CN109101464A - Based on the modified electric system sparse matrix Parallel implementation method and system of matrix - Google Patents

Abstract

It is provided in an embodiment of the present invention a kind of based on the modified electric system sparse matrix Parallel implementation method and system of matrix, wherein, the described method includes: describing the first network equation and corresponding first sparse matrix of power transmission network state before changing according to power transmission network state, the second network equation and corresponding second sparse matrix that power transmission network state is described after the power transmission network state changes are obtained；Compensation vector is obtained according to second network equation, and carries out matrix amendment using former generation back substitution process of the compensation vector to first sparse matrix and obtains second sparse matrix in the hope of solution.By calculating after power system network structure change using existing information as a result, reducing calculation amount, solution efficiency is greatly improved.

Description

Parallel solution method and system for power system sparse matrix based on matrix correction

technical field

Embodiments of the present invention relate to the technical field of power system analysis and calculation technology, and more specifically, relate to a method and system for parallel solving of a sparse matrix of a power system based on matrix correction.

Background technique

In the process of power system calculation, the solution of linear equations is a frequently encountered problem. In power flow calculation and state estimation, the realization of the Newton-Raphson method and its various improved algorithms is inseparable from the solution of the correction equation (Jacobi matrix) in the iterative process; in transient simulation, the equations and descriptions describing the state of the transmission network The equations of equipment operation are all high-order nonlinear equations, and numerical integration is required to solve them. Generally, it is necessary to use Newton’s method to differentiate them into corresponding linear equations and then iteratively solve them. In the process of such iterative solutions, Solving large systems of linear equations is also required. Therefore, optimizing the solution process of linear equations and speeding up the solution can effectively reduce the time spent on various power system calculations and improve the real-time performance of the solution.

Parallel computing is an important research content in computer science and has been developed for decades. The general process of solving problems with parallel computing is as follows: for a given application problem, first, computing scientists transform the application into a numerical or non-numerical computing problem; then computer scientists design parallel algorithms for this computing problem, and through a certain A parallel programming language to implement it; Finally, experts in the application field run application software on a specific parallel computer to solve this problem. From this, it can be naturally found that parallel computing consists of the following parts: parallel computer (hardware platform for parallel computing), parallel algorithm (theoretical basis for parallel computing), parallel programming (software support for parallel computing), parallel application (The impetus for the development of parallel computing).

Using the parallel solution method can greatly improve the efficiency of solving the sparse matrix of the power system. However, in the analysis of the power system, it is often encountered that the network structure or operating parameters change locally. In this case, if the matrix is recalculated, it is necessary to Repeated operations such as LU decomposition, previous generation and back generation, the solution process is quite complicated, and the solution efficiency is low.

Contents of the invention

Embodiments of the present invention provide a method and system for solving the above-mentioned problems in parallel or at least partially solving the above-mentioned problems based on matrix modification.

On the one hand, an embodiment of the present invention provides a parallel solution method for a sparse matrix of a power system based on matrix correction, the method comprising:

According to the first network equation describing the state of the power transmission network and the corresponding first sparse matrix before the state of the power transmission network is changed, obtain the second network equation and the corresponding second sparse matrix describing the state of the power transmission network after the state of the power transmission network is changed;

Obtaining a compensation vector according to the second network equation, and using the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix to obtain the second sparse matrix.

Further, according to the first network equation describing the state of the power transmission network and the corresponding first sparse matrix before the state of the power transmission network is changed, the second network equation and the corresponding second network equation describing the state of the power transmission network after the state of the power transmission network is changed are acquired. Sparse matrix, specifically including:

After the state of the power transmission network is changed, obtain a node-branch correlation matrix corresponding to the changed element and a diagonal matrix composed of branch admittance parameters;

According to the node-branch correlation matrix corresponding to the change element and the diagonal matrix composed of the branch admittance parameters, the first network equation describing the state of the power transmission network and the corresponding first sparse before the change according to the state of the power transmission network On the basis of the matrix, the second network equation describing the state of the power transmission network after the state of the power transmission network changes and the corresponding second sparse matrix are obtained.

Further, the obtaining the compensation vector according to the second network equation specifically includes:

Transforming the second network equation by using the matrix inversion auxiliary theorem to obtain the expression of the second sparse matrix;

Comparing and analyzing the expression of the second sparse matrix and the expression of the first sparse matrix to obtain the compensation vector.

Further, using the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix specifically includes:

Using the compensation vector to perform post-compensation, pre-compensation or mid-compensation on the previous generation back-substitution process of the first sparse matrix.

Further, the post-compensation of the previous generation back-substitution process of the first sparse matrix by using the compensation vector specifically includes:

After the calculation process of previous generation and back generation on the first sparse matrix is completed, matrix correction is performed on the first sparse matrix by using the compensation vector.

Further, using the compensation vector to perform pre-compensation on the previous generation back-substitution process of the first sparse matrix specifically includes:

Before the previous generation calculation in the previous generation back generation calculation process is performed on the first sparse matrix, the compensation vector is used to perform matrix correction on the first sparse matrix.

Further, the mid-compensation of the previous generation back-substitution process of the first sparse matrix by using the compensation vector specifically includes:

Before performing previous generation calculation and back generation calculation on the first sparse matrix in the previous generation back calculation process, the compensation vector is used to perform matrix correction on the first sparse matrix.

On the other hand, an embodiment of the present invention provides a parallel solution system for a sparse matrix of a power system based on matrix correction, and the system includes:

The acquiring module is configured to acquire the second network equation describing the state of the power transmission network after the state of the power transmission network changes and the corresponding second sparse matrix according to the first network equation describing the state of the power transmission network before the state of the power transmission network changes sparse matrix;

The compensation module is configured to obtain a compensation vector according to the second network equation, and use the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix to obtain the second sparse matrix.

In the third aspect, the embodiment of the present invention provides a parallel solution device for sparse matrix of power system based on matrix correction, including:

at least one processor; and

at least one memory communicatively coupled to the processor, wherein:

The memory stores program instructions that can be executed by the processor, and the processor can execute the above method by calling the program instructions.

In a fourth aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium, where the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the above method.

An embodiment of the present invention provides a parallel solution method and system for a sparse matrix of a power system based on matrix correction. The method includes: according to the first network equation describing the state of the power transmission network before the state of the power transmission network changes and the corresponding first sparse matrix, Obtain the second network equation describing the state of the transmission network and the corresponding second sparse matrix after the state of the transmission network is changed; obtain a compensation vector according to the second network equation, and use the compensation vector to the first sparse matrix The previous generation back-substitution process performs matrix correction to obtain the second sparse matrix. By using the existing information to calculate the result of the change of the power system network structure, the calculation amount is reduced and the solution efficiency is greatly improved.

Description of drawings

Fig. 1 is a flow chart of a parallel solution method for a sparse matrix of a power system based on matrix correction provided by an embodiment of the present invention;

Fig. 2 is a structural block diagram of a power system sparse matrix parallel solution system based on matrix correction provided by an embodiment of the present invention;

Fig. 3 is a schematic structural diagram of a parallel solving device for a sparse matrix of a power system based on matrix correction provided by an embodiment of the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are the Some, but not all, embodiments are invented. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Fig. 1 is a flow chart of a parallel solution method for a sparse matrix of a power system based on matrix correction provided by an embodiment of the present invention. As shown in Fig. 1, the method includes:

S1. According to the first network equation describing the state of the power transmission network and the corresponding first sparse matrix before the state of the power transmission network is changed, obtain the second network equation and the corresponding second sparse matrix describing the state of the power transmission network after the state of the power transmission network is changed;

S2. Obtain a compensation vector according to the second network equation, and use the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix to obtain the second sparse matrix.

In the above embodiment, according to the first network equation describing the state of the power transmission network and the corresponding first sparse matrix before the state of the power transmission network changes, the second network equation describing the state of the power transmission network after the state of the power transmission network changes and the corresponding The second sparse matrix, specifically includes:

After the state of the power transmission network is changed, obtain a node-branch correlation matrix corresponding to the changed element and a diagonal matrix composed of branch admittance parameters;

According to the node-branch correlation matrix corresponding to the change element and the diagonal matrix composed of the branch admittance parameters, the first network equation describing the state of the power transmission network and the corresponding first sparse before the change according to the state of the power transmission network On the basis of the matrix, the second network equation describing the state of the power transmission network after the state of the power transmission network changes and the corresponding second sparse matrix are obtained.

In the above embodiment, the obtaining the compensation vector according to the second network equation specifically includes:

Transforming the second network equation by using the matrix inversion auxiliary theorem to obtain the expression of the second sparse matrix;

Comparing and analyzing the expression of the second sparse matrix and the expression of the first sparse matrix to obtain the compensation vector.

Specifically, for the network equation

where Y is the node admittance matrix of the system, Inject current vectors for nodes, is the node voltage vector. When the network structure or parameters change slightly while the injected current remains unchanged, the new network equation becomes:

Among them, ΔY represents the change of the nodal admittance matrix of the system, is the corresponding node voltage. In formula (2), the generation of ΔY is generally caused by the addition, removal or parameter changes of components in power network analysis, which can be described by the node-branch correlation matrix as:

Among them, δy is a square matrix of order m, which is usually a diagonal matrix composed of branch admittance parameters, and M is a sparse matrix of order n×m, which represents the node-branch correlation matrix corresponding to the variable element.

Using the matrix inversion auxiliary theorem, formula (3) can be reduced to:

in:

c＝(δy ^-1 + M ^T Y ^-1 M) ^-1 (5)

Among them, the matrix inversion auxiliary theorem is also called the Householder formula, which gives the calculation formula of the new matrix inverse when the matrix changes locally.

For n-order non-singular matrix A, when it changes

In formula (6), is the changed matrix, M and N are n×m order matrices, a is m order non-singular matrix, m≤n, there are:

The condition is: (a ^-1 + N ^T A ^-1 M) is reversible. If the inverse A ^-1 of the original matrix A is known, the changed matrix can be calculated on the basis of A ^-1 according to formula (7) inverse of.

In the above embodiment, the use of the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix specifically includes:

Using the compensation vector to perform post-compensation, pre-compensation or mid-compensation on the previous generation back-substitution process of the first sparse matrix.

Further, the post-compensation of the previous generation back-substitution process of the first sparse matrix by using the compensation vector specifically includes:

After the calculation process of previous generation and back generation on the first sparse matrix is completed, matrix correction is performed on the first sparse matrix by using the compensation vector.

Further, using the compensation vector to perform pre-compensation on the previous generation back-substitution process of the first sparse matrix specifically includes:

Before the previous generation calculation in the previous generation back generation calculation process is performed on the first sparse matrix, the compensation vector is used to perform matrix correction on the first sparse matrix.

Further, the mid-compensation of the previous generation back-substitution process of the first sparse matrix by using the compensation vector specifically includes:

Before performing previous generation calculation and back generation calculation on the first sparse matrix in the previous generation back calculation process, the compensation vector is used to perform matrix correction on the first sparse matrix.

Specifically, in order to realize the compensation calculation of the matrix, there are the following modes according to the order of calculating the compensation amount.

1. Post-compensation

After compensation, first calculate the solution of the original matrix Then calculate the compensation amount for the solution vector The calculation mode is as follows

2. Pre-compensation

Precompensation first computes the compensation for the right-hand term Then use the compensated right-hand term To solve the matrix, the calculation mode is

3. Medium compensation

The compensation process of mid-compensation is between the previous generation and the back generation.

For the matrix Y that has completed the LU decomposition, set

Y=LU (10)

In formula (10), L is the lower triangular matrix, and U is the unit upper triangular matrix.

Then the calculation mode of the compensation is:

in, is the solution vector obtained by the previous generation, for right the amount of compensation, is the solution vector of the previous generation after compensation.

In the above embodiment, the specific implementation process of the algorithm is as follows:

1. Calculation cost analysis of the modified algorithm

The three compensation methods all need to perform a complete previous-generation back-substitution solution for the entire matrix, and the only difference is the timing of compensation application during the solution process.

For the post-compensation, the calculation of the compensation vector needs to calculate Y ^-1 M, that is, take M as the right-hand item and Y as the coefficient to perform a forward-backward solution. Among them, the previous generation process is performed on the sparse vector M, while the back generation needs to be performed on the dense vector generated by the previous generation.

For the front compensation, the calculation of the compensation vector needs to be calculated M ^T Y ^-1 , that is, M is the right-hand term, and Y ^T is the coefficient to perform a previous generation and back generation solution. The sparsity of the solution process is similar to postcompensation, but further analysis of the data-dependent structure of Y ^T is required when Y is asymmetric.

For the medium compensation, the calculation of the compensation vector needs to calculate L ^-1 M and M ^T U ^-1 , that is, take M as the right-hand term and use Y as the coefficient to perform a previous generation solution; use M as the right-hand term and Y ^T as the coefficient to perform a calculation Back to solve. For the medium compensation, the two solutions are sparse vector previous generation and back generation, so the calculation amount is minimal. When Y is a symmetric matrix, the sparse previous generation process can be further omitted by LDL decomposition.

2. Sparse vector front-generation back-substitution algorithm

For previous generations of sparse vectors, the result is generally a dense vector. Therefore, in the process of solving, only the sparse right-hand item needs to be stored sparsely, and the solution vector can be directly stored sequentially in a dense manner.

2.1. Storage of sparse vectors

For the storage of sparse vectors, you can simply use two arrays, where idx stores the position of the non-zero element, and val stores the value corresponding to the non-zero element. In addition, there should be a variable nnz to store the non-zero the number of dollars. In order to find the non-zero elements in it, normalization processing is generally performed, that is, the indexes stored in idx are arranged in strict ascending order.

2.2 Sparse vector previous generation and back generation without using DAG

When the number of calculations required is small, the DAG analysis can be omitted and the solution can be performed directly. At this time, not only can solve by row unit, but also can solve by column. In units of rows, without using the DAG solution method, it is only necessary to skip the non-zero elements in the solution process.

To use the column-priority method to solve, the coefficient matrix should be stored in the column-priority manner first, that is, use the CSC format. Its implementation is similar to CSR, except that when arranging non-zero elements, it is performed in column-first order, and the stored index is changed to colPtr and rowIdx. In particular, the transpose of a matrix is equivalent to treating its CSR storage as CSC storage without recomputation.

2.3. Using DAG's sparse vector previous generation and back generation

When DAG analysis is not used, the iteration of the sparse vector starts from the first non-zero element, but because it is impossible to judge the injection of non-zero elements after that, each row must be iterated after that, and the average calculation cost is the same as that of the complete previous iteration. generation quite.

In the case that the matrix structure has been analyzed, the nodes that need to be solved can be analyzed according to the structure of the matrix and the position of the non-zero element of the right-hand item.

For a node i, it needs to be solved if and only if it has at least one parent node that needs to be solved. We can use the depth-first search method to determine the node to be solved from the non-zero node of the right-hand item.

An embodiment of the present invention provides a parallel solution method for a sparse matrix of a power system based on matrix correction, including: obtaining the transmission network according to the first network equation describing the state of the transmission network before the state of the transmission network changes and the corresponding first sparse matrix After the state is changed, describe the second network equation and the corresponding second sparse matrix of the state of the power transmission network; obtain the compensation vector according to the second network equation, and use the compensation vector to replace the previous generation of the first sparse matrix performing matrix correction to obtain the second sparse matrix. By using the existing information to calculate the result of the change of the power system network structure, the calculation amount is reduced and the solution efficiency is greatly improved.

FIG. 2 is a matrix correction-based power system sparse matrix parallel solution system provided by an embodiment of the present invention. The system includes: an acquisition module 201 and a compensation module 202 . in:

The acquiring module 201 is used to acquire the second network equation describing the state of the power transmission network after the change of the state of the power transmission network and the corresponding second sparse matrix according to the first network equation describing the state of the power transmission network and the corresponding first sparse matrix sparse matrix. The compensation module 202 is configured to obtain a compensation vector according to the second network equation, and use the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix to obtain the second sparse matrix.

Specifically, the function and operation process of each module in the matrix correction-based power system sparse matrix parallel solution system in the embodiment of the present invention is in one-to-one correspondence with the above-mentioned method embodiments, and will not be repeated here.

An embodiment of the present invention provides a parallel solution system for sparse matrix of a power system based on matrix correction, including: an acquisition module and a compensation module, the acquisition module is used to describe the first network equation and the corresponding state of the transmission network before the state of the transmission network changes The first sparse matrix is used to obtain the second network equation describing the state of the transmission network and the corresponding second sparse matrix after the state of the transmission network is changed; the compensation module is used to obtain a compensation vector according to the second network equation, and use the compensation Vector performs matrix correction on the previous generation and back substitution process of the first sparse matrix to obtain the second sparse matrix. By using the existing information to calculate the result of the change of the power system network structure, the calculation amount is reduced and the solution efficiency is greatly improved.

As shown in Figure 3, on the basis of the above-mentioned embodiments, the embodiment of the present invention also provides a parallel solution device for sparse matrix of power system based on matrix correction, including: at least one processor 301, at least one memory 302, communication interface 303 and bus 304; wherein, the processor 301, memory 302, and communication interface 303 complete mutual communication through the bus 304; the communication interface 303 is used for communication between the modeling equipment and the communication equipment of the display device Information transmission: the memory 302 stores program instructions executable by the processor 301, and the processor 301 invokes the program instructions to execute the method as described in FIG. 1 .

The above logic instructions in the memory 302 may be implemented in the form of software functional units and when sold or used as an independent product, may be stored in a computer-readable storage medium. Based on this understanding, the essence of the technical solution of the present invention or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including Several instructions are used to make a computer device (which may be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program codes. .

An embodiment of the present invention provides a non-transitory computer-readable storage medium, the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the methods provided in the above method embodiments, for example The method includes: according to the first network equation describing the state of the transmission network and the corresponding first sparse matrix before the state of the transmission network is changed, obtaining the second network equation and the corresponding second sparse matrix describing the state of the transmission network after the state of the transmission network is changed; Obtaining a compensation vector according to the second network equation, and using the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix to obtain the second sparse matrix.

Those of ordinary skill in the art can understand that all or part of the steps for realizing the above-mentioned method embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, the It includes the steps of the above method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other various media that can store program codes.

Through the above description of the implementations, those skilled in the art can clearly understand that each implementation can be implemented by means of software plus a necessary general hardware platform, and of course also by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of software products, and the computer software products can be stored in computer-readable storage media, such as ROM/RAM, magnetic discs, optical discs, etc., including several instructions to make a computer device (which may be a personal computer, server, or network device, etc.) execute the methods described in various embodiments or some parts of the embodiments.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be Modifications are made to the technical solutions described in the foregoing embodiments, or equivalent replacements are made to some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims (10)

1. A method for parallel solution of sparse matrix of electric power system based on matrix modification, it is characterized in that, described method comprises: According to the first network equation describing the state of the power transmission network and the corresponding first sparse matrix before the state of the power transmission network is changed, obtain the second network equation and the corresponding second sparse matrix describing the state of the power transmission network after the state of the power transmission network is changed; Obtaining a compensation vector according to the second network equation, and using the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix to obtain the second sparse matrix. 2. The method according to claim 1, characterized in that, according to the first network equation describing the state of the power transmission network before the state of the power transmission network changes and the corresponding first sparse matrix, the description of the power transmission network after the state of the power transmission network is changed is obtained The second network equation of the state and the corresponding second sparse matrix specifically include: After the state of the power transmission network is changed, obtain a node-branch correlation matrix corresponding to the changed element and a diagonal matrix composed of branch admittance parameters; According to the node-branch correlation matrix corresponding to the change element and the diagonal matrix composed of the branch admittance parameters, the first network equation describing the state of the power transmission network and the corresponding first sparse before the change according to the state of the power transmission network On the basis of the matrix, the second network equation describing the state of the power transmission network after the state of the power transmission network changes and the corresponding second sparse matrix are obtained. 3. The method according to claim 1, wherein said obtaining a compensation vector according to said second network equation specifically comprises: Transforming the second network equation by using the matrix inversion auxiliary theorem to obtain the expression of the second sparse matrix; Comparing and analyzing the expression of the second sparse matrix and the expression of the first sparse matrix to obtain the compensation vector. 4. The method according to claim 1, wherein said utilizing said compensation vector to perform matrix correction on the previous generation back-substitution process of said first sparse matrix, specifically comprises: Using the compensation vector to perform post-compensation, pre-compensation or mid-compensation on the previous generation back-substitution process of the first sparse matrix. 5. The method according to claim 4, wherein said utilizing said compensation vector to carry out post-compensation to the previous generation back-substitution process of said first sparse matrix, specifically comprises: After the calculation process of previous generation and back generation on the first sparse matrix is completed, matrix correction is performed on the first sparse matrix by using the compensation vector. 6. according to the described method of claim 4, it is characterized in that, described using described compensation vector to carry out pre-compensation to the previous generation back-substitution process of described first sparse matrix, specifically comprises: Before the previous generation calculation in the previous generation back generation calculation process is performed on the first sparse matrix, the compensation vector is used to perform matrix correction on the first sparse matrix. 7. The method according to claim 4, wherein said using said compensation vector to compensate in the previous generation back-substitution process of said first sparse matrix, specifically comprises: Before performing previous generation calculation and back generation calculation on the first sparse matrix in the previous generation back calculation process, the compensation vector is used to perform matrix correction on the first sparse matrix. 8. A power system sparse matrix parallel solution system based on matrix correction, characterized in that the system includes: The acquiring module is configured to acquire the second network equation describing the state of the power transmission network after the state of the power transmission network changes and the corresponding second sparse matrix according to the first network equation describing the state of the power transmission network before the state of the power transmission network changes sparse matrix; The compensation module is configured to obtain a compensation vector according to the second network equation, and use the compensation vector to perform matrix correction on the previous generation back-substitution process of the first sparse matrix to obtain the second sparse matrix. 9. A power system sparse matrix parallel solution device based on matrix correction, characterized in that it includes: at least one processor; and at least one memory communicatively coupled to the processor, wherein: The memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the method according to any one of claims 1 to 7. 10. A non-transitory computer-readable storage medium, characterized in that the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the computer according to any one of claims 1 to 7. described method.