LR triangular decomposition method based on symmetric sparse matrix technology and non-zero element random storage

Abstract

The invention provides an LR triangular decomposition method based on a symmetric sparse matrix technology and non-zero element random storage, and belongs to the field of power system analysis and calculation. The method mainly comprises the following steps: writing Y-matrix Y (n, d) data file data stored according to a random sequence into an LR (n, d) array; obtaining a reciprocal of the diagonal element rii in the ith row, and assigning elements such as lij in the fourth column to the fifth column in the ith row of non-diagonal element group at a time according to the column proportion according to the elements such as rij in the first column to the third column in the ith row of non-diagonal element group; determining a calculation element r and a storage mode thereof according to thediagonal element, the non-zero cross element and the non-zero elimination element; calculating an element r step by step by using a quadrangle rule; solving diagonal elements zkk and elements above zkk in the Z'k matrix according to an RZ'k = E'k equation; obtaining elements on the left of zkk according to symmetry; and writing the Z matrix data into a data file. For an IEEE-300 node system, compared with a traditional LR decomposition method, the method has the advantages that the data file reading time, the LR decomposition time and the LR decomposition + back substitution time are about 5.75%, 2.16% and 6.83% and are all reduced along with increase of the system scale.

Description

technical field [0001] The invention relates to analysis and calculation in the field of power system engineering, and mainly relates to an LR triangular decomposition method based on a symmetrical sparse matrix technology and random storage of non-zero elements, and is applied to obtain a node impedance matrix. Background technique [0002] There are mainly three triangular decomposition methods widely used in power system analysis and calculation, power flow calculation, active and reactive power optimization, etc. to solve constant coefficient equations, including LR, CU, and LDU. In practical applications, the LDU decomposition method is mostly used. However, in the calculation process, the number of elements involved in the calculation of l and r elements required by the LR decomposition method to form the factor matrix is ​​relatively small, and only n intermediate matrices W need to be solved k . However, the LDU decomposition method needs to calculate the number of ...

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Problems solved by technology

And since it seeks W k 、H k The array does not take advantage of the structural characteristics of the E array elements, which increases a large number of redundant calculations; also because it calculates the Z k The order of the array is Z 1 ~ Z n , get Z k The order of array elements is z nk ~z 1k , so although the symmetry of the Z matrix elements is well known, it is difficult to use the symmetry of the Z matrix elements in this calculation method

These factors also greatly affect the calculation speed of the LDU decomposition method to obtain the Z matrix.

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