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...

Examples

Embodiment 1

[0048] Taking Formula 1 as an example, the definition of elements in the method of the present invention and the application of the symmetric sparsity technology are illustrated.

[0049] assuming l 31 ≠0, then for d 11 l under the element 31 Element to be eliminated. first define d 11 elements are diagonal elements, d 11 all u on the right 1j elements are defined as cross elements, l 31 element is defined as an elimination element, then l 31 All elements to the right are defined as computed elements.

[0050] (1) If element sparsity is not considered in the process of element elimination, it is necessary to calculate l in steps 31 All computed elements to the right of the element l 32 、d 33 , u 34 .

[0051] (2) If sparsity technology is used, only step-by-step calculation of l 31 The line on the right side of the element and the non-zero u 1j All computed elements whose columns intersect, including l 32 、d 33 , u 34 Elements (need to consider l on the left o...

Embodiment 2

[0055] Taking the n×n order node system as an example, the difference between the traditional LDU triangular decomposition method and the method of the present invention for solving Z matrix elements is compared. The comparison results are shown in Table 1.

[0056] The comparison of the traditional LDU triangular decomposition method of table 1 and the method of the present invention for solving the Z matrix element process

[0057]

[0058] It can be seen from Table 1 that:

[0059] (1) When forming the factor array of traditional LDU by the formula method, all elements of the L, D, U arrays need to be solved, and the symmetry and sparseness of the elements themselves cannot be utilized; and the method of the present invention utilizes the symmetric sparse matrix technology, and only needs Solve a small number of non-zero elements of U array and D array elements, and a small amount of non-zero elements of L array can be obtained from U array elements according to symmetr...

Embodiment 3

[0066] Using the traditional LDU triangular decomposition method ( figure 1 ), and the inventive method ( figure 2 ) Calculate the elements of the Z matrix for the Y matrix of the IEEE-30, -57, -118 node system, and compare the average calculation time of the processes of "decomposition", "regeneration" and "decomposition+regeneration". The calculation results are shown in Table 2.

[0067] Table 2 The traditional method and the method of the present invention are compared in the process time of "decomposition", "back generation" and "decomposition+back generation"

[0068]

[0069] (1) The average iteration time of the "decomposition" process:

[0070] T 1 : Traditional methods do not consider symmetric sparsity and do not use u ij = l ji properties, calculate all elements;

[0071] T 2 : the method of the present invention considers symmetric sparsity, only calculates D array elements and a small amount of U array non-zero elements, and records its position, utili...

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...

Examples

Embodiment 1

[0048] Taking Formula 1 as an example, the definition of elements in the method of the present invention and the application of the symmetric sparsity technology are illustrated.

[0049] assuming l 31 ≠0, then for d 11 l under the element 31 Element to be eliminated. first define d 11 elements are diagonal elements, d 11 all u on the right 1j elements are defined as cross elements, l 31 element is defined as an elimination element, then l 31 All elements to the right are defined as computed elements.

[0050] (1) If element sparsity is not considered in the process of element elimination, it is necessary to calculate l in steps 31 All computed elements to the right of the element l 32 、d 33 , u 34 .

[0051] (2) If sparsity technology is used, only step-by-step calculation of l 31 The line on the right side of the element and the non-zero u 1j All computed elements whose columns intersect, including l 32 、d 33 , u 34 Elements (need to consider l on the left o...

Embodiment 2

[0055] Taking the n×n order node system as an example, the difference between the traditional LDU triangular decomposition method and the method of the present invention for solving Z matrix elements is compared. The comparison results are shown in Table 1.

[0056] The comparison of the traditional LDU triangular decomposition method of table 1 and the method of the present invention for solving the Z matrix element process

[0057]

[0058] It can be seen from Table 1 that:

[0059] (1) When forming the factor array of traditional LDU by the formula method, all elements of the L, D, U arrays need to be solved, and the symmetry and sparseness of the elements themselves cannot be utilized; and the method of the present invention utilizes the symmetric sparse matrix technology, and only needs Solve a small number of non-zero elements of U array and D array elements, and a small amount of non-zero elements of L array can be obtained from U array elements according to symmetr...

Embodiment 3

[0066] Using the traditional LDU triangular decomposition method ( figure 1 ), and the inventive method ( figure 2 ) Calculate the elements of the Z matrix for the Y matrix of the IEEE-30, -57, -118 node system, and compare the average calculation time of the processes of "decomposition", "regeneration" and "decomposition+regeneration". The calculation results are shown in Table 2.

[0067] Table 2 The traditional method and the method of the present invention are compared in the process time of "decomposition", "back generation" and "decomposition+back generation"

[0068]

[0069] (1) The average iteration time of the "decomposition" process:

[0070] T 1 : Traditional methods do not consider symmetric sparsity and do not use u ij = l ji properties, calculate all elements;

[0071] T 2 : the method of the present invention considers symmetric sparsity, only calculates D array elements and a small amount of U array non-zero elements, and records its position, utili...

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