Optimization Method for Day-ahead Power Generation Plan of Hydro, Wind and Solar Power Incorporating an Interpretable Criterion for Curtailed Water

Abstract

The present invention belongs to the field of multi - energy complementary coordinated scheduling. Aiming at the key problem that the response of cascade hydropower stations to the flexibility demand of new energy easily leads to unreasonable water abandonment, an optimization method for the day - ahead power generation plan of hydropower, wind and solar integrated with an interpretable water - abandonment criterion is disclosed. First, considering the joint regulation ability of upstream and downstream reservoirs, a water - abandonment criterion for cascade hydropower stations is proposed. Based on this, an optimization model for the day - ahead power generation plan of hydropower, wind and solar is constructed, while ensuring the rationality of water abandonment and the balance of flexibility supply and demand. A linearization method of the water - abandonment criterion based on generalized disjunctive programming is proposed to transform the above - mentioned model into a mixed - integer linear programming model for solution. The present invention can effectively reduce the water abandonment of cascade hydropower stations and ensure the interpretability of water abandonment, providing technical support for the reasonable formulation of the day - ahead power generation plan of hydropower, wind and solar.

Description

Technical Field

[0001] The present invention relates to the field of multi - energy complementary coordinated scheduling, particularly to the short - term complementary coordinated scheduling of water, wind, and light, and specifically to an optimization method for the day - ahead power generation plan of water, wind, and light that couples an interpretable water abandonment criterion. Background Art

[0002] The randomness and volatility of new energy increase the flexibility requirements of the power system. Giving play to the technical advantages of the rapid start - stop and strong climbing ability of hydropower units to form a complementarity with the output processes of wind power and photovoltaic power is an important way to support the large - scale grid connection of new energy. In actual scheduling, due to the different regulation capabilities of upstream and downstream reservoirs, it is easy to generate unreasonable water abandonment when responding to the flexibility requirements of new energy.

[0003] Currently, when formulating the day - ahead power generation plan for water, wind, and light, water abandonment is generally not controlled or incorporated into the objective function in the form of a water abandonment penalty function or objective function to reduce water abandonment. It is difficult to avoid the active water abandonment of cascade hydropower stations when responding to flexibility requirements, and the positive role of the coordinated regulation ability 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) constructed a day - ahead complementary scheduling model for water, wind, and light with the water abandonment electricity as the penalty function. The patent with the application number CN201811197327.7 disclosed a method for establishing a hydropower electricity decomposition model that takes the minimum water abandonment flow as the objective function. Although the above - mentioned research can reduce water abandonment, when water can be abandoned in the calculation results cannot be controlled, 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 an optimization method for the day - ahead power generation plan of water, wind, and light that couples an interpretable water abandonment criterion. It can effectively cope with the water abandonment risk of cascade hydropower stations and improve the rationality of the day - ahead power generation plan of the water, wind, and light comprehensive base and the interpretability of water abandonment. The present invention takes a certain water, wind, and light comprehensive base in Guizhou Province as the engineering background for application testing. The results show that the present invention can effectively reduce the water abandonment volume of cascade hydropower stations and ensure the interpretability of water abandonment, providing technical support for reasonably formulating the day - ahead power generation plan of water, wind, and light.

[0005] The technical solution of the present invention:

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

[0007] Step 1) Modeling the water abandonment criterion.

[0008] To avoid unnecessary water abandonment in cascade joint scheduling due to the mismatch of the regulation capabilities of upstream and downstream reservoirs in short-term scheduling, the present invention considers the cascade hydraulic connection and proposes a water abandonment criterion for cascade hydropower stations, as Figure 1 shown, where i is the hydropower station number, numbered sequentially from upstream to downstream, and the total number of hydropower stations is I, that is, i = 1, 2,..., I; y is the number of the hydropower station with a regulating reservoir capacity that reduces the output to the minimum output, which is a variable to be optimized, and 0 ≤ y ≤ i - 1. The mathematical expression of the water abandonment criterion for cascade hydropower stations is Equation (1), that is, if hydropower station i abandons water, then hydropower station i generates electricity at the maximum output, and hydropower station i and its upstream reservoirs i - 1, i - 2,..., y + 1 are all stored to the normal high water level until a certain hydropower station y has a regulating reservoir 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 relatively high, and the flow rate required for the maximum output is less than the maximum power generation flow rate. Therefore, the water abandonment criterion for cascade hydropower stations only considers that hydropower station i reaches the maximum output and does not consider that hydropower station i generates electricity at the maximum power generation flow rate. For hydropower station i, if y = 0, it means that all the upstream reservoirs of hydropower station i do not have a regulating reservoir capacity at this time and all need to be stored to the normal high water level.

[0009]

[0010] In the formula: i is the hydropower station number, i = 1, 2,..., I; t is the time period number, t = 1, 2,..., T; is the water abandonment flow rate of hydropower station i in period t, m 3 / s; are the outputs of hydropower station i and t in period t, MW; are the output upper limits of hydropower station i and y in period t, MW; V j，t is the water storage volume of hydropower station i in period t, m 3 / s; is the upper limit of the water storage volume of hydropower station i in period t, m 3 / s; is the ramping capacity of hydropower station y, MW.

[0011] Step 2) Establishing an optimization model for the day-ahead power generation plan of hydropower, wind power and photovoltaic power.

[0012] (2.1) Objective function.

[0013] For the integrated water, wind and solar power base, the goal of formulating the daily power generation plan is to maximize the power generation benefit. Therefore, this invention takes into account the peak-valley electricity price mechanism and uses the maximum power generation benefit as the objective function.

[0014]

[0015] Where: R is the daily power generation benefit, yuan; α t is the electricity price at time period t, yuan / MWh; P t HWS is the daily power generation plan of the cascade water, wind and solar power integrated base, MW; P t W，F 、P t S，F are the predicted wind power and photovoltaic power outputs at time period t, MW; Δt is the time period length.

[0016] (2.2) Constraints of the daily power generation plan.

[0017] Water rejection criterion constraint:

[0018] When the water, wind and solar power operate in a complementary manner, the mismatch in the regulation capabilities between the upstream and downstream of the cascade hydropower stations should be avoided to generate unnecessary water rejection and improve the water energy utilization efficiency. Therefore, the water rejection criterion of the cascade hydropower stations is considered when formulating the daily power generation plan, that is, Equation (1).

[0019] Transmission channel capacity constraint:

[0020] P t HWS ≤C t max (4)

[0021] Where: is the transmission channel capacity, MW.

[0022] Water volume balance constraint:

[0023]

[0024] Where: V i，t is the water storage volume of reservoir i at the end of time period t, m 3 ; are the inflow, outflow, lateral inflow, power generation flow, and water rejection flow of hydropower station i at time period t, m 3 / s.

[0025] Water storage volume constraint:

[0026]

[0027] Where: are the upper and lower limits of the water storage volume of reservoir i, m 3 / s.

[0028] Outflow rate constraint:

[0029]

[0030] Where: are the upper and lower limits of the outflow rate of hydropower station i, m 3 / s.

[0031] Power generation flow rate constraint:

[0032]

[0033] Where: are the upper and lower limits of the power generation flow rate of hydropower station i, m 3 / s.

[0034] Output limit of hydropower station:

[0035]

[0036] Where: are the upper and lower limits of the output of hydropower station i, MW.

[0037] Ramping capacity constraint:

[0038]

[0039] Where ΔP i H，max is the ramping capacity of hydropower station i, MW.

[0040] Power generation function of hydropower station:

[0041]

[0042] Where: f i (·) is the power generation function of hydropower station i.

[0043] Initial and final water storage constraints:

[0044] V i,0 = V i begin (14)

[0045] V i,T ≥ V i end (15)

[0046] Where: V i begin and V i end are the initial and final reservoir capacities of reservoir i given, m 3 .

[0047] (2.3) Flexibility response constraint.

[0048] The prediction errors of wind power and photovoltaic power are inevitable. The hydropower station needs to adjust its output according to the flexibility requirements of wind power and photovoltaic power to ensure the balance of flexibility supply and demand. Therefore, the flexibility supply-demand balance constraint and the operation constraint of cascade hydropower stations need to be considered. In the present invention, the output uncertainty of wind power and photovoltaic power is described by scenarios. First, the probability density function and cumulative distribution function of the prediction errors of wind power and photovoltaic power in each period are fitted by the kernel density estimation method; then, the probit function is used to transform the prediction error cumulative distribution function into a Gaussian distribution, and the multi-period random variables after transformation obey the multi-dimensional Gaussian distribution; then, the maximum likelihood estimation method is used to fit the multi-variable Gaussian distribution; finally, the wind power and photovoltaic power output scenarios are obtained by sampling and reduction.

[0049] Flexibility supply-demand balance constraint:

[0050]

[0051] In the formula: is the flexibility demand of wind power and photovoltaic power at time t in scenario s, MW; is the output of the hydropower station at time t in scenario s, MW; is the flexibility supply of hydropower station i at time t in scenario s, MW; are the outputs of wind power and photovoltaic power at time t in scenario s, MW respectively.

[0052] Operation constraint of cascade hydropower stations:

[0053] When providing flexibility, the cascade hydropower stations also need to meet the operation constraints of cascade hydropower stations, including the water rejection criterion constraint, the transmission channel capacity constraint, the water volume balance constraint, the water storage capacity constraint, the out-flow constraint, the power generation flow constraint, the hydropower station output limit, the ramping capacity constraint, the hydropower station power generation function, the initial and final water storage constraints, etc. Therefore, Equation (1) and Equations (4)-(15) should also be considered in the intraday operation. These constraints are related to the scenarios, so the decision variables in these constraints are all added with the scenario subscript s. That is, in the intraday operation constraints, the decision variables V i，t 、 in Equation (1) and Equations (4)-(15) are respectively replaced by V i，s，t 、 where V i，s，t is the water storage of reservoir i at the end of time t in scenario s, m 3 ; are the inflow, outflow, power generation flow, and water rejection flow of hydropower station i at time t in scenario s, m 3 / s respectively.

[0054] Step 3) Model solution.

[0055] The optimization model of the water-wind-solar power generation plan in Step 2) contains non-linear constraints such as water abandonment criteria and hydropower generation functions, which are difficult to solve directly. In the present invention, the following method is used to transform the original model into a mixed-integer linear model and solve it using the Gurobi solver.

[0056] For the logical constraint of the water abandonment criterion, the present invention proposes a linearization method of the water abandonment criterion based on generalized disjunctive programming. First, Equation (1) is expressed as Equations (19) to (21). Equation (21) represents that U 1,i,t , U 2,i,t , U 3,i,t are all Boolean variables. Equation (20) is a logical constraint, that is, at least one of U 1,i,t , U 2,i,t , U 3,i,t takes the value of True. Equation (19) is a disjunctive formula, which contains three disjunctive terms, and each disjunctive term contains a logical variable and several constraints. The corresponding constraints are effective if and only if the logical variable is equal to True. When U 1,i,t = True or U 2,i,t = True, the hydropower station i generates electricity at the maximum output, and the reservoirs y + 1, y + 2,..., i are all stored to the normal high water level, and the output of the hydropower station y is reduced to the minimum output, then the hydropower station i can abandon water. Among them, when U 1,i,t = True, the output of the hydropower station y is reduced to the output lower limit; when U 2，i，t = True, the hydropower station y can only reduce the output according to the ramping ability. When U 3，i，t = True, the hydropower station i cannot abandon water.

[0057]

[0058] Ω({U 1,i,t , U 2,i,t , U 3,i,t ) = True (20)

[0059] U 1,i,t , U 2,i,t , U 3,i,t ∈{True, False} (21)

[0060] Furthermore, for , the big M method is used to transform Equations (19) to (21) into mixed-integer linear constraint equations (22) to (32).

[0061]

[0062]

[0063] u 1，i，t +u 2，i，t +u 3，i，t = 1 (31)

[0064] u 1，i，t ,u 2，i，t ,u 3，i，t ∈ {0, 1} (32)

[0065] In the formula: u 1,i,t 、u 2,i,t 、u 3,i,t are all introduced auxiliary variables; M is a sufficiently large constant to ensure that the response constraint is relaxed when the auxiliary variable is equal to 0.

[0066] For the hydropower generation function, the present invention uses the rectangular subdivision technique to transform it into mixed-integer linear constraints. For the convenience of expression, the subscript i of the hydropower station, the subscript t of the time period, and the subscript s of the scenario are omitted. That is, V represents the average reservoir storage volume in the time period, m 3 ; Q E represents the power generation flow rate, m 3 / s; P H represents the output of the hydropower station, MW; then the hydropower generation function P H = f(O E , V) can be transformed as follows:

[0067]

[0068] λ x，y ≥ 0, x = 1, 2,..., X, y = 1, 2,..., Y (34)

[0069]

[0070]

[0071] SOS2({γ x |x = 1, 2,...X}), SOS2({δ y |y = 1, 2,..., Y}) (40)

[0072] In the formula: x and y are the grid point subscripts of the reservoir storage volume and the power generation flow rate respectively; is the grid point of the reservoir storage volume, m 3 ; is the grid point of the power generation flow rate, m 3 / s; is the output corresponding to the grid point ; λ x,y is the weight coefficient of the grid point ; γ x 、δy respectively the weight coefficient of the row and the column where it is located; Equation (40) is γ x , δ y both obey the SOS2 constraint.

[0073] The achievements of the present invention have the following beneficial effects: The present invention proposes a criterion for abandoning water in cascade hydropower stations and its modeling method. Based on this, an optimization model for the daily power generation plan of water, wind and light is constructed, and a linearization method for the water abandonment criterion based on generalized disjunctive programming is introduced to transform the original model into a mixed-integer linear programming model for solution, effectively reducing water abandonment and improving the rationality of the daily power generation plan of water, wind and light and the interpretability of water abandonment, providing a new technical approach for the short-term scheduling of water, wind and light integrated bases. Description of the Drawings

[0074] Figure 1 is a schematic diagram of the water abandonment criterion;

[0075] Figure 2 are the statistical indicators of typical days in the dry season;

[0076] Figure 3 are the statistical indicators of typical days in the flood season;

[0077] Figure 4 is the optimized daily power generation plan for a typical day in the flood season of Comparative Model 1;

[0078] Figure 5 is the optimized daily power generation plan for a typical day in the flood season of Comparative Model 2;

[0079] Figure 6 is the optimized daily power generation plan for a typical day in the flood season of Comparative Model 3;

[0080] Figure 7 is the optimized daily power generation plan for a typical day in the flood season of the proposed model. Detailed Implementation Modes

[0081] The present invention will be further described below in conjunction with the drawings and implementation cases.

[0082] Taking a cascade hydropower, wind and solar integrated base in Guizhou Province as the engineering background, the models and methods proposed in the present invention are tested. The total installed capacity of the three hydropower stations in this cascade hydropower, wind and solar integrated base is 2478 MW, and the installed capacities of wind power and photovoltaic power are 940 MW and 1610 MW respectively. The present invention takes the above cascade hydropower, wind and solar integrated base as the optimization calculation object to analyze and verify the effectiveness of the method of the present invention. Taking January 30, 2021 and September 10, 2021 as the typical days in the dry season and flood season respectively, the model input data includes hourly runoff data, hourly predicted wind and solar power output data on the typical days in the dry season and flood season, hourly historical wind and solar predicted power output data from January 1, 2018 to December 31, 2020, hourly historical wind and solar actual power output data, basic data of cascade hydropower stations and peak-valley electricity price data.

[0083] 1) Comparison model settings:

[0084] To verify the effectiveness of the proposed cascade hydropower station water abandonment criterion, the following four models are set for comparative analysis:

[0085] (1) The proposed model: That is, the day-ahead generation plan optimization model proposed in the present invention, and this model uses the water abandonment criterion described in Equation (1) to control the water abandonment of cascade hydropower stations.

[0086] (2) Comparison model 1: Compared with the proposed model, this model does not include Constraint (1), that is, it does not consider the water abandonment criterion proposed in the present invention, nor does it use other methods to control the water abandonment of cascade hydropower stations.

[0087] (3) Comparison model 2: Compared with the proposed model, this model does not consider the water abandonment criterion described in Equation (1), and adds the abandoned water volume as a penalty term to the objective function, that is, modifies the maximum power generation benefit objective to Equation (41).

[0088] max R′ = R - E P，S -E E，S (41)

[0089]

[0090] In the formula: R′ is the objective function value after adding the water abandonment penalty; E P，S is the day-ahead planned abandoned water volume, MWh; E E，S is the expected abandoned water volume when the cascade hydropower station responds to the flexibility demand of new energy; is the daily average water consumption rate of Hydropower Station i, m 3 / s / MW, set according to historical actual operation data; Pr s is the probability of the occurrence of scenario S.

[0091] (4) Comparison Model 3: Compared with the proposed model, this model replaces the water abandonment criterion described in Equation (1) with Equation (44). According to Equation (44), if Hydropower Station i abandons water, it only needs to store water to the normal high water level and generate electricity at the maximum output. Compared with the water abandonment criterion described in Equation (1), Equation (44) does not consider the cascade reservoir joint regulation ability. Equation (44) is also transformed into a mixed-integer linear constraint by using the Generalized Disjunctive Programming, which will not be elaborated here.

[0092]

[0093] 2) Result analysis:

[0094] (1) Comparative analysis of statistical indicators:

[0095] Optimize the proposed model, Comparison Model 1, Comparison Model 2, and Comparison Model 3 respectively, and count the day-ahead planned revenue, day-ahead planned water abandonment volume, and expected water abandonment volume of scenarios. The statistical results for typical days in the dry season and flood season are shown in Figure 2 、 Figure 3 respectively. Among them, the day-ahead planned water abandonment volume and the expected water abandonment volume of scenarios are calculated by Equation (45) and Equation (46) respectively.

[0096]

[0097] In the formula: W P 、W E are the day-ahead planned water abandonment volume and the expected water abandonment volume of scenarios respectively, in m 3 .

[0098] As shown in Figure 2 , on a typical day in the dry season, the day-ahead planned revenues of the proposed model, Comparison Model 1, Comparison Model 2, and Comparison Model 3 are all 16.03 million yuan. Comparison Model 1 does not control the water abandonment of cascade hydropower stations, resulting in the day-ahead planned water abandonment volume and the expected water abandonment volume of scenarios being 16.77 million m 3 、15.66 million m 3 respectively. The proposed model, Comparison Model 2, and Comparison Model 3 adopt different water abandonment control methods, making the day-ahead planned water abandonment volume and the expected water abandonment volume of scenarios both 0. It shows that considering the water abandonment control method in the optimization model of the day-ahead power generation plan of hydropower, wind, and solar can avoid water abandonment without reducing the power generation benefit and the reliability of the day-ahead power generation plan in the dry season.

[0099] As shown in Figure 3 , on a typical day in the flood season, the day-ahead planned revenue of the proposed model is 14.01 million yuan, which is reduced by 1.01%, 1.01%, and 0.86% compared with Comparison Model 1, Comparison Model 2, and Comparison Model 3 respectively. The day-ahead planned water abandonment volume and the expected water abandonment volume of scenarios of the proposed model are 5.53 million m 3 、5.73 million m 3, it is reduced by 80.82% and 79.19% respectively compared with the comparison model 1, by 37.61% and 30.11% respectively compared with the comparison model 2, and by 26.50% and 31.32% respectively compared with the comparison model 3. It shows that the water rejection criterion considering cascade hydraulic connection proposed during the flood season can effectively reduce the water rejection volume without significantly reducing the power generation benefit.

[0100] (2) Rationality analysis of water rejection:

[0101] Taking a typical day during the flood season as an example, analyze the rationality of the proposed water rejection criterion and the interpretability of its water rejection. The day-ahead generation plans obtained by optimizing the comparison model 1, the comparison model 2, the comparison model 3, and the proposed model are respectively as Figure 4 , Figure 5 , Figure 6 , Figure 7 shown.

[0102] According to Figure 4 , the comparison model 1 does not control water rejection, resulting in concentrated water rejection of H2 and H3 from 0:00 to 1:00. Among them, the water rejection flow rate of H3 is as high as 7019 m 3 / s. However, neither H2 nor H3 is stored up to the normal high water level from 0:00 to 1:00, and there is a certain regulating storage capacity, which can reduce water rejection by increasing the water storage volume. Therefore, the comparison model 1 not only generates a large amount of concentrated water rejection, but also the rationality of water rejection is difficult to explain.

[0103] According to Figure 5 , compared with the comparison model 1, the comparison model 2 adds the rejected power as a penalty term to the objective function, which can reduce water rejection by increasing the water storage volume. However, H3 still generates water rejection from 0:00 to 1:00, and the water rejection flow rate is as high as 2460 m 3 / s, and H3 is not stored up to the normal high water level from 0:00 to 1:00, that is, the comparison model 2 still generates unreasonable water rejection.

[0104] According to Figure 6 , in the day-ahead generation plan obtained by optimizing the comparison model 3, H3 generates water rejection from 20:00 to 24:00, and the water rejection flow rate is between 214 m 3 / s and 715 m 3 / s, which is significantly reduced compared with the comparison model 1 and the comparison model 2. And when H3 rejects water, it is stored up to the normal high water level and generates electricity at the maximum output of 880 MW. However, when H3 rejects water, its upstream hydropower station H2 is not stored up to the normal high water level and does not reduce its output to the minimum output. Therefore, the water rejection flow rate of H3 can be further reduced by increasing the water storage volume of H2 to reduce the power generation flow rate and then reduce the inflow of H3.

[0105] According to Figure 7, in the daily power generation plan obtained by optimizing the proposed model, water is wasted at H3 from 20:00 to 24:00, and the water waste flow rate is between 79 m 3 / s and 587 m 3 / s. The water waste flow rate in each period is lower than that of the comparison model. When water is wasted, not only does the water level of H3 reach the normal high water level and its output reach the maximum value of 880 MW, but also the output of H2 decreases according to its ramping capacity from 20:00 to 22:00, and the output decreases to 0 from 22:00 to 24:00. This shows that the proposed water waste criterion for cascade hydropower stations can make full use of the cascade reservoir joint regulation ability, significantly reduce the water waste volume, and when water is wasted, the cascade hydropower stations have all exerted their maximum regulation ability, and the occurring water waste is more reasonable and explainable.

Claims

1. A method for optimizing the day-ahead power generation plan of water, wind and light by coupling an interpretable curtailment criterion, characterized in that The specific steps are as follows: Step 1) Modeling of the water rejection criterion: The mathematical expression of the water rejection criterion for cascade hydropower stations is Equation (1), where i is the hydropower station number, numbered sequentially from upstream to downstream, and the total number of hydropower stations is I, that is, i = 1, 2,..., I; y is the number of the hydropower station with a regulating reservoir capacity that reduces the output to the minimum output, which is a variable to be optimized, 0 ≤ y ≤ i - 1; if hydropower station i rejects water, then hydropower station i generates electricity at its maximum output, and hydropower station i and its upstream hydropower stations i - 1, i - 2,..., y + 1 are all stored up to the normal high water level until a certain hydropower station y with a regulating reservoir capacity reduces the output to the minimum output; the water rejection criterion for cascade hydropower stations only considers that hydropower station i reaches its maximum output and does not consider that hydropower station i generates electricity at its maximum discharge; for hydropower station i, if y = 0, it means that all hydropower stations upstream of hydropower station i do not have a regulating reservoir capacity at this time and all need to be stored up to the normal high water level; where: i is the hydropower station number, i = 1, 2,..., I; t is the time period number, t = 1, 2,..., T; is the water discharge of hydropower station i during time period t, m 3 / s; are the outputs of hydropower stations i and y during time period t, MW; is the upper limit of the output of hydropower station i during time period t, MW; is the lower limit of the output of hydropower station y during time period t, MW; V j，t is the water storage of hydropower station j during time period t, m 3 / s; is the upper limit of the water storage of hydropower station j during time period t, m 3 / s; is the ramping capacity of hydropower station y, MW; Step 2) Establish an optimization model for the day-ahead power generation plan of water, wind, and light: (2.1) Objective function: For the integrated water, wind, and light base, the goal of formulating the day-ahead power generation plan is to maximize the power generation benefit; therefore, considering the peak-valley electricity price mechanism, the maximum power generation benefit is used as the objective function; Where: R is the benefit of power generation on the previous day, in yuan; α t is the electricity price at time period t, in yuan / MWh; P t HWS is the daily power generation plan of the cascade water-wind-solar integrated base, in MW; P t W，F and P t S，F are the predicted wind power and photovoltaic power outputs at time period t, in MW; Δt is the time period length; (2.2) Constraints for the day-ahead power generation plan: Constraints of the water rejection criterion: When formulating the day-ahead power generation plan, the water rejection criterion for cascade hydropower stations is considered, that is, Equation (1); Constraints on the transmission channel capacity: In the formula: is the transmission channel capacity, MW; Water volume balance constraints: Where: V i，t is the water storage volume of hydropower station i at the end of period t, m 3 ; are respectively the inflow, outflow, intermediate flow, power generation flow, and water spillage flow of hydropower station i during period t, m 3 / s; Constraints on the water storage volume: Wherein: are respectively the upper and lower limits of the water storage capacity of hydropower station i, m 3 / s; Constraints on the outflow discharge: Where: are the upper and lower limits of the outflow of Hydropower Station i, respectively, in m 3 / s; Constraints on the power generation discharge: where: are the upper and lower limits of the power generation flow of hydropower station i, m 3 / s; Output limit of hydropower stations: Where: are the upper and lower limits of the output of hydropower station i, MW respectively; Constraints on the ramping capacity: where: ΔP i H,max is the ramp capacity of hydropower station i, MW; Power generation function of hydropower stations: where: f i (·) is the power generation function of hydropower station i; Constraints on the initial and final water storage volumes: V i,0 = V i begin (14) V i，T ∈ V i end (15) Where: V i begin and V i end are the initial and final reservoir capacities of the given hydropower station i, respectively, in m 3 ; (2.3) Flexibility response constraints: The uncertainty of the output of wind power and photovoltaic power is described by the output scenarios. First, the probability density function and cumulative distribution function of the prediction errors of wind power and photovoltaic power in each period are fitted using the kernel density estimation method; then, the probit function is used to transform the cumulative distribution function of the prediction errors into a Gaussian distribution, and the multi-period random variables after transformation follow a multi-dimensional Gaussian distribution; then, the maximum likelihood estimation method is used to fit the multi-variable Gaussian distribution; finally, the wind power and photovoltaic power output scenarios are obtained through sampling and reduction; Flexibility supply-demand balance constraints: Wherein: is the flexibility demand of wind power and photovoltaic power at time t in scenario s, MW; is the output of hydropower station i at time t in scenario s, MW; is the flexibility supply of hydropower station i at time t in scenario s, MW; are the outputs of wind power and photovoltaic power at time t in scenario s, MW; Operating constraints of cascade hydropower stations: When providing flexibility, cascade hydropower stations also need to meet the operating constraints of cascade hydropower stations, including constraints on water rejection criteria, transmission channel capacity, water volume balance, water storage volume, outflow discharge, power generation discharge, hydropower station output limit, ramping capacity, hydropower station power generation function, initial and final water storage volume constraints; therefore, equations (1) and (4) - (15) are considered in intraday operation; since these constraints are scenario-related, the decision variables in these constraints all add the scenario subscript s; that is, in the intraday operation constraints, the decision variables V i，t and are respectively replaced by V i，s，t and where V i，s，t is the water storage volume of hydropower station i at the end of period t in scenario s, m 3 ; are respectively the inflow discharge, outflow discharge, power generation discharge, and water rejection discharge of hydropower station i at period t in scenario s, m 3 / s; Step 3) Model solution: The optimization model for the day-ahead power generation plan of water, wind, and light in Step 2) contains non-linear constraints such as the water rejection criterion and the power generation function of hydropower, which are difficult to solve directly; the following method is used to transform the original model into a mixed-integer linear model and solve it using the Gurobi solver; For the water rejection criterion, a linearization method of the water rejection criterion based on general disjunctive programming is proposed; first, Equation (1) is expressed as Equations (19) to (21); Equation (21) represents U 1，i，t U 2，i，t U 3，i，t are all Boolean variables; Equation (20) is a logical constraint, that is, at least one of U 1，i，t U 2，i，t U 3，i，t takes the value of True; Equation (19) is a disjunctive formula, which contains three disjunctive terms, and each disjunctive term contains a logical variable and several constraints. The corresponding constraints are effective if and only if the logical variable is equal to True; when U 1，i，t = True or U 2，i，t = True, the hydropower station i generates electricity at the maximum output, and the hydropower stations y + 1, y + 2,..., i are all stored to the normal high water level, and the output of the hydropower station y is reduced to the minimum output, then the hydropower station i can reject water; among them, when U 1，i， t = True, the output of the hydropower station y is reduced to the lower limit of the output; when U 2，i，t = True, the hydropower station y can only reduce the output according to the ramping ability; when U 3，i，t = True, the hydropower station i cannot reject water; Ω({U 1，i，t , U 2，i，t , U 3，i，t ) = True (20) U 1，i，t ,U 2，i，t ,U 3，i，t ∈ {True, False} (21) Furthermore, for The big-M method is used to transform equations (19) - (21) into mixed-integer linear constraints (22) - (32). u 1，i，t +u 2，i，t +u 3，i，t =1 (31) u 1，i，t +u 2，i，t +u 3，i，t ∈ {0, 1} (32) where: u 1，i，t , u 2，i，t , u 3，i，t are all introduced auxiliary variables; M 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 subdivision technique is used to transform it into mixed-integer linear constraints. For convenience of expression, the subscript i of the hydropower station, the subscript t of the time period, and the subscript s of the scenario are omitted. That is, V represents the average water storage of the hydropower station in a time period, m 3 ; Q E represents the power generation flow rate, m 3 / s; P H represents the output of the hydropower station, MW; then the hydropower generation function P H = f(Q E , V) is transformed as follows: λ x，y ≥ 0, x = 1, 2, ..., X, y = 1, 2, ..., Y (34) SOS2({γ x | x = 1, 2, ..., X}), SOS2({δ y | y = 1, 2, ..., Y}) (40) where: \(x\) and \(y\) are the subscripts of the grid points of water storage and power generation flow respectively; is the grid point of water storage in the hydropower station, \(m^3\) 3 ; is the grid point of power generation flow, \(m^3 / s\) 3 / s; is the output corresponding to the grid point , \(MW\); \(\lambda\) x，y is the weight coefficient of the grid point ; \(\gamma\) x , \(\delta\) y are respectively the weight coefficients of the row where it is located, the weight coefficients of the column where it is located; Equation (40) means that \(\gamma\) x , \(\delta\) y both obey the SOS2 constraint.

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