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Electric power system node impedance matrix Z solving method based on CU triangular decomposition

A technology of node impedance matrix and power system, applied in the direction of complex mathematical operations, etc., can solve the problems that are not conducive to the improvement of element calculation process, the symmetry of Z array elements is not considered, and the calculation efficiency of factor array is low.

Active Publication Date: 2015-05-27
NANCHANG UNIV
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  • Abstract
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  • Application Information

AI Technical Summary

Problems solved by technology

Through the analysis, it can be found that the formula method is not conducive to the improvement of the element calculation process
Therefore, the calculation efficiency of various traditional triangular decomposition methods to form factor arrays is very low
[0005] In addition, the general traditional LDU triangular decomposition method does not consider the symmetry of the elements of the Z matrix in the process of solving the elements of the Z matrix, so there are a lot of repeated calculations for the off-diagonal elements, so the calculation time is not ideal

Method used

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  • Electric power system node impedance matrix Z solving method based on CU triangular decomposition
  • Electric power system node impedance matrix Z solving method based on CU triangular decomposition
  • Electric power system node impedance matrix Z solving method based on CU triangular decomposition

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Embodiment 1

[0052] Taking the n×n order node system as an example, the calculation process of obtaining the entire Z matrix elements is compared with the traditional LDU triangular decomposition method and the method of the present invention. The comparison results are shown in Table 1.

[0053] The traditional LDU triangular decomposition method of table 1 and the method of the present invention solve the comparison of whole Z matrix element calculation process

[0054]

[0055] It can be seen from Table 1 that:

[0056] (1) The traditional LDU triangular decomposition method is to put a column of Z k All the array elements are solved, and the process can be decomposed into LW k =E k , DH k =W k , UZ k =H k Three equations are solved. Each of these three equations has n equations, and each equation needs to solve n variables, and the total number of calculated variables is 3n 2 , while there are 2 intermediate matrix variables.

[0057] (2) The method of the present inventio...

Embodiment 2

[0063] Using the traditional LDU triangular decomposition method ( figure 1 ), and the inventive method ( figure 2 ) Obtain the entire Z matrix for the Y matrix of IEEE-30, -57, -118 node systems, and compare the average calculation time in the process of "decomposition", "regeneration" and "decomposition+regeneration". The calculation results are shown in Table 2.

[0064] Table 2 Comparison of the average calculation time of the two methods for obtaining the entire Z-array elements of each IEEE system in the process of "decomposition", "back-substitution" and "decomposition + back-substitution"

[0065]

[0066] T 1 : The average iteration time of the "decomposition" process of the traditional LDU triangular decomposition method

[0067] T 2 : The average iteration time of the inventive method "decomposition" process

[0068] T' 1 : The average iteration time of the "back-substitution" process of the traditional LDU triangular decomposition method

[0069] T' 2 ...

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Abstract

The invention relates to an electric power system node impedance matrix Z solving method based on CU triangular decomposition and belongs to the field of electric power system analysis and computing. The method mainly includes the steps of forming a node admittance matrix Y; performing quick CU triangular decomposition on the matrix Y; solving a matrix Wk through CWk=Ek; solving non-diagonal elements of a diagonal element Zkk and the diagonal element above the diagonal element Zkk of a matrix Zk through UZk=Wk; solving non-diagonal elements on the left of the diagonal element Zkk in accordance with the symmetry; writing data of a matrix Z to a data file. According to the electric power system node impedance matrix Z solving method based on CU triangular decomposition, a CU triangular decomposition method higher in calculation efficiency than a LDU triangular decomposition method is used for solving elements of the matrix Z, the symmetrical relationship between elements of a matrix Y and elements of a matrix C and a matrix U is used for quickly forming a composite matrix of a factor matrix C and a factor matrix U, and the symmetry of the matrix Z and the calculation order of elements of the matrix Zk is used for omitting back substitution solving of lower triangular elements of the matrix Z for achieving direct solving, so that the speed of formation of the matrix Z is greatly improved. Compared with the traditional LDU triangular decomposition method, the electric power system node impedance matrix Z solving method based on CU triangular decomposition has the calculation speed increased by about 33% when the method is used for IEEE-30, IEEE-57 and IEEE-118 node system checking calculation.

Description

technical field [0001] The invention belongs to the field of power system analysis and calculation, and relates to a method for obtaining a power system node impedance matrix based on CU triangular decomposition. Background technique [0002] The node impedance matrix Z is widely used in power systems and plays an important role. The traditional methods for solving the Z matrix include branch addition method, admittance matrix Y elimination element inversion method, LDU triangular decomposition method and so on. Among the commonly used traditional methods, the LDU triangular decomposition method has the fastest calculation speed, so it is used the most. Its characteristic is that it uses the triangular decomposition method suitable for solving constant coefficient linear equations. , a solution to n×n order Z matrix elements can be divided into n column matrix Z k element solution. [0003] In fact, among the various triangular decomposition methods, the A=LR or A=CU tria...

Claims

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Application Information

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IPC IPC(8): G06F17/16
Inventor 陈恳罗仁露席小青万新儒
Owner NANCHANG UNIV
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