Hybrid multilayer preprocessing method and system for ill-conditioned power flow system

Abstract

The invention discloses a hybrid multi-layer preprocessing method and system for an ill-conditioned power flow system, and mainly relates to the technical field of data calculation of a power system. Comprising the following steps: obtaining an original Jacobian matrix J based on a power flow calculation method of a power system, and executing l1 norm scaling on the original Jacobian matrix to obtain a scaled matrix; performing approximate minimum sorting on the scaling matrix to obtain a rearranged matrix; performing incomplete LU decomposition on the rearrangement matrix to obtain a decomposition matrix; and performing hybrid precondition device integration according to the scaling matrix, the rearrangement matrix and the decomposition matrix. The method has the beneficial effects that the risk of convergence failure is reduced, the decomposition efficiency is improved, and meanwhile, the precision and the calculation efficiency are balanced.

Description

Technical Field

[0001] The present invention relates to the technical field of data calculation of power systems, and in particular to a hybrid multi-layer preprocessing method and system for a pathological power flow system. Background Art

[0002] The continued growth in load demands 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 such as electric vehicles and data centers, has profoundly changed the operational characteristics of modern power systems. This integration exacerbates the challenges of large-scale ill-conditioned power flow calculations, stemming from the inherent characteristics of distribution networks, such as high R / X ratios, weak grid connections, voltage instability, and network congestion. These factors have been widely demonstrated to be the primary cause of ill-conditioned Jacobian matrices in the Newton-Raphson (NR) algorithm, leading to decreased numerical stability and hindered convergence. Although the intermittent nature and load fluctuations of RES can indirectly increase the risk of ill-conditioning by pushing the system to operational limits such as voltage collapse, the fundamental cause of numerical instability lies in the grid parameters themselves, rather than random fluctuations in RES.

[0003] Traditional solvers have problems of excessive memory consumption and poor scalability when dealing with large power grids; conventional iterative methods are prone to divergence under severe pathological conditions.

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

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

[0006] To achieve the above-mentioned purpose, the present invention is implemented through the following technical solutions:

[0007] In one aspect, a hybrid multi-layer preprocessing method for a pathological power flow system is provided, comprising the following steps:

[0008] S1: 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 scaled matrix;

[0009] S2: perform approximate minimum degree sorting on the scaling matrix to obtain the rearranged matrix;

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

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

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

[0013] S11: determining a scaling strategy, specifically: using a row and column scaling method to adjust the positions of matrix elements to enhance diagonal dominance;

[0014] S12: Calculating the norm, specifically: measuring the size of each row and each column based on the first-order norm to determine the scaling factor of 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: Check the scaling matrix to determine whether it meets the expected conditions.

[0017] Preferably, step 1 also 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 performing a normalization operation on the original Jacobian matrix J based on the calculation results.

[0018] Preferably, the step S2 is specifically: the scaling matrix J obtained in step S1 is scaled The non-zero pattern mapping of is a graph G = (V, E), where node v i Corresponding to the rows / columns of the matrix, the side e ij Corresponding to non-zero elements, calculate each node v i The approximation of , and select the node v with the minimum approximation * And eliminate, generate the permutation matrix P according to the node elimination order, and obtain the rearrangement matrix J through the permutation matrix reordered .

[0019] Preferably, the step S3 includes:

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

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

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

[0023] Preferably, in step S4, the hybrid preconditioner integration is specifically as follows:

[0024] Compute the final preconditioner:

[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] In another aspect, a pretreatment system based on the above-mentioned sick power flow system hybrid multi-layer pretreatment method is provided, comprising:

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

[0029] The rearrangement matrix calculation module is used to: perform approximate minimum degree sorting on the scaling matrix to obtain a rearrangement matrix;

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

[0031] The hybrid preconditioner integration module is used for performing hybrid preconditioner integration according to the scaling matrix, the rearrangement matrix and the decomposition matrix.

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

[0033] 1. Perform l1-norm scaling on the rows and columns of the Jacobian matrix generated in power system flow calculations, achieving a balanced magnitude of matrix elements, enhancing diagonal dominance, and improving numerical stability while maintaining matrix sparsity.

[0034] 2. By performing approximate minimum degree sorting (AMD) rearrangement on the matrix after l1 norm scaling, 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 rearranged by approximate minimum degree sorting (AMD), sparse approximate decomposition matrices L and U are generated, thereby improving the balance accuracy and computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of a hybrid multi-layer preprocessing method for a pathological power flow system of the present invention;

[0037] Figure 2 It is a structural schematic diagram of a hybrid multi-layer pretreatment system of a pathological tidal system of the present invention. DETAILED DESCRIPTION

[0038] Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiments are only used to illustrate the present invention and are not used in limiting the scope of the present invention.In addition, should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the application equally.

[0039] In the present invention, terms such as "upper", "lower", "left", "right", "front", "back", "vertical", "horizontal", "side", "bottom", etc. indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings. They are relational words determined only for the convenience of describing the structural relationships of the various parts or elements of the present invention, and do not specifically refer to any part or element in the present invention, and should not be understood as limiting the present invention.

[0040] In the present invention, terms such as "fixed connection," "connected," and "connection" should be interpreted broadly to mean a fixed connection, an integral connection, or a detachable connection; a direct connection or an indirect connection through an intermediary. Relevant researchers or technicians in this field may determine the specific meanings of these terms in the present invention based on specific circumstances, and they should not be construed as limitations of the present invention.

[0041] Example:

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

[0043] S1: 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 scaled matrix;

[0044] S2: perform approximate minimum degree sorting on the scaling matrix to obtain the rearranged matrix;

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

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

[0047] In order to improve the diagonal dominance of the Jacobian matrix generated in the power system flow calculation, the method used is based on row and column scaling technology. The core idea of this method is to adjust the scaling factors of each row and column so that the maximum element in each row and column is as close to the diagonal position as possible. The advantage of doing so is that the diagonal dominance of the matrix can be improved, thereby enhancing the stability of numerical methods (such as the Newton-Raphson method) and reducing the risk of convergence failure. Among them, the original Jacobian matrix is generated by the conventional power system flow calculation method. As described in step S1, the specific implementation steps generally include the following aspects:

[0048] S11: Determine the scaling strategy: Choose a scaling method that uses rows and columns instead of just performing operations on rows or columns separately. This allows for more flexibility in adjusting the positions of matrix elements to enhance diagonal dominance.

[0049] S12: Calculate the norm: The scale of each row and column is usually measured based on the 1st-order norm, which is crucial for determining the scaling factors of each row and column;

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

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

[0052] Through the above steps, 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 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 performing a normalization operation on the original Jacobian matrix J based on the calculation results;

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

[0055]

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

[0057] Calculate the l1 norm of each column, specifically:

[0058]

[0059] Construct the scaling factor matrix, specifically:

[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] The scaled matrix J scaled The non-zero pattern mapping of is a graph G = (V, E), where node v i Corresponding to the rows / columns of the matrix, the side e ij corresponding to non-zero elements;

[0066] 2. Approximation calculation and node elimination:

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

[0068] Select the node v with the minimum similarity * , eliminate v * , and add fill-in-edges between its neighbors;

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

[0070] 3. Generate permutation matrix:

[0071] Generate the permutation matrix P according to the node elimination order, and obtain the rearrangement matrix J through 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 to zero matrices;

[0075] S32: Incomplete decomposition iteration:

[0076] Row processing (calculation of 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: Storing sparse structures:

[0083] Only non-zero elements are kept to form sparse L and U.

[0084] In step S4, the hybrid preconditioner integration is specifically as follows:

[0085] Compute the final preconditioner:

[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 each time in the BiCGSTAB iteration. -1 , the above logic is followed.

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

Claims

1. A hybrid multi-layer preprocessing method for pathological power flow system, characterized in that: The following steps are involved: S1: 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 scaled matrix; S2: perform approximate minimum degree sorting on the scaling matrix to obtain the rearranged matrix; S3: Perform incomplete LU decomposition on the rearranged matrix to obtain a decomposition matrix; S4: Perform hybrid preconditioner integration based on the scaling matrix, rearrangement matrix, and decomposition matrix.

2. A hybrid multi-layer preprocessing method for pathological power flow system according to claim 1, characterized in that: The step S1 comprises the following steps: S11: determining a scaling strategy, specifically: using a row and column scaling method to adjust the positions of matrix elements to enhance diagonal dominance; S12: Calculating the norm, specifically: measuring the size of each row and each column based on the first-order norm to determine the scaling factor of each row and each column; 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; S14: Check the scaling matrix to determine whether it meets the expected conditions.

3. A hybrid multi-layer preprocessing method for pathological power flow system according to claim 2, characterized in that: It is characterized in that The step 1 also 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, calculating a scaling factor, and performing a normalization operation on the original Jacobian matrix J based on the calculation results.

4. A hybrid multi-layer preprocessing method for pathological power flow system according to claim 1, characterized in that: The step S2 is specifically: the scaling matrix J obtained in step S1 is scaled The non-zero pattern mapping of is a graph G = (V, E), where node v i Corresponding to the rows / columns of the matrix, the side e ij Corresponding to non-zero elements, calculate each node v i The approximation of , and select the node v with the minimum approximation * And eliminate, generate the permutation matrix P according to the node elimination order, and obtain the rearrangement matrix J through the permutation matrix reordered .

5. A hybrid multi-layer preprocessing method for pathological power flow system according to claim 1, characterized in that: The step S3 comprises: S31: Rearrange the matrix J reordered Perform sparse approximate decomposition to generate the lower triangular matrix L and the upper triangular matrix U as zero matrices; S32: perform incomplete decomposition iterations on L and U respectively; S33: After the incomplete decomposition iteration, L and U are only retained with non-zero elements to form sparse L and U.

6. A hybrid multi-layer preprocessing method for pathological power flow system according to claim 1, characterized in that: In step S4, the hybrid preconditioner integration is specifically as follows: Compute the final preconditioner: M -1 =(L·U) -1 ·P·R·C Among them, M -1 is the final preconditioner, L and U are the lower triangular matrix and upper triangular matrix respectively, P is the permutation matrix, R is the row scaling matrix, and C is the column scaling matrix.

7. A pretreatment system based on the hybrid multi-layer pretreatment method for pathological power flow system according to claim 1, characterized in that: include: The scaling matrix calculation module is used to obtain the original Jacobian matrix J based on the power system flow calculation method, and perform 1-norm scaling on the original Jacobian matrix to obtain a scaling matrix; The rearrangement matrix calculation module is used to: perform approximate minimum degree sorting on the scaling matrix to obtain a rearrangement matrix; The decomposition matrix calculation module is used to: perform incomplete LU decomposition on the rearranged matrix to obtain a decomposition matrix; The hybrid preconditioner integration module is used for performing hybrid preconditioner integration according to the scaling matrix, the rearrangement matrix and the decomposition matrix.

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