CN104239280A - Method for quickly solving nodal impedance matrix of power system - Google Patents

Abstract

The invention provides a method for quickly solving a nodal impedance matrix of a power system, and relates to the field of analytical computation of the power system. The method mainly comprises the following steps of inputting data of a nodal admittance matrix Y; establishing an augmented matrix B by the nodal admittance matrix Y and an identity matrix E together; normalizing the augmented matrix B and carrying out a Gauss-Jordan elimination method on the augmented matrix B for n times; obtaining an inverse matrix Z. At present, traditional methods for solving the nodal impedance matrix comprise an LDU (Logic Data Unit) triangular decomposition method and a Gauss elimination method, and compared with the two traditional methods, the novel method for quickly solving the nodal impedance matrix by utilizing the Gauss-Jordan elimination method, provided by the invention, has the advantages that the principle is simple and easy to understand, the computation time is reduced, the programming is convenient, and the like; compared with the traditional LDU triangular decomposition method and the Gauss elimination method, by utilizing the method for verifying systems such as an IEEE-57 node, an IEEE-118 node and an IEEE-300 node, the computation speeds can be respectively increased by about 25%-50%.

Description

A kind of method of rapid solving electric system nodal impedance matrix

Technical field

The present invention relates to Electrical power system analysis and computing field, relate generally to a kind of computing method asking for nodal impedance matrix fast.

Background technology

In Electrical power system analysis and computing, often nodal impedance matrix can be used, conventional LDU triangle decomposition method and Gaussian elimination method solution node impedance matrix in classic method.

Various triangle decomposition method is all similar to factor table method, compares and is suitable for repeatedly solving of matrix of coefficients invariant equatian.Many documents are all introduced and are solved Y inverse of a matrix matrix Z, mainly for converting to Z to solving of Z matrix by LDU triangle decomposition method _ksolving of matrix.Due to triangle decomposition method computing formula all with Gaussian elimination computing formula tight association, if do not consider repeatedly solving (in most cases onlying demand 1 inverse matrix) for multiple inverse matrix Z, triangle decomposition method in principle simple not as Gaussian elimination method directly, computing velocity is fast, more can not than desirable containing normalized Gauss-Jordan Elimination.Just calculate (calculation flow chart is shown in Fig. 1) owing to generally not relating to normalization when traditional Gaussian elimination method is used for solving inverse matrix, and LDU triangle decomposition method includes normalization calculating (calculation flow chart is shown in Fig. 2), therefore LDU triangle decomposition method is not than faster containing normalized Gaussian elimination method computing velocity.So more document when inverse matrix is asked in introduction by LDU triangle decomposition method, instead of Gaussian elimination method.But all there is principle complexity in traditional LDU triangle decomposition method and Gaussian elimination method, the problems such as computing time is long.

(1) Gaussian elimination method or LDU triangle decomposition method ask for the mode of inverse matrix

YZ＝ZY＝E (1)

Can obtain according to above formula

YZ _k＝E _k (k＝1,2,……,n)(2)

The mode that traditional Gaussian elimination method or LDU triangle decomposition method ask for inverse matrix is with formula (2), namely by asking for the Z of 1st ~ n row _kmatrix obtains Z matrix, instead of simultaneously completely obtains whole Z matrix.Because LDU triangle decomposition method calculates containing normalization, therefore LDU triangle decomposition method has the advantage in obvious computing velocity compared with Gaussian elimination method.Calculation flow chart is shown in Fig. 1 and Fig. 2 respectively.

Summary of the invention

The object of this invention is to provide a kind of rapid solving electric system nodal impedance matrix new method, the computing velocity in Electrical power system analysis and computing can have been improved.

The present invention is achieved by the following technical solutions.

First bus admittance matrix and unit matrix are formed special augmented matrix, carry out containing normalized Gauss-Yue when disappearing unit this augmented matrix more afterwards, can obtain the last solution of equation, its basic step is as follows:

Step 1: input node admittance matrix data;

Step 2: bus admittance matrix Y battle array, unit square formation E battle array build augmented matrix B=[Y E];

Step 3: to the normalization of B battle array and n Gauss-Yue when disappear first must B ⁽ⁿ⁾"=[E E ⁽ⁿ⁾"];

Step 4: obtain inverse matrix Z=E ⁽ⁿ⁾";

Step 5: Output rusults.

To augmented matrix B carry out n time containing normalized Gauss-Yue when after the new matrix E that obtains ⁽ⁿ⁾" be nodal impedance matrix Z.

In step 2 of the present invention, different from the mode of traditional LDU triangle decomposition method and Gaussian elimination method finding the inverse matrix.The augmented matrix formed in classic method forward steps is B=[Y E _k], then rows ofly ask for Z _kmatrix.The present invention utilizes the Computing Principle of Gauss-Jordan Elimination to form special augmented matrix B=[Y E] to the matrix of required inverse matrix and unit matrix, can directly obtain complete inverse matrix Z after the unit that disappears completes, and without backward steps.

In step 3 of the present invention and step 4, the special augmented matrix B formed is carried out containing normalized Gauss-Yue when obtaining B after the unit that disappears ⁽ⁿ⁾"=[Y ⁽ⁿ⁾" E ⁽ⁿ⁾"].Now Y battle array becomes n rank unit square formation Y ⁽ⁿ⁾", and n rank unit square formation E becomes n rank square formation E ⁽ⁿ⁾" battle array, E ⁽ⁿ⁾" battle array is exactly required nodal impedance matrix Z.

Because whole Z matrix of the present invention is tried to achieve simultaneously, therefore without the need to the LDU triangle decomposition method repeatedly solved mainly for equation with constant coefficient and counting yield lower not containing normalized Gaussian elimination method.Therefore the present invention can rapid solving nodal impedance matrix, and principle is simple, and programming is convenient.With the present invention to IEEE-57 ,-118, the system such as-300 nodes calculates, compare with the method for Gaussian elimination method finding the inverse matrix with traditional LDU triangle decomposition method, computing velocity can improve about 25 ~ 50% (see embodiments 1) respectively.

A kind of rapid solving electric system nodal impedance matrix new method that the present invention proposes, make use of the advantage of Gauss-Jordan Elimination in computing velocity, forms special augmented matrix and the unit that disappears to inverted matrix and unit matrix.Different from the mode of traditional LDU triangle decomposition method and Gaussian elimination method finding the inverse matrix, not rows of ask for Z _kmatrix, but solve whole Z matrix simultaneously, namely the present invention directly uses formula (1) instead of asks for inverse matrix by formula (2), and without backward steps.These features determine the speed advantage of this method.Calculation flow chart sees Fig. 3.

When asking for 1 inverse matrix Z, the computing velocity of Gauss-Jordan Elimination is not only better than Gaussian elimination method, is better than LDU triangle decomposition method too.

Accompanying drawing explanation

Fig. 1 Gaussian elimination method asks for the inverse matrix Z calculation flow chart of bus admittance matrix Y

Fig. 2 LDU triangle decomposition method asks for the inverse matrix Z calculation flow chart of bus admittance matrix Y

Fig. 3 the present invention asks for the inverse matrix Z calculation flow chart of bus admittance matrix Y

Embodiment

The present invention will be described further by following examples.

The present invention relates to a kind of new method of rapid solving electric system nodal impedance matrix, compared greatly can improve computing velocity with the method for traditional Gaussian elimination method with LDU triangle decomposition method solution node impedance matrix.The present invention also can be applicable to the inverse matrix asking for system of linear equations matrix of coefficients in Electrical power system analysis and computing fast.

Bus admittance matrix Y and whole unit matrix E is formed special augmented matrix by the present invention, and carry out containing normalized Gauss-Yue when disappearing unit this augmented matrix afterwards, the unit that disappears terminates the last solution that directly can obtain equation.

Y battle array is become special augmented matrix B=[Y E] with E formation, B battle array is unfolded as follows.

Constant term matrix F only 1 column element in traditional B battle array, and the constant term matrix E herein in B battle array has n column element.

Formula (3) is carried out containing normalized Gauss-Yue when B battle array after the unit that disappears becomes B ⁽ⁿ⁾" battle array.

Formula has Y in (4) ⁽ⁿ⁾"=E, namely contain normalized Gauss-Yue when after the unit that disappears through n time, Y matrix becomes n rank unit square formation E from n rank square formation, and E battle array becomes n rank square formation E from n rank unit matrix ⁽ⁿ⁾".Now, B ⁽ⁿ⁾" equation of battle array correspondence is Y ⁽ⁿ⁾" Z=E ⁽ⁿ⁾", with formula (1) with separating.And due to Y ⁽ⁿ⁾" therefore=E can obtain Z=E ⁽ⁿ⁾".

Therefore can obtain conclusion: the augmented matrix B=[Y E] that Y battle array and E battle array are formed carry out containing normalized Gauss-Yue when after the unit that disappears obtain new augmented matrix B ⁽ⁿ⁾" in E ⁽ⁿ⁾" battle array is exactly required Z matrix.

Embodiment 1.

To IEEE-57,118, the system such as-300 nodes carries out program calculation when not considering that element is openness, more traditional Gaussian elimination method, LDU triangle decomposition method and the present invention ask for the computing time of the inverse matrix Z of bus admittance matrix Y.Result of calculation is as shown in table 1.

The computing time that the various computing method of table 1 ask for the inverse matrix Z of Y battle array compares

As can be seen from Table 1, for IEEE-300 node system, although containing normalized LDU triangle decomposition method than not containing the computing velocity of normalized Gaussian elimination method fast about 25%, the present invention is respectively than the computing velocity respectively fast about 30 ~ 50% of traditional LDU triangle decomposition method and Gaussian elimination method.Upper table this suffice to show that advantage place of the present invention.

The present invention can adopt any one programming language and programmed environment to realize, and be adopt C++ programming language in the present embodiment, development environment is Visual C++.

Claims (1)

1. a method for rapid solving electric system nodal impedance matrix, is characterized in that according to the following steps:

Step 1: input node admittance matrix data;

Step 2: bus admittance matrix Y battle array, unit square formation E battle array build augmented matrix B=[Y E];

Step 3: to the normalization of B battle array and n Gauss-Yue when disappear first must B ⁽ⁿ⁾"=[E E ⁽ⁿ⁾"];

Step 4: obtain inverse matrix Z=E ⁽ⁿ⁾";

Step 5: Output rusults.