Method for solving nodal impedance matrix of electric system on basis of triangular decomposition method of A=LDU

Abstract

The invention discloses a method for solving a nodal impedance matrix of an electric system on the basis of a triangular decomposition method of A=LDU, and belongs to the field of analysis and computation of the electric system. The method comprises the main following steps of: forming the nodal impedance matrix Y, and carrying out LDU triangular decomposition on the matrix Y; solving hkk elements by using an equation of DHk=Wk(Ek); solving diagonal elements Zkk and off-diagonal elements above the diagonal elements Zkk of a matrix Zk for UZk=Hk; solving off-diagonal elements at the left of the diagonal element Zkk according to the symmetry; writing data of a matrix Zk to a data file. The method disclosed by the invention has the advantages that the computation of the matrix W is omitted by mainly utilizing the structural characteristics of a matrix Ek of a unit matrix E, the computation sequence of elements in the matrix Zk and the symmetry of the elements of the matrix E, the computation to a matrix H is simplified into computation to diagonal elements hkk, the computation of 50% off-diagonal elements can be omitted for the matrix Z, and the computation speed of the elements of the matrix Z is greatly increased. Compared with the traditional LDU triangular decomposition method, the method disclosed by the invention has the advantage that by carrying out checking on node systems such as IEEE-57, IEEE-118 and IEEE-300, the computation speed can be increased by about 35-45%.

Description

technical field [0001] The invention belongs to the field of power system analysis and calculation, and relates to a method for solving the node impedance matrix of the power system. 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 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. After the LDU triangular decomposition of the Y array, a The solution to the n×n order Z matrix elements is divided into n column matrix Z k element solution. [0003] However, the traditional LDU triangular decomposition method does not...

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Problems solved by technology

[0003] However, the traditional LDU triangular decomposition method does not consider the symmetry of the elements of the Z array in the process of solving the elements of the Z array, so it is necessary to calculate all the elements of the Z array, which requires a large amount of calculation and a long calculation time

In addition, E in the identity matrix E is not used k The structural characteristics of the array and the Z k The calculation order of the array elements must solve the three equations after the LDU triangular decomposition, so the actual calculation time is not ideal

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