A method for linearizing the output function of a hydropower station based on rectangular grids

Abstract

The present invention provides a method for linearizing the output function of a hydropower station based on rectangular grids, comprising: taking a binary function between the upper and lower limits of the permissible range of the average storage capacity of a reservoir period and the outflow flow as the output function of the hydropower station; equally dividing the feasible domain of the output function of the hydropower station 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 output surface of the hydropower station based on the characteristic parameters of the plane; solving the quadratic programming model to obtain the parameters of a set of plane equations that approximate the optimal output of the hydropower station; in a reservoir optimization scheduling model whose scheduling target includes maximizing the output of the hydropower station or the power generation of the hydropower station during the scheduling period, using the parameters of the plane equations obtained by solving to construct a linearized expression of the hydropower output function in the reservoir optimization scheduling model. The present invention not only avoids the introduction of integer variables, improves the solution efficiency, but also ensures the accuracy of fitting the output of the hydropower station.

Description

Technical Field

[0001] The invention relates to the cross-technical field of operations research and medium- and long-term dispatching of cascade reservoirs, and in particular to a method for linearizing a hydropower station output function based on rectangular grid points. Background Art

[0002] With the progress and development of science and technology, productivity is constantly improving, and human society is also moving from an information society to an intelligent and knowledge-based society. The demand for various information infrastructures that support transformation and upgrading is also increasing, and the demand and dependence on energy and electricity are increasing. Energy is an important driving force for the development of human society. Traditional fossil energy represented by coal, oil, and natural gas will cause serious problems such as environmental pollution and global warming that threaten human safety during use. Clean energy represented by hydropower, wind power, and solar energy has effectively improved the above problems.

[0003] As clean and renewable energy sources, wind and solar energy have the advantages of low construction cost, short construction period, and less geographical constraints compared to hydropower, so they have developed rapidly. However, due to the difficulty, low accuracy, and strong volatility of wind and light resource prediction, as the proportion of wind power and photovoltaic power generation in the new power system gradually increases, the power system will soon face the problem of difficult safe supply. Hydropower relies on the construction of reservoirs and hydropower stations to convert the energy contained in water resources into electrical energy, playing a key role in power supply. At the same time, hydropower units have the characteristics of rapid start and stop, and can undertake the functions of grid peak regulation and frequency regulation, effectively alleviating the challenges of difficult supply and demand balance and increased stability risks in the power system. In addition, through the important means of reservoir optimization scheduling, the maximum efficiency of water resources can be achieved.

[0004] As a complex optimization problem, reservoir optimization operation has been widely studied using a variety of optimization methods, including nonlinear programming (NLP), dynamic programming (DP), linear programming (LP), intelligent algorithms and heuristic algorithms (MA). Generally speaking, nonlinear models can describe complex physical systems in more detail and accuracy than linear models. Therefore, NLP is a natural choice for solving reservoir optimization operation problems. However, NLP is not mature, has difficulties in dealing with non-convex problems, and may converge to critical solutions that are not global optimal. Dynamic programming DP is widely used to solve hydropower system optimization problems, thanks to DP's ability to handle nonlinear and non-continuous objective functions and constraints, and is easy to implement its optimal staged decision-making strategy. However, with the increasing scale of hydropower systems, the use of DP is prone to the problem of "dimensionality curse". In recent years, intelligent algorithms or heuristic algorithms MA have been widely studied due to their flexibility in dealing with nonlinear complex problems, but the optimal solutions generated by intelligent algorithms in a reasonable time are inconsistent, and there are difficulties in dealing with irregular feasible domains. Generally speaking, mathematical programming methods are superior to intelligent algorithms or heuristic algorithms in solving deterministic reservoir operation problems.

[0005] Among many solution methods, LP has long been used in reservoir optimization and scheduling problems, thanks to its mature and perfect theoretical basis and its ability to solve large-scale complex engineering decision-making problems and find the optimal solution. However, reservoir optimization and scheduling is a nonlinear optimization problem. To solve such problems using LP, the objective function and constraints must be linearized, and the most important nonlinear factor comes from the hydropower output function (HOF). Therefore, in reservoir optimization and scheduling, the most important thing is to find a suitable HOF linear modeling. The method of fixing the efficiency of the hydropower station is the simplest way to linearly process the hydropower output function, but fixing the efficiency of the hydropower station ignores the head effect of the hydropower station, and the simplified model is far from the original problem. The nonlinear HOF is approximated by piecewise linearization technology, and the original problem is transformed into a mixed integer linear programming (MILP) problem that can obtain a global optimal solution. However, piecewise linearization of all nonlinear functions in the problem will introduce more integer variables, and obtaining the optimal solution in a limited time is a very challenging problem. Kang Chuanxiong (Study on Optimal Scheduling of Cascade Reservoirs Based on Linear Approximation and Water Storage Distribution Curve [PhD Dissertation]. Wuhan: Huazhong University of Science and Technology, 2018) proposed a plane convex hull linear approximation method. By dividing the feasible domain of output into rectangular grids, a plane equation is determined in each grid or grid neighborhood to approximate the actual output. However, this method selects the minimum approximate value of each rectangular grid point for evaluation in the objective function. The introduction of integer variables or special sequence sets in the solution process increases the solution time. In particular, after increasing the number of grid divisions for over-approximation, the model has the problem of being unable to stably obtain the optimal solution. Summary of the invention

[0006] The problem to be solved by the present invention is how to provide a non-convex and nonlinear hydropower station output function for the medium- and long-term scheduling of a reservoir, which is used to solve the problem that the model solution time is too long due to the introduction of too many integer variables or special sequence sets, and the model cannot stably obtain the optimal solution due to excessive approximation and increasing the number of grid divisions.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0008] A method for linearizing a hydropower station output function based on rectangular grid points, comprising:

[0009] The binary function between the average storage capacity of the reservoir during the period and the upper and lower limits of the permissible range of the outflow flow is used as the output function of the hydropower station;

[0010] The feasible domain of the hydropower station output function is equally divided into rectangular grids;

[0011] Define a corresponding plane for each rectangular grid of the feasible domain of the hydropower station output function;

[0012] A quadratic programming model for calibrating the plane cluster parameters approximating the output surface of the hydropower station is constructed based on the characteristic parameters of the defined plane;

[0013] Solving the constructed quadratic programming model to obtain parameters of a set of plane equations that approximate the optimal output of the hydropower station;

[0014] In a reservoir optimization scheduling model whose scheduling objective includes maximizing the output of a hydropower station or the amount of power generated by a hydropower station during a scheduling period, the parameters of a set of plane equations that approximate the optimal output of the hydropower station are used to construct a linear expression of the hydropower output function in the reservoir optimization scheduling model.

[0015] Furthermore, the binary function between the average storage capacity of the reservoir during the period and the upper and lower limits of the allowable range of the outflow flow is used as the output function of the hydropower station, specifically including:

[0016] The output of the hydropower station in period t is expressed as

[0017] Where P t , Q t are the output value, average storage capacity and outflow value of the reservoir in period t, in MW and million m 3 、m 3 / s, The calculation expression is:

[0018]

[0019] Among them, V t is the storage capacity of the reservoir at the beginning of period t, in million m 3 .

[0020] Furthermore, the feasible domain of the hydropower station output function is a plane area composed of the upper and lower limits of the reservoir capacity and the outflow flow rate. The feasible domain is equally divided into a number of reservoir capacity segments and outflow flow segments between the upper and lower limits of the reservoir capacity and the outflow flow rate. The reservoir capacity segments and outflow flow segments are determined by the number of segments of the reservoir capacity and the outflow flow rate, and the expression is:

[0021]

[0022] Among them, ΔV and ΔQ are the storage capacity segment length and the outflow flow segment length respectively; V max is the upper limit of the reservoir capacity at time t, V min is the lower limit of the reservoir capacity at time t, Q max is the upper limit of the outflow of the reservoir at time t, Q min is the lower limit of the outflow of the reservoir at time t, and the units of storage capacity and flow are million m 3 、m 3 / s; NV and NQ are the segment numbers of storage capacity and outbound flow respectively. The sequence numbers of storage capacity segment and outbound flow segment are:

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

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

[0025] The rectangular grids divided into the feasible domain are the areas surrounded by the equally divided storage capacity segment and the outbound flow segment. The number of the 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 output, and the serial number of the rectangular grid is defined as:

[0028] n=u(i,j)=i*NQ+j(n=0,1,···N-1)

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

[0030]

[0031] In the feasible region, the storage capacity and outbound flow are discretized into NV+1 and NQ+1 values ​​respectively, which are recorded as V(i) and Q(j). The mathematical expressions are:

[0032] V(i)=V min +i·ΔV,0≤i≤NV

[0033] Q(j)=Q min +j·ΔQ,0≤j≤NQ

[0034] For each point in the feasible region, it is expressed as [V(i),Q(j)] T .

[0035] Furthermore, each rectangular grid in the feasible region of the hydropower station has five representative grid points, namely, one central grid point and four corner grid points, with serial numbers k=0, 1, 2, 3, 4, respectively, and the corresponding rectangular grid points are expressed as:

[0036]

[0037] Furthermore, each rectangular grid in the feasible domain of the hydropower station output function is defined as a corresponding plane, wherein the plane equation corresponding to the rectangular grid n is defined as:

[0038]

[0039] in, is the value of any point (V, Q) in the grid n within the feasible region of the hydropower station on the corresponding plane, a n ,b n ,c n is the parameter of the plane corresponding to the grid n.

[0040] Furthermore, the quadratic programming model takes the minimum sum of squares of the differences between the output values ​​of all divided rectangular grid points at the calibration plane and the output values ​​at the corresponding actual output surface in the feasible domain as the objective function, and the calculation expression of the objective function is:

[0041]

[0042] in, and are the four corner points in the rectangular grid The negative and positive errors of the actual output are fitted and are all positive; α(n,k) is the weight coefficient of the kth grid point of the rectangular grid n in the feasible region of the hydropower station output, and the specific value is:

[0043]

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

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

[0046]

[0047] in, and is the output value of the kth grid point of the grid n in the feasible domain of the hydropower station at the actual output surface and on the corresponding plane, in MW;

[0048] The expression for the active plane constraint is:

[0049] Where l≠n; n,l=0,1,2,···,N-1;

[0050] Where l is the number of any rectangular grid different from plane n in the feasible region of hydropower station output;

[0051] The expression of the deviation non-negativity constraint is:

[0052] Where n=0,1,...,N-1; k=0,1,2,3.

[0053] Furthermore, the quadratic programming model constructed by solving the problem obtains a set of parameters of plane equations that approximate the optimal output of the hydropower station, which is a set of parameters a having N plane equations. n ,b n ,c n , where n = 0, 1, ..., N-1.

[0054] Furthermore, the objective function expression of the reservoir optimization scheduling model is:

[0055]

[0056] Among them, T is the total number of time periods in the scheduling period, Δt is the time period length, and O is other objective functions;

[0057] In the hydropower output constraint condition in the reservoir optimization scheduling model, the output function of the hydropower station in time period t is replaced by the inequality group formed by the parameters of a set of plane equations approximating the optimal output of the hydropower station obtained by the quadratic programming model:

[0058]

[0059] The beneficial effects of the present invention are:

[0060] Compared with the existing linearization method based on rectangular grid points, the method for linearizing the output function of a hydropower station proposed in the present invention does not introduce integer variables in the constraint conditions of the model modeling of the plane parameters for calibration, and does not need to introduce special sequence sets in the solution process, so that when the number of grid divisions in the feasible domain is the same, the time used for model solution is less; when the number of grid divisions in the feasible domain is increased to be closer to the actual output, when the number of divided grids reaches a certain number, the proposed method can still stably solve the global optimal solution of the quadratic programming, and has good stability. Applying this method to the reservoir optimization scheduling model can effectively guide the operation decision-making of cascade hydropower stations and optimize the coordinated utilization of water resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0062] Figure 1 It is a flow chart of a method for linearizing a hydropower station output function based on rectangular grid points in an embodiment;

[0063] Figure 2 An actual output diagram of a hydropower station regarding storage capacity and outflow flow based on a method for linearizing a hydropower station output function based on rectangular grid points in an embodiment;

[0064] Figure 3 A rectangular partition diagram of a feasible region of a hydropower station based on a method for linearizing a hydropower station output function based on rectangular grids in an embodiment;

[0065] Figure 4 A planar cluster approximate hydropower station output diagram of a hydropower station output function linearization method based on rectangular grid points in an embodiment;

[0066] Figure 5 This is a comparison diagram of the error between the plane cluster approximation of the hydropower station output and the actual output of a hydropower station output function linearization method based on rectangular grids in an embodiment. DETAILED DESCRIPTION

[0067] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0068] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0069] 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 term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0070] Reference Figure 1 The embodiment of the present invention provides a method for linearizing a hydropower station output function based on a rectangular grid, comprising the following steps:

[0071] Step 1: The output function of the hydropower station in period t is expressed as a binary function between the average storage capacity of the reservoir during the period and the upper and lower limits of the allowable range of the outflow flow

[0072] Step 2: Divide the feasible domain of the hydropower station output function into N equal rectangular grids;

[0073] Step 3: define a corresponding plane for each rectangular grid of the feasible domain of the hydropower station output function, that is, N plane equations;

[0074] Step 4: constructing a quadratic programming model for calibrating the plane cluster parameters approximating the output surface of the hydropower station based on the characteristic parameters of the defined plane;

[0075] Step 5: Solve the constructed quadratic programming model to obtain a set of optimal solutions, that is, a set of parameters of the plane equations that are closest to the optimal output of the hydropower station;

[0076] Step 6: In a reservoir optimization scheduling model whose scheduling objective includes maximizing the output of a hydropower station or the amount of power generated by a hydropower station during a scheduling period, a linearized expression of a hydropower output function is constructed in the reservoir optimization scheduling model using the parameters of a set of plane equations that approximate the optimal output of the hydropower station.

[0077] The method steps are described below, and the method of rectangular subdivision of the feasible domain of hydropower station output and linear expression of hydropower output function will be described in detail.

[0078] Output calculation. The output function of the hydropower station is expressed as a binary function between the average storage capacity of the reservoir during the period and the upper and lower limits of the allowable range of the outflow flow, such as Figure 2 Schematic diagram of the hydropower station output surface shown.

[0079] The output of the hydropower station in period t is expressed as

[0080] Where P t , Q t are the output value, average storage capacity and outflow value of the reservoir in period t, in MW and million m 3 、m 3 / s, The expression to be calculated is:

[0081]

[0082] Among them, V t is the storage capacity of the reservoir at the beginning of period t, in million m 3 .

[0083] Rectangular division of the feasible region of hydropower station output. Figure 3 As shown, the feasible domain of the hydropower station output function is a plane area composed of the upper and lower limits of the reservoir capacity and the outflow flow. The feasible domain is equally divided into a number of reservoir capacity segments and outflow flow segments between the upper and lower limits of the reservoir capacity and the outflow flow. The reservoir capacity segments and outflow flow segments are determined by the number of segments of the reservoir capacity and the outflow flow. The expression is:

[0084]

[0085] Among them, ΔV and ΔQ are the storage capacity segment length and the outflow flow segment length respectively; V max is the upper limit of the reservoir capacity at time t, V min is the lower limit of the reservoir capacity at time t, Q max is the upper limit of the outflow of the reservoir at time t, Q min is the lower limit of the outflow of the reservoir at time t, and the units of storage capacity and flow are million m 3 、m 3 / s. Figure 2 As shown in the figure, NV and NQ are the segment numbers of storage capacity and outbound flow respectively, and the sequence numbers of storage capacity segment and outbound flow segment are:

[0086] i=0,1,...,NV-1

[0087] j=0,1,...,NQ-1

[0088] The rectangular grids divided into the feasible domain are the areas surrounded by the equally divided storage capacity segment and the outbound flow segment. The number of the rectangular grids is:

[0089] N=NV×NQ

[0090] Where N is the total number of rectangular grids divided within the feasible region of the hydropower station output, and the serial number of the rectangular grid can be defined as:

[0091] n=u(i,j)=i*NQ+j(n=0,1,···N-1)

[0092] Among them, there is a one-to-one correspondence between any rectangular grid n and combination (i, j):

[0093]

[0094] Definition of discrete points in the feasible domain. In the feasible domain, the storage capacity and outbound flow are discretized into NV+1 and NQ+1 values ​​respectively. These values ​​are recorded as V(i) and Q(j). The mathematical expressions are:

[0095] V(i)=V min +i·ΔV,0≤i≤NV

[0096] Q(j)=Q min +j·ΔQ,0≤j≤NQ

[0097] And for each point in the feasible region, it can be expressed as [V(i),Q(j)] T .

[0098] The feasible region grid represents the grid points. Figure 3 As shown in the figure, each rectangular grid in the feasible region of the hydropower station has 5 representative grid points, namely 1 central grid point and 4 corner grid points, with serial numbers k = 0, 1, 2, 3, 4 respectively, and the corresponding rectangular grid points are expressed as:

[0099]

[0100] Rectangular grids correspond to plane equations. Define a corresponding plane for each rectangular grid in the feasible domain of the hydropower station output function, such as Figure 4 As shown, the plane equation corresponding to the grid n is defined as:

[0101]

[0102] in, is the value of any point (V, Q) in the grid n within the feasible region of the hydropower station on the corresponding plane, a n ,b n ,c n is the parameter of the plane corresponding to the grid n.

[0103] Quadratic programming model. Taking the minimum sum of the squares of the differences between the output values ​​of all divided rectangular grid points on the calibration plane and the corresponding actual output surface as the objective function, a quadratic programming model for calibrating the plane cluster parameters is established:

[0104] (1) The objective function is:

[0105]

[0106] in, and are the four corner points in the rectangular grid The negative and positive errors of the actual output are fitted and are all positive; α(n,k) is the weight coefficient of the kth grid point of the rectangular grid n in the feasible region of the hydropower station output, and the specific value is:

[0107]

[0108] (2) Constraints:

[0109] Fitting deviation constraints:

[0110]

[0111] in, and It is the output value of the kth grid point of the grid n in the feasible domain of the hydropower station at the actual output surface and on the corresponding plane, in MW.

[0112] Active plane constraints:

[0113]

[0114] Where l is the number of any rectangular grid in the feasible region of the hydropower station output that is different from the plane n.

[0115] Deviation non-negativity constraint:

[0116]

[0117] Where l is the number of any rectangular grid in the feasible region of the hydropower station output that is different from the plane n.

[0118] The decision variable in the quadratic model is the plane parameter a n ,b n ,c n The value range is not specified.

[0119] Solve the quadratic programming model. Solve the constructed quadratic programming model to obtain a set of parameters a with N plane equations that are optimal for approximating the output surface of the hydropower station. n ,b n ,c n (n=0,1,...,N-1). Figure 5 As shown,

[0120] Table 1 shows the comparison of the model solution time and the error of fitting the actual output of a reservoir under different grid division numbers in the output feasible domain according to the method of the existing model and the method of the present invention. Under the same number of grid divisions, the model solution time of the method proposed by the present invention is shorter, and the fitting error is not much different. In addition, when the number of grid divisions reaches and exceeds 196, the existing method can no longer solve the global optimal solution, while the method proposed by the present invention can still stably obtain the global optimal solution.

[0121] Table 1 Comparison of solution results of hydropower station output fitting model under different feasible domain grid division numbers

[0122]

[0123] Linearized expression of the hydropower station output function. In the reservoir optimization scheduling model where the scheduling objective includes maximizing the hydropower station output or the hydropower station power generation during the scheduling period, the objective function expression is:

[0124]

[0125] Among them, T is the total number of time periods in the scheduling period, Δt is the time period length, and O is other objective functions.

[0126] In the hydropower output constraint condition in this model, the output function of the hydropower station in period t can be replaced by the inequality group formed by this set of optimal planes:

[0127]

[0128] At this point, the linear expression of the hydropower station output function has been completed.

[0129] Evaluation of linear fitting effect. The feasible domain of the hydropower station is divided into N = 101 × 101 grids. The relative error between the fitting output determined by the plane inequality group, that is, the minimum value calculated in all plane equations at this point and the corresponding actual output value, is as follows: Figure 5 As shown, the model approximation value of the area framed by the black line is greater than the actual output, while the opposite is true for the other areas. The fitting relative error of the hydropower station in the feasible domain of output tends to be negative overall, with a maximum relative error of 25.4%. However, this reservoir condition generally does not occur and the output value is small, with an overall relative error of 0.94%, which shows that this method has good characteristics in fitting hydropower output.

[0130] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for linearizing the output function of a hydropower station based on rectangular grids, characterized in that: The steps include: The binary function between the average storage capacity of the reservoir during the period and the upper and lower limits of the permissible range of the outflow flow is used as the output function of the hydropower station; The feasible domain of the hydropower station output function is equally divided into rectangular grids; Define a corresponding plane for each rectangular grid of the feasible domain of the hydropower station output function; A quadratic programming model for calibrating the plane cluster parameters approximating the output surface of the hydropower station is constructed based on the characteristic parameters of the defined plane; Solving the constructed quadratic programming model to obtain parameters of a set of plane equations that approximate the optimal output of the hydropower station; In a reservoir optimization scheduling model whose scheduling objective includes maximizing the output of a hydropower station or the amount of power generated by a hydropower station during a scheduling period, a linearized expression of a hydropower output function is constructed in the reservoir optimization scheduling model using the parameters of a set of plane equations that approximate the optimal output of the hydropower station obtained by solving the solution; The quadratic programming model takes the minimum sum of squares of the differences between the output values ​​of all divided rectangular grid points at the calibration plane and the output values ​​at the corresponding actual output surface as the objective function. The calculation expression of the objective function is: in, and are the four corner points in the rectangular grid The negative and positive errors of the actual output are fitted and are all positive; α(n,k) is the weight coefficient of the kth grid point of the rectangular grid n in the feasible region of the hydropower station output, and the specific value is: The constraints of the quadratic programming model include fitting deviation constraints, working plane constraints, and deviation non-negativity constraints; The expression of the fitting deviation constraint is: in, and is the output value of the kth grid point of the grid n in the feasible domain of the hydropower station at the actual output surface and on the corresponding plane, in MW; The expression for the active plane constraint is: Where l≠n; n,l=0,1,2,···,N-1; Where l is the number of any rectangular grid different from plane n in the feasible region of hydropower station output; The expression of the deviation non-negativity constraint is: Where n=0,1,…,N-1; k=0,1,2,3.

2. A method for linearizing a hydropower station output function based on rectangular grid points as claimed in claim 1, characterized in that: The binary function between the average storage capacity of the reservoir during the period and the upper and lower limits of the permissible range of the outflow flow is used as the output function of the hydropower station, specifically including: The output of the hydropower station in period t is expressed as Where P t , Q t are the output value, average storage capacity and outflow value of the reservoir in period t, in MW and million m 3 、m 3 / s, The calculation expression is: Among them, V t is the storage capacity of the reservoir at the beginning of period t, in million m 3 .

3. A method for linearizing a hydropower station output function based on rectangular grid points as claimed in claim 1, characterized in that: The feasible domain of the hydropower station output function is a plane area composed of the upper and lower limits of the reservoir capacity and the outflow flow. The feasible domain is equally divided into a number of reservoir capacity segments and outflow flow segments between the upper and lower limits of the reservoir capacity and the outflow flow. The reservoir capacity segments and outflow flow segments are determined by the number of segments of the reservoir capacity and the outflow flow. The expression is: Among them, ΔV and ΔQ are the storage capacity segment length and the outflow flow segment length respectively; V max is the upper limit of the reservoir capacity at time t, V min is the lower limit of the reservoir capacity at time t, Q max is the upper limit of the outflow of the reservoir at time t, Q min is the lower limit of the outflow of the reservoir at time t, and the units of storage capacity and flow are million m 3 、m 3 / s; NV and NQ are the segment numbers of storage capacity and outbound flow respectively. The sequence numbers of storage capacity segment and outbound flow segment are: i=0,1,...,NV-1 j=0,1,...,NQ-1 The rectangular grids divided into the feasible domain are the areas surrounded by the equally divided storage capacity segment and the outbound flow segment. The number of the rectangular grids is: N=NV×NQ Where N is the total number of rectangular grids divided within the feasible region of the hydropower station output, and the serial number of the rectangular grid is defined as: n=u(i,j)=i*NQ+j(n=0,1,···N-1) Among them, there is a one-to-one correspondence between any rectangular grid n and the combination (i, j) In the feasible region, the storage capacity and outbound flow are discretized into NV+1 and NQ+1 values ​​respectively, which are recorded as V(i) and Q(j). The mathematical expressions are: V(i)=V min +i·ΔV,0≤i≤NV Q(j)=Q min +j·ΔQ,0≤j≤NQ For each point in the feasible region, it is expressed as [V(i),Q(j)] T .

4. A method for linearizing a hydropower station output function based on rectangular grid points as claimed in claim 3, characterized in that: Each rectangular grid in the feasible region of the hydropower station has 5 representative grid points, namely 1 central grid point and 4 corner grid points, with serial numbers k=0, 1, 2, 3, 4, respectively, and the corresponding rectangular grid points are expressed as:

5. A method for linearizing a hydropower station output function based on rectangular grid points as claimed in claim 1, characterized in that: Each rectangular grid in the feasible domain of the hydropower station output function is defined as a corresponding plane, wherein the plane equation corresponding to the rectangular grid n is defined as: in, is the value of any point (V, Q) in the grid n within the feasible region of the hydropower station on the corresponding plane, a n ,b n ,c n is the parameter of the plane corresponding to the grid n.

6. A method for linearizing a hydropower station output function based on rectangular grid points as claimed in claim 5, characterized in that: The quadratic programming model constructed by solving the problem obtains a set of plane equation parameters that approximate the optimal output of the hydropower station, which is a set of N plane equation parameters a n ,b n ,c n , where n = 0, 1, ..., N-1.

7. A method for linearizing a hydropower station output function based on rectangular grid points as claimed in claim 6, characterized in that: The objective function expression of the reservoir optimization operation model is: Among them, T is the total number of time periods in the scheduling period, Δt is the time period length, and O is other objective functions; In the hydropower output constraint condition in the reservoir optimization scheduling model, the output function of the hydropower station in time period t is replaced by the inequality group formed by the parameters of a set of plane equations approximating the optimal output of the hydropower station obtained by the quadratic programming model:

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