A linearization method for the output function of a hydropower station based on a simplified constraint strategy

Abstract

This invention provides a method for linearizing the power output function of a hydropower station based on a simplified constraint strategy. The method includes: equally dividing the feasible region of the power output function into rectangular grids; defining a corresponding plane for each rectangular grid; constructing a quadratic programming model for calibrating the plane cluster parameters that approximate the power output surface of the hydropower station based on the characteristic parameters of the planes and the simplified plane set corresponding to the rectangular grids generated using the simplified constraint strategy; solving the quadratic programming model to obtain a set of plane equation parameters that approximate the optimal power output of the hydropower station; and in a reservoir optimization scheduling model where the scheduling objective includes maximizing the power output or power generation of the hydropower station within the scheduling period, using the parameters of the solved plane equations to construct a linearized expression for the hydropower output function in the reservoir optimization scheduling model. This invention avoids introducing integer variables, reduces the size of the quadratic programming model while ensuring the accuracy of fitting the hydropower station's power output, and greatly improves the solution efficiency.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of operations research and long-term scheduling of cascade reservoirs, specifically a method for linearizing the output function of hydropower stations based on a simplified constraint strategy. Background Technology

[0002] The optimal reservoir scheduling problem is a typical nonlinear optimization problem. Linear programming (LP) is widely used to solve such problems due to its mature theoretical foundation. However, the solution requires linearizing the objective function and constraints, with the most significant nonlinear factor originating from the hydropower output function (HOF). Therefore, finding a suitable linearization modeling method is crucial when using LP to solve the reservoir scheduling problem. Fixing the hydropower station efficiency is the simplest way to linearize the HOF, but this ignores the head effect, resulting in a simplified model that deviates significantly from the original problem. Using piecewise linearization to approximate the nonlinear HOF transforms the original problem into a mixed-integer linear programming (MILP) problem that yields a globally optimal solution. However, piecewise linearization of all nonlinear functions introduces more integer variables, making obtaining the optimal solution within a finite time frame a very challenging task.

[0003] Kang Chuanxiong (Research on Optimal Scheduling of Cascade Reservoirs Based on Linear Approximation and Water Storage Distribution Curve [Doctoral Dissertation]. Wuhan: Huazhong University of Science and Technology, 2018) proposed a planar convex hull linear approximation method. By dividing the feasible region of output into rectangular grids, a planar equation is calibrated within each grid or its neighborhood to approximate the actual output. However, this method selects the minimum approximation value of each rectangular grid point for evaluation in the objective function. Although no integer variables are introduced in the solution process, a special sequence set is introduced when calling the mathematical solver, which increases the solution time. In particular, after increasing the number of grid divisions for over-approximation, the total number of constraints not represented by the effective planar constraints in the constructed model surges, leading to an exponential increase in the model solution time, and even the model may not be able to stably obtain the optimal solution. Summary of the Invention

[0004] The problem to be solved by this invention is how to provide a non-convex and nonlinear hydropower station output function for long-term scheduling of a reservoir, in order to solve the problems of difficulty in model solution caused by the introduction of too many integer variables or special sequence sets, and the sharp increase in model constraint scale, exponential increase in solution time, and even inability to stably obtain the optimal solution when the number of grid divisions is increased due to excessive approximation.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] A method for linearizing the output function of a hydropower station based on a simplified constraint strategy, comprising:

[0007] The feasible region of the hydropower station's output function is equally divided into rectangular grids;

[0008] Define a corresponding plane for each rectangular grid in the feasible region of the power output function of the hydropower station;

[0009] Based on the characteristic parameters of the defined plane and the simplified plane set corresponding to each rectangular grid generated by the simplified constraint strategy, a quadratic programming model for calibrating the plane cluster parameters of the hydropower station output surface is constructed.

[0010] Solving the constructed quadratic programming model yields a set of parameters for a plane equation that approximates the optimal output of the hydropower station.

[0011] In a reservoir optimization scheduling model where the scheduling objective includes maximizing the output or power generation of a hydropower station during the scheduling period, a linearized expression for the hydropower output function is constructed in the reservoir optimization scheduling model using the parameters of the set of plane equations that approximate the optimal output of the hydropower station obtained by solving the equations.

[0012] Furthermore, the simplified constraint strategy refers to a strategy that reduces the model size by simplifying some of the constraints in the effective plane when constructing the quadratic programming model, without affecting the overall constraint effect of the model.

[0013] The simplified plane set corresponding to the rectangular grid is the set of planes remaining after simplifying the plane and the redundant plane set of the plane within the feasible domain of the hydropower station. The redundant plane set of the plane is the set of planes formed by simplifying the redundant active plane constraints of the plane based on the simplification constraint strategy. That is, the redundant plane set of the plane is the set of planes corresponding to the grids whose grid center points are connected by lines that pass through the centers of other grids.

[0014] Furthermore, the power output function of the hydropower station is a bivariate function relating to the reservoir's average reservoir capacity over a given period and the upper and lower limits of the allowable outflow, specifically including:

[0015] The power output of the hydropower station during time period t is expressed as:

[0016] Where P t , Q t These represent the reservoir's power output, average reservoir capacity, and outflow during time period t, respectively, in MW and million cubic meters per second (MW and million cubic meters per second). 3 m 3 / s, The calculation expression is:

[0017]

[0018] Among them, V t The reservoir capacity at the beginning of time period t is expressed in millions of cubic meters. 3

[0019] Furthermore, the feasible region of the hydropower station's output function is a planar region composed of the upper and lower limits of the reservoir capacity and the allowable outflow. This feasible region is then equally divided into several capacity segments and outflow segments, where the number of capacity and outflow segments is determined by the number of segments, as expressed in the following expression:

[0020]

[0021]

[0022] Where ΔV and ΔQ are the lengths of the storage capacity segment and the outflow segment, respectively; V max V represents the upper limit of the reservoir's capacity at time t. min Let Q be the lower limit of the reservoir's capacity at time t. max Let Q be the upper limit of the outflow from the reservoir at time t. min Let be the lower limit of the outflow from the reservoir at time t, where the reservoir capacity and flow rate are in millions of cubic meters per second (M³). 3 m 3 / s; NV and NQ are the number of segments for storage capacity and outbound flow, respectively, and the sequence numbers for storage capacity segment and outbound flow segment are as follows:

[0023] i = 0, 1, ..., NV-1

[0024] j = 0, 1, ..., NQ-1

[0025] The feasible region is divided into rectangular grids, which are areas enclosed by equally divided storage capacity segments and outflow flow segments. The number of rectangular grids is:

[0026] N = NV × NQ

[0027] Where N is the total number of rectangular grids divided within the feasible region of the hydropower station's output, and the index of the rectangular grid is defined as follows:

[0028] n=u(i,j)=i*NQ+j(n=0,1,···N-1)

[0029] There is a one-to-one correspondence between any rectangular grid n and the combination (i,j).

[0030]

[0031] Within the feasible region, the storage capacity and outflow are discretized into NV+1 and NQ+1 values, respectively, denoted as V(i) and Q(j), and their mathematical expressions are as follows:

[0032] V(i)=V min +i·ΔV,0≤i≤NV

[0033] Q(j)=Q min +j·ΔQ,0≤j≤NQ

[0034] Each point within the feasible region is represented as [V(i), Q(j)] T .

[0035] Furthermore, each rectangular grid within the feasible power output domain of the hydropower station has 5 representative grid points: 1 central grid point and 4 corner grid points, with indices k = 0, 1, 2, 3, 4, respectively. The corresponding rectangular grid points are represented as follows:

[0036]

[0037] Furthermore, each rectangular grid within the feasible region of the hydropower station's output function is defined with a corresponding plane, meaning there is a one-to-one correspondence between the rectangular grids and the planes. The plane index corresponding to the rectangular grid is the same as the index of the rectangular grid itself. The plane equation for plane n corresponding to rectangular grid n is defined as follows:

[0038]

[0039] in, For any point (V,Q) within grid n in the feasible domain of the hydropower station's output, a represents the value of that point on the corresponding plane n. n ,b n ,c n Let n be the planar characteristic parameters of the plane n corresponding to grid n.

[0040] Furthermore, the quadratic programming model takes minimizing the sum of the squares of the differences between the force values ​​at the calibration plane and the corresponding force values ​​at the actual force surfaces of all rectangular grid points within the feasible region as its objective function. The expression for the objective function is as follows:

[0041]

[0042] in, and These are the four corner grid points in the rectangular grid. The fitting of the actual power output includes both negative and positive errors, all of which are positive; α(n,k) is the weight coefficient of the k-th grid point of the rectangular grid n within the feasible domain of the hydropower station's power output, with specific values ​​as follows:

[0043]

[0044] Furthermore, the constraints of the quadratic programming model include fitting deviation constraints, effective plane constraints, and deviation non-negativity constraints.

[0045] The expression for the fitting deviation constraint is:

[0046]

[0047] in, and The output values, in MW, are the output values ​​of the kth grid point of grid n within the feasible domain of the hydropower station at the actual output surface and on the corresponding plane.

[0048] The effective plane constraint is a constraint constructed from the simplified plane set corresponding to each rectangular mesh generated using a simplified constraint strategy. The expression is:

[0049]

[0050] Where Θ(n) is the set of simplified planes generated by the simplified constraint strategy within the feasible domain of the hydropower station's output n, and u is the index of any plane in the set of simplified planes;

[0051] The simplified set of planes Θ(n) within the feasible region of the hydropower station's output is the set of planes remaining after removing plane n and its redundant planes within the feasible region of the hydropower station, expressed as:

[0052]

[0053] Where i,s and j,z are the segment numbers of the reservoir capacity V and outflow Q, respectively, and Δ represents the segment distance length between the rectangular grids n and u corresponding to plane n and u in the V or Q direction, expressed as:

[0054]

[0055] The expression for the non-negativity constraint of the deviation is:

[0056] Where n = 0, 1, ..., N-1; k = 0, 1, 2, 3.

[0057] Furthermore, the quadratic programming model constructed by solving yields a set of parameters for a set of plane equations that approximate the optimal output of the hydropower station, which is a set of parameters a with N plane equations. n ,b n ,c n , where n = 0, 1, ..., N-1.

[0058] Furthermore, the objective function expression of the reservoir optimization scheduling model is:

[0059]

[0060] Where T is the total number of time periods in the scheduling period, Δt is the time period length, and O is the other objective function;

[0061] In the hydropower output constraints of the reservoir optimization scheduling model, the output function of the hydropower station in time period t is replaced by a set of inequalities formed by the parameters of a set of plane equations that approximate the optimal output of the hydropower station obtained from the quadratic programming model:

[0062]

[0063] The beneficial effects of this invention are:

[0064] The proposed linearization method for hydropower station output functions based on a simplified constraint strategy, compared to existing linearization methods based on rectangular grid points, does not introduce integer variables into the constraints of the model for calibrating plane parameters, nor does it require the introduction of special sequence sets during the solution process. Furthermore, it reduces the time required for model solving while maintaining fitting accuracy. When the number of feasible region grids is increased to more closely approximate the actual output, the proposed method still results in a relatively smaller model size even after a certain number of grids are established. It can still stably and efficiently solve for the global optimal solution of the quadratic programming problem, demonstrating good stability. Applying this method to reservoir optimization scheduling models can effectively guide the operational decisions of cascade hydropower stations and optimize the coordinated utilization of water resources. Attached Figure Description

[0065] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0066] Figure 1 This is a flowchart of a method for linearizing the output function of a hydropower station based on a simplified constraint strategy, as described in the embodiment.

[0067] Figure 2 This is an example of a hydropower station's actual output diagram with respect to reservoir capacity and outflow rate, based on a hydropower station output function linearization method using a simplified constraint strategy.

[0068] Figure 3 This is a rectangular partition diagram of the feasible region of a hydropower station, which is an embodiment of a method for linearizing the output function of a hydropower station based on a simplified constraint strategy.

[0069] Figure 4 This is a schematic diagram of the simplified working plane of a hydropower station output function linearization method based on a simplified constraint strategy in an embodiment. Detailed Implementation

[0070] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0071] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0072] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0073] Reference Figure 1 This invention provides a method for linearizing the output function of a hydropower station based on a simplified constraint strategy, comprising the following steps:

[0074] Step 1: The power output function of a hydropower station during time period t is expressed as a bivariate function between the average reservoir capacity and the upper and lower limits of the allowable outflow range during the same period.

[0075] Step 2: Divide the feasible region of the power output function of the hydropower station into N rectangular grids;

[0076] Step 3: Define a corresponding plane for each rectangular grid of the feasible region of the hydropower station's output function, i.e., N plane equations;

[0077] Step 4: Based on the characteristic parameters of the defined plane and the simplified plane set corresponding to each rectangular grid generated by the simplified constraint strategy, construct a quadratic programming model for calibrating the plane cluster parameters of the hydropower station output surface.

[0078] Step 5: Solve the constructed quadratic programming model to obtain a set of optimal solutions, that is, the parameters of the set of plane equations that best approximate the optimal output of the hydropower station;

[0079] Step 6: In the reservoir optimization scheduling model where the scheduling objective includes maximizing the output or power generation of the hydropower station during the scheduling period, the parameters of the set of plane equations that approximate the optimal output of the hydropower station obtained by solving are used to construct a linearized expression of the hydropower output function in the reservoir optimization scheduling model.

[0080] The steps described below will be detailed in relation to the rectangular partitioning of the feasible region of hydropower station output, the quadratic programming model constructed based on the simplified constraint strategy, and the method for linearizing the hydropower output function.

[0081] Output calculation. The output function of the hydropower station is expressed as a bivariate function relating the average reservoir capacity over time and the upper and lower limits of the allowable outflow, such as... Figure 2 The diagram shows the output surface of the hydropower station.

[0082] The output of a hydropower station during time period t is expressed as:

[0083] Where P t , Q t These represent the reservoir's power output, average reservoir capacity, and outflow during time period t, respectively, in MW and million cubic meters per second (MW and million cubic meters per second). 3 m 3 / s, The expression for calculation is:

[0084]

[0085] Among them, V t The reservoir capacity at the beginning of time period t is expressed in millions of cubic meters. 3 .

[0086] The feasible region for the output of a hydropower station is divided into rectangular sections. For example... Figure 3 As shown, the feasible region of the hydropower station's output function is a planar region composed of the upper and lower limits of the reservoir capacity and the allowable outflow. This feasible region is then equally divided into several capacity segments and outflow segments, where the number of capacity and outflow segments is determined by the number of segments. The expression is as follows:

[0087]

[0088]

[0089] Where ΔV and ΔQ are the lengths of the storage capacity segment and the outflow segment, respectively; V max V represents the upper limit of the reservoir's capacity at time t. min Let Q be the lower limit of the reservoir's capacity at time t. max Let Q be the upper limit of the outflow from the reservoir at time t.min Let be the lower limit of the outflow from the reservoir at time t, where the reservoir capacity and flow rate are in millions of cubic meters per second (M³). 3 m 3 / s. For example... Figure 2 As shown, NV and NQ are the number of segments for storage capacity and outbound flow, respectively. The segment numbers for storage capacity and outbound flow are as follows:

[0090] i = 0, 1, ..., NV-1

[0091] j = 0, 1, ..., NQ-1

[0092] The feasible region is divided into rectangular grids, which are areas enclosed by equally divided storage capacity segments and outflow flow segments. The number of rectangular grids is:

[0093] N = NV × NQ

[0094] Where N is the total number of rectangular grids divided within the feasible region of the hydropower station's output, and the index of the rectangular grid can be defined as:

[0095] n=u(i,j)=i*NQ+j(n=0,1,···N-1)

[0096] There is a one-to-one correspondence between any rectangular grid n and the combination (i,j):

[0097]

[0098] Discrete points are defined within the feasible region. Within the feasible region, the storage capacity and outflow are discretized into NV+1 and NQ+1 values, respectively, denoted as V(i) and Q(j). Their mathematical expressions are:

[0099] V(i)=V min +i·ΔV,0≤i≤NV

[0100] Q(j)=Q min +j·ΔQ,0≤j≤NQ

[0101] Furthermore, each point within the feasible region can be represented as [V(i), Q(j)]. T .

[0102] The feasible region grid is represented by grid points. For example... Figure 3 As shown, each rectangular grid within the feasible power output domain of the hydropower station has 5 representative grid points: 1 central grid point and 4 corner grid points, with indices k = 0, 1, 2, 3, 4, and the corresponding rectangular grid points are represented as follows:

[0103]

[0104] Rectangular grids correspond to plane equations. For each rectangular grid within the feasible region of the hydropower station's output function, a corresponding plane is defined; that is, there is a one-to-one correspondence between the rectangular grids and the planes. The plane index corresponding to a rectangular grid is the same as the index of the rectangular grid itself. For example... Figure 4 As shown, the plane equation of the plane n corresponding to grid n is defined as:

[0105]

[0106] in, For any point (V,Q) within grid n in the feasible domain of the hydropower station's output, a represents the value of a on the corresponding plane. n ,b n ,c n Let n be the planar characteristic parameters of the plane n corresponding to grid n.

[0107] Quadratic programming model. A quadratic programming model for the calibration plane cluster parameters is established, with the objective function being to minimize the sum of the squares of the differences between the force values ​​at the calibration plane and the corresponding force values ​​at the actual force surfaces of all rectangular grid points within the feasible region.

[0108] (1) The objective function is:

[0109]

[0110] in, and These are the four corner grid points in the rectangular grid. The fitting of the actual power output includes both negative and positive errors, all of which are positive; α(n,k) is the weight coefficient of the k-th grid point of the rectangular grid n within the feasible domain of the hydropower station's power output, with specific values ​​as follows:

[0111]

[0112] (2) Constraints:

[0113] Fitting bias constraint:

[0114]

[0115] in, and The output values, in MW, are the output values ​​of the k-th grid point of grid n within the feasible domain of the hydropower station at the actual output surface and on the corresponding plane.

[0116] The effective plane constraints are constructed from the set of simplified planes corresponding to each rectangular mesh n generated by the simplified constraint strategy:

[0117]

[0118] Where Θ(n) is the set of simplified planes generated by the simplified constraint strategy for plane n within the feasible domain of hydropower station output, and u is the index of any plane in the set of simplified planes;

[0119] The simplified constraint strategy refers to a strategy that reduces the model size by simplifying some of the effective plane constraints when constructing the quadratic programming model, without affecting the overall constraint effect of the model.

[0120] The simplified plane set corresponding to the rectangular grid is the set of planes remaining after simplifying plane n and the redundant plane set of plane n within the feasible domain of the hydropower station. The redundant plane set of plane n is the set formed by simplifying the planes corresponding to the effective plane constraints of plane n based on the simplification constraint strategy. Specifically, it is the set of planes corresponding to the grids whose center points of the grids corresponding to plane n pass through the centers of other grids.

[0121] The simplified set of planes Θ(n) within the feasible region of the hydropower station's output is the set of planes remaining after simplifying plane n and its redundant planes within the feasible region of the hydropower station, such as... Figure 4 As shown, the plane corresponding to the white rectangular grid is the redundant plane of plane n, and the planes corresponding to all the remaining dark grids form the simplified plane set Θ(n). The expression is as follows:

[0122]

[0123] Where i, s and j, z are the segment numbers of the reservoir capacity V and outflow Q, respectively. Δ represents the segment distance length in the V or Q direction between the rectangular grids n and u corresponding to plane n and u, and its expression is:

[0124]

[0125] Deviation nonnegativity constraint:

[0126]

[0127] Where l is the index of any rectangular grid that is different from plane n within the feasible domain of the hydropower station's output.

[0128] In the quadratic model, the decision variable is the plane parameter a. n ,b n ,c n The range of its values ​​is not specified.

[0129] Solving the quadratic programming model: Solving the constructed quadratic programming model yields a set of parameters 'a' with N plane equations that approximate the optimal output surface of the hydropower station. n ,b n ,cn (n = 0, 1, ..., N-1).

[0130] Table 1 compares the model solution time and the error in fitting the actual output of a reservoir under different grid numbers within the feasible output domain using existing models and the method described in this invention. Under the same grid number, the method proposed in this invention has a shorter model solution time while maintaining fitting accuracy. Furthermore, the proposed method requires even less time when achieving better fitting accuracy. Moreover, when the number of grids reaches or exceeds 196, existing methods can no longer find the global optimum, while the method proposed in this invention can still quickly and stably obtain the global optimum.

[0131] Table 1 Comparison of solution results of the power output fitting model for hydropower stations under different numbers of feasible region grid divisions.

[0132]

[0133] Linearized expression of hydropower station output function. In the reservoir optimization scheduling model where the scheduling objective includes maximizing the hydropower station's output or power generation during the scheduling period, the objective function expression is:

[0134]

[0135] Where H is the total number of cascade hydropower stations, h is the sequence number of the hydropower station / reservoir, T is the total number of time periods during the scheduling period, Δt is the duration of the time period, and O is the other objective function.

[0136] In the hydropower output constraints of this model, the output function of hydropower station h in time period t can be expressed by a set of inequalities formed by this set of optimal planes:

[0137]

[0138] This completes the linearized expression of the power output function of the hydropower station.

[0139] Table 2 Comparison of simulation results for typical years of medium- and long-term power generation scheduling of cascade reservoirs.

[0140]

[0141]

[0142] Table 2 shows the scheduling results of the LP model for medium- and long-term power generation optimization scheduling of cascade reservoirs constructed using existing model methods and the method proposed in this invention, under different typical annual runoff processes, based on the same number of grid divisions. It can be seen that the optimization scheduling results of the method proposed in this invention are quite close to those of existing methods, especially the minimum output results for the ten-day period are consistent, which reflects the effectiveness of the linear processing HOF proposed in this invention.

[0143] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for linearizing the output function of a hydropower station based on a simplified constraint strategy, characterized in that, Includes the following steps: The feasible region of the hydropower station's output function is equally divided into rectangular grids; Define a corresponding plane for each rectangular grid in the feasible region of the power output function of the hydropower station; Based on the characteristic parameters of the defined plane and the simplified plane set corresponding to each rectangular grid generated by the simplified constraint strategy, a quadratic programming model for calibrating the plane cluster parameters of the hydropower station output surface is constructed. Solving the constructed quadratic programming model yields a set of parameters for a plane equation that approximates the optimal output of the hydropower station. In a reservoir optimization scheduling model where the scheduling objective includes maximizing the output or power generation of hydropower stations during the scheduling period, the parameters of the set of plane equations approximating the optimal output of hydropower stations obtained by solving are used to construct a linearized expression of the hydropower output function in the reservoir optimization scheduling model. The parameters of the set of plane equations approximating the optimal output of hydropower stations are applied in the reservoir optimization scheduling model to guide the operation decisions of cascade hydropower stations and optimize the coordinated utilization of water resources. The quadratic programming model takes minimizing the sum of the squares of the differences between the force values ​​at the calibration plane and the corresponding force values ​​at the actual force surfaces of all rectangular grid points within the feasible region as its objective function. The expression for the objective function is as follows: ； in, and These are the four corner grid points in the rectangular grid. The fitting of the actual output force includes both negative and positive errors, and both are positive values. Rectangular grid within the feasible region for hydropower station output The The weight coefficients for each grid point are specifically set as follows: ； The constraints of the quadratic programming model include fitting deviation constraints, active plane constraints, and deviation non-negativity constraints. The expression for the fitting deviation constraint is: ； in, and Grid within the feasible region for hydropower station output The The output values ​​of each grid point at the actual output surface and the corresponding plane are in MW; N is the total number of grids in the feasible region of the hydropower station's output. The effective plane constraint is a constraint constructed from the simplified plane set corresponding to each rectangular mesh generated using a simplified constraint strategy. The expression is: ； in Planar surface within the feasible area for hydropower station output The simplified plane set generated by the simplification constraint strategy Let be any plane index in the simplified plane set; The feasible area of ​​the hydropower station's output plane Simplified planar set To eliminate the plane within the feasible output region of the hydropower station and the plane The set of planes remaining after the redundant planes is expressed as: ； in, and Reservoir capacity Outbound flow The segment number, where Represented as a plane With plane Corresponding rectangular grid Between or The length of the segmented distance in the direction is expressed as: ; The expression for the non-negativity constraint of the deviation is: ； The objective function expression of the reservoir optimization scheduling model is: ； Where T is the total number of time periods in the scheduling period. Let O be the time period and O be other objective functions; For hydroelectric power station Output value during a given time period For reservoir Storage capacity during a given time period For reservoir Outbound flow during a specific time period; In the hydropower output constraints of the reservoir optimization scheduling model, the hydropower station is... The output function for a given time period is replaced by a set of inequalities formed by the parameters of a set of plane equations that approximate the optimal output of the hydropower station, obtained from the quadratic programming model: ； For grid Corresponding plane The planar feature parameters, where .

2. The method for linearizing the output function of a hydropower station based on a simplified constraint strategy as described in claim 1, characterized in that: The simplified constraint strategy refers to the strategy of reducing the model size by simplifying some of the effective plane constraints when constructing the quadratic programming model without affecting the overall constraint effect of the model. The simplified plane set corresponding to the rectangular grid is the set of planes remaining after simplifying the plane and the redundant plane set of the plane within the feasible region of the hydropower station output. The redundant plane set of the plane is the set of planes corresponding to the redundant effective plane constraints of the plane based on the simplified constraint strategy. That is, the redundant plane set of the plane is the set of planes corresponding to the grids whose grid center points are connected by lines that pass through the centers of other grids.

3. The method for linearizing the output function of a hydropower station based on a simplified constraint strategy as described in claim 1, characterized in that: The power output function of the hydropower station is a bivariate function relating to the reservoir's average reservoir capacity over a given period and the upper and lower limits of the allowable outflow range, specifically including: Hydropower station The output during a time period is expressed as ; in , , Reservoirs at The power output, average storage capacity, and outflow rate for each time period are expressed in MW, millions of m³, and m³ / s, respectively. The calculation expression is: ； in, For the reservoir in The initial storage capacity at the start of the period, in millions of cubic meters (m³).

4. The method for linearizing the output function of a hydropower station based on a simplified constraint strategy as described in claim 1, characterized in that: The feasible region of the hydropower station's output function is a planar area composed of the upper and lower limits of the reservoir capacity and the allowable outflow. This feasible region is then equally divided into several capacity segments and outflow segments, where the number of capacity and outflow segments is determined by the number of segments. The expression is as follows: ； ； in, and These are the length of the storage capacity segment and the length of the outflow segment, respectively. For the reservoir at all times The upper limit of the storage capacity, For the reservoir at all times The lower limit of the storage capacity, For the reservoir at all times The upper limit of outbound flow. For the reservoir at all times The lower limit of the outbound flow rate, with storage capacity and flow rate in millions of m³ and m³ / s, respectively; NV and NQ are the number of segments for storage capacity and outbound flow rate, respectively, and the sequence numbers for storage capacity segment and outbound flow rate segment are as follows: ； ； The feasible region is divided into rectangular grids, which are areas enclosed by equally divided storage capacity segments and outflow flow segments. The number of rectangular grids is: ； Where N is the total number of rectangular grids divided within the feasible region of the hydropower station's output, and the index of the rectangular grid is defined as follows: ； For any rectangular grid With combination They all have a one-to-one correspondence. ； Within the feasible region, storage capacity and outflow are discretized as follows: and There are 10 values, denoted as 10 ... and The mathematical expression is: ； ； For each point within the feasible region, it is represented as: .

5. The method for linearizing the output function of a hydropower station based on a simplified constraint strategy as described in claim 4, characterized in that: Each rectangular grid within the feasible power output domain of the hydropower station has 5 representative grid points: 1 central grid point and 4 corner grid points, with the following numbers: And the corresponding rectangular grid points are represented as: 。 6. The method for linearizing the output function of a hydropower station based on a simplified constraint strategy as described in claim 1, characterized in that: The feasible region of the hydropower station's output function defines a corresponding plane for each rectangular grid, meaning there is a one-to-one correspondence between the rectangular grid and the plane. The plane index corresponding to the rectangular grid is the same as the index of the rectangular grid itself. Corresponding plane The equation of a plane is defined as: ； in, Grid within the feasible region for hydropower station output any point inside In the corresponding plane The value on, For grid Corresponding plane Planar characteristic parameters.

7. The method for linearizing the output function of a hydropower station based on a simplified constraint strategy as described in claim 6, characterized in that: The quadratic programming model constructed by solving yields a set of parameters for a set of plane equations that approximate the optimal output of the hydropower station. This set of parameters consists of N plane equations. ,in .

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