Random Generation of Non-Zero Elements and Method of Forming Jacobian Matrix of Electric Power System

Abstract

The random generation of non-zero elements and the method of forming the Jacobian matrix of the power system relate to the field of power system analysis and calculation, and mainly include the following steps: establish a Y(n, d′) array that stores triangular non-zero elements on the Y array in random order partitions ; According to the line branch data i, j, r, x, k, respectively calculate the self-admittance and mutual admittance of the node, and then accumulate S according to the relationship between the column number j and m 1i or S 2i And stored in PQ area or PV area in random order; according to S 1i , S 2i The value of the two-dimensional Y(n, d′) array will remove the vacant cells, and write the Y(n, d′) data file in a one-dimensional compact format for calling; the Y(n, d′) data file Write the data into the Y(n, d) array; calculate P according to the parameters of the Y(n, d) array according to the symmetric random segmentation i , Q i ;According to Y array element and J ij 、J ji Correspondence between non-zero element positions of subarrays and J ij 、J ji The corresponding relationship between the elements of the sub-array and their respective values ​​is symmetrically formed in a J-array in the manner of (two rows + two columns) / time. The speed of each link of the method is better than that of the traditional method.

Description

technical field [0001] The invention belongs to the field of power system analysis and calculation, and relates to a method for randomly generating non-zero elements and forming a power system Jacobian matrix. Background technique [0002] Node admittance matrix Y and Jacobian matrix J, which are widely used in power system calculations, are extremely sparse matrices, where Y matrix is ​​symmetric and J matrix is ​​asymmetric. But if the element structure of J array is replaced by J ij Sub-array representation, except for the balance node, the element structure of Y array is the same as that of J in J array ij The subarray structure is exactly the same. In addition, although the J array is asymmetrical, the J in the J array ij Subarray with J ji The non-zero position of the sub-array is almost symmetrical, and this feature makes the elements of the Y array and the J in the J array ij Subarray and J ji The elements of the sub-arrays are closely related, but the traditio...

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Problems solved by technology

In the traditional method, the Y(n, 2n) storage method is simple and intuitive when the sparseness of the Y elements is not considered, and it is convenient to process the Y array data, but the storage of a large number of zero elements requires a large storage unit, which leads to It takes longer to write Y(n, 2n) data files

The element structure in the Y(n, 2n) array is similar to the element structure in the J array, and the J array can be easily formed by using the Y(n, 2n) array, but because the elements of the Y array and the J array are not used ij Subarray and J ji The relationship of subarray elements and J ij Subarray with J ji The relationship between subarray elements, the efficiency of forming J array is not high

[0004] In the traditional method, the coordinate method, sequential method, and linked list method, which consider the sparseness of Y array elements, greatly reduce the storage units, but because the diagonal elements are stored separately from the non-zero non-diagonal elements, not only the storage structure is complicated, but also the It is conducive to data retrieval, modification, and application, and the storage method has no clear correspondence with the element structure of the Y array and J array, and there is no partition storage for the Y array elements, so it cannot reflect the relationship between the Y array elements and the J array elements. ij Subarray and J ji The relationship of subarray elements and J ij Subarray with J ji The relationship between the elements of the sub-array, so the above-mentioned relationship cannot be used, resulting in the fact that the reading and writing speed of the data file cannot reach the best, and the speed of forming the J array is not ideal.

In addition, no matter whether the sparsity is considered or not in the traditional method, the node active power P i and reactive power Q i The calculation efficiency is not high

[0005] Document ① (A method for quickly calculating polar coordinate Newton-Raphson method power flow based on symmetric sparse matrix technology: China, [ZL 201510770899.X]) proposes to use symmetric sparse matrix technology to quickly Form J matrix and eliminate elements to calculate power flow. Although the storage method of triangular non-zero elements on Y matrix is ​​given, the specific calculation and formation method is not given, and in the process of forming Y matrix j 1 2 ---6 Requirements require the application of a large number of loops and judgment statements, which also leads to low calculation efficiency; and in the process of forming the Y array, the Y array data of the PQ node and the PV node are not stored in partitions, resulting in the need for a large number of judgment statements when forming the J array by subsequent use. Also reduce the computational efficiency; and although J array is formed, J ij 、J ji The corresponding relationship between the non-zero element positions of the sub-array, but the corresponding relationship between the values ​​of each element in the polar coordinate Newton method is not used, which also greatly reduces the calculation efficiency of the diagonal elements and non-diagonal elements of the J array

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