A method and system for mixed multi-layer preprocessing of a sick power flow system

Abstract

This invention discloses a hybrid multi-layer preprocessing method and system for ill-conditioned power flow systems, primarily relating to the field of power system data computation technology. The method includes the following steps: obtaining the original Jacobian matrix J based on a power flow computation method, and performing l1-norm scaling on the original Jacobian matrix to obtain a scaling matrix; sorting the scaling matrix by approximate minimum degree to obtain a rearranged matrix; performing incomplete LU decomposition on the rearranged matrix to obtain a decomposition matrix; and integrating the hybrid preconditioners based on the scaling matrix, rearranged matrix, and decomposition matrix. The beneficial effects of this invention are that it reduces the risk of convergence failure, improves decomposition efficiency, and balances accuracy and computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of data computing technology for power systems, specifically a hybrid multi-layer preprocessing method and system for ill-conditioned power flow systems. Background Technology

[0002] The continuous growth in load demand on existing infrastructure, coupled with the widespread integration of renewable energy sources (RES) such as solar, wind, and energy storage, as well as dynamic loads like electric vehicles and data centers, has profoundly altered the operating characteristics of modern power systems. This integration exacerbates the challenges of large-scale ill-conditioned power flow calculations, stemming from inherent characteristics of distribution networks such as high R / X ratios, weak grid connections, voltage instability, and network congestion. These factors have been widely recognized as the primary cause of ill-conditioned Jacobian matrix in the Newton-Raphson (NR) algorithm, leading to decreased numerical stability and hindered convergence. Although the intermittency of RES and load volatility can indirectly increase the risk of ill-conditioned behavior by pushing the system towards operational limits such as voltage collapse, the fundamental cause of numerical instability lies in the grid parameters themselves, rather than the random fluctuations of RES.

[0003] Traditional solvers suffer from excessive memory consumption and poor scalability when dealing with large power grids; while conventional iterative methods are prone to divergence under severely ill-conditioned conditions.

[0004] Therefore, there is an urgent need for a hybrid multi-layer preprocessing method consisting of first-order norm scaling, AMD rearrangement, and incomplete ILU decomposition to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a hybrid multilayer preprocessing method and system for pathological power flow systems, which reduces the risk of convergence failure, improves decomposition efficiency, and balances accuracy and computational efficiency.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] On the one hand, a hybrid multilayer preprocessing method for pathological power flow systems is provided, including the following steps:

[0008] S1: Obtain the original Jacobian matrix J based on the power flow calculation method of the power system, and perform l1 norm scaling on the original Jacobian matrix to obtain the scaling matrix;

[0009] S2: Sort the scaling matrix by approximate minimum degree to obtain the rearranged matrix;

[0010] S3: Perform incomplete LU decomposition on the rearranged matrix to obtain the decomposed matrix;

[0011] S4: Perform hybrid preconditioner integration based on the scaling matrix, rearrangement matrix, and decomposition matrix.

[0012] Preferably, step S1 includes the following steps:

[0013] S11: Determine the scaling strategy, specifically: use row and column scaling methods to adjust the position of matrix elements to enhance the diagonal advantage;

[0014] S12: Calculate the norm, specifically: measure the size of each row and each column based on the first-order norm, used to determine the scaling factor for each row and each column;

[0015] S13: Based on the scaling strategy of step S11 and the norm of step S12, the original Jacobian matrix is ​​scaled. Specifically, the original Jacobian matrix is ​​multiplied by the corresponding diagonal scaling matrices R and C to obtain the scaling matrix J. scaled =R·J·C, where R is the row scaling matrix, C is the column scaling matrix, and J is the original Jacobian matrix;

[0016] S14: Verify the scaling matrix to determine if it meets the expected conditions.

[0017] Preferably, step 1 further includes: performing an l1 normalization operation on the original Jacobian matrix J, including: calculating the l1 norm of each row, calculating the l1 norm of each column, constructing a scaling factor matrix, and normalizing the original Jacobian matrix J based on the calculation results.

[0018] Preferably, step S2 specifically involves: scaling the matrix J obtained in step S1... scaled The non-zero pattern is mapped to the graph G = (V, E), where node v i The corresponding row / column of the matrix, edge e ij For each non-zero element, calculate v for each node. i The approximation is determined, and the node with the minimum approximation is selected. * Then eliminate the nodes, generate a permutation matrix P according to the node elimination order, and obtain the rearrangement matrix J from the permutation matrix. reordered .

[0019] Preferably, step S3 includes:

[0020] S31: Rearrange matrix J reordered Perform a sparse approximate decomposition to generate a lower triangular matrix L and an upper triangular matrix U that are zero matrices;

[0021] S32: Perform incomplete decomposition iterations on L and U respectively;

[0022] S33: After incomplete decomposition and iteration of L and U, only non-zero elements are retained to form sparse L and U.

[0023] Preferably, in step S4, the integration of the hybrid preconditioner specifically involves:

[0024] The final preconditioner is calculated:

[0025] M -1 =(L·U) -1 ·P·R·C

[0026] Where R is the row scaling matrix, C is the column scaling matrix, and J is the original Jacobian matrix.

[0027] On the other hand, a preprocessing system based on the above-mentioned hybrid multilayer preprocessing method for pathological power flow systems is provided, comprising:

[0028] The scaling matrix calculation module is used to: obtain the original Jacobian matrix J based on the power system flow calculation method, and perform l1 norm scaling on the original Jacobian matrix to obtain the scaling matrix;

[0029] The rearrangement matrix calculation module is used to: sort the scaling matrix by approximately minimum degree to obtain the rearranged matrix;

[0030] The decomposition matrix calculation module is used to: perform incomplete LU decomposition on the rearranged matrix to obtain the decomposition matrix;

[0031] The hybrid preconditioner integration module is used to integrate hybrid preconditioners based on scaling matrices, rearrangement matrices, and decomposition matrices.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] 1. The Jacobian matrix generated in the power flow calculation is scaled by the l1 norm of the rows and columns, which achieves a balance of the magnitude of the matrix elements, enhances the diagonal advantage, improves numerical stability, and maintains the sparsity of the matrix.

[0034] 2. By performing an approximate minimum degree sort (AMD) rearrangement on the matrix after scaling with l1 norm, the non-zero structure of the matrix is ​​optimized, the amount of padding in LU decomposition is reduced, and the decomposition efficiency is further improved.

[0035] 3. By performing threshold-based ILU decomposition on the matrix after rearranging by Approximate Minimum Degree Sort (AMD), sparse approximate decomposition matrices L and U are generated, thereby improving the balance accuracy and computational efficiency. Attached Figure Description

[0036] Figure 1 This is a flowchart of a hybrid multilayer preprocessing method for a pathological power flow system according to the present invention;

[0037] Figure 2 This is a schematic diagram of the structure of a hybrid multilayer pretreatment system for a pathological power flow system according to the present invention. Detailed Implementation

[0038] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined in this application.

[0039] In this invention, terms such as "upper," "lower," "left," "right," "front," "back," "vertical," "horizontal," "side," and "bottom" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used only to facilitate the description of the structural relationships of the various components or elements of this invention and do not specifically refer to any component or element in this invention. They should not be construed as limiting the invention.

[0040] In this invention, terms such as "fixed connection," "connected," and "linked" should be interpreted broadly, indicating a fixed connection, an integral connection, or a detachable connection; a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can determine the specific meaning of these terms in this invention based on the specific circumstances, and they should not be construed as limitations on the invention.

[0041] Example:

[0042] like Figure 1 As shown, this embodiment provides a hybrid multilayer preprocessing method for a pathological power flow system, including the following steps:

[0043] S1: Obtain the original Jacobian matrix J based on the power flow calculation method of the power system, and perform l1 norm scaling on the original Jacobian matrix to obtain the scaling matrix;

[0044] S2: Sort the scaling matrix by approximate minimum degree to obtain the rearranged matrix;

[0045] S3: Perform incomplete LU decomposition on the rearranged matrix to obtain the decomposed matrix;

[0046] S4: Perform hybrid preconditioner integration based on the scaling matrix, rearrangement matrix, and decomposition matrix.

[0047] To improve the diagonal dominance of the Jacobian matrix generated in power system power flow calculations, a scaling technique based on rows and columns is employed. The core idea of ​​this method is to adjust the scaling factors of each row and column so that the largest element in each row and column is as close as possible to the diagonal. This improves the diagonal dominance of the matrix, thereby enhancing the stability of numerical methods (such as the Newton-Raphson method) and reducing the risk of convergence failure. The original Jacobian matrix is ​​generated using conventional power system power flow calculation methods. As described in step S1, the specific implementation steps typically include the following aspects:

[0048] S11: Determine the scaling strategy: Choose to use a scaling method that uses both rows and columns, rather than operating on rows or columns individually. This allows for more flexible adjustment of the matrix element positions to enhance the diagonal advantage.

[0049] S12: Calculate the norm: The size of each row and column is usually measured based on the first-order norm, which is crucial for determining the scaling factor for each row and column;

[0050] S13: Scaling the Jacobian Matrix: By multiplying by the corresponding diagonal scaling matrices R and C, where R is the row scaling matrix and C is the column scaling matrix, the Jacobian matrix is ​​adjusted to obtain a new matrix J. scaled =R·J·C;

[0051] S14: Evaluate the scaling effect: Check whether the scaled matrix meets the expected conditions, such as: the modulus of the diagonal elements is close to 1, while the modulus of the sub-diagonal elements does not exceed 1.

[0052] By following the steps above, the diagonal dominance of the Jacobian matrix can be systematically improved, thereby enhancing the stability and reliability of large-scale power flow analysis.

[0053] Step 1 also includes: performing l1 normalization on the original Jacobian matrix J, including: calculating the l1 norm of each row, calculating the l1 norm of each column, constructing a scaling factor matrix, and normalizing the original Jacobian matrix J based on the calculation results;

[0054] Specifically, the l1 norm of each row is calculated as follows:

[0055]

[0056] If r i =0, then let r = 0. i =1 to avoid division by zero;

[0057] Calculate the l1 norm of each column as follows:

[0058]

[0059] Construct the scaling factor matrix as follows:

[0060] Row scaling factor matrix

[0061] Column scaling factor matrix

[0062] Normalize the original Jacobian matrix J: J scaled =R·J·C.

[0063] Step S2 includes:

[0064] 1. Construct an adjacency graph:

[0065] Scaled matrix J scaled The non-zero pattern is mapped to the graph G = (V, E), where node v i The corresponding row / column of the matrix, edge e ij Corresponding to non-zero elements;

[0066] 2. Approximation calculation and node elimination:

[0067] Calculate v for each node i Approximation: Where N(i) is the set of direct neighbors;

[0068] Select its minimum approximation node v * Eliminate v * And add fill-in edges between its neighbors;

[0069] Dynamically update the approximation of the remaining nodes;

[0070] 3. Generate the permutation matrix:

[0071] Generate a permutation matrix P based on the node elimination order, and then obtain a rearrangement matrix J from the permutation matrix. reordered =P·J scaled ·P T .

[0072] Step S3 includes:

[0073] S31: Initialize the decomposition matrix:

[0074] Initialize the lower triangular matrix L and the upper triangular matrix U as zero matrices;

[0075] S32: Incomplete decomposition iteration:

[0076] Line processing (calculating L):

[0077] For each row i, calculate from left to right If |L ij |<τ·max k |A ik |, then discard L ij (Set to 0);

[0078] Column processing (calculation I):

[0079] For each column j, calculate from left to right If |I ij |<τ·maxk |A ik |, then discard U ij (Set to 0);

[0080] The decomposition process satisfies:

[0081]

[0082] S33: Sparse storage structure:

[0083] Only non-zero elements are retained, forming sparse L and U.

[0084] In step S4, the integration of the hybrid preconditioner specifically involves:

[0085] The final preconditioner is calculated:

[0086] M -1 =(L·U) -1 ·P·R·C

[0087] Where R is the row scaling matrix, C is the column scaling matrix, and J is the original Jacobian matrix;

[0088] After the final preconditioner calculation is completed, the preconditioner M is applied in each BiCGSTAB iteration. -1 In all cases, the above logic shall be followed.

[0089] The above is a detailed description of the preferred embodiments of the present invention, but the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions to the transaction features between nodes without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A hybrid multilayer preprocessing method for a pathological power flow system, characterized in that, Includes the following steps: S1: Obtaining the original Jacobian matrix based on power system flow calculation methods And perform on the original Jacobian matrix. Norm scaling yields the scaling matrix; specifically, it includes: S11: Determine the scaling strategy, specifically: use row and column scaling methods to adjust the position of matrix elements to enhance the diagonal advantage; S12: Calculate the norm, specifically: measure the size of each row and each column based on the first-order norm, used to determine the scaling factor for each row and each column; S13: Based on the scaling strategy in step S11 and the norm in step S12, scale the original Jacobian matrix, specifically by multiplying the original Jacobian matrix by the corresponding diagonal scaling matrix. and , thus obtaining the scaling matrix ,in For row scaling matrices, For column scaling matrices, This is the original Jacobian matrix; S14: Verify the scaling matrix to determine if it meets the expected conditions; S2: Sort the scaling matrix by approximate minimum degree to obtain the rearranged matrix; specifically: The scaling matrix obtained in step S1 Non-zero pattern mapping is a graph , among which, nodes The corresponding rows / columns and edges of the matrix For each non-zero element, calculate the value of each node. The approximation is determined, and the node with the minimum approximation is selected. Then eliminate them, and generate a permutation matrix according to the order of node elimination. The rearrangement matrix is ​​obtained by using the permutation matrix. S3: Perform incomplete LU decomposition on the rearranged matrix to obtain the decomposed matrix; specifically including: S31: Rearrange the matrix Perform sparse approximate decomposition to generate a lower triangular matrix. and upper triangular matrix It is a zero matrix; S32: respectively for and Perform incomplete decomposition iterations; S33: After incomplete decomposition and iteration and Only non-zero elements are retained, forming a sparse structure. and S4: Perform hybrid preconditioner integration based on the scaling matrix, rearrangement matrix, and decomposition matrix.

2. The hybrid multilayer preprocessing method for a pathological power flow system according to claim 1, characterized in that, Step 1 further includes: processing the original Jacobian matrix. implement Normalization operations include: calculating the normalization value of each row. Norm, calculate the norm of each column Norm, calculate scaling factor, and use the calculation results to analyze the original Jacobian matrix. Perform normalization.

3. The method for hybrid multilayer preprocessing of a pathological power flow system according to claim 1, characterized in that, In step S4, the integration of the hybrid preconditioner specifically involves: The final preconditioner is calculated: in, For the final preconditioner, , These are lower triangular matrices and upper triangular matrices, respectively. Let be the permutation matrix. For row scaling matrices, Scale the matrix for columns.

4. A preprocessing system based on the hybrid multilayer preprocessing method for pathological power flow systems as described in any one of claims 1-3, characterized in that, include: The scaling matrix calculation module is used to: obtain the original Jacobian matrix based on power system power flow calculation methods. And perform on the original Jacobian matrix. Norm scaling yields the scaling matrix; The rearrangement matrix calculation module is used to: sort the scaling matrix by approximately minimum degree to obtain the rearranged matrix; The decomposition matrix calculation module is used to: perform incomplete LU decomposition on the rearranged matrix to obtain the decomposition matrix; The hybrid preconditioner integration module is used to integrate hybrid preconditioners based on scaling matrices, rearrangement matrices, and decomposition matrices.

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