Cascade reservoir distributed robust flood control optimization scheduling method considering flood forecast error

Abstract

The invention discloses a cascade reservoir distributed robust flood control optimization scheduling method considering flood forecast errors, and the method comprises the steps: building an uncertainty set of the flood forecast errors based on statistical information, and fully considering the distribution rule of the flood forecast errors; meanwhile, a distributed robust optimization scheduling model is constructed with the minimum flow maximum value of the downstream control station, and the optimal error amplification coefficient is selected with the scheduling scheme risk as the index, so that the water resource utilization efficiency can be improved on the premise of effectively controlling the flow of the downstream station; therefore, safety of downstream flood control sites is guaranteed and economic benefits are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of hydropower energy system scheduling, and in particular to a distributed robust flood control optimization scheduling method for cascade reservoirs considering flood forecast errors. Background Art

[0002] Cascade reservoir scheduling is an effective means to cope with flood disasters. However, the inaccuracy of flood prediction makes it difficult to anticipate the actual discharge flow of cascade reservoirs, further bringing difficulties to the prediction of the flow process at flood control stations downstream of cascade reservoirs, resulting in situations where the limit flow is exceeded, seriously threatening the safety of downstream cities. Therefore, how to consider flood forecast errors in cascade reservoir flood control scheduling and improve the utilization efficiency of water resources on the premise of ensuring flood control safety is of great significance for ensuring people's life and property safety and improving the economic benefits of cascade reservoirs.

[0003] In the prior art, stochastic programming and robust optimization are effective means to solve optimization problems involving random variables. Stochastic programming describes random variables through chance constraints and design of scenario distribution functions. Stochastic programming assumes that random variables follow a certain distribution function and solves the model by minimizing the expectation under the distribution function. However, in practice, it is difficult to obtain the true distribution function of random variables, and often an empirical distribution is used instead, which leads to computational difficulties in stochastic programming and the results are difficult to conform to the actual flood process due to the deviation of the distribution function. Robust optimization, on the other hand, uses a set of random variables to describe the range of values of random variables and performs optimization calculations in the worst case within the set of random variables. However, in the actual scheduling process, the worst case of flood forecast errors rarely occurs, which results in the calculation results of robust optimization often being too conservative and difficult to make full use of flood resources. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above deficiencies and provide a distributed robust flood control optimization scheduling method for cascade reservoirs considering flood forecast errors, which can reduce scheduling deviation, make full use of flood resources, and effectively control flood control scheduling risks.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a distributed robust flood control optimization scheduling method for cascade reservoirs considering flood forecast errors, comprising the following steps:

[0006] S1, collect historical flood forecast data, calculate flood forecast error statistical indicators, determine the relationship between the magnitude of flood flow and the variance of forecast errors, and construct an uncertain set of flood forecast errors with the expected value and variance data of flood forecast errors;

[0007] S2. Construct an objective function with the minimum maximum flow of the downstream control site of cascade reservoirs under the worst flood forecasting error in the flood forecasting error uncertainty set. Take the water balance of cascade hydropower stations, the constraints of the initial and final water levels of cascade hydropower stations, and the upper and lower limits of the downstream discharge and storage capacity of cascade hydropower station reservoirs as constraints to establish a distributed robust optimization scheduling model, where the flow of the downstream reservoir site of cascade reservoirs is expressed as Q D =Q 末 +Q 区 , where Q D represents the flow of the downstream flood control site, Q 末 represents the discharge of the most downstream reservoir in the cascade reservoir, and Q 区 represents the inter-basin confluence between the most downstream reservoir in the cascade reservoir and the downstream control site;

[0008] S3. Solve the distributed robust optimization scheduling model to obtain the discharge of each reservoir in the cascade reservoir, and then calculate the risk value P F of the current scheduling plan. The risk value P F is defined as the probability that the flow of the downstream flood control site exceeds the limit flow, and the specific expression is P F =P(Q D >Q L ), where Q L represents the flood control limit flow of the downstream control site;

[0009] S4. If the risk value P F of the current scheduling plan is large, increase the variance amplification coefficient k in the flood forecasting error uncertainty set and re-execute S3. If the risk value P F of the current scheduling plan is small, decrease the variance amplification coefficient k in the flood forecasting error uncertainty set and re-execute S3. If the risk value of the current scheduling plan is moderate, record the variance amplification coefficient in the current flood forecasting error uncertainty set as k, so as to determine the optimal distributed robust optimization scheduling model;

[0010] S5. Obtain real-time flood forecasting data and input it into the optimal distributed robust optimization scheduling model. Determine the forecast error variance value according to the real-time flood forecasting data, solve the optimal distributed robust optimization scheduling model, obtain the real-time downstream discharge process of cascade reservoirs, and thus obtain the flood control optimization scheduling plan of cascade reservoirs.

[0011] Further, in S1, calculate the flood forecasting error statistical index and determine the relationship between the flood flow magnitude and the forecast error variance, specifically including,

[0012] S11. Calculate the error between the prediction result obtained by the flood prediction method and the measured value, and calculate the mean value μ of the forecast error;

[0013] S12. Calculate the variance value σ of the prediction error under different predicted flows 2 , and obtain the prediction error variances corresponding to different predicted flows

[0014] Furthermore, the calculation method of μ is as follows: where N represents the total number of prediction error samples, and d n represents the prediction error of the nth sample, and n is a natural number greater than or equal to 1;

[0015] The calculation method of is as follows: M represents the number of prediction error samples of the predicted flow , and d m represents the mth prediction error sample of the predicted flow , and m is a natural number greater than or equal to 1, represents the mean value of the prediction error corresponding to the predicted flow.

[0016] Further, in S1, the construction of the flood prediction error uncertainty set is specifically as follows:

[0017]

[0018] where represents the constructed flood prediction error uncertainty set, represents the probability distribution of the flood prediction error, represents the real number space of dimension J, and J represents the dimension of the flood prediction error d, represents the set of all probability distributions of dimension , d and represent the flood prediction error and the auxiliary variable respectively, represents the expectation under the distribution 2 , μ represents the expected value of the flood prediction error, and σ represents the variance value of the flood prediction error,

[0019] Furthermore, the is specifically expressed in the following form: d and

[0020] - are the upper and lower limits of the flood prediction error respectively, and d j , μ j and u j represent the jth values in the prediction error vector, the prediction error expected value vector, and the auxiliary vector respectively.

[0021] Furthermore, in S2, the specific process of establishing the distributed robust optimization scheduling model is as follows:

[0022]

[0023] V i,1 =V i,begin ,V i,T+1 =V i,end

[0024] where Q represents the discharge of each reservoir in each cascade stage, X represents the decision space, is the flood forecast error uncertainty set constructed above, which contains all possible values of the flood forecast error distribution T represents the length of the scheduling period, Q t represents the flow at the downstream section in the t-th period, Q l represents the flood control limit flow of the downstream section, V i,t represents the storage capacity of the i-th hydropower station at time t, and the natural inflow and discharge are I i,y and Q i,t , d i,t represents the natural inflow forecast error of the i-th hydropower station at time t, which is 0 if there is no natural inflow, Z i represents the set of numbers of the upstream reservoirs of the i-th reservoir. The water flow delay period from the z-th reservoir to the i-th reservoir is τ z,i , where the single-step scheduling period length is Δt; where Q i and are the lower and upper limits of the discharge of the i-th reservoir respectively, V i and are the lower and upper limits of the storage capacity of the i-th reservoir respectively, V i,begin and V i,end are the storage capacities at the start and end of the calculation of the i-th reservoir respectively.

[0025] Furthermore, the risk value P F of the scheduling plan in S3 is specifically,

[0026] where T represents the number of periods in the scheduling period, P t represents the probability that the flow at the control site exceeds the limit water level at time t, specifically expressed as where f(Q t ) represents the probability density function of the flow at the control site in each period, Q t represents the flow at the downstream section in the t-th period;

[0027] Further, the variance amplification coefficient k in S4 is specifically as follows: The variance amplification coefficient k is a real number greater than 0. When k = 1, the variance is the statistical variance of the flood forecast error. When k < 1, the flood forecast error variance is reduced. When k > 1, the flood forecast error is amplified. That is, the larger the variance amplification coefficient, the larger the uncertainty set of the flood forecast error.

[0028] Further, determining the forecast error variance value according to the real-time flood forecast data in S5 is specifically as follows:

[0029] According to the relationship between the flood flow magnitude determined in S1 and the forecast error variance, if the real-time flood forecast Q r is the same as the historical flood flow, directly query the corresponding forecast error variance. If they are different, perform interpolation based on two adjacent historical flood flows. The calculation method is where Q 左 and Q 右 are respectively the left and right two flows closest to the real-time flood forecast Q r , and σ 右 2 and σ 左 2 are respectively the variance values corresponding to Q 左 and Q 右 ;

[0030] Further, solving the distributed robust optimization scheduling model in S5 is specifically as follows:

[0031] Based on the duality theory and linear decision rules, the distributed robust optimization scheduling model is transformed into a mixed-integer programming model under the flood forecast error uncertainty set, and then solved using the GUROBI solver.

[0032] Advantages of the present invention:

[0033] 1. The present invention proposes a method for constructing an uncertain set of flood forecasting errors based on historical flood forecasting error statistical information, which can reduce the scheduling deviation, make full use of flood resources, and effectively control the flood control scheduling risk. The present invention calculates the mean of historical flood forecasting errors, further calculates the forecasting error variances corresponding to different flows, determines the relationship between the flood flow magnitude and the forecasting error variance, defines a variance amplification factor to adjust the size of the flood forecasting error uncertain set, determines the variance amplification factor with the scheduling scheme risk as an index, and constructs the flood forecasting error uncertain set according to the optimal variance amplification factor, so as to more accurately describe the distribution law of flood forecasting errors and improve the safety of the scheduling process; at the same time, the present invention takes the minimum of the maximum flow at the downstream control site of cascade reservoirs as the goal, constructs a distributed robust optimization scheduling model to handle the uncertainty of flood forecasting errors, and can effectively control the flow process at the downstream flood control site in the event of a flood in the basin, obtaining a more safe and reliable scheduling result.

[0034] 2. The method of the present invention constructs an uncertain set of flood forecasting errors based on statistical information, fully considering the distribution law of flood forecasting errors. At the same time, the method constructs a distributed robust optimization scheduling model with the minimum of the maximum flow at the downstream control site, and selects the optimal error amplification factor with the scheduling scheme risk as an index, which can improve the water resource utilization efficiency on the premise of effectively controlling the flow magnitude at the downstream site, thus ensuring the safety of the downstream flood control site and improving the economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic flow chart of a distributed robust flood control optimization scheduling method for cascade reservoirs considering flood forecasting errors. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0037] As Figure 1 shown, a flood control optimization scheduling method for cascade reservoirs considering flood forecasting errors, the method includes the following steps:

[0038] S1. Collect historical flood forecasting data, calculate the statistical indexes of flood forecasting errors, determine the relationship between the flood flow magnitude and the forecasting error variance, and construct an uncertain set of flood forecasting errors with the expected value and variance data of flood forecasting errors;

[0039] S2. Construct an objective function by minimizing the maximum value of the flow at the downstream control site of the cascade reservoirs under the worst flood forecasting error in the flood forecasting error uncertainty set. Use the water balance of the cascade hydropower stations, the constraints on the initial and final water levels of the cascade hydropower stations, and the upper and lower limits of the discharge and storage capacity of the cascade hydropower station reservoirs as constraints to establish a distributed robust optimization scheduling model, where the flow at the downstream reservoir site of the cascade reservoir is expressed as Q D =Q 末 +Q 区 , where Q D represents the flow at the downstream flood control site, Q 末 represents the discharge from the most downstream reservoir in the cascade reservoir, and Q 区 represents the catchment between the most downstream reservoir in the cascade reservoir and the downstream control site;

[0040] S3. Solve the distributed robust optimization scheduling model to obtain the discharge from each reservoir in the cascade reservoir, and then calculate the risk value P F of the current scheduling plan. The risk value P F is defined as the probability that the flow at the downstream flood control site exceeds the limit flow, and the specific expression is P F =P(Q D >Q L ), where Q L represents the flood control limit flow of the downstream control site;

[0041] S4. If the risk value P F of the current scheduling plan is too large, increase the variance amplification coefficient k in the flood forecasting error uncertainty set and re - execute S3. If the risk value P F of the current scheduling plan is too small, decrease the variance amplification coefficient k in the flood forecasting error uncertainty set and re - execute S3. If the risk value of the current scheduling plan is appropriate, record the variance amplification coefficient in the current flood forecasting error uncertainty set as k, so as to determine the optimal distributed robust optimization scheduling model;

[0042] S5. Obtain real - time flood forecasting data and input it into the optimal distributed robust optimization scheduling model. Determine the variance value of the forecasting error according to the real - time flood forecasting data, solve the optimal distributed robust optimization scheduling model, obtain the real - time discharge process of the cascade reservoir, and thus obtain the flood control optimal scheduling plan of the cascade reservoir.

[0043] That is, in the method of the present invention, first, the statistical information of the historical flood forecast error data is calculated, and the flood forecast error uncertainty set is constructed with the variance amplification factor with the best risk of the scheduling scheme to obtain the best distributed robust optimization scheduling model. Then, the real-time flood forecast data is obtained and input into the best distributed robust optimization scheduling model. By solving the best distributed robust optimization scheduling model, the outflow process of each reservoir in the cascade reservoir is obtained, so as to obtain the flood control optimization scheduling scheme of the cascade reservoir.

[0044] In this embodiment, calculating the flood forecast error statistical index in S1 to determine the relationship between the flood flow magnitude and the forecast error variance specifically includes:

[0045] S11, calculating the error between the prediction result obtained by the flood prediction method and the measured value, calculating the mean value μ of the forecast error, and the calculation method is where N represents the total number of forecast error samples, d n represents the prediction error of the nth sample, and n is a natural number greater than or equal to 1;

[0046] S12, calculating the forecast error variance value σ 2 under different forecast flows, and obtaining the forecast error variances corresponding to different forecast flows The calculation method is where M represents the number of forecast error samples of the forecast flow d represents the mth forecast error sample of the forecast flow m and m is a natural number greater than or equal to 1, represents the mean value of the forecast error corresponding to the forecast flow ;

[0047] In this embodiment, constructing the flood forecast error uncertainty set specifically is:

[0048]

[0049] where represents the constructed flood forecast error uncertainty set, represents the probability distribution of the flood forecast error, represents the real number space of dimension J, and J represents the dimension of the flood forecast error d, represents the set of all probability distributions of dimension d and respectively represent the flood forecast error and the auxiliary variable, represents the expectation under the distribution , μ represents the expected value of the flood forecast error, and σ 2 represents the variance value of the flood forecast error, is the support set of flood forecast error, specifically expressed in the following form: d are the upper and lower limits of the flood forecast error, respectively, and d j , μ j and u j represent the j-th values in the forecast error vector, the forecast error expectation vector, and the auxiliary vector, respectively.

[0050] In this embodiment, the establishment of the cascade reservoir distributed robust flood control optimization scheduling model is specifically as follows:

[0051]

[0052]

[0053] V i,1 = V i,begin , V i,T+1 = V i,end

[0054] where Q represents the discharge of each reservoir in the cascade at each time period, X represents the decision space, is the uncertainty set of flood forecast error constructed above, which contains all possible values of the flood forecast error distribution , T represents the length of the scheduling time period, Q t represents the flow of the downstream section at the t-th time period, Q l represents the flood control limit flow of the downstream section. V i,t represents the storage capacity of the i-th hydropower station at time t, and the natural inflow and discharge are I i,t and Q i,t , d i,t represents the natural inflow forecast error of the i-th hydropower station at time t, which is 0 if there is no natural inflow, and Z i represents the set of numbers of the upstream reservoirs of the i-th reservoir, and the water flow delay period from the z-th reservoir to the i-th reservoir is τ z,i , where the single-step scheduling time period is Δt. Among them Q i and are the lower and upper limits of the discharge of the i-th reservoir, respectively, V i and are the lower and upper limits of the storage capacity of the i-th reservoir, respectively, V i,begin and V i,end are the storage capacities at the start and end of the calculation of the i-th reservoir, respectively.

[0055] In this embodiment, the variance amplification coefficient k is specifically a real number greater than 0. When k is 1, the variance is the statistical variance of the flood forecast error. When k is less than 1, the flood forecast error variance is reduced. When k is greater than 1, the flood forecast error is amplified. That is, the larger the variance amplification coefficient, the larger the uncertainty set of the flood forecast error.

[0056] In this embodiment, the risk value P of the scheduling plan in S3 F , specifically, its calculation method is where T represents the number of time periods in the scheduling period, and P t represents the probability that the flow rate of the control station at time t exceeds the limit water level, specifically expressed as where f(Q t ) represents the probability density function of the flow rate of the control station in each time period, and Q t represents the flow rate of the downstream section at the t-th time period;

[0057] In this embodiment, determining the forecast error variance value according to the real-time flood forecast data in S5 is specifically as follows: According to the relationship between the flood flow magnitude determined in S1 and the forecast error variance, if the real-time flood forecast Q r is the same as the historical flood flow, the corresponding forecast error variance is directly queried. If they are different, interpolation is performed based on two adjacent historical flood flows, and the calculation method is where Q 左 and Q 右 are respectively the left and right two flow rates closest to the real-time flood forecast Q r , and σ 右 2 and σ 左 2 are respectively the variance values corresponding to Q 左 and Q 右 ;

[0058] In this embodiment, solving the distributed robust optimization scheduling model in S5 is specifically as follows: Based on the duality theory and linear decision rules, the distributed robust optimization scheduling model is converted into a mixed-integer programming model under the flood forecast error uncertainty set, and then the GUROBI solver is used for solving.

[0059] The main principle of converting the distributed robust optimization scheduling model into a mixed-integer programming model using the duality theory and linear decision rules is as follows:

[0060] The part of the distributed robust optimization scheduling model that is difficult to solve directly is mainly the objective function part where the downstream site flow rate can be expressed as where represents the outflow of the most downstream hydropower station in the cascade hydropower station at time t, It represents the catchment flow from the most downstream hydropower station in the cascade hydropower station to the flood control section at time t. Substituting it into the objective function, we get the following form:

[0061]

[0062] Further linearizing it, it can be transformed into the following form:

[0063]

[0064] The water balance constraint in the operation process of the cascade hydropower station is an equality constraint that must be satisfied. However, due to the uncertainty of the inflow, the reservoir storage V and the discharge Q cannot be determined simultaneously. Therefore, in this embodiment, the reservoir storage V is selected as the decision variable, and the discharge Q is the recourse variable, which is determined by the forecast error d and the auxiliary variable u. To transform it into a finite-dimensional decision variable, it is restricted by the method of linear decision rules. After being transformed by the linear decision rules, Q i,t is in the following form:

[0065] Q i,t = A i,t d + B i,t u + C i,t

[0066] where A is a matrix decision variable of dimension I×T×T, B is a matrix decision variable of dimension I×(T + 1)×(T + 1), C is a matrix decision variable of dimension I×T, I is the number of cascade reservoirs, and T is the length of the operation period.

[0067] The model after linearization and linear decision rule processing is as follows:

[0068]

[0069] Q i,t = A i,t d + B i,t u + C i,t

[0070]

[0071] V i,1 = V i, b eg i n , V i,T+1 = V i,end

[0072] According to the robust duality theory, the above model can be further transformed into a robust optimization model, in the following specific form:

[0073]

[0074] r + s ′ d + t ′ u ≥ y

[0075]

[0076] V i ,1 = V i,begin , V i,T+1 = V i,end

[0077] t ≥ 0

[0078] Q i,t = A i,t d + B i,t u + C i,t

[0079]

[0080] wherein are decision variables of 1 dimension, T dimensions and T dimensions respectively, and μ and σ 2 are the expectation and variance of the forecast error in the flood forecast uncertainty set respectively, is the support set of the forecast error d and the auxiliary variable u.

[0081] Then, by using the cone duality theory to transform the second-order cone constraint in the above model, the form of mixed-integer programming can be obtained. With the help of the GUROBI solver, the mixed-integer programming model can be solved to obtain the flow process of each reservoir in the cascade reservoirs. The GUROBI solver is an existing solving tool, and the solving process thereof will not be introduced in detail in this embodiment.

[0082] Next, the scheduling method proposed by the present invention will be further described by taking the cascade reservoirs of Wudongde, Baihetan, Xiluodu and Xiangjiaba in the lower reaches of the Jinsha River, and the design flood data of the Lizhuang control station in 1982 with a frequency of 1% as an example.

[0083] First, obtain the historical flood forecast data and measured data in the lower reaches of the Jinsha River. Subtract the forecast data from the measured data to obtain the historical flood forecast error. Calculate the mean value of the flood forecast error, merge the forecast samples of the same historical flood flow, and calculate the sample variance corresponding to each different flow. In this embodiment, without loss of generality, set the sample mean of the forecast error to 0. The variance sizes corresponding to some different flows are shown in Table 1:

[0084] Table 1 Variance values corresponding to different flows

[0085] <![CDATA[Flow rate (m 3 / s)]]> Variance value (10×4) 21400 15.90 21900 17.81 22600 20.67 23300 23.74 23900 26.54 24500 29.50 24900 31.56 25100 32.62 25500 34.78 25900 37.01 26300 39.32 28205 51.23 28735 54.83 29475 60.05 30105 64.69 30320 66.31 30530 67.91 31710 77.27 31490 75.48 31710 77.27 31940 79.17 32160 81.00

[0086] Taking the minimum of the maximum downstream control site flow as the goal, a target function is constructed, and constraint conditions such as the water balance constraint of cascade reservoirs, the initial and final water level constraints of cascade reservoirs, and the upper and lower limits of the downstream discharge flow and storage capacity of cascade reservoirs are constructed. Based on the target function and constraint conditions, a distributed robust optimization scheduling model is established, and the model is solved with the design flood data of Lizhuang control site in 1982 and a frequency of 1% as the input to obtain the downstream discharge flow and water level process of each reservoir, and then the risk of the scheduling scheme is calculated, as shown in Table 2.

[0087] Table 2 Risks of scheduling schemes corresponding to different variance amplification coefficients

[0088] Variance amplification factor 0.49 0.64 0.81 1.00 1.21 1.44 1.69 Scheduling plan risk (%) 1.42 1.24 1.0 0.90 0.78 0.67 0.60

[0089] It can be concluded from the table that as the variance amplification coefficient increases, the risk of the flood scheduling process also decreases. This is because the larger the variance amplification coefficient, the larger the range of the flood forecast error uncertainty set. For distributed robust optimization, the worst case in the flood forecast error uncertainty set is taken for scheduling calculation, and the risk of the scheduling scheme is also lower. The dispatcher can select the optimal variance amplification coefficient according to the dispatching experience.

[0090] Obtain real-time flood forecast data, construct a multi-scenario uncertainty set of wind and light power output with a variance amplification coefficient of 0.9, take the minimum of the maximum downstream control site flow as the goal to construct a target function, construct constraint conditions such as the water balance constraint of cascade reservoirs, the initial and final water level constraints of cascade reservoirs, and the upper and lower limits of the downstream discharge flow and storage capacity of cascade reservoirs, and establish a distributed robust flood control optimization scheduling model for cascade reservoirs based on the target function and constraint conditions; solve the distributed robust optimization scheduling model to obtain the outflow and water level process of each reservoir in the cascade reservoir, that is, obtain the flood control optimization scheduling scheme of the cascade reservoir.

[0091] To verify the advantages of the method of the present invention, the scheduling results of the method of the present invention and the deterministic method and robust optimization method in the prior art in the test set are compared, as shown in Table 3.

[0092] Table 3 Performances of scheduling results of different scheduling methods in the test set

[0093] Scheduling plan risk Power generation (100 million kWh) Deterministic optimization 4.98％ 86.39 Distributed robust optimization 1.0％ 86.22 Robust optimization 0.28％ 84.66

[0094] As can be seen from the table, the risk of the deterministic model without considering flood forecast errors is the highest, the risk of the robust optimization model considering all situations is the lowest, and the risk of the distributionally robust optimization model that abandons extreme conditions and considers most situations lies between the two. However, high risk corresponds to high economic benefits. The power generation of cascade reservoirs during the scheduling period is ranked from large to small as follows: deterministic optimization model, distributionally robust optimization model, and robust optimization model. The risk of the scheduling scheme obtained by distributionally robust optimization is slightly higher than that of robust optimization, but the power generation is 244 million kWh higher than that of robust optimization, verifying the good performance of the flood control optimal scheduling method for cascade reservoirs proposed by the present invention.

[0095] The embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention should be the technical solutions recited in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recited in the claims. That is, the equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A distributed robust flood control optimal operation method for cascade reservoirs considering flood forecasting errors, characterized in that: It includes the following steps: S1. Collect historical flood forecast data, calculate the statistical indexes of flood forecast errors, determine the relationship between the flood flow magnitude and the forecast error variance, and construct a flood forecast error uncertainty set with the expected value and variance data of flood forecast errors; S2, construct an objective function by minimizing the maximum value of the flow at the downstream control site of the cascade reservoir under the worst flood forecasting error in the flood forecasting error uncertainty set, and establish a distributed robust optimization scheduling model with the water balance of the cascade hydropower stations, the constraints of the initial and final water levels of the cascade hydropower stations, and the upper and lower limits of the downstream discharge and storage capacity of the cascade reservoir. The flow at the downstream reservoir site of the cascade reservoir is expressed as Q D =Q 末 +Q 区 , where Q D represents the flow at the downstream flood control site, Q 末 represents the outflow from the most downstream reservoir in the cascade reservoir, and Q 区 represents the catchment between the most downstream reservoir in the cascade reservoir and the downstream control site; S3. Solve the distributed robust optimization scheduling model to obtain the outflow of each reservoir in the cascade reservoir, and then calculate the risk value P of the current scheduling plan. F , the risk value P F is defined as the probability that the flow at the downstream flood control site exceeds the limit flow, and the specific expression is P F = P(Q D > Q L ), where Q L represents the flood control limit flow of the downstream control site; S4. If the risk value P of the current scheduling plan F is large, increase the variance amplification coefficient k in the flood forecast error uncertainty set, and re-execute S3. If the risk value P of the current scheduling plan F is small, decrease the variance amplification coefficient k in the flood forecast error uncertainty set, and re-execute S3. If the risk value of the current scheduling plan is moderate, record the variance amplification coefficient in the current flood forecast error uncertainty set as k, so as to determine the optimal distributed robust optimization scheduling model; S5. Obtain real-time flood forecast data and input it into the optimal distributed robust optimization scheduling model. Determine the forecast error variance value according to the real-time flood forecast data, solve the optimal distributed robust optimization scheduling model, obtain the real-time cascade reservoir discharge flow process, and thus obtain the flood control optimal scheduling scheme of the cascade reservoir.

2. A distributed robust flood control optimal operation method for cascade reservoirs considering flood forecast errors according to claim 1, characterized in that: In the above S1, calculating the statistical indexes of flood forecast errors and determining the relationship between the flood flow magnitude and the forecast error variance specifically includes: S11. Calculate the error between the prediction result obtained by the flood prediction method and the measured value, and calculate the mean value μ of the forecast error; S12. Calculate the prediction error variance value σ under different predicted flows 2 , and obtain different predicted flows corresponding to the prediction error variance 3. A cascaded reservoir distributed robust optimal operation method considering flood forecasting error according to claim 2, characterized in that: The μ calculation method is as follows: where N represents the total number of forecast error samples, and d n represents the prediction error of the nth sample, and n is a natural number greater than or equal to 1; The calculation method is as follows: M represents the number of forecast error samples of the forecast flow , d m represents the m-th forecast error sample of the forecast flow , where m is a natural number greater than or equal to 1 represents the mean value of the forecast error corresponding to the forecast flow ​ 4. A cascaded reservoir distributed robust optimal operation method considering flood forecasting errors according to claim 1, characterized in that: In the above S1, the construction of the flood forecast error uncertainty set is specifically as follows: Among them represents the constructed uncertainty set of flood forecasting error represents the probability distribution of flood forecasting error represents the real number space of dimension J, where J represents the dimension of flood forecasting error d represents the dimension of the set of all probability distributions, where d and represent flood forecasting error and auxiliary variable respectively represents the expectation under the distribution μ represents the expected value of flood forecasting error, and σ 2 represents the variance value of flood forecasting error is the support set of flood forecasting error 5. A cascaded reservoir distributed robust optimal operation method considering flood forecast error according to claim 4, characterized in that: The is specifically expressed in the following form: d and are respectively the upper and lower limits of the flood forecasting error, and d j , μ j and u j respectively represent the j-th values in the forecasting error vector, the forecasting error expectation vector, and the auxiliary vector.

6. A distributed robust optimal operation method for cascade reservoirs considering flood forecasting errors according to claim 1, characterized in that: In the above S2, the establishment of the distributed robust optimization scheduling model is specifically as follows: V i,1 = V i,begin , V i,T+1 = V i,end Among them, Q represents the discharge of each reservoir in each cascade during each period, and X represents the decision space. is the uncertainty set of flood forecast error constructed above, which contains the distribution of flood forecast error for all possible values. T represents the length of the scheduling period, and Q t represents the flow at the downstream section at the t-th period, and Q l represents the flood control limit flow of the downstream section, and V i,t represents the storage capacity of the i-th hydropower station at time t. The natural inflow and the discharge are I i,t and Q i,t , and d i,t represents the natural inflow forecast error of the i-th hydropower station at time t. If there is no natural inflow, it is 0, and Z i represents the set of numbers of the upstream reservoirs of the i-th reservoir. The water flow delay period from the z-th reservoir to the i-th reservoir is τ z,i , where the single-step scheduling period length is Δt; among them Q i and are respectively the lower limit and the upper limit of the discharge of the i-th reservoir, V i and are respectively the lower limit and the upper limit of the storage capacity of the i-th reservoir, and V i,begin and V i,end are respectively the storage capacity at the start and the end of the calculation of the i-th reservoir.

7. A distributed robust optimal operation method for cascade reservoirs considering flood forecasting errors according to claim 1, characterized in that: The risk value P of the scheduling scheme in S3 F , specifically where \(T\) represents the number of periods in the scheduling period, and \(P\) t represents the probability that the flow rate at the control site at time \(t\) exceeds the limit water level, specifically expressed as where \(f(Q\) t ) represents the probability density function of the flow rate at the control site for each period, and \(Q\) t represents the flow rate at the downstream section in the \(t\)-th period.

8. A cascaded reservoir distributed robust optimal operation method considering flood forecasting error according to claim 1, characterized in that: In the above S4, the variance amplification coefficient k is specifically that the variance amplification coefficient k is a real number greater than 0. When k is 1, the variance is the statistical variance of the flood forecast error. When k is less than 1, the flood forecast error variance is reduced. When k is greater than 1, the flood forecast error is amplified, that is, the larger the variance amplification coefficient, the larger the flood forecast error uncertainty set.

9. A distributed robust optimal operation method for cascade reservoirs considering flood forecasting errors according to claim 1, characterized in that: In the above S5, determining the forecast error variance value according to the real-time flood forecast data is specifically as follows: According to the relationship between the flood flow magnitude determined in S1 and the forecast error variance, if the real-time flood forecast Q r is the same as the historical flood flow, directly query the corresponding forecast error variance; if not, perform interpolation based on two adjacent historical flood flows. The calculation method is where Q 左 and Q 右 are respectively the left and right two flows closest to the real-time flood forecast Q r , and σ 右 2 and σ 左 2 are respectively the variance values corresponding to Q 左 and Q 右 .

10. A distributed robust optimal operation method for cascade reservoirs considering flood forecasting errors according to claim 1, characterized in that: In the above S5, the solution of the distributed robust optimization scheduling model is specifically as follows: Based on the duality theory and the linear decision rule, convert the distributed robust optimization scheduling model into a mixed integer programming model under the flood forecast error uncertainty set, and then use the GUROBI solver to solve it.

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