Method for solving node impedance matrix of electric system on basis of Gaussian elimination method of sparse symmetric matrix technology

Abstract

The invention belongs to the field of power system analysis and computing and discloses a method for solving a node impedance matrix of an electric system on the basis of a Gaussian elimination method of a sparse symmetric matrix technology. The method mainly comprises the following steps that a node admittance matrix Y is formed; the matrix Y and a matrix En form an augmented matrix Bn=[YEn]; elimination is carried out on the matrix Bn according to the spare symmetry to obtain Bn(n-1)'=[Y(n-1)'En(n-1)']; according to Y(n-1)'Zn=En(n-1)', sparseness and symmetry, elements above and on the left of a diagonal element Znn of a matrix Zn are solved; a matrix Y(k-1)' is obtained according to the Y(n-1)'; elements above and on the left of a diagonal element Zkk of the matrix Zk are obtained according to Y(k-1)'Zk=Ek(k-1)', sparseness and symmetry. By the utilization of the symmetric sparseness, all invalid computation of the previous generation process is avoided, and computation of about 50% of nonzero elements is reduced; by the utilization of the characteristics of the E matrix element structure and the sparseness of upper triangle elements, the elements of the matrix Zk are obtained in a back substitution mode according to a symmetry mode, and back substitution computation is greatly accelerated. The method can check IEEE-30, -57 and -118 node systems and the like, and the computation speed for the IEEE-118 node system can be improved by 96-97% compared with a traditional Gaussian elimination method and an LDU triangular decomposition method.

Description

technical field [0001] The invention belongs to the field of power system analysis and calculation, and relates to a method for obtaining the node impedance matrix of the power system. Background technique [0002] In the power system, the traditional LDU triangular decomposition method is generally used, and some literatures also introduce the non-normalized Gaussian elimination method to obtain the node impedance matrix Z. When these two methods solve the Z matrix, the solution to the n*n order Z matrix is ​​generally converted into n Z k Array (Z 1 ~ Z n ) for the solution of the entire column of elements, the symmetry of the elements of the Z array is not used for calculation, that is, only Z is not calculated k Diagonal element Z in the array kk and above element Z k-1,k ~ Z 1k , and then according to Z k-1,k ~ Z 1k Directly get the element Z to the left of the diagonal element k,k-1 ~ Z k1 . Thus computing the entire column Z k array element way to calculat...

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Problems solved by technology

Although these storage methods can save a lot of storage units, the calculation speed has not reached the optimal effect, and the structure of these storage methods is complex, and the storage of diagonal elements and non-diagonal elements separately also makes the access process cumbersome. , which is not conducive to the processing of data in symmetric matrices

In fact, these storage methods are mainly to reduce the storage unit, which has no advantage in simplifying the calculation process or increasing the calculation speed.

Moreover, these storage methods are mainly used in the Gaussian elimination method, and the application in the triangular decomposition method is more complicated.

And because the traditional sparse matrix technology generally does not consider the characteristics of the matrix element structure to store non-zero elements, it needs to form another storage matrix, so the principle is complicated and the calculation speed is slow

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