A quadratic programming based field flattening design method

Abstract

The application provides a photovoltaic power station optimal field design method suitable for a fieldless drainage requirement area; the method takes the minimum excavation and filling amount of the whole field as an objective function, takes the field slope ratio and the excavation and filling balance (or the difference given value) as a constraint condition, integrates a local coefficient matrix and a vector into a global coefficient matrix and a vector, finally converts the field design problem into a mathematical problem of seeking a quadratic programming optimal solution, and obtains an optimal field square scheme by solving the mathematical problem.

Description

Technical Field

[0001] This invention relates to a site leveling design method based on quadratic programming, which is mainly applicable to the site leveling design of photovoltaic power stations in areas such as Gobi Desert and other deserts where there are no site drainage requirements. Background Technology

[0002] Photovoltaic modules are typically arranged in a north-south orientation, with the panels able to rotate east-west to face the sun. To minimize mutual shading between adjacent east-west facing panels, the east-west slope of the photovoltaic site needs to be controlled within a certain range (generally not exceeding 2%). In desert areas, photovoltaic panels are often cleaned using small cleaning robots that crawl along the north-south direction of the panels. The maximum crawling slope of the cleaning robot determines the maximum north-south slope of the site (generally not exceeding 6%).

[0003] Large-scale photovoltaic power plants often occupy tens of square kilometers. In areas with significant topographical variations, such as deserts, the earthwork volume for photovoltaic site leveling can reach millions or even tens of millions of cubic meters, resulting in a massive engineering project. Traditional site leveling design methods require first dividing the photovoltaic site into blocks, then using site leveling software to design the leveling for each block, and finally considering the coordination of boundaries between blocks. Traditional methods are extremely time-consuming and labor-intensive, limiting the number of blocks to a maximum of a dozen or so. Furthermore, it's difficult to effectively connect the blocks and determine the merits of different leveling schemes; multiple schemes must be compared before a relatively optimal one is selected. Traditional site leveling methods are labor-intensive, inefficient, and involve large amounts of excavation and filling. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the background technology by providing a site leveling design method based on quadratic programming. This method divides the photovoltaic site into continuous blocks, uses the minimum excavation and fill volume of the entire site as the objective function, and uses the site slope ratio and the balance (or difference between) of excavation and fill volume as linear constraints. It integrates the global coefficient matrix and vectors using local coefficient matrices and vectors, and finally obtains the optimal site leveling scheme by finding the optimal solution of quadratic programming.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A site leveling design method based on quadratic programming, characterized by the following steps:

[0007] S1. Raw terrain data processing: Extract site coordinate data and generate terrain interpolation function F;

[0008] S2. Site Block Division and Coding: Divide the photovoltaic site into rectangular blocks, number the nodes, edges, and blocks, and record the node coordinates, edge and block node composition to form a topological structure; let n be the number of blocks, nodes, and edges respectively. el n ndn ed ;

[0009] S3. Initialize the global initial quadratic coefficient matrix Q, the global initial linear coefficient vector f, the global inequality constraint coefficient matrix A, the global inequality constraint constant vector b, and the global equality constraint coefficient vector A. eq Global equality constraint constant b eq ;

[0010] S4. Generate the local quadratic coefficient matrix Q for each block in order of block number. i Local first-order coefficient vector f i Local equality constraint coefficient vector A eqi Local equality constraints often b eqi And then integrate them into the corresponding global matrices and vectors in sequence;

[0011] S5. Generate the local inequality constraint coefficient matrix A for each edge according to the edge numbering order. i Local inequality constraints on constant vector b i And then integrate them into the corresponding global matrices and vectors in sequence;

[0012] S6. Correct the global equality constraint constant b eqi ;

[0013] S7. Solving the quadratic programming problem:

[0014]

[0015]

[0016] S8. Forming the site leveling design surface: Connect all adjacent nodes based on the design elevations of each node obtained from the quadratic programming solution to form the final site leveling design surface;

[0017] Steps S4 and S5 are not sequential.

[0018] Furthermore, the global quadratic coefficient matrix Q is n nd ×n nd 1-order matrix.

[0019] Furthermore, the global first-order coefficient vector f is n nd ×1 dimensional vector.

[0020] Furthermore, the global inequality constraint coefficient matrix A is 2n. ed ×n nd 1-order matrix.

[0021] Furthermore, in step S7, a numerical method is used to iteratively solve the quadratic programming problem.

[0022] In a second aspect of the present invention, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the steps of the above-described quadratic programming-based field leveling design method.

[0023] In a third aspect of the invention, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the program, implements the steps of the above-described quadratic programming-based field plan design method.

[0024] The beneficial effects of this invention are:

[0025] 1) Optimal solution: The optimal field leveling scheme can be obtained by finding the optimal solution of the field leveling problem through quadratic programming, and the optimal solution of the photovoltaic field leveling problem is obtained theoretically.

[0026] 2) Good applicability: This method can be used for site leveling design in different photovoltaic site leveling projects, only the boundary conditions such as block division and slope requirements are different.

[0027] 3) Fast design speed: By programming the design method, the site leveling scheme design can be completed in a very short time. Attached Figure Description

[0028] Figure 1 A schematic diagram showing the original site area division and numbering;

[0029] Figure 2 A schematic diagram of grid division for a certain area;

[0030] Figure 3 A site leveling diagram and original site layout diagram are provided.

[0031] Figure 4 Design drawings for a photovoltaic power station using a traditional partial planar site leveling design scheme;

[0032] Figure 5 for Figure 4 The design drawings of a certain photovoltaic power station adopting the site leveling design scheme of the present invention.

[0033] In the attached diagram: 100 - Original site; 200 - Block division line; 300 - Coordinate system; 400 - North arrow; 500 - Grid division line; 600 - Final design site plan. Detailed Implementation

[0034] Referring to the accompanying drawings, this embodiment provides a photovoltaic site leveling design method based on quadratic programming, comprising the following steps:

[0035] S1 - Generates the terrain interpolation function F.

[0036] Using the original terrain elevation point data (x, y, z) as samples, a two-dimensional terrain interpolation function F is generated. F is used to calculate the ground elevation value z0 = F(x0, y0) for a given plane coordinate (x0, y0).

[0037] S2 - Site Block Division and Coding: Based on the photovoltaic matrix layout, the entire site is divided into blocks, and all blocks, nodes, and edges are numbered. The number of blocks, nodes, and edges is denoted as n. el n nd n ed .

[0038] The photovoltaic site is divided into several rectangular blocks using straight lines parallel to the east-west and north-south directions. The size of each block is determined based on the arrangement of the photovoltaic matrix and the dimensions of the photovoltaic modules. Nodes, edges, and blocks are numbered, and the coordinates of nodes, the node composition of edges and blocks, and other information are recorded to form a topological structure.

[0039] like Figure 1 As illustrated, this embodiment uses 4 east-west straight lines and 6 north-south straight lines to divide the site into 15 blocks. The blocks are numbered 1, 2, ... 15, ①, ②, ... Let n be the node number, and (1), (2), ..., (38) be the edge number. In this example, n el =15, n nd =24, n ed =38.

[0040] S3 - Set the global initial coefficient matrix and vector, including:

[0041] The global initial quadratic coefficient matrix Q is n. nd ×n nd A zero matrix of order Q; in this example, Q is a 24×24 zero matrix.

[0042] A global initial coefficient vector f, where f is n nd A zero vector of order ×1, in this example, f is a zero vector of order 24×1;

[0043] The global inequality constraint coefficient matrix A is 2n. ed ×n nd A is a zero matrix of order 76×24; in this example, A is a zero matrix of order 76×24.

[0044] The global inequality constraint is a constant vector b, where b is 2n. ed b is a zero vector of order 76×1 in this example;

[0045] Global equality constraint coefficient vector A eq A eqFor 1×n nd A is a zero-dimensional vector. eq It is a zero vector of order 1×24;

[0046] Global equality constraint constant b eq b eq It is zero.

[0047] S4 - Generate the local quadratic coefficient matrix Q for each block in order of block number. i Local first-order coefficient vector f i Local equality constraint coefficient vector A eqi Local equality constraint constant b eqi Then, integrate them sequentially into the corresponding global matrices and vectors (constants). Perform the following operations on all blocks sequentially until completion.

[0048] like Figure 2 As shown, for block i, i = 1, 2…15, the four nodes of the block are numbered a, b, c, d in a clockwise direction, and their corresponding coordinates are: (x a ,y a ), (x b ,y b ), (x c ,y c ), (x d ,y d The corresponding ground elevation is: z a ,z b ,z c ,z d Calculated using the interpolation function F. The block is divided into several rectangular grids on the horizontal plane by east-west and north-south straight lines. In this example, the block is divided into 4 rows (y-direction) and 5 columns (x-direction), for a total of 20 grids. The center coordinates of each grid are denoted as (x...). j ,y j Elevation value z of each grid center j The area of ​​each grid cell is calculated using the interpolation function F. j ,,j=1,2…20。

[0049] Calculate the quadratic coefficients A for each grid. j B j C j D j , j = 1, 2…20.

[0050]

[0051]

[0052]

[0053]

[0054] Local quadratic coefficient matrix Q i for:

[0055]

[0056] Local first-order coefficient vector f i for:

[0057]

[0058] Local equality constraint coefficient matrix A eqi for:

[0059]

[0060] Local equality constraint constant vector b eqi for:

[0061]

[0062] The local quadratic coefficient matrix Q i Local first-order coefficient vector f i Integrate these values ​​into the global quadratic coefficient matrix Q and the global linear coefficient vector f respectively: Update the values ​​in the a, b, c, and d-th rows and columns a, b, c, and d of Q, respectively, and add them to Q. i The values ​​in columns 1 to 4 of rows 1 to 4 are used as the new values; the values ​​of items a, b, c, and d in f are updated by adding f to them respectively. i The values ​​of items 1 through 4 are used as new values.

[0063] Let the equality constraint coefficient matrix A eqi Local equality constraint constant vector b eqi Each is integrated into the global equality constraint coefficient matrix A. eq Global equality constraint constant vector b eq Chinese: Update A eq Add A to the values ​​of terms a, b, c, and d in the equation. eqi The values ​​of items 1 through 4 are used as new values; update b. eq Add b to it eqi As a new value.

[0064] S5 - Generate the local inequality constraint coefficient matrix A for each edge according to the edge numbering order. i Local inequality constraints on constant vector b i Then, integrate them sequentially into the corresponding global matrices and vectors. Perform the following operations on all edges sequentially until completion.

[0065] like Figure 2As shown, for block i, the operation is explained by taking edges numbered p and q in different directions. Edge p is a north-south edge with nodes numbered a and b at both ends; edge q is an east-west edge with nodes numbered a and c at both ends. The local inequality constraint coefficient matrix A for edge p is shown. p and local inequality constraints on constant vector b p They are respectively:

[0066]

[0067] b p =(y b -y a )×[k sn k ns ] T

[0068] Where, k sn k is the maximum permissible slope ratio of the site from south to north. ns k represents the maximum permissible slope ratio of the site from north to south. ns k sn ≥0.

[0069] q-edge local inequality constraint coefficient matrix A q and local inequality constraints on constant vector b q They are respectively:

[0070]

[0071] b q =(x c -x a )×[k we k ew ] T

[0072] Where, k we k is the maximum permissible slope ratio of the site from west to east. ew k is the maximum permissible slope ratio of the site from east to west. ew k we ≥0.

[0073] Let the local inequality constraint coefficient matrix A of edge p be... p Local inequality constraints on constant vector b p Integrate into global matrix A and vector b: Update the values ​​corresponding to columns a and b in rows 2p-1 and 2p of matrix A, respectively, changing them to A. p The values ​​corresponding to columns 1 and 2 in rows 1 and 2; update the values ​​of items 2p-1 and 2p in b, changing them to b respectively. p The first and second values. The same operation is used to change the local inequality constraint coefficient matrix A of edge q. qLocal inequality constraints on constant vector b q Integrate into the global matrix A and vector b.

[0074] S6 - Correction of global equality constraint constant b eq

[0075] Assuming the final site leveling plan requires that the fill volume be dtV greater than the excavation volume, then the correction b is... eq The value is b eq +dtV. For site leveling schemes requiring cut-fill balance, dtV = 0.

[0076] S7 - Solving Quadratic Programming Problems

[0077] After calculating each coefficient matrix, the field leveling problem is transformed into a quadratic programming optimization problem:

[0078]

[0079]

[0080] Where h represents the elevation of each node in the leveling scheme to be solved, and n represents the elevation of each node. ed Using a 1×1 dimensional vector, solve the above quadratic programming optimization problem to obtain the design elevation h values ​​of each node in the optimal field leveling scheme.

[0081] S8 - Forms the site leveling design surface, connecting the design elevation h of each adjacent node to form the final site leveling design surface, such as... Figure 3 The number 600 in the middle refers to.

[0082] The application of this invention in a photovoltaic power station project illustrates the comparison between the effects of this invention and previous methods.

[0083] A photovoltaic power station covers an area of ​​2.7 square kilometers and has an installed photovoltaic capacity of 283MW. During the bidding phase of this project, a traditional partial planar approach was used for site leveling design, dividing the entire site into six areas, each with its own planar site leveling design, such as... Figure 4 As shown, the lighter-colored areas represent excavation, and the darker-colored areas represent fill. The total excavation volume for this project is 839,600 m³. 3 The total fill volume was 842,400 m³. 3 The design took approximately 40 hours.

[0084] If the site leveling design is carried out using the method of this invention, the entire site is divided into 4286 zones, such as... Figure 5 As shown, the lighter-colored areas represent excavation, and the darker-colored areas represent fill. The total excavation volume for this project is 352,500 m³. 3 The total fill volume was 348,900 m³. 3The design process takes approximately 2 hours. Compared to traditional methods, this invention saves about 58% of the excavation and filling work and reduces design time by about 95%.

[0085] This method can be implemented as a software module for data processing. The invention can be implemented using software plus the necessary general-purpose hardware platform. For example, it can be implemented using existing processors, or by a dedicated processor used for this or other purposes in a suitable system, or by a hardwired system. Embodiments of the invention also include non-transitory computer-readable storage media, which include machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available medium accessible by a general-purpose or special-purpose computer or other machine with a processor. For example, such machine-readable media can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the required program code in the form of machine-executable instructions or data structures and can be accessed by a general-purpose or special-purpose computer or other machine with a processor. When information is transmitted or provided to a machine via a network or other communication connection (hardwired, wireless, or a combination of hardwired and wireless), that connection is also considered a machine-readable medium.

Claims

1. A site leveling design method based on quadratic programming, characterized in that, Includes the following steps: S1. Raw terrain data processing: Extract site coordinate data and generate terrain interpolation function F; S2. Site Block Division and Coding: Divide the photovoltaic site into rectangular blocks, number the nodes, edges, and blocks, and record the node coordinates, edge and block node composition to form a topological structure; let n be the number of blocks, nodes, and edges respectively. el n nd n ed ; S3. Initialize the global initial quadratic coefficient matrix Q, the global initial linear coefficient vector f, the global inequality constraint coefficient matrix A, the global inequality constraint constant vector b, and the global equality constraint coefficient vector A. eq Global equality constraint constant b eq ; S4. Generate the local quadratic coefficient matrix Q for each block in order of block number. i Local first-order coefficient vector f i Local equality constraint coefficient vector A eqi Local equality constraints often b eqi And then integrate them into the corresponding global matrices and vectors in sequence; S5. Generate the local inequality constraint coefficient matrix A for each edge according to the edge numbering order. i Local inequality constraints on constant vector b i And then integrate them into the corresponding global matrices and vectors in sequence; S6. Correct the global equality constraint constant b eqi ; S7. Solving the quadratic programming problem: S8. Forming the site leveling design surface: Connect all adjacent nodes based on the design elevations of each node obtained from the quadratic programming solution to form the final site leveling design surface; Steps S4 and S5 are not sequential.

2. The site leveling design method based on quadratic programming according to claim 1, characterized in that: The global quadratic coefficient matrix Q is n nd ×n nd 1-order matrix.

3. The site leveling design method based on quadratic programming according to claim 1, characterized in that: The global first-order coefficient vector f is n nd ×1 dimensional vector.

4. The site leveling design method based on quadratic programming according to claim 1, characterized in that: The global inequality constraint coefficient matrix A is 2n ed ×n nd 1-order matrix.

5. The site leveling design method based on quadratic programming according to claim 1, characterized in that: In step S7, a numerical method is used to iteratively solve the quadratic programming problem.

6. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the quadratic programming-based site leveling design method as described in any one of claims 1 to 5.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the quadratic programming-based site leveling design method as described in any one of claims 1 to 5.

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