Flexible support method for step hydroelectric generating unit under vibration zone spanning constraint

Abstract

The present application belongs to the field of hydroelectric optimal dispatching operation, and discloses a flexible support method for cascade hydroelectric generating units under the consideration of vibration zone crossing constraint. The present application can improve the hydroelectric reserve flexibility by reasonable dispatching of the hydroelectric generating unit operation state under the premise of ensuring the operation reliability of the hydroelectric generating unit. The technical scheme is as follows: firstly, a flexible support model for the hydroelectric generating unit under the consideration of vibration zone crossing constraint is constructed; secondly, the solution of the flexible support model for the hydroelectric generating unit under the consideration of vibration zone crossing constraint is considered; and finally, a flexible allocation model considering the vibration zone of the unit is constructed. The flexible support method for the cascade hydroelectric generating unit under the consideration of vibration zone crossing constraint provided by the present application can effectively improve the hydroelectric reserve flexibility under the premise of ensuring the operation reliability of the hydroelectric generating unit, and is more practical and operable, thereby providing a new technical approach for the support dispatching of the hydroelectric generating unit flexibility under the consideration of vibration zone crossing constraint.

Description

Technical Field

[0001] This invention belongs to the field of hydropower optimized scheduling and operation, and specifically relates to a scheduling method for cascade hydropower units to support the flexibility of new energy grid connection. Background Technology

[0002] With rapid economic development, society's demand for energy continues to grow, and electricity, with its unique advantages, has become one of the important energy sources for promoting rapid social development.

[0003] As the proportion of new energy sources connected to the power system continues to rise, their absorption problem is becoming increasingly prominent. Joint dispatching of hydropower and renewable energy can ensure the effective utilization of renewable energy, thereby fully leveraging the flexibility of hydropower and meeting the grid's absorption needs. However, currently installed large-scale hydro-turbine generator units often exhibit single or even multiple vibration zones due to mechanical, electromagnetic, and hydraulic factors. To ensure the reliable and stable operation of the power system, in-depth research into the impact of these vibration zones on the output and reserve flexibility of hydro-turbine generator units is of great practical significance. Furthermore, due to the inherent high-dimensional nonlinear characteristics of hydropower dispatching, this problem is also a key and challenging aspect of further improving the reliability of hydropower in ensuring the grid connection of new energy sources under the new circumstances.

[0004] For the reasons mentioned above, this invention combines the safe operation and optimized scheduling of hydropower units, constructing a model that considers the unit vibration zone and constraints for crossing the vibration zone; it proposes a definition method for hydropower flexibility under vibration zone constraints; and based on the above research, a flexibility allocation model is constructed to study the allocation of hydropower flexibility in the actual scheduling process. Taking a two-stage hydropower station in southwestern my country as the engineering background, simulation calculations are completed under the actual scheduling conditions of the system. The results show that the unit operating state obtained by the hydropower flexibility support model based on considering constraints for crossing the vibration zone can avoid long-term operation in the vibration zone and frequent crossing of the vibration zone, effectively improving the overall safety benefits of the power system. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method for supporting the flexibility of grid connection of new energy by cascade hydropower units under the constraint of vibration zone crossing, so as to effectively avoid the risks of hydropower units operating in the vibration zone for a long time and frequently crossing the vibration zone, thereby improving the safety and reliability of the system.

[0006] Technical solution of the present invention:

[0007] The method for flexible support of cascade hydropower units under vibration zone crossing constraints includes: (1) constructing a flexible support model for hydropower units under vibration zone crossing constraints; (2) solving the flexible support model for hydropower units under vibration zone crossing constraints; and (3) constructing a flexible allocation model considering the vibration zone of the units. The following steps are followed to complete the flexible support scheduling of cascade hydropower units for new energy grid connection under vibration zone crossing constraints:

[0008] Step (1): To fully leverage the flexibility of hydropower and ensure the effective utilization of renewable energy, a support model for the flexibility of hydropower units under the constraint of vibration zone crossing is constructed. The construction of the model includes the establishment of objective function and constraint conditions, including conventional constraints, unit operation constraints considering the vibration zone, and hydropower unit flexibility constraints considering the vibration zone.

[0009] Step 1.1 Objective Function

[0010] To mitigate the impact of wind and solar power output fluctuations on system stability, the system needs sufficient flexibility in both upward and downward adjustments. The average reserve flexibility of hydropower units during the dispatch period is used as an indicator to measure the optimization of hydropower unit dispatch within the system. The objective function is:

[0011]

[0012] In the formula: This indicates the flexibility of adjusting the output of a hydropower unit during time period t, expressed in MW. N represents the downward adjustment flexibility of the hydropower unit's output during time period t, in MW; F represents the average adjustment flexibility of the hydropower unit during the dispatch period, in MW; T Represents the set of time periods;

[0013] Step 1.2 Conventional Constraints

[0014] Common constraints include water balance constraints, outflow limits, boundary constraints, net head constraints, power plant output constraints, unit start-up and shutdown time constraints, and residual load ramping constraints.

[0015] 1) Water balance constraint

[0016] V h，t+1 =V h，t +(i h，t +q h-1，t -q h，t )τ t

[0017] In the formula: V h，t The reservoir capacity of hydropower station h at the end of time period t is represented by m. 3 i h，t The average inflow of hydropower station h over time period t is expressed in m³.3 / s;q h，t The average outflow from the reservoir of hydropower station h during time period t is expressed in m³. 3 / s;τ t The duration of the scheduling period is expressed in seconds; the water balance constraint defines the relationship between reservoir capacities under the spatial and temporal interaction of cascade hydropower stations.

[0018] 2) Outbound flow constraints

[0019] q h，t =g h，t +lw h，t

[0020] Where: g h，t This represents the power generation flow of hydropower station h during time period t, in m. 3 ;lw h，t The average discharge flow of the hydropower station h during time period t is expressed in m. 3 / s; Set the water discharge to 0, i.e., lw h，t =0;

[0021] 3) Boundary constraints

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] In the formula: V h，t , These represent the lower and upper limits of the reservoir capacity (h) for the hydropower station during time period (t), respectively. 3 ; q h，t , Let represent the lower and upper limits of the outflow from the hydropower station during the time period t (h), respectively, in m³ / s; g h，t , These represent the lower and upper limits of the power generation flow of the hydropower station h during time period t, respectively, and m. 3 / s; This indicates that the initial storage capacity during the scheduling period is V. h，1 The final storage capacity is V. h，T m 3 ;

[0028] 4) Constraints related to water purification head

[0029]

[0030]

[0031] d h，t =fd h (q h，t )

[0032] hl h，t =fl h，u (g h，t )

[0033] h h，t =u h，t -d h，t -hl h，t

[0034]

[0035] In the formula: The reservoir capacity of hydropower station h during time period t is expressed in m³. h，t The value of fu represents the average upstream water level of the hydropower station during time period t. h (·) represents the water level-reservoir capacity function; d h，t fd represents the average tailwater level of the hydropower station during time period t, in meters. h (·) represents the tailwater level discharge function; hl h，t The value of fl represents the head loss of the hydropower station during time period t, expressed in m. h，u (·) represents the head loss function; h h，t p represents the average net head (m) of the hydropower station h during time period t. h，t This represents the power output of the hydropower station h during time period t, in MW. Let h be the power generation characteristic function of the hydropower station;

[0036] 5) Power plant output constraints

[0037]

[0038]

[0039] In the formula: P h，u，t , This represents the lower and upper limits of the output of the u-th generating unit of the hydropower station h during time period t, in MW; This represents the set of generating units contained in power plant h; Φ h , This represents the lower and upper limits of reservoir output h, in MW.

[0040] 6) Unit start-up and shutdown time constraints

[0041] Define the unit state variable r h，u，t If r h，u，t =1, which means that the u-th generating unit of hydropower station h is in operation during time period t; otherwise, r h，u，t =0 indicates that the unit is in a stopped state; define the unit start-up operation variable. like This indicates that the u-th generating unit of the hydropower station h performs the unit start-up operation during time period t; otherwise... Define unit shutdown operation variables like This indicates that the u-th generating unit of hydropower station h will be shut down during time period t; otherwise...

[0042]

[0043]

[0044]

[0045] In the formula: These represent the shortest time interval between the start-up and shutdown of the u-th generating unit in hydropower station h, respectively.

[0046] 7) Residual load ramping constraint

[0047]

[0048] σ t =|d t -d t+1 |

[0049]

[0050] Where: σ t Represents the absolute value of the ramp-up of the remaining load in time period t and the next time period, in MW; D represents the maximum absolute value of the ramp-up of the remaining load in time period t and the next time period, in MW; t N represents the load of the day-ahead forecasting system in time period t, in MW; H P represents the set of power station numbers; wt This represents the wind power output (MW) predicted for time period t. st This represents the predicted photovoltaic output in MW for the current period t; d t The remaining system load during time period t is expressed in MW.

[0051] Step 1.3 Considering the unit's operating constraints in the vibration zone

[0052] The constraints on unit operation in the vibration zone include constraints on long-term operation of the unit in the vibration zone and constraints on the unit crossing the vibration zone.

[0053] 1) Constraints to avoid long-term operation of the unit in the vibration zone:

[0054]

[0055] 2) Unit crossing vibration zone constraints:

[0056]

[0057]

[0058]

[0059]

[0060] In the formula: This represents the lower and upper limits, in MW, of the output of the u-th generating unit of the hydropower station during the time period t within the safe operating zone z. This represents the set of all safe operating zones for the u-th generating unit of the hydropower station during time period t; C h，u，t z represents the variable used to determine whether the operating state of the u-th generating unit of hydropower station h is the same in time period t and t+1; h，u，t This indicates the safe operating zone of the u-th generating unit of hydropower station h during time period t; This indicates the number of times the u-th generating unit of the hydropower station h crosses the vibration zone; This represents the upper limit of the number of times the u-th generating unit of the hydropower station h crosses the vibration zone;

[0061] Step 1.4 Considering the flexibility constraints of the hydropower unit in the vibration zone

[0062]

[0063]

[0064] In the formula: These represent the safe operating zones (z, z) of the u-th generating unit of hydropower station h during time period t. h，u，t The lower and upper limits of output, in MW;

[0065] Step (2): Solving the flexible support model of the hydropower unit under the constraint of vibration zone crossing

[0066] The unit output calculation constraints and unit operation constraints considering the vibration zone crossing constraints in the flexible support model of the hydropower unit are both nonlinear, which makes the flexible support model of the hydropower unit considering the vibration zone crossing constraints a nonlinear optimization problem that is difficult to solve directly.

[0067] Step 2.1 Linearization of hydropower unit output and flexibility constraints considering the vibration zone

[0068] Introducing unit safety operation variable s h，u，t , is used to represent the safe operating zone of the u-th generating unit of the hydropower station h during time period t, so as to realize the calculation of the output and flexibility constraints of the hydropower unit under the consideration of the vibration zone into a form that meets the constraints of the MILP method;

[0069] Equation (2) can be constructed as follows:

[0070]

[0071] In the formula: Let represent the lower and upper limit vectors of the output of the u-th generating unit of hydropower station h in each safe operating zone during time period t;

[0072] Equations (7)-(8) are constructed as follows:

[0073]

[0074]

[0075] Step 2.2 Linearization of the constraint on the number of times the unit crosses the vibration zone

[0076] Based on the positive infinity norm of vectors, the transformation of equations (3) to (4) is completed, realizing the statistics of the number of times the unit crosses the vibration zone in adjacent time periods. Then, the equivalent linearization is completed by using the relevant expression of the element index of the unit's safe operation variable, solving the problem of ||·|| +∞ Nonlinear problems;

[0077] 1) Construct equations (3)-(5) as follows:

[0078]

[0079] In the formula: ||·|| +∞ Let be the positive infinity norm of the vector;

[0080] 2) Equations (3) to (5) are further constructed as follows:

[0081]

[0082] In the formula: The variable s represents the safe operation of the u-th generating unit of the hydropower station during time period t. h，u，t The dimension is the number of safe operating zones for the u-th generating unit of the hydropower station during time period t. The variable s represents the safe operation of the generator unit. h，u，t The d-th element;

[0083] Step 2.3 uses a triangulation method based on convex combinations to linearize the output calculation constraints.

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] In the formula: λ h，t，u，k With y h，t，u The auxiliary variables introduced are: u, representing the triangle number of the triangulation; k, representing the vertex number of the triangle; and N. U N represents the set of numbers that divide the triangle, N3 represents the set of integers from 1 to 3, and H represents the set of numbers that divide the triangle. h，u，k With Q h，u，k This represents the triangulation grid points of the three-dimensional surface used for force calculation.

[0091] Step (3): Construct a flexible allocation model that considers the vibration zone

[0092] By solving the flexibility support model of hydropower units considering the vibration zone crossing constraint, this study investigates the allocation of unit flexibility in actual scheduling process, obtained from the traditional flexibility model and the flexibility model considering the vibration zone.

[0093] Step 3.1 Objective Function

[0094] To balance the impact of the deviation between the actual and predicted output of each unit, the absolute value of the difference between the current output deviation and the average flexibility supply is used as an auxiliary optimization parameter δ. h，u，t , with all units δ h，u，t The sum is used as an indicator to measure the optimization of flexible allocation, and the objective function is:

[0095]

[0096] Where: δ h，u，t The absolute value, in MW, represents the difference between the actual output of the u-th generating unit of hydropower station h and the planned output of the previous day during time period t, and the average flexible supply of all generating units.

[0097] Step 3.2 Constraints

[0098]

[0099] P t de =(P t wp +P t sp )-(P t wr +P t sr (16)

[0100]

[0101]

[0102]

[0103] In the formula: This indicates the planned output (MW) of the u-th generating unit of the hydropower station h before day t, obtained by considering strict constraints on the vibration zone. This represents the actual power output (MW) of the u-th generating unit of hydropower station h during time period t. These represent the planned output of the u-th generating unit of the hydropower station h before day t. Located in safe operating zone z h，u，t The lower and upper limits of output, in MW; These represent the planned and actual wind power outputs for the day-ahead period t, respectively, in MW; These represent the planned and actual power output of the photovoltaic system during time period t, respectively, in MW. This represents the difference between the planned and actual power output of the wind turbine at time t, expressed in MW. This represents the change in actual power output of hydropower units compared to the planned output on the previous day, expressed in MW, during time period t, in order to reduce the fluctuation of wind and solar power output.

[0104] Step 3.3 Model Solving

[0105] The solution results of the flexible allocation model considering the vibration zone show that the unit output process obtained by the flexible support model of the hydropower unit considering the vibration zone crossing constraint can ensure that the unit flexibility is smoothly executed by each unit while avoiding the unit vibration zone, thus ensuring the safety and reliability of the unit.

[0106] The beneficial effects of this invention are as follows: This invention constructs a flexible support model for hydropower units considering vibration zone crossing constraints, establishes unit operation constraints and flexible constraints considering vibration zone crossing constraints, and transforms the model into a mixed integer linear programming model by introducing auxiliary variables for safe operation and the positive infinity norm of vectors. The effectiveness of the flexible support model for hydropower units considering vibration zone crossing constraints is thoroughly verified through the constructed flexible allocation model considering vibration zone crossing constraints, providing a new technical approach for the support scheduling of flexible hydropower units considering vibration zone crossing constraints. Attached Figure Description

[0107] Figure 1 This is the power output process of each unit of the XW power plant; where (a) is the traditional constraint model; (b) is the vibration zone constraint model; and (c) is the vibration zone strict constraint model.

[0108] Figure 2 It is the power output process of each unit of the MW power plant; among them, (a) is the traditional constraint model; (b) is the vibration zone constraint model; (c) is the vibration zone strict constraint model;

[0109] Figure 3 It represents the number of times the unit crosses the vibration zone; where (a) is the XW power plant; and (b) is the MW power plant.

[0110] Figure 4 The standby flexibility of hydropower units in different time periods is obtained from the traditional flexibility model; where (a) is the flood season scenario and (b) is the dry season scenario.

[0111] Figure 5 The standby flexibility of the hydropower unit in each time period is obtained by considering the vibration zone flexibility model; where (a) is the flood season scenario; and (b) is the dry season scenario.

[0112] Figure 6 This is a flowchart of the solution process for the flexible allocation model considering the vibration zone;

[0113] Figure 7 This is the power output process of each unit in the traditional flexibility model; where (a) is the XW power plant; and (b) is the MW power plant.

[0114] Figure 8 The output process of each unit is considered in the flexibility model of the vibration zone; where (a) is the XW power station; (b) is the MW power station. Detailed Implementation

[0115] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0116] This invention uses a two-stage hydropower station in southwestern my country as a specific research object to verify the model and method proposed in this paper. Reservoirs XW and MW are located upstream and downstream of the cascade system, respectively, each containing six generating units. The operating range of all units includes a corresponding vibration zone. In this invention, the scheduling calculation cycle is one day, and the calculation period is 24 hours. Simulation calculations are performed based on collected wind and solar power output prediction and actual data, combined with different research objectives and models. When the constructed model considers strict constraints on the vibration zone, a maximum number of vibration zone crossings is set. It was 4 times.

[0117] (1) Using the traditional flexibility algorithm as the objective function, the following models were constructed: Model 1 is the traditional algorithm model; Model 2 is the model considering vibration zone constraints; and Model 3 is the model considering the number of vibration zone crossings constraints. The output process of each unit in each model was solved, such as... Figures 1-2 As shown in the figure. The calculation results show that, compared with the model constructed by the traditional algorithm, the model constructed by considering the constraint of the number of times the vibration zone is crossed can reduce the time when each unit operates in the vibration zone for a long time to 0, effectively avoid the situation where the unit operates in the vibration zone for a long time, and ensure the stable operation of the unit. Figure 3 The model demonstrates the number of times each unit crosses the vibration zone in different models. The model constructed with consideration of the constraint on the number of times the unit crosses the vibration zone keeps the number of times the unit crosses the vibration zone within the limit, which significantly improves the overall safety benefits of the system.

[0118] (2) A flexibility constraint model considering the vibration zone and a traditional flexibility constraint model were constructed. The solution results were used to calculate the unit flexibility using different flexibility calculation methods. The calculation results are shown in Table 1. The results show that the unit operating status obtained by using the flexibility constraint model considering the vibration zone is not significantly different from the solution of the traditional flexibility constraint model, even if the unit's average reserve flexibility is calculated using the traditional flexibility algorithm. However, if the traditional flexibility constraint model is used, and the unit flexibility is to be obtained while avoiding the unit's vibration zone, the calculation result will lose a larger range of unit flexibility compared to the solution of the flexibility constraint model considering the vibration zone. The unit operating status obtained by using the flexibility constraint model considering the vibration zone can better meet engineering requirements in real-time scheduling and has a relatively more sufficient adjustment margin.

[0119] Table 1 Average Standby Flexibility of Hydropower Units (MW)

[0120]

[0121]

[0122] (3) Construct a flexibility model considering the vibration zone and a traditional flexibility model, and perform simulation analysis under flood season and dry season scenarios respectively. Figures 4-5 The standby flexibility of hydropower units under different scenarios and time periods is demonstrated using two flexibility models. The results show that the distribution of the vibration zone of the hydropower unit affects its available flexibility. When the vibration zone is mainly distributed in the low-output range, it will restrict the average standby flexibility when the unit output is low, resulting in the average standby flexibility obtained by the unit in the dry season being lower than that in the flood season.

[0123] (4) Substitute the solution results of the flexibility model considering the vibration zone and the traditional flexibility model into the flexibility allocation model considering the vibration zone. The calculation process is as follows: Figure 6 As shown, the allocation of unit flexibility during the scheduling process is analyzed, and the output process of each unit is solved, as follows. Figures 6-7 As shown in the figure. The results indicate that the day-ahead schedule of the unit, obtained based on the flexibility model considering the vibration zone, can ensure the smooth execution of unit flexibility while avoiding the unit vibration zone during the scheduling process, effectively guaranteeing the safety and reliability of unit operation during the scheduling period.

[0124] In summary, the flexible support method for cascade hydropower units considering vibration zone crossing constraints proposed in this invention can effectively improve the flexibility of hydropower standby while ensuring the operational reliability of hydropower units. It is practical and operable, and provides a new technical approach for supporting and scheduling the flexibility of hydropower units considering vibration zone crossing constraints.

Claims

1. A flexible support method for cascade hydropower units considering vibration zone crossing constraints, characterized in that, The steps are as follows: Step (1): To fully leverage the flexibility of hydropower and ensure the effective utilization of renewable energy, a support model for the flexibility of hydropower units under the constraint of vibration zone crossing is constructed, including the establishment of objective function and constraint conditions. The constraint conditions include conventional constraints, unit operation constraints considering the vibration zone, and hydropower unit flexibility constraints considering the vibration zone. Step 1.1 Objective Function To mitigate the impact of wind and solar power output fluctuations on system stability, the system needs sufficient flexibility in both upward and downward adjustments. The average reserve flexibility of hydropower units during the dispatch period is used as an indicator to measure the optimization of hydropower unit dispatch within the system. The objective function is: In the formula: This indicates the flexibility of adjusting the output of a hydropower unit during time period t, expressed in MW. N represents the downward adjustment flexibility of the hydropower unit's output during time period t, in MW; F represents the average adjustment flexibility of the hydropower unit during the dispatch period, in MW; T Represents the set of time periods; Step 1.2 Conventional Constraints Common constraints include water balance constraints, outflow limits, boundary constraints, net head constraints, power plant output constraints, unit start-up and shutdown time constraints, and residual load ramping constraints. 1) Water balance constraint V h,t+1 =V h,t +(i h,t +q h-1,t -q h,t )τ t In the formula: V h,t The reservoir capacity of hydropower station h at the end of time period t is represented by m. 3 ; i h,t The average inflow of hydropower station h over time period t is expressed in m³. 3 / s;q h,t The average outflow from the reservoir of hydropower station h during time period t is expressed in m³. 3 / s;τ t The duration of the scheduling period is expressed in seconds; the water balance constraint defines the relationship between reservoir capacities under the spatial and temporal interaction of cascade hydropower stations. 2) Outbound flow constraints q h,t =g h,t +lw h,t Where: g h,t This represents the power generation flow of hydropower station h during time period t, in m. 3 ;lw h,t The average discharge flow of the hydropower station h during time period t is expressed in m. 3 / s; Set the water discharge to 0, i.e., lw h,t =0; 3) Boundary constraints In the formula: V h,t , These represent the lower and upper limits of the reservoir capacity (h) for the hydropower station during time period (t), respectively. 3 ; q h,t , These represent the lower and upper limits of the outflow from the hydropower station during the time period h and t, respectively. 3 / s; g h,t , Let m represent the lower and upper limits of the power generation flow of the hydropower station h during time period t, respectively. 3 / s; This indicates that the initial storage capacity during the scheduling period is V. h,1 The final storage capacity is V. h,T m 3 ; 4) Constraints related to water purification head d h,t =fd h (q h,t ) hl h,t =fl h,u (g h,t ) h h,t u h,t -d h,t -hl h,t In the formula: The reservoir capacity of hydropower station h during time period t is represented by m. 3 ;u h,t The value of fu represents the average upstream water level of the hydropower station during time period t. h (·) represents the water level-reservoir capacity function; d h,t fd represents the average tailwater level of the hydropower station during time period t, in meters. h (·) represents the tailwater level discharge function; hl h,t The value of fl represents the head loss of the hydropower station during time period t, expressed in m. h,u (·) represents the head loss function; h h,t p represents the average net head (m) of the hydropower station h during time period t. h,t This represents the power output of the hydropower station h during time period t, in MW. Let h be the power generation characteristic function of the hydropower station; 5) Power plant output constraints In the formula: P h,u,t , This represents the lower and upper limits of the output of the u-th generating unit of the hydropower station h during time period t, in MW; This represents the set of generating units contained in power plant h; Φ h , This represents the lower and upper limits of reservoir output h, in MW. 6) Unit start-up and shutdown time constraints Define the unit state variable r h,u,t If r h,u,t =1, which means that the u-th generating unit of hydropower station h is in operation during time period t; otherwise, r h,u,t =0 indicates that the unit is in a stopped state; define the unit start-up operation variable. like This indicates that the u-th generating unit of the hydropower station h performs the unit start-up operation during time period t; otherwise... Define unit shutdown operation variables like This indicates that the u-th generating unit of hydropower station h will be shut down during time period t; otherwise... In the formula: These represent the shortest time interval between the start-up and shutdown of the u-th generating unit in hydropower station h, respectively. 7) Residual load ramping constraint s t =|d t -d t+1 | In the formula: σ t Represents the absolute value of the ramp-up of the remaining load in time period t and the next time period, in MW; D represents the maximum absolute value of the ramp-up of the remaining load in time period t and the next time period, in MW; t N represents the load of the day-ahead forecasting system in time period t, in MW; H P represents the set of power station numbers; wt This represents the wind power output (MW) predicted for time period t. st This represents the predicted photovoltaic output in MW for the period t; d t The system's remaining load during time period t is expressed in MW. Step 1.3 Considering the unit's operating constraints in the vibration zone The constraints on unit operation in the vibration zone include constraints on long-term operation of the unit in the vibration zone and constraints on the unit crossing the vibration zone. 1) Constraints to avoid long-term operation of the unit in the vibration zone: 2) Unit crossing vibration zone constraints: In the formula: This represents the lower and upper limits, in MW, of the output of the u-th generating unit of the hydropower station during the time period t within the safe operating zone z. This represents the set of all safe operating zones for the u-th generating unit of the hydropower station during time period t; C h,u,t z represents the variable used to determine whether the operating state of the u-th generating unit of hydropower station h is the same in time period t and t+1; h,u,t This indicates the safe operating zone of the u-th generating unit of hydropower station h during time period t; This indicates the number of times the u-th generating unit of the hydropower station h crosses the vibration zone; This represents the upper limit of the number of times the u-th generating unit of the hydropower station h crosses the vibration zone; Step 1.4 Considering the flexibility constraints of the hydropower unit in the vibration zone In the formula: These represent the safe operating zones (z, z) of the u-th generating unit of the hydropower station h during time period t. h,u,t The lower and upper limits of output, in MW; Step (2): Solving the flexible support model of the hydropower unit under the constraint of vibration zone crossing The unit output calculation constraints and unit operation constraints considering the vibration zone crossing constraints in the flexible support model of the hydropower unit are both nonlinear, which makes the flexible support model of the hydropower unit considering the vibration zone crossing constraints a nonlinear optimization problem that is difficult to solve directly. Step 2.1 Linearization of hydropower unit output and flexibility constraints considering the vibration zone Introducing unit safety operation variable s h,u,t , is used to represent the safe operating zone of the u-th generating unit of the hydropower station h during time period t, so as to realize the calculation of the output and flexibility constraints of the hydropower unit under the consideration of the vibration zone into a form that meets the constraints of the MILP method; Equation (2) can be constructed as follows: In the formula: Let represent the lower and upper limit vectors of the output of the u-th generating unit of hydropower station h in each safe operating zone during time period t; Equations (7)-(8) are constructed as follows: Step 2.2 Linearization of the constraint on the number of times the unit crosses the vibration zone Based on the positive infinity norm of vectors, the transformation of equations (3) to (4) is completed, realizing the statistics of the number of times the unit crosses the vibration zone in adjacent time periods. Then, the equivalent linearization is completed by using the relevant expression of the element index of the unit's safe operation variable, solving the problem of ||·|| +∞ Nonlinear problems; 1) Construct equations (3)-(5) as follows: In the formula: ||·|| +∞ Let be the positive infinity norm of the vector; 2) Equations (3) to (5) are further constructed as follows: In the formula: The variable s represents the safe operation of the u-th generating unit of the hydropower station during time period t. h,u,t The dimension is the number of safe operating zones for the u-th generating unit of the hydropower station during time period t. The variable s represents the safe operation of the generator unit. h,u,t The d-th element; Step 2.3 uses a triangulation method based on convex combinations to linearize the output calculation constraints. In the formula: λ h,t,u,k With y h,t,u The auxiliary variables introduced are: u, representing the triangle number of the triangulation; k, representing the vertex number of the triangle; and N. U N represents the set of numbers that divide the triangle, N3 represents the set of integers from 1 to 3, and H represents the set of numbers that divide the triangle. h,u,k With Q h,u,k The triangulation points represent the grid points of the three-dimensional surface used for force calculation; Step (3): Construct a flexible allocation model that considers the vibration zone By solving the flexibility support model of hydropower units considering the vibration zone crossing constraint, this study investigates the allocation of unit flexibility in actual scheduling process between the traditional flexibility model and the flexibility model considering the vibration zone. Step 3.1 Objective Function To balance the impact of the deviation between the actual and predicted output of each unit, the absolute value of the difference between the current output deviation and the average flexibility supply is used as an auxiliary optimization parameter δ. h,u,t , with all units δ h,u,t The sum is used as an indicator to measure the optimization of flexible allocation, and the objective function is: Where: δ h,u,t The absolute value, in MW, represents the difference between the actual output of the u-th generating unit of hydropower station h and the planned output at time period t and the average flexible supply of all generating units. Step 3.2 Constraints P t de =(P t wp +P t sp )-(P t wr +P t sr ) (16) In the formula: This indicates the planned output (MW) of the u-th generating unit of the hydropower station h before day t, obtained by considering strict constraints on the vibration zone. This represents the actual power output (MW) of the u-th generating unit of hydropower station h during time period t. These represent the planned output of the u-th generating unit of the hydropower station h before day t. Located in safe operating zone z h,u,t The lower and upper limits of output, in MW; These represent the planned and actual wind power outputs for the day-ahead period t, respectively, in MW; These represent the planned and actual power output of the photovoltaic system during time period t, respectively, in MW. This represents the difference between the planned and actual power output of the wind turbine at time t, expressed in MW. This represents the change in actual power output of hydropower units compared to the planned output on the previous day, expressed in MW, during time period t, in order to reduce the fluctuation of wind and solar power output. Step 3.3 Model Solving The solution results of the flexible allocation model considering the vibration zone show that the unit output process obtained by the flexible support model of the hydropower unit considering the vibration zone crossing constraint can ensure that the unit flexibility is smoothly executed by each unit while avoiding the unit vibration zone, thus ensuring the safety and reliability of the unit.

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