The Method of Obtaining Power System Node Impedance Matrix Based on LDU Decomposition Based on Sparse Technology

Abstract

The invention discloses a method for calculating a nodal impedance matrix Z of a power system based on a sparse symmetric matrix technology by virtue of improved LDU triangular decomposition, and belongs to the field of analytical calculation of power systems. The method comprises the following steps of reading a data file; forming a nodal admittance matrix Y; performing LDU triangular decomposition on the matrix Y to calculate, L, D and U factor matrixes according to symmetry and sparsity; only calculating an element hkk according to DHk=Ek; calculating a diagonal element Zkk of a Zk matrix and elements above the diagonal element Zkk according to the element sparsity of the U matrix; calculating elements on the left of the element Zkk according to symmetry; writing Z matrix data into the data file. According to the method, LDU triangular decomposition is performed on the matrix Y by virtue of a process method according to symmetry and sparsity, so that the triangular decomposition speed is greatly increased; structural characteristics of a unit matrix E are utilized, the calculation of the elements in the U matrix is eliminated, only the hkk element is calculated according to DHk=Ek, and the sparsity of the elements of the U matrix is used for solving the equation UZk=Hk, so that the back substitution solving speed is greatly increased; when the method is used for checking IEEE-30, -57 and -118 node systems, the calculation speed of the method can be increased by about 84 to 98 percent compared with that of a conventional 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 to obtain the node impedance matrix Z. But in fact, the traditional method does not consider the symmetry and sparsity of L and U array elements in the process of triangular decomposition, and does not consider the use of the characteristics of the structure of E array elements and the sparsity of U array elements in the process of back substitution, so that Computational efficiency is greatly reduced. [0003] When the traditional LDU triangular decomposition method performs triangular decomposition on the Y array, each element is formed in one step by calculation formula in the form of "┘" (reverse L) or in the form of "row" (referred to as the formula method). Therefore...

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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 especially bad for data processing in symmetric matrices

In fact, these storage methods are mainly to reduce the storage unit, and there is no special advantage in simplifying the storage process or increasing the storage speed.

Moreover, these storage methods are mainly used in the Gaussian elimination method, and are difficult to be used in the triangular decomposition method of the formula method.

And because the traditional sparse matrix technology generally does not consider the characteristics of the matrix element structure to store non-zero elements, the above storage method cannot take advantage of the symmetry and sparseness of the L, U factor matrix elements when using the formula method to perform LDU triangular decomposition. Sex and other characteristics

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