CN107808237B - A real-time flood control risk analysis and calculation method for parallel reservoir groups - Google Patents

Abstract

The invention discloses a kind of parallel reservoir group Real time Flood risk Analytic Calculation Methods, the described method comprises the following steps: (1) establishing the mathematic(al) representation of uncertain factor, obtain the marginal distribution function of uncertain factor；(2) it is based on Copula function, solves the joint probability density distribution function of multidimensional uncertain factor；(3) multi-reservoir Technique for Real-time Joint Operation of Flood risk model is established, each moment multi-reservoir flood control operation risk is parsed；(4) calculating of multi-reservoir Technique for Real-time Joint Operation of Flood risk.The present invention considers influence of the correlation between uncertain factor to multi-reservoir Technique for Real-time Joint Operation of Flood risk, has acquired the analytic sensitivity of each moment multi-reservoir Technique for Real-time Joint Operation of Flood risk, and computational efficiency is high, is easily achieved, and has stronger versatility.

Description

A real-time flood control risk analysis and calculation method for parallel reservoir groups

technical field

The invention belongs to the risk assessment of flood control dispatching of reservoirs, and in particular relates to a real-time flood control risk analysis and calculation method for parallel reservoir groups.

Background technique

The real-time flood control scheduling of reservoir groups is one of the important technical means for flood control and disaster mitigation in the basin, which can improve the benefits of flood control projects with a small investment. However, there are many uncertain factors in the existing real-time flood control scheduling of reservoir groups, including the uncertainty of the inflow process of the reservoir group, the uncertainty of the outflow process of the reservoir group, and the uncertainty of the interval flood forecasting process. These uncertain factors lead to the uncertainty of the combined flow process of the downstream public flood control points, which has a certain impact on the flood control decision-making and has certain risks. Therefore, the real-time flood control scheduling risk assessment of reservoir groups has important academic significance and practical value. Quantitative calculations.

At present, the existing real-time flood control scheduling risk assessment methods for reservoir groups mainly have the following shortcomings: (1) it is difficult to obtain the joint probability density distribution function of multi-dimensional uncertainty factors; (2) the stochastic simulation method calculates the real-time flood control scheduling risk of reservoir groups, The computational efficiency is not high and the versatility is not enough, and it needs to be remodeled for different systems.

SUMMARY OF THE INVENTION

Purpose of the invention: Aiming at the above-mentioned deficiencies of the prior art, the present invention provides a real-time flood control risk analysis and calculation method for parallel reservoir groups to evaluate the risk problems caused by uncertain factors in the real-time flood control analysis of parallel reservoir groups.

Technical solution: a real-time flood control risk analysis and calculation method for parallel reservoir groups, comprising the following steps:

(1) Establish the mathematical expression of the uncertainty factor, and solve the marginal distribution function of the uncertainty factor;

(2) Based on the Copula function, solve the joint probability density distribution function of multi-dimensional uncertainty factors;

(3) Establish a real-time flood control dispatch risk model for reservoir groups, and analyze the flood control dispatch risks of reservoir groups at each moment;

(4) Calculation of real-time flood control dispatch risk for reservoir groups.

Further, the uncertainty factors in step (1) include the inflow of the reservoir group, the outflow of the reservoir group and the uncertainty of interval flood forecasting.

Further, described step (2) comprises the steps:

(2.1) Define H(q ₁ (t), q ₂ (t), q ₃ (t)) as the joint probability of the outflow random process of reservoir 1, the outflow random process of reservoir 2, and the interval flood outflow random process Distribution function, the calculation formula is as follows:

H(q ₁ (t),q ₂ (t),q ₃ (t))=C(F(q ₁ (t)),F(q ₂ (t)),F(q ₃ (t))) (1)

In the formula, q ₁ (t) is the random process of the outflow flow of reservoir 1 at time t; q ₂ (t) is the random process of outflow flow of reservoir 2 at time t; q ₃ (t) is the flow of the downstream flood control section at time t. Interval flood stochastic process; F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)) are uncertainty factors respectively - the outflow stochastic process of reservoir 1 q ₁ (t) , the marginal distribution function of the outflow random process q ₂ (t) of reservoir 2, and the interval flood random process q ₃ (t); C is the Copula function;

(2.2) Define h(q ₁ (t), q ₂ (t), q ₃ (t)) as the joint probability density function of the outflow random process of reservoir 1, the outflow random process of reservoir 2, and the interval flood random process ,Calculated as follows:

In the formula, f(q _i (t)) is the probability density function of the uncertainty factor q _i (t), i=1, 2, 3, c(F(q ₁ (t)), F(q ₂ ( t)), F(q ₃ (t)) is the probability density function of the Copula function C(F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)).

Further, the Copula function described in step (2) includes 3 kinds of calculation formulas, and the expressions are as follows:

Among them, α(t) is the parameter of Copula function;

Further, the specific steps of the step (3) are as follows:

Define the real-time flood control dispatch risk Risk(t) of the reservoir group as the probability that the combined flow process of the public flood control points exceeds the safe flow threshold of the flood control section at time t, and connect the uncertain factors in step (1) through the Copula function to obtain the real-time flood control of the reservoir group. The calculation formula of scheduling risk Risk(t) is:

In the formula, Risk(t) represents the real-time flood control dispatch risk of the reservoir group system at time t; Q(t) represents the combined flow process of the public flood control points at time t; Q _C (t) represents the safe flow threshold of the flood control section at time t, which is desirable Safe discharge of public flood control point; Ω ₀ ={q ₁ (t)+q ₂ (t)+q ₃ (t)>Q _C (t)}, Ω ₁ is the integral conversion interval corresponding to Ω ₀ .

Further, described step (4) comprises the steps:

(4.1) Obtaining the operation data of the reservoir group and real-time forecasting of the mean value process and error distribution of inflow discharge, and the mean value process and error distribution of interval flood forecasting;

(4.2) According to the flood control scheduling rules of the reservoir, carry out the flood adjustment calculation of the reservoir, and calculate the random process of the outflow flow of the reservoir;

(4.3) Select Copula function as uncertainty factor - joint probability of outflow random process q ₁ (t) of reservoir 1, outflow random process q ₂ (t) of reservoir 2, and interval flood random process q ₃ (t) Distribution function.

(4.4) According to the selected Copula function, the real-time flood control dispatch risk of the reservoir group at each moment is calculated.

Beneficial effects: Compared with the prior art, the present invention has significant effects as follows: 1. Considering the impact of the correlation between uncertain factors on the risk of real-time flood control and dispatching of reservoir groups, the risk assessment method for real-time flood control and dispatching of reservoir groups considers more factors; Comprehensive; 2. The analytical calculation formula of the real-time flood control dispatch risk of reservoir groups at each moment is established by the Copula function; 3. The analytical calculation method has high calculation efficiency, is easy to implement, and has strong generality.

Description of drawings

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

Fig. 2 is the schematic diagram of the parallel reservoir group system of the present invention;

FIG. 3 is a schematic flow chart of calculation steps of the present invention.

Detailed ways

In order to further illustrate the technical solutions disclosed in the present invention, a detailed description is given below with reference to the accompanying drawings and specific embodiments of the description.

The method comprehensively considers the uncertainty of the inflow process of the reservoir group, the uncertainty of the outflow process of the reservoir group, and the uncertainty of the interval flood forecasting process, and considers the correlation between the uncertain factors, and is established by the Copula function theory. Based on the joint probability density distribution function of the above uncertainty factors, the definition of real-time flood control dispatch risk of reservoir groups is proposed, and the analytical calculation formula of real-time flood control dispatch risk of reservoir groups at each moment is obtained.

As shown in Figure 1, a real-time flood control risk analysis and calculation method for parallel reservoir groups includes the following steps:

Step 1: Propose the mathematical expression of the uncertainty factor, and solve the marginal distribution function of the uncertainty factor:

(1.1) Define Q _i (t) as the random process of the inflow flow of reservoir i at time t, and the calculation formula is as follows:

in, is the mean value of the random process of inflow flow of reservoir i at time t; ξ _i (t) is the forecast error of inflow flow of reservoir i at time t, and ξ _i (t) obeys a normal distribution, that is, Distribution parameters is the mean square error of the inflow forecast error of reservoir i, which can be obtained from the hydrological forecast model. Then the random process q _i (t) of the inflow flow of reservoir i at time t also obeys a normal distribution, that is,

Then, define q ₃ (t) as the interval flood random process of the downstream flood control section at time t, and the calculation formula is as follows:

in, is the mean value of the stochastic process of flood in the interval at time t, that is, the deterministic hydrological forecast result; ξ ₃ (t) is the interval flood forecast error at time t, and ξ ₃ (t) obeys a normal distribution, that is, Distribution parameters is the mean square error of interval flood forecast error, which can be obtained from the hydrological forecast model. Then the interval flood random process q ₃ (t) of the downstream flood control section at time t also obeys the normal distribution, that is,

(1.2) Define q _i (t) as the random process of the outflow flow of reservoir i at time t, and the calculation formula is as follows:

in, is the mean value of the random process of the outflow flow of reservoir i at time t; η _i (t) is the outflow flow error of reservoir i at time t, and η _i (t) obeys a normal distribution, that is, Then the random process q _i (t) of the outflow flow of reservoir i at time t also obeys the normal distribution, that is, Distribution parameters is the mean square error of the outflow flow error of reservoir i, and the calculation steps are as follows:

1) Random process according to the inflow flow of reservoir i and interval flood stochastic process distribution, here the Latin hypercube sampling is preferred to generate samples of M groups of inbound flow processes and a sample of interval flood processes

2) According to the flood control scheduling rules of the reservoir i, the flood regulation calculation of the reservoir is carried out through the principle of water balance, and the outflow flow process sample of the reservoir i is calculated.

3) Fitting the distribution of the random process of the outflow flow of reservoir i at each moment according to the sample of the outflow flow process of reservoir i

Step 2: Based on the Copula function, solve the joint probability density distribution function of multi-dimensional uncertainty factors:

Define H(q ₁ (t), q ₂ (t), q ₃ (t)) as the uncertainty factor - the outflow random process of reservoir 1 q ₁ (t), the outflow random process of reservoir 2 q ₂ (t ), and the joint probability distribution function of the interval flood random process q ₃ (t), according to the Copula function theory, the following formula is used to calculate:

H(q ₁ (t),q ₂ (t),q ₃ (t))=C(F(q ₁ (t)),F(q ₂ (t)),F(q ₃ (t))) (9)

Among them, F(q ₁ (t)), F(q ₂ (t)), and F(q ₃ (t)) are the uncertainty factors of the outflow random process q ₁ (t) of reservoir 1 and the outflow of reservoir 2, respectively. The marginal distribution functions of the flow random process q ₂ (t) and the interval flood random process q ₃ (t), C is the Copula function.

The Copula function used in this example includes the following three types:

Wherein, α(t) is a parameter of the Copula function. In this embodiment, the maximum likelihood method is preferably used to estimate the parameters of the Copula function.

Take the partial derivatives on both sides of Equation (9) to obtain the uncertainty factors—the outflow random process q ₁ (t) of reservoir 1, the outflow random process q ₂ (t) of reservoir 2, and the interval flood random process q ₃ (t) ), the joint probability density function is as follows:

Among them, f(q _i (t)) is the probability density function of the uncertainty factor q _i (t), i=1, 2, 3;

h(q ₁ (t), q ₂ (t), q ₃ (t)) is the uncertainty factor of the outflow random process of reservoir 1 q ₁ (t), the outflow random process of reservoir 2 q ₂ (t), and the joint probability density function of the interval flood stochastic process q ₃ (t);

c(F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)) are Copula functions C(F(q ₁ (t)), F(q ₂ (t)) , the probability density function of F(q ₃ (t)).

In this embodiment, the K-S test method is used to test the three types of Copula functions in formula (10) respectively, and the backup Copula functions of uncertain factors are screened, and then the OLS criterion is used in this embodiment to evaluate the goodness of fit of the backup Copula functions. , so that the Copula function with the best fit is selected as the joint probability distribution of uncertainty factors, where the OLS value of each Copula function is calculated by the following formula:

in, is the uncertainty factor - the empirical cumulative probability value of the outflow random process q ₁ (t) of reservoir 1, the outflow random process q ₂ (t) of reservoir 2, and the interval flood random process q ₃ (t); is the theoretical cumulative probability value of the uncertainty factor - the outflow random process q ₁ (t) of reservoir 1, the outflow random process q ₂ (t) of reservoir 2, and the interval flood random process q ₃ (t).

Step 3, establish a real-time flood control scheduling risk model of the reservoir group, and analyze the flood control scheduling risk of the reservoir group at each moment.

The real-time flood control dispatch risk of reservoir groups is defined as the probability Risk(t) that the combined flow process of public flood control points exceeds the safety flow threshold of the flood control control section, which means that there is a probability Risk(t) at time t that the combined flow process of public flood control points will exceed the safety of the flood control control section. Traffic thresholds provide decision makers with risk information for risk decisions. Substituting Equation (11) into Equation (1), the analytical calculation formula of Risk(t) for the real-time flood control dispatch risk of reservoir groups at each moment is obtained:

Among them, Q _C (t) represents the safe flow threshold of the flood control control section at time t, which can be taken as the safe discharge of the public flood control point; Ω ₀ ={q ₁ (t)+q ₂ (t)+q ₃ (t)>Q _C (t)}, Ω ₁ is the integral conversion interval corresponding to Ω ₀ .

Step 4: Calculation of real-time flood control scheduling risk for reservoir groups.

Carry out the application of the real-time flood control scheduling risk model of the reservoir group. In this embodiment, the recursive algorithm is used to calculate the real-time flood control scheduling risk of the reservoir group at each moment. The flow of the algorithm is shown in FIG. 3 and mainly includes the following solving steps:

(1) Obtain the operation data of the reservoir group, including the flood control scheduling rules of the reservoir, the water level storage capacity curve, the discharge capacity curve, the starting water level, the design flood level, the check flood level, and the reservoir crest elevation and other characteristic values;

(2) The process of obtaining the mean value of real-time forecast inflow of reservoir groups Interval Flood Forecast Mean Process Inbound flow forecast error ξ _i (t), i=1,2, interval flood forecast error ξ ₃ (t);

(3) According to the distribution of the random process of the inflow flow and the random process of the interval flood of the reservoir group, in this embodiment, Latin hypercube sampling is used to generate the samples of the M groups of inflow processes and a sample of interval flood processes

(4) According to the flood control scheduling rules of the reservoir i, the flood regulation calculation of the reservoir is carried out through the principle of water balance, and the outflow flow process sample of the reservoir i is calculated.

(5) According to formula (8), calculate the distribution parameters of the random process of the outflow flow of reservoir i and

(6) Select the backup Copula function and perform the K-S test;

(7) Calculate the OLS value of this Copula function according to formula (12), compare the OLS values of the alternate Copula functions, and select the Copula function with the smallest OLS value as the uncertainty factor - the outflow random process of reservoir 1 q ₁ (t) , the joint probability distribution function of the outflow random process q ₂ (t) of reservoir 2, and the interval flood random process q ₃ (t);

(8) According to the selected Copula function and formula (13), set the safe flow threshold Q _C (t) of the public flood control point, and calculate the real-time flood control dispatch risk of the reservoir group at each moment.

Claims (5)

1. A parallel reservoir group real-time flood control risk analysis and calculation method is characterized by comprising the following steps: the method comprises the following steps:

(1) three uncertainty factors of the random process of the warehousing flow of each reservoir, the random process of the ex-warehouse flow of each reservoir and the random process of interval flood forecast are considered; establishing a mathematical expression of uncertainty factors, expressing each uncertainty factor random process as an error random process on which the mean value is superposed, and describing an edge distribution function of the uncertainty factors by adopting normal distribution;

(2) based on the flood control dispatching rules of all reservoirs, converting the inlet flow random process of all the reservoirs into the outlet flow random process of all the reservoirs through random simulation and reservoir flood regulation calculation; solving a joint probability density distribution function of multi-dimensional uncertainty factors comprising a random process of the warehouse-out flow of each reservoir and a random process of interval flood forecast based on a Copula function;

(3) defining the reservoir group real-time flood control scheduling risk as the probability that the combined flow process of public flood control points exceeds the safety flow threshold of a flood control section; analyzing and obtaining flood control scheduling risks of the reservoir groups at each moment through direct integration of joint probability density distribution functions of multi-dimensional uncertainty factors of the outflow process and interval flood process of each reservoir;

(4) acquiring real-time operation data of reservoirs, a process of forecasting warehousing flow of each reservoir and an error process thereof, and an interval flood process and an error process thereof; and establishing a joint probability density distribution function of multidimensional uncertainty factors in the random process of the warehouse-out flow of each reservoir and the random process of interval flood forecasting through a Copula function, and calculating the real-time flood control dispatching risk of the reservoir group.

2. The method for analyzing and calculating the risk of flood control in parallel of the reservoir groups according to claim 1, wherein the method comprises the following steps: the step (2) comprises the following steps:

(2.1) definition of H (q)₁(t),q₂(t),q₃(t)) is a combined probability distribution function of the random process of the delivery flow of the reservoir 1, the random process of the delivery flow of the reservoir 2 and the random process of the interval flood forecast, and the calculation formula is as follows:

H(q₁(t),q₂(t),q₃(t))＝C(F(q₁(t)),F(q₂(t)),F(q₃(t))) (1)

in the formula, q₁(t) is a random process of the delivery flow of the reservoir 1 at the moment t; q. q.s₂(t) is a random process of the delivery flow of the reservoir 2 at the moment t; q. q.s₃(t) is an interval flood random process of a downstream flood control section at the time t; f (q)₁(t))、F(q₂(t))、F(q₃(t)) random process q of discharge flow of reservoir 1, respectively, as uncertainty factor₁(t) reservoir2 random process q of flow out of warehouse₂(t) and Interval flood forecasting stochastic Process q₃(t) an edge distribution function; c is a Copula function;

(2.2) definition of h (q)₁(t),q₂(t),q₃(t)) is a combined probability density function of the random process of the delivery flow of the reservoir 1, the random process of the delivery flow of the reservoir 2 and the random process of the interval flood forecast, and the calculation formula is as follows:

in the formula, f (q)_i(t)) is an uncertainty factor q_i(t), i ═ 1,2,3 probability density function, c (F (q)₁(t)),F(q₂(t)),F(q₃(t)) is the Copula function C (F (q)₁(t)),F(q₂(t)),F(q₃(t)) probability density function.

3. The method for analyzing and calculating the risk of flood control in parallel of the reservoir groups according to claim 1, wherein the method comprises the following steps: the Copula function described in step (2) includes 3 calculation formulas, and the expression is as follows:

wherein α (t) is a parameter of Copula function, F (q)₁(t)) is a random process (q) of the delivery flow of the reservoir 1₁(t)) edge distribution function, F (q)₂(t)) is a random process (q) of the delivery flow of the reservoir 2₂(t)) edge distribution function, F (q)₃(t)) random process (q) of flood forecasting for intervals₃(t)) edge distribution function.

4. The method for analyzing and calculating the risk of flood control in parallel of the reservoir groups according to claim 1, wherein the method comprises the following steps: the step (3) comprises the following specific steps:

defining the real-time flood control scheduling risk Risk (t) of the reservoir group as the probability that the combined flow process of the public flood control points at the time t exceeds the safe flow threshold of the flood control section, and connecting uncertainty factors in the step (1) through a Copula function to obtain a calculation formula of the real-time flood control scheduling risk Risk (t) of the reservoir group, wherein the calculation formula is as follows:

in the formula, Risk (t) represents the real-time flood control scheduling risk of the reservoir group system at the time t; q (t) represents the combined flow process of the public flood control point at the time t; q_C(t) the safe flow threshold of the flood control section at the moment t is shown, and the safe discharge of a public flood control point can be taken; omega₀＝{q₁(t)+q₂(t)+q₃(t)＞Q_C(t)}，Ω₁Is corresponding to omega₀The integral conversion interval of (1); f (q)₁(t)) is a random process (q) of the delivery flow of the reservoir 1₁(t)) edge distribution function, F (q)₂(t)) is a random process (q) of the delivery flow of the reservoir 2₂(t)) edge distribution function, F (q)₃(t)) random process (q) of flood forecasting for intervals₃(t)) an edge distribution function; h (q)₁(t),q₂(t),q₃(t)) is a combined probability density function of the random process of the delivery flow of the reservoir 1, the random process of the delivery flow of the reservoir 2 and the random process of the interval flood forecast.

5. The method for analyzing and calculating the risk of flood control in parallel of the reservoir groups according to claim 1, wherein the method comprises the following steps: the step (4) comprises the following steps:

(4.1) acquiring operation data of a reservoir group, and forecasting the average value process and error distribution of the flow entering the reservoir group in real time, and forecasting the average value process and error distribution of the flood in an interval;

(4.2) carrying out reservoir flood regulation calculation according to the reservoir flood control regulation rule, and calculating the random process of the reservoir delivery flow;

(4.3) selecting Copula function as uncertainty factor-stochastic process q of outflow from reservoir 1₁(t) reservoir 2 outflow randomization procedure q₂(t) and Interval flood randomization procedure q₃(t) a joint probability distribution function;

and (4.4) calculating the real-time flood control scheduling risk of the reservoir group at each moment according to the selected Copula function.