertainty of design flood, the influence of factors such as uncertainty of probability distribution function parameters, uncertainty of probability distribution function types, uncertainty of samples and the like on a design flood peak value or flood is mainly disclosed by adopting a Bayes theory or a Monte Carlo method, and multi-dimensional design flood uncertainty research is developed on the basis of simulating the correlation of the design flood peak value and the flood by using a Copula function. Reis et al sampled the distribution parameters using a markov-monte carlo (MCMC) sampling method, quantitatively evaluated the uncertainty of the parameters and demonstrated the effectiveness of the bayes method. Yin and the like adopt Copula functions to construct a combined distribution model of peak flow and flood, and adopt a parameter Bootstrap sampling method to evaluate the influence of sample uncertainty on the calculation of a two-variable combined flood design value. Guo et al analyzed the influence of uncertainty of edge distribution type and uncertainty of samples on the two-dimensional combined design value of flood peak and rainfall in frequency calculation by introducing the maximum entropy theory. Lufan et al take the Dangjiang mouth reservoir as an example, adopt a Bayesian MCMC method based on Metropolis-Hastings sampling algorithm to estimate the posterior distribution of the design flood, and carry out frequency analysis accordingly. The beam loyalty and the like research the uncertainty of the parameters and the function types of the probability distribution function in the hydrologic design value calculation, and provide a hydrologic frequency analysis method based on the Bayesian theory. Huimines et al investigated the effect of sample uncertainty on hydrologic design values using the boottrap method and evaluated it quantitatively. Zhengetering and the like provide a flood control project design flood risk assessment method considering uncertainty, a non-uniform flood sequence is fitted according to mixed probability distribution, the mixed distribution is resampled, and the influence of sample uncertainty on design flood risk calculation is assessed by adopting a bias correction and acceleration algorithm. In addition to the uncertainty of designing the flood peak value and the magnitude, the uncertainty of designing the flood process line (such as the occurrence time of the flood peak, the shape of the flood process line, and the like) is also an important factor influencing the reservoir flood control dispatching rule, and the past research is less involved in simultaneously considering the uncertainty of designing the flood peak value, the magnitude and the process line.
As described above, uncertainty in designing floods necessarily affects the scale of hydraulic and hydroelectric engineering design and its operational management. The method comprises the steps of constructing a combined distribution model of the flood peak and the flood volume by using the plum singing and the like, randomly sampling, generating a flood process based on different flood categories, calculating reservoir dispatching risks corresponding to different risk factor combinations by using a Monte Carlo method, and providing a certain reference for reasonably utilizing flood resources. A C-PBU (Copula-based Parametric Bootstrap Uncertainty) model for describing bivariate design flood Uncertainty is established by Yi Jia Bo, Guosheng, and the like, the influence of Uncertainty of a joint design value on the highest regulated flood level of a reservoir is analyzed, and the Uncertainty of the water level in different typical flood processes is compared. The method is characterized in that a flood random simulation method considering peak type and frequency is provided at the Yan side and the like, peak type coefficients and peak occurrence time are introduced, random simulation of flood characteristic quantity and flood process lines of different types is carried out, the method is applied to flood control dispatching calculation, and the method has important significance for formulation of reservoir flood control dispatching rules and risk analysis. Requena and the like adopt Copula functions to construct joint distribution of peak flood volume, generate multi-field design flood based on actual measurement flood process, and evaluate overtopping risk of the dam. In conclusion, scholars at home and abroad carry out a great deal of research on the aspect of evaluating the influence of uncertainty of design flood on flood control safety of a reservoir, but most of the research adopts the existing flood control rules of the reservoir in the process, neglects that the existing flood control rules of the reservoir are obtained under the assumption of the certainty of the design flood, and has natural contradiction with the starting point of the research, namely the uncertainty of the calculation of the design flood which is not negligible.
Disclosure of Invention
The invention aims to provide a reservoir flood control risk scheduling method under the design flood comprehensive uncertainty, which aims at the multi-dimensional uncertainty of a design flood peak value, magnitude and a process line, establishes a reservoir flood control optimal scheduling model based on CVaR (conditional value at risk) risk measurement indexes for carrying out risk measurement, and provides support for making an actual flood control scheduling decision.
The technical scheme adopted by the invention is as follows: the reservoir flood control risk scheduling method under the flood comprehensive uncertainty is designed, and specifically comprises the following steps:
step 1, estimating a joint distribution function H (H, y; theta) to C (F (H; theta) by a maximum likelihood methodh),F(y；θy)；θ0) Is (theta) is given as the parameter vector of (theta)h,θy；θ0) In the function, variables h and y are the annual maximum flood peak value and magnitude respectively;
step 2, based on the combined distribution function, a Monte Carlo method is applied to extract a two-dimensional sample with the length equal to the length of the actually measured data from the combined distribution function, and the two-dimensional sample is randomly extracted for N times;
step 3, estimating parameters of each group of simulation samples by adopting a maximum likelihood method to obtain N groups of joint distribution function parameter vectors;
step 4, calculating two-dimensional joint design values under different recurrence period types under each group of parameter vectors;
step 5, calculating the design flood under the multidimensional uncertainty based on the two-dimensional joint design value under each group of parameter vectors;
and 6, establishing a reservoir flood control optimal scheduling model based on the CVaR risk measurement indexes, and realizing flood control risk scheduling.
The present invention is also characterized in that,
the two-dimensional joint design values under different types of the recurrence periods are calculated in step 4 specifically,
probability K that the probability W of the joint distribution of the characteristic quantities is less than or equal to t at a given probability level te (0,1)cThe expression of (a) is:
Kc(t)＝P(W≤t)＝P(C(u,v)≤t) (1)
in formula (1): c (u, v) is a Copula function, KcFor a kendall measure, P represents the probability;
then with KcIndicated kendall recurrence period TkComprises the following steps:
Figure RE-GDA0003384845250000041
calculating a combined design value of flood by adopting a most probable combination method, wherein the most probable combined design value is a combined design value which is the maximum corresponding to the combined probability density of flood peak and flood volume under the condition of meeting a specified flood control standard T, and the calculation formula of the combined design value of flood is as follows:
Figure RE-GDA0003384845250000042
f(x,y)＝c(u,v)f(x)f(y) (4)
in formula (3): (x)m,ym) For the joint design value of the flood,
Figure RE-GDA0003384845250000044
the method is characterized in that the method is an isoline formed by peak amount combinations with the same recurrence period, and f (x, y) is a combined probability density function of a flood peak and a flood amount;
in formula (4): f (x), f (y) are edge probability density functions respectively; c (u, v) is a probability density function of Copula.
The step 5 specifically comprises the following steps:
the dimensionless flood accumulation curve is equally divided into K time periods, and the dimensionless time is carried out at the time
Figure RE-GDA0003384845250000043
Corresponding dimensionless cumulative flood volume is FiThen the dimensionless flood volume per time interval is Pi＝Fi-Fi-1F for each period of each flood processiOr PiAs input, classifying the data by adopting a K-means clustering method based on Euclidean distance;
for the classified flood process, F is firstly carried outiOr PiCarrying out logarithmic transformation, namely, transforming the constrained related non-normal multivariable into the unconstrained related non-normal multivariable, carrying out normal transformation by adopting a Johnson system function to transform the constrained related non-normal multivariable into the related standard normal multivariable, carrying out orthogonal transformation by Cholesky decomposition to transform the independent standard normal multivariable into the independent standard normal multivariable, and finally generating the independent standard normal multivariable by adopting Monte Carlo simulation to carry out inverse transformation;
and fusing the generated dimensionless flood process line with the flood peak and the flood volume obtained by simulation in a variable magnification mode, so that a complete flood process can be generated, and a plurality of designed flood sequences are obtained.
The step 6 specifically comprises the following steps:
establishing a target function, namely a reservoir flood control optimal scheduling model:
minG(x)＝(1-λ)E(x)+λCVaR(x) (5)
in the formula (5), x is the maximum flood regulation storage capacity of each flood, g (x) is the sum of potential risk and expected risk in the reservoir dispatching process under the influence of uncertainty factors, e (x) is the expectation of the maximum flood regulation storage capacity, λ is a risk coefficient, the value range of λ belongs to (0,1), and the conditional risk value CVaR is calculated according to the formula:
CVaRβ(x)＝VaRβ(x)+E[f(x,y) VaRβ(x)|f(x,y)≥VaRβ(x)]
＝E[f(x,y)|f(x,y)≥VaRβ(x)] (6)
in the formula (6), β represents the degree of risk aversion,
VaRβ(Zmax)＝E[Zmax|Zmax≥VaR(Zmax)] (7)；
equation (5) satisfies the following constraint:
and (3) water balance constraint:
Vt+1＝Vt+(Qt-qt)×Δt (8)，
reservoir capacity constraint:
Vmin≤Vt≤Vmax (9)，
reservoir water level constraint:
Zmin≤Zt≤Zmax (10)，
and (4) restriction of the drainage capacity:
qt≤f(qt) (11)，
and (4) limiting the discharge amount change:
|qt-qt-1|≤Δq (12)
in formulae (8) to (12), Vt、ZtFor reservoir level and water storage capacity at the current time interval, Vt+1For the next period of reservoir storage capacity, Qt、qtRespectively the average warehousing flow and the ex-warehouse flow in the current time period, Vmin、VmaxAnd Zmin、ZmaxThe maximum value and the minimum value of the water storage capacity and the water level of the reservoir respectively, and f (qt) is the discharge capacity of the reservoir at the moment t.
The risk coefficient lambda in the reservoir flood control optimization scheduling model is valued according to the risk preference degree of scheduling personnel, and when the value of lambda is 0, the scheduling personnel do not avoid risks and actively pursue the risks; when lambda is more than 0 and less than or equal to 0.5, the willingness degree of the dispatcher to avoid risks is low; when the lambda is more than 0.5 and less than or equal to 1, the willingness degree of the dispatcher to avoid the risk is higher.
The invention has the beneficial effects that:
the reservoir flood control risk scheduling method under the flood comprehensive uncertainty is designed, the design flood peak value, the magnitude and the process uncertainty are comprehensively considered, the reservoir flood control optimal scheduling method based on the CVaR risk value index is provided, and a decision maker can be assisted to make flood control scheduling decisions under different risk coefficients in practice, so that the flood damage of a drainage basin can be reduced, and the reasonable design scale of the water conservancy and hydropower engineering can be made.
Drawings
FIG. 1 is a sampling chart of a one-hundred-year-old recurrence period;
FIG. 2 is a classification diagram of a flood process line;
FIG. 3 is a graph of the results of a class II flood process simulation;
fig. 4 is a flood process line graph of different categories after fusion, in which fig. 4(a) is a category I flood process line graph, fig. 4(b) is a category II flood process line graph, and fig. 4(c) is a category III flood process line graph;
FIG. 5 is a graph of mean, CVaR versus risk factor;
fig. 6 is a graph showing changes in the storage capacity of the reservoir under different risk factors, where fig. 6(a) is a graph showing changes in the storage capacity of the reservoir when λ is 0, fig. 6(b) is a graph showing changes in the storage capacity of the reservoir when λ is 0.2, fig. 6(c) is a graph showing changes in the storage capacity of the reservoir when λ is 0.4, fig. 6(d) is a graph showing changes in the storage capacity of the reservoir when λ is 0.6, fig. 6(e) is a graph showing changes in the storage capacity of the reservoir when λ is 0.8, and fig. 6(f) is a graph showing changes in the storage capacity of the reservoir when λ is 1.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Examples
The embodiment provides a reservoir flood control risk scheduling method under the design flood comprehensive uncertainty by taking an healthy reservoir in an upstream drainage basin of Hanjiang as an example, and specifically comprises the following steps:
step 1, estimating a joint distribution function H (H, y; theta) to C (F (H; theta) by a maximum likelihood methodh),F(y；θy)；θ0) Is (theta) is given as the parameter vector of (theta)h,θy；θ0) In the function, variables h and y are the annual maximum flood peak value and magnitude respectively;
the method specifically comprises the following steps:
1) selecting edge distribution functions with higher fitting degree for flood peak and maximum three-day flood data from Pearson type III, Gamma distribution, Lognist distribution, Gp distribution, Gev distribution and Norm distribution respectively, adopting a root mean square error criterion and an AICc criterion to carry out inspection of goodness of fit, and selecting Gamma distribution as the edge distribution type of the flood peak and the maximum three-day flood according to inspection result values;
2) selecting a proper coupling function from Clayton, Frank and Gumbel types, estimating parameters of joint distribution by adopting a maximum likelihood method, then selecting a Copula function type with higher fitting degree by adopting an AICc criterion and a BIC criterion, and selecting a distribution function combination with smaller AICc and BIC values from the Copula function types, so that the Gumbel Copula function is selected as a joint distribution function of a flood peak and a maximum three-day flood.
Step 2, based on the combined distribution function, a Monte Carlo method is applied to extract a two-dimensional sample with the length equal to the length of the actually measured data from the combined distribution function, and the two-dimensional sample is randomly extracted for N times;
the method specifically comprises the following steps:
according to the obtained edge distribution type of the flood peak and the maximum three-day flood volume, a calculation formula of a second recurrence period is combined, a most probable combination method is adopted to calculate and obtain a combined design value under a second recurrence period standard, and the flood prevention standard of an Ankang reservoir is one hundred years, so that the original sample is resampled for multiple times by taking the design flood of one hundred years as an example and adopting a Monte Carlo method, and the peak volume combined design value under the second recurrence period is obtained, and the result is shown in figure 1.
Step 3, estimating parameters of each group of simulation samples by adopting a maximum likelihood method to obtain N groups of joint distribution function parameter vectors;
step 4, calculating two-dimensional joint design values under different recurrence period types under each group of parameter vectors;
the two-dimensional joint design values under different types of the recurrence periods are calculated in step 4 specifically,
probability K that the probability W of the joint distribution of the characteristic quantities is less than or equal to t at a given probability level te (0,1)cThe expression of (a) is:
Kc(t)＝P(W≤t)＝P(C(u,v)≤t) (1)
in formula (1): c (u, v) is a Copula function, KcIs kendall measure, P denotes probability;
then with KcIndicated kendall recurrence period TkComprises the following steps:
Figure RE-GDA0003384845250000081
calculating a combined design value of flood by adopting a most probable combination method, wherein the most probable combined design value is a combined design value which is the maximum corresponding to the combined probability density of flood peak and flood volume under the condition of meeting a specified flood control standard T, and the calculation formula of the combined design value of flood is as follows:
Figure RE-GDA0003384845250000091
f(x,y)＝c(u,v)f(x)f(y) (4)
in formula (3): (x)m,ym) For the joint design value of the flood,
Figure RE-GDA0003384845250000092
the method is characterized in that the method is an isoline formed by peak amount combinations with the same recurrence period, and f (x, y) is a combined probability density function of a flood peak and a flood amount;
in formula (4): f (x), f (y) are edge probability density functions respectively; c (u, v) is a probability density function of Copula.
Step 5, calculating the design flood under the multidimensional uncertainty based on the two-dimensional joint design value under each group of parameter vectors;
the method specifically comprises the following steps:
1) carrying out dimensionless treatment on the selected complete warehousing flood process of 36 pools of the Ankang reservoir from 1954 to 2009; dividing a flood process line into 12 sections according to flood characteristics of the Hanjiang river basin, wherein the time interval is 3 hours;
2) the flood process types of the health station are classified into 3 types by adopting a K-means clustering method, and the result is shown in figure 2. Through analysis of different types of floods, it can be seen that the flood peak of the health station does not appear in a later time period basically, and conforms to the flood characteristics of the area;
3) converting a dimensionless flood volume accumulation curve into an unconstrained related non-normal multivariable by adopting logarithmic conversion, performing normal conversion by adopting a Johnson distribution system, performing inverse conversion by adopting Monte Carlo to randomly simulate a normal random variable, and finally solving flood processes of different types; taking the class II flood process as an example for simulation, the simulation result is shown in figure 3;
4) fusing the simulated dimensionless flood process line and the flood characteristic quantity by adopting a zoom ratio method, thereby forming a complete flood process; the result is shown in FIG. 4, wherein the flood type in FIG. 4(a) is type I, and the peak flow is 26314.12m3The flood volume is 42.72 hundred million m3When the peak time is near the front, the flood rises and falls sharply; FIG. 4(b) Peak flood flow 28822.87m3The flood volume is 59.50 hundred million m3The flood peak occurs in the middle and is near the front, and belongs to the II-class flood; FIG. 4(c) Peak flood flow 29488.65m3The flood volume is 60.16 hundred million m3The peak time is the middle later, and belongs to the class III flood process;
through the steps, the flood processes of different types of any field can be simulated at random, the uniqueness of typical flood process line selection in the traditional flood design process is overcome, and a basis can be provided for flood control planning design.
Step 6, establishing a reservoir flood control optimized dispatching model based on CVaR risk measurement indexes to realize flood control risk dispatching;
the step 6 specifically comprises the following steps:
establishing a target function, namely a reservoir flood control optimal scheduling model:
minG(x)＝(1-λ)E(x)+λCVaR(x) (5)
in the formula (5), x is the maximum flood regulation storage capacity of each flood, G (x) is the sum of potential risk and expected risk in the reservoir dispatching process under the influence of uncertainty factors, E (x) is the expectation of the maximum flood regulation storage capacity, lambda is a risk coefficient, the value range of lambda belongs to (0,1), the risk coefficient lambda in the reservoir flood control optimization dispatching model is valued according to the risk preference degree of a dispatcher, and when the value of lambda is 0, the dispatcher does not avoid the risk and actively pursue the risk; when lambda is more than 0 and less than or equal to 0.5, the willingness degree of the dispatcher to avoid risks is low; when lambda is more than 0.5 and less than or equal to 1, the willingness degree of the dispatcher to avoid risks is higher;
the conditional risk value CVaR is calculated according to the formula:
CVaRβ(x)＝VaRβ(x)+E[f(x,y) VaRβ(x)|f(x,y)≥VaRβ(x)]
＝E[f(x,y)|f(x,y)≥VaRβ(x)] (6)
in the formula (6), β represents the degree of risk aversion,
VaRβ(Zmax)＝E[Zmax|Zmax≥VaR(Zmax)] (7)；
equation (5) satisfies the following constraint:
and (3) water balance constraint:
Vt+1＝Vt+(Qt-qt)×Δt (8)，
reservoir capacity constraint:
Vmin≤Vt≤Vmax (9)，
reservoir water level constraint:
Zmin≤Zt≤Zmax (10)，
and (4) restriction of the drainage capacity:
qt≤f(qt) (11)，
and (4) limiting the discharge amount change:
|qt-qt-1|≤Δq (12)
in formulae (8) to (12), Vt、ZtFor reservoir level and water storage capacity at the current time interval, Vt+1For the next period of reservoir storage capacity, Qt、qtRespectively the average warehousing flow and the ex-warehouse flow in the current time period, Vmin、VmaxAnd Zmin、ZmaxThe maximum value and the minimum value of the water storage capacity and the water level of the reservoir respectively, and f (qt) is the discharge capacity of the reservoir at the moment t.
In order to verify the effectiveness of a reservoir flood control optimization scheduling model based on CVaR risk measurement indexes, 50 floods of each type with a recurrence period of one hundred years are selected as input; analyzing the influence of different risk coefficients on reservoir dispatching decision and corresponding mean-CVaR targets, enabling the parameter lambda to be {0, 0.2,0.4,0.6,0.8 and 1}, enabling the risk aversion degree beta to be a fixed value of 0.95, solving a model by adopting a particle swarm algorithm, and obtaining dispatching rules under different risk coefficients lambda, so that the mean value of the maximum reservoir capacity of flood regulation, the CVaR and the corresponding mean-CVaR value are obtained through statistics, and fig. 5 shows the relation between the mean value, the CVaR and the risk coefficients;
taking the class II flood process as an example, 100 hundred year designed flood processes are selected to be brought into the scheduling model, and the change processes of the storage capacity at different times are obtained through statistics, as shown in fig. 6. As can be seen from fig. 6(a) - (f), the class II flood is a flood process with a peak present time being earlier, and it can be seen that under different risk coefficients, the reservoir capacity changes little at the initial flood-expansion stage, and the reservoir capacity fluctuates significantly during the peak present period, and the time for maintaining a higher water level is longer, and it is difficult to return to the flood limit water level at the end of the scheduling period.
From the perspective of reservoir planning, uncertainty in designing floods has a great impact on flood safety. In view of the above, under such high uncertainty, if the reservoir needs to maintain the original design standard, the flood control storage capacity can be increased by reducing the flood limit water level in advance, or the reservoir can be emptied by increasing the flood forecast accuracy in advance, so as to ensure the flood control safety.

Claims (5)

1. The reservoir flood control risk scheduling method under the design flood comprehensive uncertainty is characterized by comprising the following steps:
step 1, estimating a joint distribution function H (H, y; theta) to C (F (H; theta) by a maximum likelihood methodh),F(y；θy)；θ0) Is (theta) is given as the parameter vector of (theta)h,θy；θ0) In the function, variables h and y are the annual maximum flood peak value and magnitude respectively;
step 2, based on the combined distribution function, a Monte Carlo method is applied to extract a two-dimensional sample with the length equal to the length of the actually measured data from the combined distribution function, and the two-dimensional sample is randomly extracted for N times;
step 3, estimating parameters of each group of simulation samples by adopting a maximum likelihood method to obtain N groups of joint distribution function parameter vectors;
step 4, calculating two-dimensional joint design values under different recurrence period types under each group of parameter vectors;
step 5, calculating the design flood under the multidimensional uncertainty based on the two-dimensional joint design value under each group of parameter vectors;
and 6, establishing a reservoir flood control optimal scheduling model based on the CVaR risk measurement indexes, and realizing flood control risk scheduling.
2. The method for dispatching flood control risk of reservoir under the synthetic uncertainty of design flood as claimed in claim 1, wherein the calculating of two-dimensional joint design values under different recurrence period types in step 4 is specifically,
probability K that the probability W of the joint distribution of the characteristic quantities is less than or equal to t at a given probability level te (0,1)cThe expression of (a) is:
Kc(t)＝P(W≤t)＝P(C(u,v)≤t) (1)
in formula (1): c (u, v) is a Copula function, KcFor a kendall measure, P represents the probability;
then with KcIndicated kendall recurrence period TkComprises the following steps:
Figure FDA0003237327360000021
calculating a combined design value of flood by adopting a most probable combination method, wherein the most probable combined design value is a combined design value which is the maximum corresponding to the combined probability density of flood peak and flood volume under the condition of meeting a specified flood control standard T, and the calculation formula of the combined design value of flood is as follows:
Figure FDA0003237327360000022
f(x,y)＝c(u,v)f(x)f(y) (4)
in formula (3): (x)m,ym) For the joint design value of the flood,
Figure FDA0003237327360000023
the method is characterized in that the method is an isoline formed by peak amount combinations with the same recurrence period, and f (x, y) is a combined probability density function of a flood peak and a flood amount;
in formula (4): f (x), f (y) are edge probability density functions respectively; c (u, v) is a probability density function of Copula.
3. The method for dispatching flood control risk of a reservoir under the design flood comprehensive uncertainty of claim 1, wherein the step 5 is specifically as follows:
the dimensionless flood accumulation curve is equally divided into K time periods, and the dimensionless time is carried out at the time
Figure FDA0003237327360000024
Corresponding dimensionless cumulative flood volume is FiThen the dimensionless flood volume per time interval is Pi＝Fi-Fi-1F for each period of each flood processiOr PiAs input, classifying the data by adopting a K-means clustering method based on Euclidean distance;
for the classified flood process, F is firstly carried outiOr PiCarrying out logarithmic transformation, namely, transforming the constrained related non-normal multivariable into the unconstrained related non-normal multivariable, carrying out normal transformation by adopting a Johnson system function to transform the constrained related non-normal multivariable into the related standard normal multivariable, carrying out orthogonal transformation by Cholesky decomposition to transform the independent standard normal multivariable into the independent standard normal multivariable, and finally generating the independent standard normal multivariable by adopting Monte Carlo simulation to carry out inverse transformation;
and fusing the generated dimensionless flood process line with the flood peak and the flood volume obtained by simulation in a variable magnification mode, so that a complete flood process can be generated, and a plurality of designed flood sequences are obtained.
4. The method for dispatching flood control risk of reservoir under design flood comprehensive uncertainty of claim 2, wherein the step 6 is specifically as follows:
establishing a target function, namely a reservoir flood control optimal scheduling model:
minG(x)＝(1-λ)E(x)+λCVaR(x) (5)
in the formula (5), x is the maximum flood regulation storage capacity of each flood, g (x) is the sum of potential risk and expected risk in the reservoir dispatching process under the influence of uncertainty factors, e (x) is the expectation of the maximum flood regulation storage capacity, λ is a risk coefficient, the value range of λ belongs to (0,1), and the conditional risk value CVaR is calculated according to the formula:
CVaRβ(x)＝VaRβ(x)+E[f(x,y) VaRβ(x)|f(x,y)≥VaRβ(x)]
＝E[f(x,y)|f(x,y)≥VaRβ(x)] (6)
in the formula (6), β represents the degree of risk aversion,
VaRβ(Zmax)＝E[Zmax|Zmax≥VaR(Zmax)] (7)；
equation (5) satisfies the following constraint:
and (3) water balance constraint:
Vt+1＝Vt+(Qt-qt)×Δt (8)，
reservoir capacity constraint:
Vmin≤Vt≤Vmax (9)，
reservoir water level constraint:
Zmin≤Zt≤Zmax (10)，
and (4) restriction of the drainage capacity:
qt≤f(qt) (11)，
and (4) limiting the discharge amount change:
|qt-qt-1|≤Δq (12)
in formulae (8) to (12), Vt、ZtFor reservoir level and water storage capacity at the current time interval, Vt+1For the next period of reservoir storage capacity, Qt、qtRespectively the average warehousing flow and the ex-warehouse flow in the current time period, Vmin、VmaxAnd Zmin、ZmaxThe maximum value and the minimum value of the water storage capacity and the water level of the reservoir respectively, and f (qt) is the discharge capacity of the reservoir at the moment t.
5. The method for designing reservoir flood control risk scheduling under flood comprehensive uncertainty as claimed in claim 4, wherein a risk coefficient λ in the reservoir flood control optimized scheduling model is taken according to risk preference degree of a scheduler, and when the value of λ is 0, the scheduler neither avoids risk nor actively pursues risk; when lambda is more than 0 and less than or equal to 0.5, the willingness degree of the dispatcher to avoid risks is low; when lambda is more than 0.5 and less than or equal to 1, the willingness degree of the dispatcher to avoid risks is higher.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114297875A (en) * 2022-01-04 2022-04-08 西安理工大学 Non-consistency hydrological frequency analysis method based on traceability reconstruction method

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