Water-wind-light day-ahead power generation plan optimization method coupled with interpretable discarding rule

Abstract

The invention belongs to the field of multi-energy complementary coordinated dispatching, and discloses a water-wind-light day-ahead power generation plan optimization method coupled with an interpretable discarding rule in order to solve the key problem that unreasonable water discarding is easily caused when cascade hydropower stations respond to new energy flexibility requirements. Firstly, upstream and downstream reservoir linkage adjusting capacity is considered, and a cascade hydropower station discarding rule is provided; on the basis, a water-wind-light day-ahead power generation plan optimization model is constructed, and meanwhile water abandoning rationality and flexible supply-demand balance are guaranteed; and proposing a standard discarding rule linearization method based on generalized disjunction programming to convert the model into a mixed integer linear programming model for solving. According to the method, the abandoned water of the cascade hydropower station can be effectively reduced, the interpretability of the abandoned water is ensured, and a technical support is provided for reasonably formulating a water-wind-light day-ahead power generation plan.

Description

Technical Field

[0001] The present invention relates to the field of multi-energy complementary coordinated scheduling, in particular to short-term complementary coordinated scheduling of water, wind and solar power, and specifically to a method for optimizing day-ahead power generation plans of water, wind and solar power by coupling an interpretable water abandonment criterion. Background Art

[0002] The randomness and volatility of new energy sources increase the flexibility requirements of the power system. Taking advantage of the rapid start and stop and strong ramp-up capability of hydropower units, and complementing them with wind power and photovoltaic power output processes, is an important way to support large-scale grid connection of new energy sources. In actual dispatching, due to the different regulation capabilities of upstream and downstream reservoirs, unreasonable water abandonment is prone to occur in response to the flexibility requirements of new energy sources.

[0003] At present, when formulating the day-ahead power generation plan for hydropower, wind and solar power, water abandonment is generally not controlled or included in the objective function in the form of water abandonment penalty function or objective function to reduce water abandonment. It is difficult to avoid the active abandonment of water by cascade hydropower stations in response to flexibility needs, and the positive role of the linkage regulation capacity of upstream and downstream reservoirs in reducing water abandonment is ignored, and the rationality of water abandonment is difficult to explain. For example, the literature (Jin X, Liu B, Liao S, et al. A wasserstein metric-based distributionally robust optimization approach for reliable-economic equilibrium operation of hydro-wind-solar energy systems [J]. Renewable Energy, 2022, 196: 204–219) uses the abandoned water flow as a penalty function to construct a water-wind-solar day-ahead complementary scheduling model. The patent with application number CN201811197327.7 uses the minimum abandoned water flow as the objective function to disclose a method for establishing a hydropower electricity decomposition model that takes into account peak regulation and water abandonment. Although the above research can reduce water abandonment, the calculation results cannot control when the water can be abandoned, and the rationality of water abandonment is difficult to explain. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for optimizing the day-ahead power generation plan of water, wind and solar power plants coupled with an interpretable water abandonment criterion. It can effectively deal with the risk of water abandonment in cascade hydropower stations and improve the rationality of the day-ahead power generation plan of water, wind and solar power integrated bases and the interpretability of water abandonment. The present invention uses a water, wind and solar power integrated base in Guizhou Province as the engineering background for application testing. The results show that the present invention can effectively reduce the amount of water abandoned by cascade hydropower stations and ensure the interpretability of water abandonment, providing technical support for the rational formulation of day-ahead power generation plans for water, wind and solar power plants.

[0005] Technical solution of the present invention:

[0006] A method for optimizing the day-ahead power generation plan of water, wind and solar power plants coupled with an interpretable water abandonment criterion includes: modeling the water abandonment criterion, establishing a water, wind and solar power day-ahead power generation plan optimization model, and solving the model. The specific steps are as follows:

[0007] Step 1) Modeling of water abandonment criteria.

[0008] In order to avoid unnecessary water abandonment caused by mismatch of upstream and downstream reservoir regulation capacity in short-term dispatching, the present invention considers the hydraulic connection of cascades and proposes water abandonment criteria for cascade hydropower stations, such as Figure 1 As shown, The hydropower stations are numbered from upstream to downstream. The total number of hydropower stations is ,Right now ; is the number of the hydropower station with the ability to adjust the reservoir capacity to reduce the output to the minimum output, is the variable to be optimized, The mathematical expression of the water abandonment criterion of cascade hydropower stations is formula (1), that is, if the hydropower station If water is abandoned, the hydropower station According to the maximum output power generation, and hydropower station and its upstream reservoir , ,..., The water level is stored to the normal high level until a hydropower station It has the function of regulating the storage capacity to reduce the output to the minimum output. Generally, when the reservoir is stored to the normal high water level, the power generation efficiency is high, and the flow required for the maximum output is less than the maximum power generation flow. Therefore, the water abandonment criterion of the cascade hydropower station only considers the hydropower station Reaching maximum output, ignoring hydropower stations Generate electricity at the maximum power flow rate. ,like , it means that the hydropower station All reservoirs upstream of it do not have the regulating capacity at this time and all need to store water to normal high levels.

[0009] (1)

[0010] Where: Number the hydroelectric power station. ; is the time period number, ; for Time-limited hydropower station Abandoned water flow, m 3 / s; , They are Time-limited hydropower station , Output, MW; , They are Time-limited hydropower station , Output upper limit, MW; for Time-limited hydropower station Water storage capacity, m 3 / s; for Time-limited hydropower station Upper limit of water storage capacity, m 3 / s; For hydropower station Ramp capacity, MW.

[0011] Step 2) Establish a day-ahead power generation plan optimization model for hydropower, wind power and solar power.

[0012] (2.1) Objective function.

[0013] For a hydropower, wind and solar power integrated base, the goal of formulating a day-ahead power generation plan is to maximize power generation benefits. Therefore, the present invention considers the peak-valley electricity price mechanism and takes the maximum power generation benefit as the objective function.

[0014] (2)

[0015] (3)

[0016] Where: is the day-ahead power generation benefit, yuan; For the period The electricity price, RMB / MWh; The day-ahead power generation plan for the cascade hydro-wind-solar integrated base, MW; The predicted Wind power and photovoltaic output during the period, MW; The length of the period.

[0017] (2.2) Day-ahead power generation schedule constraints.

[0018] Water abandonment criteria constraints:

[0019] When hydropower, wind power and solar power are in complementary operation, unnecessary water abandonment caused by mismatch in upstream and downstream regulation capacity of cascade hydropower should be avoided to improve water energy utilization efficiency. Therefore, the water abandonment criterion of cascade hydropower stations is considered when formulating the day-ahead power generation plan, that is, formula (1).

[0020] Transmission channel capacity constraints:

[0021] (4)

[0022] Where: is the transmission channel capacity, MW.

[0023] Water balance constraints:

[0024] (5)

[0025] (6)

[0026] (7)

[0027] Where: For the reservoir exist Water storage at the end of the period, m 3 ; Hydropower Station exist Inflow, outflow, interval flow, power generation flow, and abandoned water flow in the time period, m 3 / s.

[0028] Water storage capacity constraints:

[0029] (8)

[0030] Where: , Reservoirs The upper and lower limits of water storage capacity, m 3 / s.

[0031] Outbound traffic constraints:

[0032] (9)

[0033] Where: , Hydropower Station The upper and lower limits of the outbound flow, m 3 / s.

[0034] Power generation flow constraints:

[0035] (10)

[0036] Where: , Hydropower Station The upper and lower limits of power generation flow, m 3 / s.

[0037] Output limits of hydropower stations:

[0038] (11)

[0039] Where: , Hydropower Station Upper and lower limits of output, MW.

[0040] Climbing capacity constraints:

[0041] (12)

[0042] Where: For hydropower station Ramp capacity, MW.

[0043] Hydropower station power generation function:

[0044] (13)

[0045] Where: For hydropower station The power generation function.

[0046] Initial and final water storage capacity constraints:

[0047] (14)

[0048] (15)

[0049] Where: , For the given reservoirs Initial and final storage capacity, m 3 .

[0050] (2.3) Flexibility response constraints.

[0051] The prediction error of wind power and photovoltaic output is inevitable. Hydropower stations need to adjust the output of hydropower stations according to the flexibility requirements of wind power and photovoltaics to ensure the balance of flexibility supply and demand. Therefore, it is necessary to consider the flexibility supply and demand balance constraints and the operation constraints of cascade hydropower stations. The present invention describes the uncertainty of wind power and photovoltaic output scenarios. First, the kernel density estimation method is used to fit the probability density function and cumulative distribution function of the prediction errors of wind power and photovoltaics in each time period; then, the probit function is used to convert the cumulative distribution function of the prediction error into a Gaussian distribution. After the conversion, the multi-time period random variables obey the multi-dimensional Gaussian distribution; then, the maximum likelihood estimation method is used to fit the multivariate Gaussian distribution; finally, the wind power and photovoltaic output scenarios are obtained by sampling and reduction.

[0052] Flexibility supply and demand balance constraints:

[0053] (16)

[0054] (17)

[0055] (18)

[0056] Where: For the scene Time Flexibility requirements for wind power and photovoltaic power, MW; For hydropower station In the scene Time Output, MW; For hydropower station In the scene Time of flexibility supply, MW; Wind power and photovoltaic power in the scene Time Output, MW.

[0057] Operation constraints of cascade hydropower stations:

[0058] When providing flexibility, cascade hydropower stations also need to meet the operating constraints of cascade hydropower stations, including water abandonment criteria constraints, transmission channel capacity constraints, water balance constraints, water storage constraints, outflow constraints, power generation flow constraints, hydropower station output limits, ramp capacity constraints, hydropower station power generation functions, initial and final water storage constraints, etc. Therefore, equations (1) and (4) to (15) should also be considered in daily operation. These constraints are related to scenarios, so the decision variables in these constraints are all increased by the scenario subscript That is, in the intraday operation constraints, the decision variables in equations (1) and (4) to (15) are Replace with .in, For the reservoir exist Scenario Water storage at the end of the period, m 3 ; Hydropower Station exist Scenario Inflow, outflow, power generation and abandoned water flow in the period, m 3 / s.

[0059] Step 3) Solve the model.

[0060] The hydropower, wind and solar power day-ahead power generation plan optimization model in step 2) contains nonlinear constraints such as water abandonment criteria and hydropower generation function, which is difficult to solve directly. The present invention adopts the following method to convert the original model into a mixed integer linear model and solves it using the Gurobi solver.

[0061] Aiming at the logical constraint of water abandonment criterion, this paper proposes a linearization method of water abandonment criterion based on generalized disjunctive programming. Firstly, equation (1) is expressed as equation (19) to equation (21). Equation (21) means are Boolean variables. Formula (20) is a logical constraint, that is, At least one of them is True. Formula (19) is a disjunctive formula, which contains three disjuncts. Each disjunct contains a logical variable and several constraints. The corresponding constraint is valid if and only if the logical variable is equal to True. or When the hydropower station According to the maximum output power generation, and the reservoir , ,..., The water level is stored to the normal high level, and the hydropower station If the output is reduced to the minimum output, the hydropower station The water can be discarded. When the hydropower station Reduce the output to the lower limit; when When the hydropower station The output can only be reduced according to the climbing ability. When the hydropower station Can’t discard water.

[0062] (19)

[0063] (20)

[0064] (twenty one)

[0065] Further, , , the big M method is used to transform equations (19) to (21) into mixed integer linear constraints (22) to (32).

[0066] (twenty two)

[0067] (twenty three)

[0068] (twenty four)

[0069] (25)

[0070] (26)

[0071] (27)

[0072] (28)

[0073] (29)

[0074] (30)

[0075] (31)

[0076] (32)

[0077] Where: All are auxiliary variables introduced; is a constant large enough to ensure that the response constraint is relaxed when the auxiliary variable is equal to 0.

[0078] For the hydropower generation function, the present invention uses rectangular partitioning technology to transform it into mixed integer linear constraints. For the convenience of expression, the subscript of the hydropower station is omitted. , Time period subscript , scene subscript , that is, Represents the average water storage capacity of the reservoir during the period, m 3 ;by Represents the power generation flow, m 3 / s; represents the output of the hydropower station, MW; then the hydropower station power generation function Can be converted as follows:

[0079] (33)

[0080] (34)

[0081] (35)

[0082] (36)

[0083] (37)

[0084] (38)

[0085] (39)

[0086] (40)

[0087] Where: , are the grid point subscripts for water storage capacity and power generation flow, respectively; is the grid point for reservoir water storage, m 3 ; is the grid point for power generation flow, m3 / s; Grid points Corresponding output, MW; Grid points The weight coefficient of , They are The line The weight coefficient of the column where the , All are subject to SOS2 constraints.

[0088] The results of the present invention have the following beneficial effects: The present invention proposes a water abandonment criterion and a modeling method for cascade hydropower stations, and on this basis, constructs an optimization model for the day-ahead power generation plan of water, wind and solar power plants, and introduces a water abandonment criterion linearization method based on generalized disjunctive programming to convert the original model into a mixed integer linear programming model for solving it, which effectively reduces water abandonment, improves the rationality of the day-ahead power generation plan of water, wind and solar power plants and the explainability of water abandonment, and provides a new technical approach for short-term scheduling of water, wind and solar power integrated bases. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a schematic diagram of the water abandonment criterion;

[0090] Figure 2 It is a statistical indicator of a typical day during the dry season;

[0091] Figure 3 It is a statistical indicator of a typical day during the flood season;

[0092] Figure 4 It is the day-ahead power generation plan for typical days in the flood season optimized by comparison model 1;

[0093] Figure 5 It is the day-ahead power generation plan for typical days in the flood season optimized by comparison model 2;

[0094] Figure 6 It is the day-ahead power generation plan optimized on a typical day in the flood season compared with model 3;

[0095] Figure 7 It is the day-ahead power generation plan for typical days in the flood season optimized by the proposed model. DETAILED DESCRIPTION

[0096] The present invention is further described below in conjunction with the accompanying drawings and implementation examples.

[0097] The model and method proposed in the present invention are tested with a cascade water, wind and solar integrated base in Guizhou Province as the engineering background. The three hydropower stations of the cascade water, wind and solar integrated base have a total installed capacity of 2478MW, and the installed capacities of wind power and photovoltaic power are 940MW and 1610MW respectively. The present invention takes the above-mentioned cascade water, wind and solar integrated base as the optimization calculation object to analyze and verify the effectiveness of the method of the present invention. January 30, 2021 and September 10, 2021 are taken as typical days of the dry season and flood season respectively. The model input data include hourly runoff data on typical days of the dry season and flood season, hourly predicted wind and solar output data, hourly historical predicted wind and solar output data from January 1, 2018 to December 31, 2020, hourly historical actual wind and solar output data, basic data of cascade hydropower stations and peak and valley electricity price data.

[0098] 1) Comparison model settings:

[0099] In order to verify the effectiveness of the proposed cascade hydropower station abandonment criteria, the following four models are set up for comparative analysis:

[0100] (1) The proposed model: that is, the day-ahead power generation plan optimization model proposed in the present invention, which uses the water abandonment criterion described in formula (1) to control the water abandonment of cascade hydropower stations.

[0101] (2) Comparative model 1: Compared with the proposed model, this model does not contain constraint formula (1), that is, it does not consider the water abandonment criterion proposed in this invention, nor does it use other methods to control the water abandonment of cascade hydropower stations.

[0102] (3) Comparative model 2: Compared with the proposed model, this model does not consider the water abandonment criterion described in formula (1), and adds the amount of water abandoned as a penalty term into the objective function, that is, the maximum power generation benefit target is modified to formula (41).

[0103] (41)

[0104] (42)

[0105] (43)

[0106] Where: is the objective function value after adding the water abandonment penalty; is the planned abandoned hydropower volume a day ago, MWh; The expected amount of hydropower abandoned when cascade hydropower stations respond to the flexibility needs of renewable energy; for Average daily water consumption rate of hydropower station, m 3 / s / MW, set according to historical actual operation data; For the scene Probability of occurrence.

[0107] (4) Comparative model 3: Compared with the proposed model, this model replaces the water abandonment criterion described in equation (1) with equation (44). According to equation (36), if the hydropower station Abandon water, only need hydropower station The water is stored to the normal high water level and generates electricity at the maximum output. Compared with the water abandonment criterion described in formula (1), formula (36) does not consider the linkage regulation capacity of cascade reservoirs. Formula (36) also uses generalized disjunctive programming to transform into mixed integer linear constraints, which will not be repeated here.

[0108] (44)

[0109] 2) Result analysis:

[0110] (1) Comparative analysis of statistical indicators:

[0111] The proposed model, comparative model 1, comparative model 2, and comparative model 3 are optimized respectively, and the day-ahead planned revenue, day-ahead planned water abandonment, and scenario water abandonment expectations are counted. The statistical results of typical days in the dry season and flood season are as follows: Figure 2 , Figure 3 As shown. Among them, the planned water abandonment amount and the expected water abandonment amount in the scenario are calculated using formula (45) and formula (46) respectively.

[0112] (45)

[0113] (46)

[0114] Where: , are the planned water abandonment amount and the expected water abandonment amount in the scenario, respectively, m 3 .

[0115] like Figure 2 As shown in the figure, the planned revenues of the proposed model, comparative model 1, comparative model 2, and comparative model 3 on a typical dry day are all 16.03 million yuan. Comparative model 1 does not control the water abandonment of cascade hydropower stations, resulting in the planned water abandonment and the expected water abandonment in the scenario being 16.77 million m 3 , 15.66 million m 3 The proposed model, comparative model 2, and comparative model 3 respectively use different water abandonment control methods to make the planned water abandonment amount and the expected water abandonment amount in the scenario both 0. This shows that considering the water abandonment control method in the water, wind, and solar power day-ahead power generation plan optimization model can avoid water abandonment during the dry season without reducing the power generation efficiency and the reliability of the day-ahead power generation plan.

[0116] like Figure 3As shown in the figure, on a typical day in the flood season, the proposed model's planned revenue is 14.01 million yuan, which is 1.01%, 1.01%, and 0.86% lower than that of comparison model 1, comparison model 2, and comparison model 3, respectively. The proposed model's planned water abandonment volume and scenario expected water abandonment volume are 5.53 million m 3 5.73 million m 3 , which are respectively reduced by 80.82% and 79.19% compared with the comparison model 1, by 37.61% and 30.11% compared with the comparison model 2, and by 26.50% and 31.32% compared with the comparison model 3. This indicates that the proposed water abandonment criterion considering the cascade hydraulic connection during the flood season can effectively reduce the amount of water abandonment without significantly reducing the power generation efficiency.

[0117] (2) Analysis on rationality of water abandonment:

[0118] Taking a typical day in the flood season as an example, the rationality of the proposed water abandonment criterion and the interpretability of water abandonment are analyzed. The day-ahead power generation plans obtained by optimizing the comparison model 1, comparison model 2, comparison model 3, and the proposed model are shown in the figure below: Figure 4 , Figure 5 , Figure 6 , Figure 7 shown.

[0119] according to Figure 4 Compared with model 1, which does not control the water abandonment, H2 and H3 abandon water in a concentrated manner from 0:00 to 1:00, and the water abandonment flow of H3 is as high as 7019 m 3 / s. However, H2 and H3 did not store up to the normal high water level from 0:00 to 1:00, and had a certain regulating storage capacity, which could reduce water abandonment by increasing water storage. Therefore, compared with model 1, not only a large amount of concentrated water abandonment occurred, but also the rationality of water abandonment was difficult to explain.

[0120] according to Figure 5 Compared with comparison model 1, comparison model 2 adds abandoned water power as a penalty term into the objective function, which can reduce abandoned water by increasing water storage capacity. However, H3 still generates abandoned water from 0:00 to 1:00, and the abandoned water flow rate is as high as 2460 m 3 / s, and H3 did not store up to the normal high water level from 0:00 to 1:00, that is, the comparison model 2 still produced unreasonable water abandonment.

[0121] according to Figure 6 In the day-ahead power generation plan obtained by optimizing and comparing model 3, H3 generates abandoned water from 20:00 to 24:00, and the abandoned water flow is 214 m 3 / s~715 m 3 / s, which is significantly lower than that of comparison model 1 and comparison model 2, and H3 is stored to the normal high water level and generates electricity at the maximum output of 880MW when abandoning water. However, when H3 abandons water, its upstream hydropower station H2 does not store water to the normal high water level and does not reduce the output to the minimum output. Therefore, the power generation flow can be reduced by increasing the water storage capacity of H2, thereby reducing the inflow flow of H3 and further reducing the abandoned water flow of H3.

[0122] according to Figure 7 In the day-ahead power generation plan obtained by optimizing the proposed model, H3 generates abandoned water from 20:00 to 24:00, and the abandoned water flow is 79 m 3 / s~587 m 3 / s, and the abandoned water flow in each period is lower than that of the comparison model. When abandoning water, not only does H3 store to the normal high water level and the output reaches the maximum value of 880MW, but H2 also reduces its output according to its climbing capacity from 20:00 to 22:00, and its output is reduced to 0 from 22:00 to 24:00. This shows that the proposed cascade hydropower station abandonment criterion can make full use of the linkage regulation capacity of cascade reservoirs and significantly reduce the amount of abandoned water. Moreover, when abandoning water, the cascade hydropower stations have exerted their maximum regulation capacity, and the abandoned water is more reasonable and explainable.

Claims

1. A method for optimizing the day-ahead power generation plan of water, wind and solar power coupled with an interpretable water abandonment criterion, characterized in that: The specific steps are as follows: Step 1) Modeling of water abandonment criteria: The mathematical expression of the water abandonment criterion of cascade hydropower stations is formula (1), where The hydropower stations are numbered from upstream to downstream. The total number of hydropower stations is ,Right now ; is the number of the hydropower station with the ability to adjust the reservoir capacity to reduce the output to the minimum output, is the variable to be optimized, If the hydropower station If water is abandoned, the hydropower station According to the maximum output power generation, and hydropower station and its upstream reservoir , ,..., The water level is stored to the normal high level until a hydropower station It has the function of regulating the reservoir capacity to reduce the output to the minimum output; the cascade hydropower station abandonment criterion only considers the hydropower station Reaching maximum output, ignoring hydropower stations Generate electricity at the maximum power flow rate; for hydropower stations ,like , it means that the hydropower station All reservoirs upstream of it have no regulating storage capacity at this time and need to store water to normal high levels; (1) Where: Number the hydroelectric power station. ; is the time period number, ; for Time-limited hydropower station Abandoned water flow, ; , They are Time-limited hydropower station , Output, MW; , They are Time-limited hydropower station , Output upper limit, MW; for Time-limited hydropower station Water storage capacity, m 3 / s; for Time-limited hydropower station Upper limit of water storage capacity, m 3 / s; For hydropower station Ramp capacity, MW; Step 2) Establish a hydropower, wind and solar power day-ahead power generation plan optimization model: (2.1) Objective function: For the integrated water, wind and solar base, the goal of formulating the day-ahead power generation plan is to maximize the power generation benefits; therefore, the peak-valley electricity price mechanism is considered, and the maximum power generation benefits are taken as the objective function; (2) (3) Where: is the day-ahead power generation benefit, yuan; For the period The electricity price, RMB / MWh; The day-ahead power generation plan for the cascade hydro-wind-solar integrated base, MW; The predicted Wind power and photovoltaic output during the period, MW; is the time period length; (2.2) Day-ahead power generation plan constraints: Water abandonment criteria constraints: When formulating the day-ahead power generation plan, the water abandonment criterion of cascade hydropower stations is considered, that is, formula (1); Transmission channel capacity constraints: (4) Where: is the transmission channel capacity, MW; Water balance constraints: (5) (6) (7) Where: For the reservoir exist The water storage at the end of the period, ; , , , , Hydropower Station exist Inflow, outflow, interval flow, power generation flow, and abandoned water flow in the time period, m 3 / s; Water storage capacity constraints: (8) Where: , Reservoirs The upper and lower limits of water storage capacity, m 3 / s; Outbound traffic constraints: (9) Where: , Hydropower Station The upper and lower limits of the outbound flow, m 3 / s; Power generation flow constraints: (10) Where: , Hydropower Station The upper and lower limits of power generation flow, m 3 / s; Output limits of hydropower stations: (11) Where: , Hydropower Station The upper and lower limits of output, MW; Climbing capacity constraints: (12) Where: For hydropower station Ramp capacity, MW; Hydropower station power generation function: (13) Where: For hydropower station The power generation function; Initial and final water storage capacity constraints: (14) (15) Where: , For the given reservoirs Initial and final storage capacity, m 3 ; (2.3) Flexibility response constraints: The uncertainty of wind power and photovoltaic output scenarios is described. First, the kernel density estimation method is used to fit the probability density function and cumulative distribution function of the wind power and photovoltaic forecast errors in each period. Then, the probit function is used to transform the forecast error cumulative distribution function into a Gaussian distribution. After the transformation, the multi-period random variables obey the multi-dimensional Gaussian distribution. Then, the maximum likelihood estimation method is used to fit the multivariate Gaussian distribution. Finally, the wind power and photovoltaic output scenarios are obtained by sampling and reduction. Flexibility supply and demand balance constraints: (16) (17) (18) Where: For the scene Time Flexibility requirements for wind power and photovoltaic power, MW; For hydropower station In the scene Time Output, MW; For hydropower station In the scene Time of flexibility supply, MW; Wind power and photovoltaic power in the scene Time Output, MW; Operation constraints of cascade hydropower stations: When providing flexibility, cascade hydropower stations also need to meet the operating constraints of cascade hydropower stations, including water abandonment criteria constraints, transmission channel capacity constraints, water balance constraints, water storage constraints, outflow constraints, power generation flow constraints, hydropower station output limits, ramp capacity constraints, hydropower station power generation functions, and initial and final water storage constraints. Therefore, equations (1) and (4) to (15) should also be considered in daily operation. These constraints are related to scenarios, so the decision variables in these constraints are all added with scenario subscripts. ; That is, in the intraday operation constraints, the decision variables in equations (1) and (4) to (15) are , , , , , Replace with , , , , , ;in, For the reservoir exist Scenario Water storage at the end of the period, m 3 ; , , , Hydropower Station exist Scenario Inflow, outflow, power generation and abandoned water flow in the period, m 3 / s; Step 3) Model solution: The optimization model for the day-ahead power generation plan of hydropower, wind power and solar power in step 2) contains the water abandonment criterion and the nonlinear constraints of the hydropower generation function, which is difficult to solve directly. The following method is used to transform the original model into a mixed integer linear model, and the Gurobi solver is used to solve it; According to the abandonment criterion, a linearization method of the abandonment criterion based on generalized disjunctive programming is proposed. First, equation (1) is expressed as equations (19) to (21). Equation (21) represents , , are Boolean variables; Formula (20) is a logical constraint, that is, , , At least one of them is True; Formula (19) is a disjunctive formula, which contains three disjuncts. Each disjunct contains a logical variable and several constraints. The corresponding constraint is valid if and only if the logical variable is equal to True; or When the hydropower station According to the maximum output power generation, and the reservoir , ,..., The water level is stored to the normal high level, and the hydropower station If the output is reduced to the minimum output, the hydropower station Water can be discarded; When the hydropower station Reduce the output to the lower limit; when When the hydropower station The output can only be reduced according to the climbing ability; when When the hydropower station You can’t abandon water; (19) (20) (21) Further, , , the Big M method is used to transform equations (19) to (21) into mixed integer linear constraints (22) to (32); (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) Where: , , All are introduced auxiliary variables; is a constant to ensure that the response constraint is relaxed when the auxiliary variable is equal to 0; For the hydropower generation function, the rectangular partitioning technique is used to transform it into a mixed integer linear constraint. For the convenience of expression, the subscript of the hydropower station is omitted. , Time period subscript , scene subscript , that is, Represents the average water storage capacity of the reservoir during the period, m 3 ;by Represents the power generation flow, m 3 / s; represents the output of the hydropower station, MW; then the hydropower station power generation function The conversion is as follows: (33) (34) (35) (36) (37) (38) (39) (40) Where: , are the grid point subscripts for water storage capacity and power generation flow, respectively; is the grid point for reservoir storage capacity, ; is the grid point for power generation flow, m 3 / s; Grid points Corresponding output, MW; Grid points The weight coefficient of , They are The line The weight coefficient of the column where the , All are subject to SOS2 constraints.

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