A static N-1 fast evaluation method based on admittance matrix fast triangular decomposition

Abstract

This invention discloses a fast static N-1 evaluation method based on rapid triangular decomposition of the admittance array, comprising: reading in basic power grid data to form an admittance array and an admittance array; selecting one disconnected line, performing correlation matrix element analysis, and performing triangular decomposition on the corresponding rows of the admittance array and the admittance array based on the correlation elements; performing overload range analysis of secondary DC power flow based on the modified and re-triangularly decomposed admittance array; and performing static N-1 evaluation based on the re-triangularly decomposed admittance array and the initial current vector. This invention solves the efficiency problem of static N-1 calculation analysis based on the admittance array and improves its accuracy. It defines the analysis range based on the DC power flow conductance array, and then reduces the computational load of triangular analysis based on the non-zero element influence range analysis of the admittance array triangular decomposition, comprehensively improving the efficiency and accuracy of static N-1 calculation and enhancing the efficiency of power grid icing system safety analysis.

Description

Technical Field

[0001] This invention relates to the field of power dispatching and operation technology, and in particular to a static N-1 fast evaluation method based on fast triangular decomposition of admittance array. Background Technology

[0002] Ice accumulation on transmission lines can impact the safety and stability of the power grid, especially after widespread icing. Rapid grid analysis is crucial, and static security analysis is an essential component of overall grid security analysis. Static security analysis methods typically include rapid analysis approaches and detailed power flow-based analysis methods. A combination of both is generally used, allowing for a balance between speed and accuracy by conducting detailed analysis based on rapid assessment.

[0003] Rapid analysis methods generally employ approximations to improve computational speed, but their accuracy is somewhat lower, serving a filtering function. Examples include compensation methods and methods based on DC power flow. Static N-1 analysis can also be achieved by modifying and calculating the admittance matrix derived from power grid simulation analysis. This method is relatively simple and easy to understand. However, since the admittance matrix is ​​generally quite large, the workload of triangulation after modification is considered substantial, severely limiting computational speed and leading to its rarity in practical applications. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the aforementioned existing problems, the present invention is proposed.

[0006] Therefore, this invention provides a static N-1 fast evaluation method based on fast triangular decomposition of the admittance matrix to solve the problem that the workload of triangular decomposition after the admittance matrix is ​​large, which seriously limits the calculation speed and results in low efficiency and limited use in practical applications.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution, including:

[0008] Read in the basic power grid data to form the susceptance array and the admittance array;

[0009] Select one disconnected line, perform correlation matrix element analysis, and perform triangular decomposition on the corresponding rows of the susceptance and admittance arrays based on the correlation elements.

[0010] Based on the modified and re-triangularly decomposed susceptance array, the overload range of secondary DC power flow is analyzed.

[0011] Static N-1 evaluation is performed based on the admittance matrix and initial current vector obtained from the retriangulation.

[0012] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, the basic power grid data includes power flow data and power flow calculation results data.

[0013] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, the method further includes: performing initial calculations after forming the susceptance array and admittance array; completing the initial triangular decomposition based on the susceptance array and admittance array formed from the power grid basic data; performing initial DC power flow calculations to obtain the initial angle θ0 of all nodes; and deriving the injected current vector I of all nodes based on the initial power flow calculation results. equ0 .

[0014] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, before performing correlation matrix element analysis, the selected disconnected line is modified by deleting the elements corresponding to the disconnected line on the susceptance array and admittance array.

[0015] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of the admittance matrix described in this invention, wherein: the element analysis of the correlation matrix is ​​performed by arbitrarily selecting either the susceptance matrix or the admittance matrix, including,

[0016] A1: Create an array to store node numbers, and store the node numbers on both sides of the broken branch;

[0017] A2: Extract the first node number ibus from the array;

[0018] A3: Find the first non-zero element to the left of the diagonal element in the row corresponding to node number ibus in the matrix;

[0019] A4: Store the column number corresponding to the non-zero element into the node number array;

[0020] A5: Continue searching in the matrix for the next non-zero element to the left of the diagonal element in the row corresponding to node number ibus;

[0021] A6: If a next non-zero element exists, return A4; otherwise, proceed to the next step.

[0022] A7: Select the next node number ibus in the node number array;

[0023] A8: If there is a next node number, return A3; otherwise, end the entire search process.

[0024] A9: Retain all nodes in the node number array, sort them in ascending order of node number, and store them. The node number is the row number.

[0025] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, wherein: the triangular decomposition of the corresponding rows of the susceptance array and admittance array based on correlation elements includes:

[0026] Read in the array storing the associated node numbers;

[0027] Select the first node ibus[i], i = 1;

[0028] Perform permametric transformation on row ibus[i], that is, all non-zero elements on the right except for the diagonal elements;

[0029] Eliminate all non-zero elements in the ibus[i]th column of the lower triangular matrix. That is, check if the ibus[i]th column element of all subsequent associated rows is non-zero. If it is, use the ibus[i]th row element to eliminate it; otherwise, skip it. Continue until all non-zero elements in the ibus[i]th column become 0.

[0030] Select the next node, i.e., i = i + 1; if all associated rows have been processed, the calculation is complete and exit; otherwise, return to the standardization operation and continue processing the ibus[i + 1] row.

[0031] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, wherein: the overload range analysis of the secondary DC power flow yields new angles θ of each node;

[0032] The power change rate of the line is estimated based on the change in the angle difference between the two sides of the line.

[0033] Lines with a power change rate exceeding a certain limit are identified as overloaded lines and stored.

[0034] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, the power change rate is expressed as:

[0035]

[0036] The restriction is expressed as follows:

[0037] λ>λ lim

[0038] Where, θ i0 θ j0It calculates the initial angle θ on both sides of the branch. i θ j It is the angle between the two sides after the break, λ lim To determine the standard for the rate of change.

[0039] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, the static N-1 evaluation based on the re-triangular decomposition of admittance array and initial current vector includes calculating a new voltage V.

[0040] For overloaded lines identified in DC power flow analysis, calculate the line current, determine whether they are overloaded, and store all overloaded lines.

[0041] As a preferred embodiment of the static N-1 fast evaluation method based on fast triangular decomposition of admittance array described in this invention, the new voltage V is represented as:

[0042] V = Y -1 I equ0

[0043] Among them, I equ0 The injected current vector is determined based on the initial state; Y is the system admittance matrix.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention solves the efficiency problem of static N-1 calculation analysis based on admittance array and improves the accuracy. It defines the analysis range based on DC power flow conductance array, and then reduces the calculation amount of triangular analysis based on the non-zero element influence range analysis of admittance array triangular decomposition. It comprehensively improves the efficiency and accuracy of static N-1 calculation and improves the efficiency of power grid icing system safety analysis. Attached Figure Description

[0045] 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:

[0046] Figure 1 This is a schematic diagram of the overall process of the static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix according to an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of the correlation matrix element analysis process in the static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix according to an embodiment of the present invention;

[0048] Figure 3This is a schematic diagram of the fast triangular decomposition process based on the correlation matrix in the static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix according to an embodiment of the present invention. Detailed Implementation

[0049] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0050] 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.

[0051] 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.

[0052] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0053] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0054] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0055] Example 1

[0056] Reference Figure 1-3 As an embodiment of the present invention, a static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix is ​​provided, comprising:

[0057] S1: Read in the basic power grid data and form the susceptance array and admittance array;

[0058] Furthermore, the basic data of the power grid includes power flow data and the calculation results of power flow.

[0059] Specifically, power flow data includes information on all power grid lines, transformers, and other branches, as well as generator and load power. The calculated power flow results include node voltage and generator output information.

[0060] Furthermore, this also includes initial calculations after the susceptance and admittance arrays are formed. These initial calculations include: completing the initial triangulation of the susceptance and admittance arrays based on the power grid's fundamental data; performing initial DC power flow calculations to obtain the initial angles θ0 of all nodes; and deriving the injected current vector I of all nodes based on the initial power flow calculation results. equ0 .

[0061] S2: Select one disconnected line, perform correlation matrix element analysis, and perform triangular decomposition on the corresponding rows of the susceptance and admittance arrays based on the correlation elements;

[0062] Furthermore, before performing correlation matrix element analysis, the selected disconnected line is modified by deleting the elements corresponding to the disconnected line on the susceptance and admittance arrays.

[0063] Furthermore, see Figure 2 The correlation matrix element analysis involves randomly selecting either the susceptance matrix or the admittance matrix for analysis, including:

[0064] A1: Create an array to store node numbers, and store the node numbers on both sides of the broken branch;

[0065] A2: Extract the first node number ibus from the array;

[0066] A3: Find the first non-zero element to the left of the diagonal element in the row corresponding to node number ibus in the matrix;

[0067] A4: Store the column number corresponding to the non-zero element into the node number array;

[0068] A5: Continue searching in the matrix for the next non-zero element to the left of the diagonal element in the row corresponding to node number ibus;

[0069] A6: If a next non-zero element exists, return A4; otherwise, proceed to the next step.

[0070] A7: Select the next node number ibus in the node number array;

[0071] A8: If there is a next node number, return A3; otherwise, end the entire search process.

[0072] A9: Retain all nodes in the node number array, sort them in ascending order of node number, and store them. The node number is the row number.

[0073] It should be noted that the purpose of the above analysis steps is to modify the admittance matrix elements of the nodes on both sides of the disconnected line. Before proceeding with the subsequent calculations, it is necessary to find the affected rows based on the non-zero element distribution of the admittance matrix. The reason for arbitrarily choosing either the susceptance matrix or the admittance matrix is ​​that the search results for the two matrices are the same in this step.

[0074] Furthermore, see Figure 3 In the diagram, n represents the number of associated nodes, and i and j represent the sequence numbers. Based on the associated elements, a triangular decomposition is performed on the corresponding rows of the susceptance and admittance arrays, including:

[0075] Read in the array storing the associated node numbers;

[0076] Select the first node ibus[i], i = 1;

[0077] Perform permametric transformation on row ibus[i], that is, all non-zero elements on the right except for the diagonal elements;

[0078] Eliminate all non-zero elements in the ibus[i]th column of the lower triangular matrix. That is, check if the ibus[i]th column element of all subsequent associated rows is non-zero. If it is, use the ibus[i]th row element to eliminate it; otherwise, skip it. Continue until all non-zero elements in the ibus[i]th column become 0.

[0079] Select the next node, i.e., i = i + 1; if all associated rows have been processed, the calculation is complete and exit; otherwise, return to the standardization operation and continue processing the ibus[i + 1] row.

[0080] It should be noted that the purpose of the above analysis steps is to re-triangulate the admittance matrix when some variables are modified. Based on all the associated node numbers obtained in the initial calculation steps, triangulation is performed only on the corresponding rows, while the triangulation results of other rows remain unchanged. This part applies to both susceptance and admittance matrices.

[0081] S3: Based on the modified and re-triangularly decomposed susceptance array, perform overload range analysis of secondary DC power flow.

[0082] Furthermore, the overload range analysis of the secondary DC power flow yields new angles θ for each node;

[0083] The power change rate of the line is estimated based on the change in the angle difference between the two sides of the line.

[0084] Lines with a power change rate exceeding a certain limit are identified as overloaded lines and stored.

[0085] Specifically, the rate of change of power is expressed as:

[0086]

[0087] The restrictions are expressed as:

[0088] λ>λ lim

[0089] Where, θ i0 θ j0 It calculates the initial angle θ on both sides of the branch. i θ j It is the angle between the two sides after the break, λ lim It is the standard for judging the rate of change, which needs to be determined according to the actual situation. Generally, 0.05 can be selected.

[0090] It should be noted that the range of this restriction can be set according to actual needs and operational experience.

[0091] S4: Static N-1 evaluation based on the admittance matrix and initial current vector obtained from the retriangulation.

[0092] Furthermore, a static N-1 evaluation is performed based on the admittance matrix and initial current vector obtained from the retriangulation, including the calculation of the new voltage V.

[0093] For overloaded lines identified in DC power flow analysis, calculate the line current, determine whether they are overloaded, and store all overloaded lines.

[0094] Specifically, the new voltage V is expressed as:

[0095] V = Y -1 I equ0

[0096] Among them, I equ0 The injected current vector is determined based on the initial state; Y is the system admittance matrix.

[0097] It should also be noted that the above analysis is for a single circuit breaker; the same method applies to other circuit breaks. The overall approach first involves reading in the basic data of the power grid to form the susceptance and admittance arrays, which serve as the basis for all subsequent calculations. Then, static N-1 calculations are performed on each line that needs to be broken until all calculations are completed. Each calculation includes several parts: matrix correlation element analysis, fast triangular decomposition of the admittance array based on correlation elements, overload range analysis based on DC power flow, and fast static N-1 analysis based on the admittance array.

[0098] Although the admittance matrix is ​​relatively large, it is a sparse matrix. Therefore, the impact of each modification on the admittance matrix is ​​actually quite limited. By leveraging the sparsity of the admittance matrix and combining it with the triangular decomposition order to extract the affected non-zero elements, the computational cost of triangular analysis can be significantly reduced, thereby greatly improving computational speed. Furthermore, in static N-1 fast analysis, the overload range can be defined first based on the sensitivity information of the DC power flow before performing specific calculations, thus improving computational efficiency.

[0099] Example 2

[0100] Referring to Table 1, an embodiment of the present invention provides a static N-1 fast evaluation method based on fast triangular decomposition of admittance array. To verify its beneficial effects, a comparison of two schemes is provided.

[0101] Currently, typical power grids have tens of thousands of nodes. Taking a scale of 10,000 nodes as an example, the corresponding matrix typically has around 40,000 to 60,000 non-zero elements. If the admittance matrix is ​​modified during the calculation, the matrix needs to be re-triangularly decomposed starting from the row to be modified. Thus, the computational workload is related to the position of the row being modified. The first row has the highest computational workload, involving all non-zero elements; the last row has the lowest. On average, calculations are typically required for several thousand rows of data, involving tens of thousands of non-zero elements. Using the method in this example, the number of rows that need modification for a single node is typically on the order of tens of rows. Compared to the original method, the average computational workload is approximately 1%, thus significantly improving the calculation speed.

[0102] Table 1 Comparison of Calculation Amount

[0103] Number of lines Non-zero elements Traditional methods 3-4 thousand lines 40,000 to 60,000 Optimization methods Lines 30-40 400-600

[0104] Overall, this invention extracts the associated row numbers of disconnected lines based on the sparsity characteristics of the admittance matrix, the basic method of triangulation, and the rules. In the process of re-triangulation, only the associated rows are recalculated, avoiding the need to recalculate the entire matrix. This greatly reduces the amount of computation in the triangulation process and improves the overall computational efficiency.

[0105] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A static N-1 fast evaluation method based on admittance matrix fast triangular decomposition, characterized in that, include: Read in the basic power grid data to form the susceptance array and the admittance array; After forming the susceptance and admittance arrays, initial calculations are performed. These initial calculations include: completing the initial triangulation of the susceptance and admittance arrays based on the power grid fundamental data; and performing initial DC power flow calculations to obtain the initial angles of all nodes. ; Based on the initial power flow calculation results, the injected current vectors of all nodes are deduced. ; Before performing correlation matrix element analysis, select one disconnected line and modify the selected disconnected line by deleting the elements corresponding to the disconnected line on the susceptance and admittance arrays. Perform correlation matrix element analysis, and based on the correlation elements, perform triangular decomposition of the corresponding rows of the susceptance and admittance matrices, including: Read in the array storing the associated node numbers; Select the first node ibus[i], i=1; Perform permametric transformation on row ibus[i], that is, all non-zero elements on the right except for the diagonal elements; Eliminate all non-zero elements in the ibus[i]th column of the lower triangular matrix. That is, determine whether the ibus[i]th column element of all subsequent associated rows is non-zero. If it is, use the ibus[i]th row element to eliminate it; otherwise, skip it; until all non-zero elements in the ibus[i]th column become 0. Select the next node, i.e., i = i + 1; if all associated rows have been processed, the calculation is complete and exit; otherwise, return to the standardization operation and continue processing rows ibus[i + 1]. The correlation matrix element analysis involves analyzing either the susceptance matrix or the admittance matrix, including: A1: Create an array to store node numbers, and store the node numbers on both sides of the broken branch; A2: Extract the first node number ibus from the array; A3: Find the first non-zero element to the left of the diagonal element in the row corresponding to node number ibus in the matrix; A4: Store the column number corresponding to the non-zero element into the node number array; A5: Continue searching in the matrix for the next non-zero element to the left of the diagonal element in the row corresponding to node number ibus; A6: If a next non-zero element exists, return A4; otherwise, proceed to the next step. A7: Select the next node number ibus in the node number array; A8: If there is a next node number, return A3; otherwise, end the entire search process. A9: Retain all nodes in the node number array, sort them in ascending order of node number and store them, where the node number is the row number; Based on the modified and re-triangularly decomposed susceptance array, the overload range of secondary DC power flow is analyzed. Static N-1 evaluation is performed based on the admittance matrix and initial current vector obtained from the retriangulation.

2. The static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix as described in claim 1, characterized in that, The power grid basic data includes power flow data and power flow calculation results.

3. The static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix as described in claim 2, characterized in that, The overload range analysis of the secondary DC power flow yields new angles for each node. ; The power change rate of the line is estimated based on the change in the angle difference between the two sides of the line. Lines with a power change rate exceeding a certain limit are identified as overloaded lines and stored.

4. The static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix as described in claim 3, characterized in that, The power change rate is expressed as: The restriction is expressed as follows: in, , It calculates the initial angles on both sides of the branch. , It is the angle on both sides after it is broken. To determine the standard for the rate of change.

5. The static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix as described in claim 4, characterized in that, The static N-1 evaluation based on the re-triangulated admittance matrix and initial current vector includes calculating the new voltage. ; For overloaded lines identified in DC power flow analysis, calculate the line current, determine whether they are overloaded, and store all overloaded lines.

6. The static N-1 fast evaluation method based on fast triangular decomposition of admittance matrix as described in claim 5, characterized in that, The new voltage , is represented as: in, The injected current vector is determined based on the initial state; It is the system admittance matrix.

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