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CN113128757B - Optimal design method of reservoir water level during flood season considering the influence of inter-basin water transfer - Google Patents

Optimal design method of reservoir water level during flood season considering the influence of inter-basin water transfer
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CN113128757B
CN113128757BCN202110390810.2ACN202110390810ACN113128757BCN 113128757 BCN113128757 BCN 113128757BCN 202110390810 ACN202110390810 ACN 202110390810ACN 113128757 BCN113128757 BCN 113128757B
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reservoir
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张晓琦
许继军
刘攀
姚立强
许斌
鄢波
孙可可
周涛
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Bureau of Hydrology Changjiang Water Resources Commission
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Abstract

Translated fromChinese

本发明提供一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法,包括以下步骤:步骤1,推求考虑跨流域调水影响下的水库汛期分期入库流量;步骤2,建立考虑跨流域调水影响下水库汛期分期洪水过程间的联合分布函数;步骤3,构建适用于水库调度领域的水库防洪损失条件风险价值评价指标;步骤4,推求考虑跨流域调水影响下的水库分期汛限水位优化设计方案。本发明能够在水库开展分期汛限水位优化组合的过程中考虑跨流域调水工程对水库入库洪水过程的影响,从而为水库工程与跨流域调水工程之间的有效衔接提供思路。

Figure 202110390810

The present invention provides an optimization design method for the limited water level during flood season of a reservoir considering the influence of cross-basin water transfer. Joint distribution function between flood stages in the flood season under the influence of cross-basin water transfer; Step 3, construct the risk value evaluation index of reservoir flood control loss conditions suitable for the field of reservoir management; Step 4, calculate the reservoir stages under the influence of cross-basin water transfer Optimal design scheme of flood-limited water level. The invention can consider the influence of the cross-basin water transfer project on the flood process of the reservoir in the process of carrying out the staged flood-limited water level optimization combination of the reservoir, thereby providing an idea for the effective connection between the reservoir project and the cross-basin water transfer project.

Figure 202110390810

Description

Translated fromChinese
考虑跨流域调水影响下的水库分期汛限水位优化设计方法Optimal design method of reservoir water level during flood season considering the influence of inter-basin water transfer

技术领域technical field

本发明涉及水库调度技术领域,具体是一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法。The invention relates to the technical field of reservoir dispatching, in particular to a method for optimizing the design of the flood-limited water level of a reservoir by stages under the influence of cross-basin water diversion.

背景技术Background technique

由于受季风气候影响,我国降水分布不均,从而导致我国水资源呈现时空分布不均的特征。水库是协调流域水资源进行合理配置的主要工程措施。目前,水文学者以水库(群)为研究对象,在水资源调配理论与方法层面已取得了大量的科研成果,并逐步形成了较为成熟的技术方法体系;但水库对水资源的调蓄作用多局限于流域干或支流范围内。对此,跨流域调水是通过大规模的人工方法从余水的流域向缺水流域大量调水,以便促进缺水区域的经济发展和缓解流域用水矛盾,可与水库进行水工程联合运用,从而实现水资源在流域“宏观”与“微观”双重尺度上的安全高效协调分配。跨流域调水工程的具体实施通常需要先分析流域洪水资源分布特征并明确水库水源区可调水量,然后从水库坝前修建引水工程将余水调至受水区。因此,新时期开展水库(群)洪水资源化利用研究需要考虑跨流域调水会对水库入库洪水过程产生影响这一前提条件,这也是实现水工程(水库与跨流域调水工程)间联合调度、流域水资源优化配置的关键。其中,汛限水位是水库优化调度的关键特征水位参数,以此为切入点开展水库调度与跨流域调水工程联合运用是值得探究的。Due to the influence of the monsoon climate, the distribution of precipitation in my country is uneven, which leads to the uneven distribution of water resources in time and space in my country. Reservoir is the main engineering measure to coordinate the rational allocation of water resources in the basin. At present, hydrologists take reservoirs (groups) as their research objects, and have achieved a lot of scientific research results in the theory and method of water resources allocation, and gradually formed a relatively mature technical method system; but the role of reservoirs in regulating and storing water resources Most are confined to the main or tributary of the watershed. In this regard, inter-basin water transfer is to transfer a large amount of water from the remaining water basin to the water-deficient basin through large-scale artificial methods, so as to promote the economic development of the water-deficient area and alleviate the contradiction of water use in the basin. It can be used in conjunction with the reservoir for water engineering. So as to realize the safe and efficient coordinated distribution of water resources on the "macro" and "micro" scales of the basin. The specific implementation of the inter-basin water transfer project usually requires analyzing the distribution characteristics of flood resources in the basin and clarifying the adjustable water volume in the reservoir water source area, and then constructing a water diversion project in front of the reservoir dam to transfer the remaining water to the water receiving area. Therefore, in the new era, the research on the utilization of flood resources in reservoirs (groups) needs to consider the precondition that cross-basin water transfer will affect the flood process of the reservoir inflow. The key to scheduling and optimal allocation of water resources in the basin. Among them, the limited water level during the flood season is the key characteristic water level parameter for the optimal operation of the reservoir. Taking this as the starting point to carry out the joint application of the reservoir operation and the inter-basin water transfer project is worth exploring.

在现有的技术中存在如下问题:(1)现有水库分期汛限水位优化设计研究未考虑跨流域调水工程对入库洪水过程的影响;(2)目前针对水库分期汛限水位优化设计研究主要以传统洪水风险率作为防洪标准进行评价,在径流变化环境下适用性存在可探讨的空间。There are the following problems in the existing technology: (1) The existing research on the optimal design of the flood-limited water level of the existing reservoir does not consider the impact of the cross-basin water transfer project on the flood process; The research mainly uses the traditional flood risk rate as the flood control standard for evaluation, and there is room for discussion in the applicability under the environment of runoff change.

发明内容SUMMARY OF THE INVENTION

本发明是为了解决上述问题而进行的,目的在于提供一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法,该方法能够在水库开展洪水资源化利用的过程中考虑跨流域调水工程对水库入库洪水过程的影响,为水库工程与跨流域调水工程之间的有效衔接提供思路,从而兼顾流域内外水资源的合理配置。The present invention is carried out to solve the above problems, and the purpose is to provide a method for optimizing the design of the flood-limited water level of the reservoir by stages under the influence of cross-basin water transfer. The influence of water engineering on the flooding process of reservoir entry provides ideas for the effective connection between reservoir engineering and inter-basin water transfer engineering, so as to take into account the rational allocation of water resources inside and outside the basin.

本发明提供了一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法,包括以下步骤:The present invention provides a method for optimizing the design of the flood-limited water level of a reservoir by stages under the influence of cross-basin water transfer, comprising the following steps:

步骤1:推求考虑跨流域调水影响下的水库汛期分期入库流量;Step 1: Calculate the inflow flow of the reservoir during the flood season considering the influence of inter-basin water transfer;

步骤2:根据步骤1推求得到的水库汛期分期入库流量建立考虑跨流域调水影响下水库汛期分期洪水过程间的联合分布函数,确定分期洪水量级特征参数之间的联合分布关系及条件发生概率;Step 2: Establish the joint distribution function between the floods of the reservoir during the flood season under the influence of the inter-basin water transfer, and determine the joint distribution relationship between the characteristic parameters of the flood season and the condition occurrence probability;

步骤3:引入经济学条件风险价值理论,构建适用于水库调度领域的水库防洪损失条件风险价值评价指标,并在步骤2确定的分期洪水量级特征参数之间的条件发生概率基础上推求水库在整个汛期可能发生潜在防洪损失的计算式;Step 3: Introduce the conditional value-at-risk theory of economics, construct a conditional value-at-risk evaluation index for reservoir flood control losses suitable for the field of reservoir dispatching, and calculate the conditional probability of occurrence between the characteristic parameters of the staged flood magnitude determined instep 2. Calculation formula for potential flood control losses that may occur throughout the flood season;

步骤4:以步骤3构建的防洪损失条件风险价值指标为主要防洪约束条件,建立水库分期汛限水位优化设计模型,并求解水库分期汛限水位优化设计模型得到考虑跨流域调水影响下的水库分期汛限水位优化设计方案。Step 4: Taking the value-at-risk index of the flood control loss condition constructed in step 3 as the main flood control constraint, establish the optimal design model for the flood-limited water level of the reservoir by stages, and solve the optimal design model of the reservoir's flood-limited water level by stages to obtain the reservoir considering the influence of cross-basin water transfer. Optimal design scheme of limited water level during flood season.

进一步的,步骤1具体包括:Further,step 1 specifically includes:

步骤1-1,采用汛期分期研究领域常用的变点分析法,将水库汛期分期划分为前汛期D1和后汛期D2两期,或前汛期D1、主汛期D2和后汛期D3三期,分期数记为M,并对应将第j年各分期Ti时段内入库流量记为

Figure RE-GDA0003086137890000021
整个汛期时段长度
Figure RE-GDA0003086137890000022
其中j=1,…,N,N为实测入库径流序列年数,t=1,…,Ti,i=1,…,M;Step 1-1, using the change point analysis method commonly used in the field of flood season research, divide the reservoir flood season into two phases: the pre-flood period D1 and the post-flood period D2 , or the pre-flood period D1 , the main flood period D2 and the post-flood period D3 Three phases, the number of phases is recorded as M, and the corresponding inbound flow in each phase Ti in the j-th year is recorded as
Figure RE-GDA0003086137890000021
The length of the entire flood season
Figure RE-GDA0003086137890000022
Among them, j=1,...,N, N is the number of years of the measured inflow runoff sequence, t=1,...,Ti , i=1,...,M;

步骤1-2,将汛期跨流域调水工程的最大引水能力记为QY,并将其纳入汛期各分期洪水特性分析中,推求考虑跨流域调水影响下的水库各年汛期入库流量

Figure RE-GDA0003086137890000023
Step 1-2, record the maximum water diversion capacity of the cross-basin water diversion project in the flood season as QY , and incorporate it into the flood characteristic analysis of each stage in the flood season, and calculate the inflow flow of the reservoir in each flood season under the influence of the inter-basin water diversion.
Figure RE-GDA0003086137890000023

Figure RE-GDA0003086137890000024
Figure RE-GDA0003086137890000024

进一步的,步骤2具体包括:Further,step 2 specifically includes:

步骤2-1,根据步骤1推求得到的各年考虑跨流域调水影响下的水库入库流量

Figure RE-GDA0003086137890000025
分别统计计算汛期各分期Di的洪水特征参数值序列,统一记为变量
Figure RE-GDA0003086137890000026
(X={Q,W},a={p,3d,7d,15d,30d}),具体包括洪峰值
Figure RE-GDA0003086137890000031
最大3天洪量值
Figure RE-GDA0003086137890000032
最大7天洪量值
Figure RE-GDA0003086137890000033
最大15天洪量值
Figure RE-GDA0003086137890000034
最大30天洪量值
Figure RE-GDA0003086137890000035
Step 2-1, according to the inflow flow of the reservoir under the influence of inter-basin water transfer in each year calculated according tostep 1
Figure RE-GDA0003086137890000025
Statistically calculate the sequence of flood characteristic parameter values of each stage Di in the flood season, and record them as variables
Figure RE-GDA0003086137890000026
(X={Q, W}, a={p, 3d, 7d, 15d, 30d}), specifically including the flood peak
Figure RE-GDA0003086137890000031
Maximum 3-day flood value
Figure RE-GDA0003086137890000032
Maximum 7-day flood value
Figure RE-GDA0003086137890000033
Maximum 15-day flood value
Figure RE-GDA0003086137890000034
Maximum 30-day flood value
Figure RE-GDA0003086137890000035

步骤2-2,依据Copula函数原理,构建考虑跨流域调水影响下各分期内入库洪水量级特征参数之间的联合分布关系:Step 2-2, based on the Copula function principle, construct the joint distribution relationship between the characteristic parameters of the magnitude of the inflow flood in each stage under the influence of inter-basin water transfer:

Figure RE-GDA0003086137890000036
Figure RE-GDA0003086137890000036

式中:

Figure RE-GDA0003086137890000037
为变量
Figure RE-GDA0003086137890000038
的边缘分布函数,
Figure RE-GDA0003086137890000039
为变量
Figure RE-GDA00030861378900000310
的联合分布函数,Cλ(·)为Copula联结函数,λ为Copula函数的参数,可由其与Kendall秩相关系数的关系求得;where:
Figure RE-GDA0003086137890000037
as variable
Figure RE-GDA0003086137890000038
The marginal distribution function of ,
Figure RE-GDA0003086137890000039
as variable
Figure RE-GDA00030861378900000310
The joint distribution function of , Cλ (·) is the Copula connection function, and λ is the parameter of the Copula function, which can be obtained from its relationship with the Kendall rank correlation coefficient;

步骤2-3,依据步骤2-2建立的联合分布关系,推求各分期洪水量级特征参数之间的条件发生概率;Step 2-3, according to the joint distribution relationship established in step 2-2, infer the conditional probability of occurrence between the characteristic parameters of flood magnitude in each stage;

分期Di客观发生时间早于分期Di+1,当给定分期Di洪水量级特征参数

Figure RE-GDA00030861378900000311
时,记为洪水风险事件Ai,分期Di+1洪水量级特征参数
Figure RE-GDA00030861378900000312
记为洪水风险事件Ai+1,分期Di和分期Di+1洪水量级特征参数之间的条件发生概率计算式为:The objective occurrence time of stage Di is earlier than that of stage Di+1 , when the characteristic parameters of flood magnitude of stage Di are given
Figure RE-GDA00030861378900000311
, it is recorded as flood risk event Ai , and the characteristic parameters of flood magnitude in stages Di+1
Figure RE-GDA00030861378900000312
Denoted as the flood risk event Ai+1 , the calculation formula of the conditional probability of occurrence between the characteristic parameters of the flood magnitude of the stage Di and the stage Di+1 is:

Figure RE-GDA00030861378900000313
Figure RE-GDA00030861378900000313

式中,X={Q,W},a={p,3d,7d,15d,30d},

Figure RE-GDA00030861378900000314
Figure RE-GDA00030861378900000315
分别为分期Di和分期Di+1洪水量级特征参数的阈值,根据防洪对象的防洪标准确定。where X={Q, W}, a={p, 3d, 7d, 15d, 30d},
Figure RE-GDA00030861378900000314
and
Figure RE-GDA00030861378900000315
are the thresholds of the characteristic parameters of the flood magnitude of the stage Di and the stage Di+1 respectively, which are determined according to the flood control standards of the flood control object.

进一步的,步骤3具体包括:Further, step 3 specifically includes:

步骤3-1,根据经济学条件风险价值理论的定义,将其拓展于水库调度领域并建立水库防洪损失条件风险价值评价指标;Step 3-1, according to the definition of economic conditional value-at-risk theory, expand it to the field of reservoir dispatching and establish reservoir flood control loss conditional value-at-risk evaluation index;

条件风险价值的含义为,在一定置信水平α条件下,损失超过阈值Fα的平均水平,其通用表达式如下:The meaning of conditional value-at-risk is the average level of loss exceeding the threshold Fα under a certain confidence level α, and its general expression is as follows:

Figure RE-GDA0003086137890000041
Figure RE-GDA0003086137890000041

式中:y为决策变量,θ为随机变量,L(y,θ)为损失函数,max和Fα分别为损失函数最大值、置信水平α下的函数值,f(·)为防洪损失的概率密度函数;In the formula: y is the decision variable, θ is a random variable, L(y, θ) is the loss function, max and Fα are the maximum value of the loss function and the function value under the confidence level α, respectively, and f( ) is the flood control loss. Probability density function;

根据水库调洪演算原理,选取决策变量为水库汛限水位、随机变量为入库洪水量级构建各分期防洪损失函数

Figure RE-GDA0003086137890000042
并在条件风险价值指标通用表达式(5)的基础上推求水库在置信水平αi条件下、分期Di的防洪损失条件风险价值指标
Figure RE-GDA0003086137890000043
如下:According to the principle of reservoir flood regulation, the decision variable is selected as the flood limit water level of the reservoir, and the random variable is selected as the flood level of the reservoir to construct the flood control loss function of each stage.
Figure RE-GDA0003086137890000042
And on the basis of the general expression (5) of the conditional value-at-risk index, the conditional value-at-risk index of the flood control loss of the reservoir under the condition of confidence level αi and in stages Di is calculated.
Figure RE-GDA0003086137890000043
as follows:

Figure RE-GDA0003086137890000044
Figure RE-GDA0003086137890000044

式中:

Figure RE-GDA0003086137890000045
为分期Di的水库汛限水位,
Figure RE-GDA0003086137890000046
为分期Di的入库洪水量级,
Figure RE-GDA0003086137890000047
为分期Di时段内相应于置信水平αi的阈值,
Figure RE-GDA0003086137890000048
为分期Di内损失函数
Figure RE-GDA0003086137890000049
的最大值,
Figure RE-GDA00030861378900000410
为分期Di内防洪损失的概率密度函数;where:
Figure RE-GDA0003086137890000045
is the flood-limited water level of the reservoir in stage Di ,
Figure RE-GDA0003086137890000046
is the inbound flood magnitude of the stage Di ,
Figure RE-GDA0003086137890000047
is the threshold corresponding to the confidence level αi in the period of stage Di ,
Figure RE-GDA0003086137890000048
is the loss function within the stage Di
Figure RE-GDA0003086137890000049
the maximum value of ,
Figure RE-GDA00030861378900000410
is the probability density function of flood control loss in the period Di ;

设分期Di内洪水风险事件

Figure RE-GDA00030861378900000411
发生概率为P(Ai),则置信水平αi与洪水风险率P(Ai)满足关系式P(Ai)+αi=1;Set the flood risk event within the period Di
Figure RE-GDA00030861378900000411
The occurrence probability is P(Ai ), then the confidence level αi and the flood risk rate P(Ai ) satisfy the relational expression P(Ai )+αi =1;

步骤3-2,在步骤2-3确定的各分期洪水量级特征参数之间的条件发生概率计算式的基础上,结合洪水风险事件发生的固有自然特性,推求水库在整个汛期时段可能发生的潜在防洪损失CVaRα计算式:Step 3-2, on the basis of the calculation formula of the conditional probability of occurrence between the characteristic parameters of the flood magnitudes of each stage determined in step 2-3, combined with the inherent natural characteristics of flood risk events, infer the possible occurrence of the reservoir during the entire flood season. Calculation formula of potential flood protection loss CVaRα :

Figure RE-GDA00030861378900000412
Figure RE-GDA00030861378900000412

式中:X={Q,W},a={p,3d,7d,15d,30d},X和a可根据水库自身面临的入库洪水特性进行选择,P(Ai)为分期Di洪水风险事件Ai的发生概率, P(Ai+1|Ai)表征当给定分期Di洪水风险事件Ai发生时,分期Di+1洪水风险事件 Ai+1发生的条件概率,见式(4);

Figure RE-GDA0003086137890000051
αi=1-P(Ai),其中i=1,…,M。In the formula: X={Q, W}, a={p, 3d, 7d, 15d, 30d}, X and a can be selected according to the characteristics of the inflow flood faced by the reservoir itself, P(Ai ) is the stage Di The occurrence probability of flood risk event Ai , P(Ai+1 |Ai ) represents the conditional probability of occurrence of flood risk event Ai+1 in stage Di+1 when flood risk event Ai occurs in given stage Di , see formula (4);
Figure RE-GDA0003086137890000051
αi =1-P(Ai ), where i=1, . . . , M.

进一步的,步骤4中以水库现状设计汛限水位方案对应的汛期防洪损失条件风险价值βα为防洪约束条件,建立水库分期汛限水位优化设计模型;水库分期汛限水位优化设计模型的目标函数和主要约束条件如下:Further, in step 4, the flood control loss condition risk valueβα corresponding to the flood control loss condition in flood season corresponding to the current design of the reservoir is used as the flood control constraint condition, and the optimal design model of the reservoir water level is established by stages; and the main constraints are as follows:

Figure RE-GDA0003086137890000052
Figure RE-GDA0003086137890000052

Figure RE-GDA0003086137890000053
Figure RE-GDA0003086137890000053

式中:

Figure RE-GDA0003086137890000054
代表各分期汛限水位优化组合方案,B(·)代表水库汛期兴利效益,CVaRα(·)代表相应于水库分期汛限水位优化组合方案
Figure RE-GDA0003086137890000055
的防洪损失条件风险价值,其计算过程中的随机变量
Figure RE-GDA0003086137890000059
采用的是考虑跨流域调水影响后的入库洪水过程;
Figure RE-GDA0003086137890000056
代表分期汛限水位现状组合方案,βα(·)代表相应于水库分期汛限水位现状组合方案的防洪损失条件风险价值,其计算过程中的随机变量
Figure RE-GDA0003086137890000057
采用天然入库洪水过程,即未受跨流域调水影响下的入库洪水过程。where:
Figure RE-GDA0003086137890000054
Represents the optimal combination scheme of the flood-limited water level in each stage, B(·) represents the benefit of the reservoir during the flood season, and CVaRα (·) represents the optimal combination scheme corresponding to the flood-limited water level of the reservoir by stages
Figure RE-GDA0003086137890000055
The Flood Loss Conditional VaR, a random variable in its calculation process
Figure RE-GDA0003086137890000059
The inflow flood process after considering the influence of inter-basin water transfer is adopted;
Figure RE-GDA0003086137890000056
βα (·) represents the conditional risk value of flood control loss corresponding to the current combination scheme of the flood-limited water level of the reservoir by stages, and the random variable in the calculation process
Figure RE-GDA0003086137890000057
The natural inflow flood process is adopted, that is, the inflow flood process without the influence of inter-basin water transfer.

进一步的,步骤2-2中Copula函数包括二元正态Copula函数、二元t-Copula 函数、二元Archimedean-Copula函数,采用离差平方和最小准则OLS来选取OLS 最小的Copula函数表达形式作为联结函数,OLS的计算公式如下:Further, in step 2-2, the Copula function includes a bivariate normal Copula function, a bivariate t-Copula function, and a bivariate Archimedean-Copula function, and the OLS minimum sum of squared deviation criterion is used to select the expression form of the Copula function with the smallest OLS as the expression form. The link function, the calculation formula of OLS is as follows:

Figure RE-GDA0003086137890000058
Figure RE-GDA0003086137890000058

式中,n为样本数,Pei、Pi分别为经验频率和理论频率。In the formula, n is the number of samples, and Pei and Pi are the empirical frequency and the theoretical frequency, respectively.

与现有技术相比,本发明的有益效果在于:Compared with the prior art, the beneficial effects of the present invention are:

(1)本发明提出了一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法,该方法能够在水库开展洪水资源化利用的过程中考虑跨流域调水工程对水库入库洪水过程的影响,为水库工程与跨流域调水工程之间的有效衔接提供思路,从而兼顾流域内外水资源的合理配置;(1) The present invention proposes an optimal design method for the flood-limited water level of the reservoir by stages considering the influence of cross-basin water transfer. The influence of the process provides ideas for the effective connection between the reservoir project and the inter-basin water transfer project, so as to take into account the rational allocation of water resources inside and outside the basin;

(2)本发明所提出的一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法中所构建的水库汛期分期防洪损失条件风险价值指标CVaRα,可通过耦合汛期各分期内防洪损失条件风险价值

Figure RE-GDA0003086137890000061
及两个相邻分期间洪水事件发生的条件概率,推求水库整个汛期调度决策时段的潜在防洪损失值,从而为水库各分期汛限水位组合提供优化思路。(2) The conditional value-at-risk index CVaRα of the flood control loss condition of the reservoir during the flood season, which is constructed in the optimal design method for the flood-limited water level of the reservoir by stages under the influence of the cross-basin water transfer proposed by the present invention, can be coupled with the flood control in each stage of the flood season. loss condition value at risk
Figure RE-GDA0003086137890000061
And the conditional probability of flood events in two adjacent sub-periods, the potential flood control loss value of the reservoir during the whole flood season scheduling decision-making period is calculated, so as to provide an optimization idea for the combination of the flood-limited water level in each sub-period of the reservoir.

附图说明Description of drawings

图1是本发明实施例提供的一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法的流程示意图;Fig. 1 is a schematic flow chart of a method for optimizing the design of the reservoir's flood-limited water level by stages under the influence of cross-basin water transfer provided by an embodiment of the present invention;

图2是本发明实施例构建考虑跨流域调水影响下各分期内入库洪水量级特征参数之间的联合分布关系示意图;2 is a schematic diagram of the joint distribution relationship between the characteristic parameters of the magnitude of the inflow flood in each phase under the consideration of the influence of cross-basin water transfer in an embodiment of the present invention;

图3(a)是本发明实施例水库分期汛限水位优化设计模型推求的分期汛限水位组合方案解集示意图;图3(b)是本发明实施例不同的分期汛限水位组合方案对应的条件风险价值CVaRα和效益目标值B的关系图。Fig. 3 (a) is a schematic diagram of the solution set of the combination scheme of the flood-limited water level in different stages according to the embodiment of the present invention; Plot of conditional value-at-risk CVaRalpha and benefit target value B.

具体实施方式Detailed ways

为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明的一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present invention.

如图1所示,本实施例所提供的一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法包括以下步骤:As shown in FIG. 1 , a method for optimizing the design of reservoir water level with limited flood season by stages under the influence of inter-basin water transfer provided by this embodiment includes the following steps:

步骤1,推求考虑跨流域调水影响下的水库汛期分期入库流量过程,具体实现如下:Step 1: Calculate the inflow process of the reservoir during the flood season under the influence of inter-basin water transfer. The specific implementation is as follows:

步骤1-1,采用汛期分期研究领域常用的变点分析法,将水库汛期分期划分为前汛期D1和后汛期D2两期,或前汛期D1、主汛期D2和后汛期D3三期,分期数记为M,并对应将第j年各(j=1,…,N,N为实测入库径流序列年数)分期Ti时段内入库流量记为

Figure RE-GDA0003086137890000071
整个汛期时段长度
Figure RE-GDA0003086137890000072
Step 1-1, using the change point analysis method commonly used in the field of flood season research, divide the reservoir flood season into two phases: the pre-flood period D1 and the post-flood period D2 , or the pre-flood period D1 , the main flood period D2 and the post-flood period D3 For the third phase, the number of phases is recorded as M, and the corresponding inbound flow in each phase Ti in the jth year (j=1, .
Figure RE-GDA0003086137890000071
The length of the entire flood season
Figure RE-GDA0003086137890000072

步骤1-2,将汛期跨流域调水工程的最大引水能力记为QY(通常汛期跨流域调水可达到最大引水能力),并将其纳入汛期各分期洪水特性分析中,推求考虑跨流域调水影响下的水库各年汛期入库流量

Figure RE-GDA0003086137890000073
Step 1-2, record the maximum water diversion capacity of the cross-basin water diversion project in the flood season as QY (usually, the cross-basin water diversion in the flood season can reach the maximum water diversion capacity), and incorporate it into the flood characteristic analysis of each stage in the flood season, and calculate the cross-basin consideration. Reservoir inflow in flood seasons under the influence of water transfer
Figure RE-GDA0003086137890000073

Figure RE-GDA0003086137890000074
Figure RE-GDA0003086137890000074

步骤2,根据步骤1推求得到的水库汛期分期入库流量建立考虑跨流域调水影响下水库汛期分期洪水过程间的联合分布函数,确定分期洪水量级特征参数之间的联合分布关系及条件发生概率,具体实现如下:Step 2: According to the inflow of the reservoir during the flood season obtained instep 1, establish a joint distribution function between the flood processes of the reservoir during the flood season under the influence of cross-basin water transfer, and determine the joint distribution relationship between the characteristic parameters of the flood season and the condition occurrence. probability, which is implemented as follows:

步骤2-1,根据步骤1-2推求得到的各年考虑跨流域调水影响下的水库入库流量

Figure RE-GDA0003086137890000075
分别统计计算汛期各分期Di的洪水特征参数值序列,统一记为变量
Figure RE-GDA0003086137890000076
(X={Q,W},a={p,3d,7d,15d,30d}),具体包括洪峰值
Figure RE-GDA0003086137890000077
最大3天洪量值
Figure RE-GDA0003086137890000078
最大7天洪量值
Figure RE-GDA0003086137890000079
最大15天洪量值
Figure RE-GDA00030861378900000710
最大30天洪量值
Figure RE-GDA00030861378900000711
Step 2-1, the inflow flow of the reservoir under the influence of inter-basin water transfer in each year calculated according to step 1-2
Figure RE-GDA0003086137890000075
Statistically calculate the sequence of flood characteristic parameter values of each stage Di in the flood season, and record them as variables
Figure RE-GDA0003086137890000076
(X={Q, W}, a={p, 3d, 7d, 15d, 30d}), specifically including the flood peak
Figure RE-GDA0003086137890000077
Maximum 3-day flood value
Figure RE-GDA0003086137890000078
Maximum 7-day flood value
Figure RE-GDA0003086137890000079
Maximum 15-day flood value
Figure RE-GDA00030861378900000710
Maximum 30-day flood value
Figure RE-GDA00030861378900000711

步骤2-2,依据Copula函数原理,构建考虑跨流域调水影响下各分期内入库洪水量级特征参数之间的联合分布关系(如图2):Step 2-2, according to the principle of Copula function, construct the joint distribution relationship between the characteristic parameters of the magnitude of the inflow flood in each stage under the influence of inter-basin water transfer (as shown in Figure 2):

Figure RE-GDA00030861378900000712
Figure RE-GDA00030861378900000712

式中:

Figure RE-GDA00030861378900000713
为变量
Figure RE-GDA00030861378900000714
的边缘分布函数,
Figure RE-GDA00030861378900000715
为变量
Figure RE-GDA00030861378900000716
的联合分布函数,Cλ(·)为Copula联结函数,λ为Copula函数的参数,可由其与Kendall秩相关系数的关系求得;where:
Figure RE-GDA00030861378900000713
as variable
Figure RE-GDA00030861378900000714
The marginal distribution function of ,
Figure RE-GDA00030861378900000715
as variable
Figure RE-GDA00030861378900000716
The joint distribution function of , Cλ (·) is the Copula connection function, and λ is the parameter of the Copula function, which can be obtained from its relationship with the Kendall rank correlation coefficient;

常用的Copula函数有二元正态Copula函数,二元t-Copula函数,二元Archimedean-Copula函数,采用离差平方和最小准则(OLS)来选取OLS最小的Copula函数表达形式作为联结函数,OLS的计算公式如下:Commonly used Copula functions include the binary normal Copula function, the binary t-Copula function, and the binary Archimedean-Copula function. The minimum sum of squared deviation criterion (OLS) is used to select the expression form of the Copula function with the smallest OLS as the link function. OLS The calculation formula is as follows:

Figure RE-GDA0003086137890000081
Figure RE-GDA0003086137890000081

式中,n为样本数,Pei、Pi分别为经验频率和理论频率;In the formula, n is the number of samples, and Pei and Pi are the empirical and theoretical frequencies, respectively;

步骤2-3,依据步骤2-2建立的联合分布关系,推求各分期洪水量级特征参数之间的条件发生概率;Step 2-3, according to the joint distribution relationship established in step 2-2, infer the conditional probability of occurrence between the characteristic parameters of flood magnitude in each stage;

由于分期Di客观发生时间早于分期Di+1,因此,当给定分期Di洪水量级特征参数

Figure RE-GDA0003086137890000082
时(记为洪水风险事件Ai),分期Di+1洪水量级特征参数
Figure RE-GDA0003086137890000083
(记为洪水风险事件Ai+1),分期Di和分期Di+1洪水量级特征参数之间的条件发生概率计算式为:Since the objective occurrence time of stage Di is earlier than that of stage Di+1 , when the characteristic parameters of flood magnitude of stage Di are given,
Figure RE-GDA0003086137890000082
time (denoted as flood risk event Ai ), stage Di+1 flood magnitude characteristic parameters
Figure RE-GDA0003086137890000083
(denoted as the flood risk event Ai+1 ), the conditional probability of occurrence between the characteristic parameters of the flood magnitude of the stage Di and the stage Di+1 is calculated as:

Figure RE-GDA0003086137890000084
Figure RE-GDA0003086137890000084

式中,X={Q,W},a={p,3d,7d,15d,30d},

Figure RE-GDA0003086137890000085
Figure RE-GDA0003086137890000086
分别为分期Di和分期Di+1洪水量级特征参数的阈值,可根据防洪对象的防洪标准确定;where X={Q, W}, a={p, 3d, 7d, 15d, 30d},
Figure RE-GDA0003086137890000085
and
Figure RE-GDA0003086137890000086
are the thresholds of the characteristic parameters of the flood magnitude of the stage Di and the stage Di+1 respectively, which can be determined according to the flood control standard of the flood control object;

步骤3,引入经济学条件风险价值理论,构建适用于水库调度领域的水库防洪损失条件风险价值评价指标,并在步骤2确定的分期洪水量级特征参数之间的条件发生概率基础上推求水库在整个汛期可能发生潜在防洪损失的计算式,具体实现如下:Step 3: Introduce the conditional value-at-risk theory of economics to construct a conditional value-at-risk evaluation index suitable for reservoir flood control losses in the field of reservoir scheduling, and based on the conditional probability of occurrence among the characteristic parameters of the staged flood magnitude determined instep 2, calculate the value of the reservoir at risk. The formula for calculating the potential flood control losses that may occur throughout the flood season is as follows:

步骤3-1,条件风险价值的含义为,在一定置信水平α条件下,损失超过阈值Fα的平均水平,其通用表达式如下:Step 3-1, the meaning of conditional value-at-risk is that, under a certain confidence level α, the loss exceeds the average level of the threshold value Fα , and its general expression is as follows:

Figure RE-GDA0003086137890000087
Figure RE-GDA0003086137890000087

式中:y为决策变量,θ为随机变量,L(y,θ)为损失函数,max和Fα分别为损失函数最大值、置信水平α下的函数值,f(·)为防洪损失的概率密度函数;In the formula: y is the decision variable, θ is a random variable, L(y, θ) is the loss function, max and Fα are the maximum value of the loss function and the function value under the confidence level α, respectively, and f( ) is the flood control loss. Probability density function;

根据水库调洪演算原理构建各分期防洪损失函数

Figure RE-GDA0003086137890000091
并在条件风险价值指标通用表达式(5)的基础上推求水库在置信水平αi条件下、分期Di的防洪损失条件风险价值指标
Figure RE-GDA0003086137890000092
如下:Constructing the flood control loss function of each stage according to the principle of reservoir flood regulation
Figure RE-GDA0003086137890000091
And on the basis of the general expression (5) of the conditional value-at-risk index, the conditional value-at-risk index of the flood control loss of the reservoir under the condition of confidence level αi and in stages Di is calculated.
Figure RE-GDA0003086137890000092
as follows:

Figure RE-GDA0003086137890000093
Figure RE-GDA0003086137890000093

式中:

Figure RE-GDA0003086137890000094
为分期Di的水库汛限水位,
Figure RE-GDA0003086137890000095
为分期Di的入库洪水量级,
Figure RE-GDA0003086137890000096
为分期Di时段内相应于置信水平αi的阈值,
Figure RE-GDA0003086137890000097
为分期Di内损失函数
Figure RE-GDA0003086137890000098
的最大值,
Figure RE-GDA0003086137890000099
为分期Di内防洪损失的概率密度函数;where:
Figure RE-GDA0003086137890000094
is the flood-limited water level of the reservoir in stage Di ,
Figure RE-GDA0003086137890000095
is the inbound flood magnitude of the stage Di ,
Figure RE-GDA0003086137890000096
is the threshold corresponding to the confidence level αi in the period of stage Di ,
Figure RE-GDA0003086137890000097
is the loss function within the stage Di
Figure RE-GDA0003086137890000098
the maximum value of ,
Figure RE-GDA0003086137890000099
is the probability density function of flood control loss in the period Di ;

设分期Di内洪水风险事件

Figure RE-GDA00030861378900000910
发生概率为P(Ai),则置信水平αi与洪水风险率P(Ai)满足关系式P(Ai)+αi=1;Set the flood risk event within the period Di
Figure RE-GDA00030861378900000910
The occurrence probability is P(Ai ), then the confidence level αi and the flood risk rate P(Ai ) satisfy the relational expression P(Ai )+αi =1;

步骤3-2,在步骤2-3构建的各分期洪水量级特征参数之间的条件发生概率计算式的基础上,结合洪水风险事件发生的固有自然特性,推求水库在整个汛期时段可能发生的潜在防洪损失CVaRα计算式:Step 3-2, on the basis of the calculation formula of the conditional probability of occurrence among the characteristic parameters of flood magnitudes of each stage constructed in step 2-3, combined with the inherent natural characteristics of flood risk events, infer the possible occurrence of the reservoir during the entire flood season. Calculation formula of potential flood protection loss CVaRα :

Figure RE-GDA00030861378900000911
Figure RE-GDA00030861378900000911

式中:X={Q,W},a={p,3d,7d,15d,30d},X和a可根据水库自身面临的入库洪水特性进行选择,P(Ai)为分期Di洪水风险事件Ai的发生概率, P(Ai+1|Ai)表征当给定分期Di洪水风险事件Ai发生时,分期Di+1洪水风险事件 Ai+1发生的条件概率,见式(4);

Figure RE-GDA00030861378900000912
αi=1-P(Ai) (i=1,…,M);In the formula: X={Q, W}, a={p, 3d, 7d, 15d, 30d}, X and a can be selected according to the characteristics of the inflow flood faced by the reservoir itself, P(Ai ) is the stage Di The occurrence probability of flood risk event Ai , P(Ai+1 |Ai ) represents the conditional probability of occurrence of flood risk event Ai+1 in stage Di+1 when flood risk event Ai occurs in given stage Di , see formula (4);
Figure RE-GDA00030861378900000912
αi =1-P(Ai ) (i=1,...,M);

步骤4,以步骤3构建的防洪损失条件风险价值指标为主要防洪约束条件,建立水库分期汛限水位优化设计模型,并求解得到考虑跨流域调水影响下的水库分期汛限水位优化设计方案,请参阅图3(a)和图3(b),其中图3(a)为水库分期汛限水位优化设计模型推求的分期汛限水位组合方案解集示意图,图3(b) 为不同的分期汛限水位组合方案对应的条件风险价值CVaRα和效益目标值B的关系图。Step 4, take the flood control loss condition risk value index constructed in step 3 as the main flood control constraint condition, establish the optimal design model of the reservoir's flood-limited water level by stages, and solve the optimal design scheme of the reservoir's flood-limited water level by stages considering the influence of cross-basin water transfer, Please refer to Figure 3(a) and Figure 3(b), in which Figure 3(a) is a schematic diagram of the solution set of the combination scheme of the flood-limited water level in different stages calculated by the optimal design model for the flood-limited water level of the reservoir, and Figure 3(b) is a diagram of different stages The relationship between the conditional value-at-risk CVaRα and the benefit target value B corresponding to the combination scheme of the flood-limited water level.

具体的,在步骤3的基础上,以水库现状设计汛限水位方案对应的汛期防洪损失条件风险价值(记为βα)为防洪约束条件,推求在不增加防洪风险的基础上可行的水库分期汛限水位优化方案;水库分期汛限水位优化设计模型的目标函数和主要约束条件如下:Specifically, on the basis of step 3, taking the flood control loss condition risk value (denoted as βα ) corresponding to the flood control loss condition in the flood season corresponding to the current design of the reservoir in the flood season as the flood control constraint condition, infer the feasible reservoir stages without increasing the flood control risk. Optimal scheme of flood-limited water level; the objective function and main constraints of the optimal design model for flood-limited water level of the reservoir by stages are as follows:

Figure RE-GDA0003086137890000101
Figure RE-GDA0003086137890000101

Figure RE-GDA0003086137890000102
Figure RE-GDA0003086137890000102

式中:

Figure RE-GDA0003086137890000103
代表各分期汛限水位优化组合方案,B(·)代表水库汛期兴利效益(比如发电量、供水量等),CVaRα(·)代表相应于水库分期汛限水位优化组合方案
Figure RE-GDA0003086137890000104
的防洪损失条件风险价值,其计算过程中的随机变量
Figure RE-GDA0003086137890000105
采用的是考虑跨流域调水影响后的入库洪水过程;
Figure RE-GDA0003086137890000106
代表分期汛限水位现状组合方案,βα(·)代表相应于水库分期汛限水位现状组合方案的防洪损失条件风险价值,其计算过程中的随机变量
Figure RE-GDA0003086137890000107
采用天然入库洪水过程,即未受跨流域调水影响下的入库洪水过程。where:
Figure RE-GDA0003086137890000103
Represents the optimal combination scheme of the flood-limited water level in each stage, B(·) represents the benefit of the reservoir during the flood season (such as power generation, water supply, etc.), and CVaRα (·) represents the optimal combination scheme corresponding to the flood-limited water level of the reservoir by stages
Figure RE-GDA0003086137890000104
The Flood Loss Conditional VaR, a random variable in its calculation process
Figure RE-GDA0003086137890000105
The inflow flood process after considering the influence of inter-basin water transfer is adopted;
Figure RE-GDA0003086137890000106
βα (·) represents the conditional risk value of flood control loss corresponding to the current combination scheme of the flood-limited water level of the reservoir by stages, and the random variable in the calculation process
Figure RE-GDA0003086137890000107
The natural inflow flood process is adopted, that is, the inflow flood process without the influence of inter-basin water transfer.

以上所述,仅为本发明的具体实施方式,但本发明的保护范围并不局限于此,任何属于本技术领域的技术人员在本发明揭露的技术范围内,可轻易想到的变化或替换,都应涵盖在本发明的保护范围之内。因此,本发明的保护范围应该以权利要求的保护范围为准。The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, All should be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (2)

Translated fromChinese
1.一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法,其特征在于,包括以下步骤:1. a method for optimizing the design of reservoir water level in flood season under consideration under the influence of cross-basin water transfer, is characterized in that, comprises the following steps:步骤1:推求考虑跨流域调水影响下的水库汛期分期入库流量;Step 1: Calculate the inflow flow of the reservoir during the flood season considering the influence of inter-basin water transfer;步骤2:根据步骤1推求得到的水库汛期分期入库流量建立考虑跨流域调水影响下水库汛期分期洪水过程间的联合分布函数,确定分期洪水量级特征参数之间的联合分布关系及条件发生概率;Step 2: Establish the joint distribution function between the floods of the reservoir during the flood season under the influence of the inter-basin water transfer, and determine the joint distribution relationship between the characteristic parameters of the flood season and the condition occurrence probability;步骤3:引入经济学条件风险价值理论,构建适用于水库调度领域的水库防洪损失条件风险价值评价指标,并在步骤2确定的分期洪水量级特征参数之间的条件发生概率基础上推求水库在整个汛期可能发生潜在防洪损失的计算式;Step 3: Introduce the conditional value-at-risk theory of economics, construct a conditional value-at-risk evaluation index for reservoir flood control losses suitable for the field of reservoir dispatching, and calculate the conditional probability of occurrence between the characteristic parameters of the staged flood magnitude determined in step 2. Calculation formula for potential flood control losses that may occur throughout the flood season;步骤4:以步骤3构建的水库防洪损失条件风险价值评价指标为主要防洪约束条件,建立水库分期汛限水位优化设计模型,并求解水库分期汛限水位优化设计模型得到考虑跨流域调水影响下的水库分期汛限水位优化设计方案;Step 4: Taking the risk value evaluation index of the flood control loss condition of the reservoir constructed in step 3 as the main flood control constraint, establish the optimal design model of the reservoir's flood-limited water level by stages, and solve the optimal design model of the reservoir's flood-limited water level by stages. The optimal design scheme for the flood-limited water level of the reservoir by stages;步骤1具体包括:Step 1 specifically includes:步骤1-1,采用汛期分期研究领域变点分析法,将水库汛期分期划分为前汛期D1和后汛期D2两期,或前汛期D1、主汛期D2和后汛期D3三期,分期数记为M,并对应将第j年各分期Ti时段内入库流量记为
Figure FDA0003603948180000011
整个汛期时段长度
Figure FDA0003603948180000012
其中j=1,…,N,N为实测入库径流序列年数,t=1,…,Ti,i=1,…,M;Step 1-1, using the change point analysis method of the flood season research field, divide the reservoir flood season into two phases: the pre-flood period D1 and the post-flood period D2 , or the three periods of the pre-flood period D1 , the main flood period D2 and the post-flood period D3 , the number of instalments is recorded as M, and the corresponding inbound flow in each phase Ti in the j-th year is recorded as
Figure FDA0003603948180000011
The length of the entire flood season
Figure FDA0003603948180000012
Among them, j=1,...,N,N is the number of years of the measured inflow runoff sequence, t=1,...,Ti , i=1,...,M;步骤1-2,将汛期跨流域调水工程的最大引水能力记为QY,并将其纳入汛期各分期洪水特性分析中,推求考虑跨流域调水影响下的水库各年汛期入库流量
Figure FDA0003603948180000013
Step 1-2, record the maximum water diversion capacity of the cross-basin water diversion project in the flood season as QY , and incorporate it into the flood characteristic analysis of each stage in the flood season, and calculate the inflow flow of the reservoir in each flood season under the influence of the inter-basin water diversion.
Figure FDA0003603948180000013
Figure FDA0003603948180000014
Figure FDA0003603948180000014
步骤2具体包括:Step 2 specifically includes:步骤2-1,根据步骤1推求得到的考虑跨流域调水影响下的水库各年汛期入库流量
Figure FDA0003603948180000015
分别统计计算汛期各分期Di的洪水特征参数值序列,统一记为变量
Figure FDA0003603948180000016
其中X={Q,W},a={p,3d,7d,15d,30d},具体包括洪峰值
Figure FDA0003603948180000021
最大3天洪量值
Figure FDA0003603948180000022
最大7天洪量值
Figure FDA0003603948180000023
最大15天洪量值
Figure FDA0003603948180000024
最大30天洪量值
Figure FDA0003603948180000025
Step 2-1, according to the calculation of step 1, the inflow of the reservoir in each flood season under the influence of inter-basin water transfer
Figure FDA0003603948180000015
Statistically calculate the sequence of flood characteristic parameter values of each stage Di in the flood season, and record them as variables
Figure FDA0003603948180000016
where X={Q,W}, a={p,3d,7d,15d,30d}, including the peak value of Hong
Figure FDA0003603948180000021
Maximum 3-day flood value
Figure FDA0003603948180000022
Maximum 7-day flood value
Figure FDA0003603948180000023
Maximum 15-day flood value
Figure FDA0003603948180000024
Maximum 30-day flood value
Figure FDA0003603948180000025
步骤2-2,依据Copula函数原理,构建考虑跨流域调水影响下各分期内入库洪水量级特征参数之间的联合分布关系:Step 2-2, based on the Copula function principle, construct the joint distribution relationship between the characteristic parameters of the magnitude of the inflow flood in each stage under the influence of inter-basin water transfer:
Figure FDA0003603948180000026
Figure FDA0003603948180000026
式中:
Figure FDA0003603948180000027
为变量
Figure FDA0003603948180000028
的边缘分布函数,
Figure FDA0003603948180000029
为变量
Figure FDA00036039481800000210
的联合分布函数,Cλ(·)为Copula联结函数,λ为Copula函数的参数,由其与Kendall秩相关系数的关系求得;
where:
Figure FDA0003603948180000027
as variable
Figure FDA0003603948180000028
The marginal distribution function of ,
Figure FDA0003603948180000029
as variable
Figure FDA00036039481800000210
The joint distribution function of , Cλ (·) is the Copula connection function, and λ is the parameter of the Copula function, which is obtained from its relationship with the Kendall rank correlation coefficient;
步骤2-3,依据步骤2-2建立的联合分布关系,推求各分期洪水量级特征参数之间的条件发生概率;Step 2-3, according to the joint distribution relationship established in step 2-2, infer the conditional probability of occurrence between the characteristic parameters of flood magnitude in each stage;分期Di客观发生时间早于分期Di+1,当给定分期Di洪水量级特征参数
Figure FDA00036039481800000211
时,记为洪水风险事件Ai,分期Di+1洪水量级特征参数
Figure FDA00036039481800000212
记为洪水风险事件Ai+1,分期Di和分期Di+1洪水量级特征参数之间的条件发生概率计算式为:
The objective occurrence time of stage Di is earlier than that of stage Di+1 , when the characteristic parameters of flood magnitude of stage Di are given
Figure FDA00036039481800000211
, it is recorded as flood risk event Ai , and the characteristic parameters of flood magnitude in stages Di+1
Figure FDA00036039481800000212
Denoted as the flood risk event Ai+1 , the calculation formula of the conditional probability of occurrence between the characteristic parameters of the flood magnitude of the stage Di and the stage Di+1 is:
Figure FDA00036039481800000213
Figure FDA00036039481800000213
式中,X={Q,W},a={p,3d,7d,15d,30d},
Figure FDA00036039481800000214
Figure FDA00036039481800000215
分别为分期Di和分期Di+1洪水量级特征参数的阈值,根据防洪对象的防洪标准确定;
In the formula, X={Q,W}, a={p,3d,7d,15d,30d},
Figure FDA00036039481800000214
and
Figure FDA00036039481800000215
are the thresholds of the characteristic parameters of the flood magnitude of the stage Di and the stage Di+1 respectively, which are determined according to the flood control standards of the flood control object;
步骤3具体包括:Step 3 specifically includes:步骤3-1,根据经济学条件风险价值理论的定义,将其拓展于水库调度领域并建立水库防洪损失条件风险价值评价指标;Step 3-1, according to the definition of economic conditional value-at-risk theory, expand it to the field of reservoir dispatching and establish reservoir flood control loss conditional value-at-risk evaluation index;条件风险价值的含义为,在置信水平α条件下,损失超过阈值Fα的平均水平,其通用表达式如下:The meaning of conditional value-at-risk is, under the condition of confidence level α, the average level that the loss exceeds the threshold value Fα , and its general expression is as follows:
Figure FDA0003603948180000031
Figure FDA0003603948180000031
式中:y为决策变量,θ为随机变量,L(y,θ)为损失函数,max和Fα分别为损失函数最大值、置信水平α下的函数值,f(·)为防洪损失的概率密度函数;In the formula: y is the decision variable, θ is a random variable, L(y, θ) is the loss function, max and Fα are the maximum value of the loss function and the function value under the confidence level α, respectively, and f( ) is the flood control loss. Probability density function;根据水库调洪演算原理,选取决策变量为水库汛限水位、随机变量为入库洪水量级构建各分期防洪损失函数
Figure FDA0003603948180000032
并在条件风险价值指标通用表达式(5)的基础上推求水库在置信水平αi条件下、分期Di的防洪损失条件风险价值指标
Figure FDA0003603948180000033
如下:
According to the principle of reservoir flood regulation, the decision variable is selected as the flood limit water level of the reservoir, and the random variable is selected as the flood level of the reservoir to construct the flood control loss function of each stage.
Figure FDA0003603948180000032
And on the basis of the general expression (5) of the conditional value-at-risk index, the conditional value-at-risk index of the flood control loss of the reservoir under the condition of confidence level αi and in stages Di is calculated.
Figure FDA0003603948180000033
as follows:
Figure FDA0003603948180000034
Figure FDA0003603948180000034
式中:
Figure FDA0003603948180000035
为分期Di的水库汛限水位,
Figure FDA0003603948180000036
为分期Di的入库洪水量级,
Figure FDA0003603948180000037
为分期Di时段内相应于置信水平αi的阈值,
Figure FDA0003603948180000038
为分期Di内损失函数
Figure FDA0003603948180000039
的最大值,
Figure FDA00036039481800000310
为分期Di内防洪损失的概率密度函数;
where:
Figure FDA0003603948180000035
is the flood-limited water level of the reservoir in stage Di ,
Figure FDA0003603948180000036
is the inbound flood magnitude of the stage Di ,
Figure FDA0003603948180000037
is the threshold corresponding to the confidence level αi in the period of stage Di ,
Figure FDA0003603948180000038
is the loss function within the stage Di
Figure FDA0003603948180000039
the maximum value of ,
Figure FDA00036039481800000310
is the probability density function of flood control loss in the period Di ;
设分期Di内洪水风险事件
Figure FDA00036039481800000311
发生概率为P(Ai),则置信水平αi与分期Di内洪水风险事件
Figure FDA00036039481800000312
发生概率P(Ai)满足关系式P(Ai)+αi=1;
Set the flood risk event within the period Di
Figure FDA00036039481800000311
The probability of occurrence is P(Ai ), then the confidence level αi and the flood risk event in the stage Di
Figure FDA00036039481800000312
The occurrence probability P(Ai ) satisfies the relational expression P(Ai )+αi =1;
步骤3-2,在步骤2-3确定的各分期洪水量级特征参数之间的条件发生概率计算式的基础上,结合洪水风险事件发生的固有自然特性,推求水库在整个汛期时段可能发生的潜在防洪损失CVaRα计算式:Step 3-2, on the basis of the calculation formula of the conditional probability of occurrence between the characteristic parameters of the flood magnitudes of each stage determined in step 2-3, combined with the inherent natural characteristics of flood risk events, infer the possible occurrence of the reservoir during the entire flood season. Calculation formula of potential flood protection loss CVaRα :
Figure FDA00036039481800000313
Figure FDA00036039481800000313
式中:X={Q,W},a={p,3d,7d,15d,30d},X和a根据水库自身面临的入库洪水特性进行选择,P(Ai)为分期Di洪水风险事件Ai的发生概率,P(Ai+1|Ai)表征当给定分期Di洪水风险事件Ai发生时,分期Di+1洪水风险事件Ai+1发生的条件概率,见式(4);
Figure FDA0003603948180000041
αi=1-P(Ai),其中i=1,…,M;
In the formula: X={Q,W}, a={p,3d,7d,15d,30d}, X and a are selected according to the characteristics of the inflow flood faced by the reservoir itself, and P(Ai ) is the stage Di flood The occurrence probability of the risk event Ai , P(Ai+1 |Ai ) represents the conditional probability that the flood risk event Ai+1 of the stageDi+1 occurs when the flood risk event Ai of the given stage Di occurs, See formula (4);
Figure FDA0003603948180000041
αi =1-P(Ai ), where i=1,...,M;
步骤4中以水库现状设计汛限水位方案对应的汛期防洪损失条件风险价值βα为防洪约束条件,建立水库分期汛限水位优化设计模型;水库分期汛限水位优化设计模型的目标函数和主要约束条件如下:In step 4, the flood control loss condition risk valueβα corresponding to the current design of the flood-limited water level scheme of the reservoir is used as the flood control constraint condition, and the optimal design model of the reservoir's flood-limited water level by stages is established; The conditions are as follows:
Figure FDA0003603948180000042
Figure FDA0003603948180000042
Figure FDA0003603948180000043
Figure FDA0003603948180000043
式中:
Figure FDA0003603948180000044
代表各分期汛限水位优化组合方案,B(·)代表水库汛期兴利效益,CVaRα(·)代表相应于水库分期汛限水位优化组合方案
Figure FDA0003603948180000045
的防洪损失条件风险价值,其计算过程中的随机变量
Figure FDA0003603948180000046
采用的是考虑跨流域调水影响后的入库洪水过程;
Figure FDA0003603948180000047
代表分期汛限水位现状组合方案,βα(·)代表相应于水库分期汛限水位现状组合方案的防洪损失条件风险价值,其计算过程中的随机变量
Figure FDA0003603948180000048
采用未受跨流域调水影响下的入库洪水过程。
where:
Figure FDA0003603948180000044
Represents the optimal combination scheme of the flood-limited water level in each stage, B(·) represents the benefit of the reservoir during the flood season, and CVaRα (·) represents the optimal combination scheme corresponding to the flood-limited water level of the reservoir by stages
Figure FDA0003603948180000045
The Flood Loss Conditional VaR, a random variable in its calculation process
Figure FDA0003603948180000046
The inflow flood process after considering the influence of inter-basin water transfer is adopted;
Figure FDA0003603948180000047
βα (·) represents the conditional risk value of flood control loss corresponding to the current combination scheme of the flood-limited water level of the reservoir by stages, and the random variable in the calculation process
Figure FDA0003603948180000048
The inflow flood process without the influence of inter-basin water transfer was adopted.
2.根据权利要求1所述的一种考虑跨流域调水影响下的水库分期汛限水位优化设计方法,其特征在于:步骤2-2中Copula函数包括二元正态Copula函数、二元t-Copula函数、二元Archimedean-Copula函数,采用离差平方和最小准则OLS来选取OLS最小的Copula函数表达形式作为联结函数,OLS的计算公式如下:2. a kind of reservoir water level optimization design method considering the influence of cross-basin water transfer according to claim 1, it is characterized in that: in step 2-2, Copula function comprises binary normal Copula function, binary t -Copula function, binary Archimedean-Copula function, using the OLS criterion of the smallest sum of squared deviations to select the expression form of the Copula function with the smallest OLS as the link function. The calculation formula of OLS is as follows:
Figure FDA0003603948180000049
Figure FDA0003603948180000049
式中,n为样本数,Pei、Pi分别为经验频率和理论频率。In the formula, n is the number of samples, and Pei and Pi are the empirical frequency and the theoretical frequency, respectively.
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