CN109344361B  Method for quickly forming Jacobian matrix in power system load flow calculation  Google Patents
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Abstract
A method for quickly forming a Jacobian matrix in power system load flow calculation comprises the following steps: establishing an array Y (n, d) for only storing triangular nonzero elements on the Y array according to a random sequence, and controlling the reading and application of the nonzero elements by using the nonzero element number; accumulating and calculating the selfadmittance of the i and j nodes; respectively calculating the mutual admittance of the i and j nodes, and accumulating and calculating S according to the number of the mutual admittance_{i}(ii) a Writing the Y (n, d) array into a data file; reading the Y (n, d) data file and randomly calculating the active current I of the node according to the parameters of the Y (n, d) array_{pi}And a reactive current I_{qi}(ii) a According to Y array elements and J_{ij}And J_{ji}Calculating the elements of the J array by using Y (n, d) array elements and simultaneously according to a tworow + twocolumn mode according to the corresponding relation of the positions of the nonzero elements of the subarrays; according to I_{pi}、I_{qi}And correcting all diagonal elements to form a complete J array. The calculation speed of forming and storing the Yarray data file, reading the Yarray data file and forming the Jarray is greatly superior to that of the traditional method, and the advantages are more obvious along with the increase of the system scale.
Description
Technical Field
The invention belongs to the field of analysis and calculation of an electric power system, and relates to a method for randomly storing triangular nonzero elements on an admittance matrix and quickly forming a Jacobian matrix in load flow calculation of the electric power system.
Background
The extremely sparse node admittance matrix Y and the Jacobian matrix J are widely applied to power system calculation, wherein the Y matrix is symmetrical, and the J matrix is asymmetrical. But if the element structure of the J array is J_{ij}The submatrix represents that the structure of Y matrix elements and J in the J matrix except the balanced nodes_{ij}The subarrays are identical in structure. It can also be seen at this point that, although the Jarray is asymmetric, in the Jarray, J_{ij}Subarrays and J_{ji}The nonzero positions of the subarrays are almost symmetrical, and the characteristic causes the elements of the Y array and the J in the J array_{ij}Subarrays and J_{ji}The element relationship of the subarray is close, but the relationship cannot be utilized in the process of forming the J array by the traditional method, so that the forming time of the J array is too long.
In the conventional method, all elements of a Y array are stored in a Y (n,2n) storage mode without considering the sparsity of the Y elements. This form is simple and intuitive and facilitates the processing of Yarray data, but requires more memory cells for storage of a large number of zero elements and results in longer time for reading and writing Y (n,2n) data files. Although the structure of the elements in the Y (n,2n) array is similar to that of the elements in the J array, the J array can be conveniently formed by using the Y (n,2n) array, but the Y array elements and the J array elements are not used_{ij}Subarrays and J_{ji}The relationship of the subarray elements makes the formation of a Jarray inefficient.
Although storage units of a coordinate method, a sequence method and a linked list method considering sparsity of Yarray elements in the traditional method are greatly reduced, diagonal elements and nonzero nondiagonal elements are separately stored, so that the storage structure is complex, data retrieval, modification and application are not facilitated, the storage mode of the coordinate method, the sequence method and the linked list method has no definite corresponding relation with the element structures of the Yarray and the Jarray, and the Yarray elements and the Jarray cannot be reflected_{ij}Subarrays and J_{ji}The relationship of the subarray elements does not utilize the symmetry of the Y array elements, so that the speed of forming the Y array or the J array is not particularly ideal.
Document [1 ]](a method for rapidly forming and reading and writing electric power system node admittance matrix data based on sparse matrix technology, China, [ ZL 201410539178.3]2017.02.15), the storage method of Y (n,22) for generating upper triangular array nonzero elements is provided, and the storage method of the upper triangular nonzero elements of the Y array is also provided, but the symmetry of the Y array elements is also utilized, but the storage method does not use the symmetry of the Y array elementsGiving a specific calculation flow; j in the process of forming Y matrix_{1}<j_{2}<j_{3}<j_{4}<j_{5}<j_{6}The requirement of (2) needs to apply a large amount of circulation and judgment statements, which also causes low calculation efficiency; according to the method, the active and reactive currents I of the nodes are calculated because the lower triangular nonzero elements are inconvenient to obtain_{pi}And I_{qi}Node active and reactive power P_{i}And Q_{i}Diagonal element H in J matrix_{ii}、N_{ii}、M_{ii}、L_{ii}It also causes inconvenience in calculation; the method also does not utilize the structure of the Yarray element and J_{ij}And J_{ji}The corresponding relation of the positions of the nonzero elements of the subarray forms a Jarray.
Disclosure of Invention
The invention provides a method for randomly storing triangular nonzero elements on an admittance matrix of an electric power system and quickly forming a Jacobian matrix in load flow calculation of the electric power system to overcome the defects of the prior art.
The invention is realized by the following technical scheme.
The invention relates to a method for quickly forming a Jacobian matrix in power flow calculation of a power system, which comprises the following steps of:
step 1: establishing an array Y (n, d) for only storing triangular nonzero elements on the Y array according to a random sequence;
defining the number of ungrounded branches of the maximum triangular connection on each node in the system as l_{max}Creating an array that stores only the triangular nonzero elements on the array of Y's as Y (n, d), where d is 3 x l_{max}+4, divide the Y (n, d) array into 3 groups, as follows:
group 1: number of nonzero elements S_{i}Only 1 row, storing the sum S of the nondiagonal elements of the upper triangle which is connected with the diagonal elements but does not include the diagonal elements in the Y array_{i}(ii) a Form Y matrix S_{i}Generated by program accumulation, S_{i}The method can ensure that the Yarray parameters can be accurately and quickly read and the Jarray elements can be calculated, so that the reading of redundant data and the calculation of elements can be avoided;
group 2: the diagonal element groups have 3 rows and respectively store the row number i and the parameter g of the diagonal element_{ii}、b_{ii}；
Group 3: there may be at most l in nonzero nondiagonal tuples_{max}In small groups, maximum number of columns is 3l_{max}And (4) columns. But the actual number of the connecting branches of the triangle on each node is l_{i}Thus, there is l in the nonzero offdiagonal tuples in each row_{i}Small group with 3l of actual columns_{i}And (4) columns. Therefore, the nonzero nondiagonal tuple is three rows and one group which respectively and randomly stores the row number j and the parameter g of all nonzero nondiagonal elements of the upper triangle connected with the diagonal element i_{ij}、b_{ij}That is, the column numbers and their corresponding parameters of each subgroup in the nonzero nondiagonal tuple can be stored in random order without requiring j_{1}<j_{2}<j_{3}<j_{4}<j_{5}<j_{6}And the like.
The structure of the Y (n, d) array is shown in Table 1.
Table 1 shows the storage form of the array elements of Y (n, d).
Step 2: reading data i, j, r, x and k of each line branch of the system, and accumulating and calculating the selfadmittance of the nodes i and j; respectively calculating the mutual admittance between the i and j nodes, and cumulatively calculating S according to the number of the triangular mutual admittance on each node_{i}；
(1) Selfadmittance of the i and j nodes is respectively stored in a line number column i and a parameter column g 'of the diagonal tuple of the ith line'_{ii}、b′_{ii}And row number column j and parameter column g 'of jth row diagonal tuple'_{jj}、b′_{jj}And respectively comparing the selfadmittance of the subsequently increased i and j nodes with g'_{ii}、b′_{ii}Or g'_{jj}、b′_{jj}Accumulating until the completion;
(2) if i<j, then is the upper triangle element, can directly connect the Ith row S_{i}The value is added by 1, the mutual admittance of the i and j nodes is calculated and stored in the S th row of the nonzero offdiagonal tuple_{i}In the subgroup, the initial column number is T3 (S)_{i}+1) 1, i.e. storing its column number j and parameter g, respectively_{ij}、b_{ij}In the Tth columnColumn T + 2;
(3) if i>j, then is the lower triangle element, the S of the j row_{j}The value is added by 1, the mutual admittance of the i and j nodes is calculated and stored in the S th row of the nonzero and diagonal tuple_{j}In the subgroup, the initial column number is T3 (S)_{j}+1) 1, i.e. storing its column number i and parameter g, respectively_{ji}、b_{ji}In the Tth column to the T + 2th column, the calculation process is equivalent to exchanging the row numbers and the column numbers of the lower triangular elements, and calculating the corresponding upper triangular elements;
(4) the whole Y (n, d) array can be obtained by the circulation.
Since the reading sequence of the branch data is random, and the column number of each row of nonzero elements in the upper triangle is determined by the node number of the readin branch parameter, the column number and the parameter stored in each row in the Y (n, d) array are also random and are not arranged in sequence. The storage mode can save a large amount of judgments in the cycle statement, thereby greatly accelerating the forming speed of the Y array, and the random storage of the Y array elements does not influence the forming of the J array, and can also utilize the J array in the J array_{ij}And J_{ji}And the corresponding relation of the positions of the nonzero elements of the subarrays quickly forms a Jarray.
And step 3: writing the Y (n, d) array into the data file.
And 4, step 4: reading a Y (n, d) data file and randomly and sectionally calculating the active current I of the node according to the parameters of the Y (n, d) array_{pi}And node reactive current I_{qi}；
In the conventional calculation method of the power system I_{pi}And I_{qi}The calculation formula of (a) is as follows:
as can be seen from equation (1), I is calculated_{pi}、I_{qi}The invention only stores diagonal elements of Y array and nonzero elements of upper triangle, and has no nonzero elements of lower triangle_{pi}、I_{qi}A new method. At this time, the formula(1) The formula (2) is rewritten.
Wherein, Delta I_{p,ij}、ΔI_{q,ij}Is represented by_{pi}、I_{qi}The jth of the summation terms, i.e. Δ I_{p,ij}＝g_{ij}e_{j}b_{ij}f_{j}、ΔI_{q,ij}＝g_{ij}f_{j}+b_{ij}e_{j}. If only the ith row element of the Y array is nonzero in the a, b and c columns_{pi}＝ΔI_{p,ia}+ΔI_{p,ib}+ΔI_{p,ic}And I_{qi}＝ΔI_{q,ia}+ΔI_{q,ib}+ΔI_{q,ic}. Then, according to the symmetry of the Y array, I of the a, b and c rows can be simultaneously and randomly calculated in a segmentation manner_{pa}、I_{pb}、I_{pc}And I_{qa}、I_{qb}、I_{qc}In delta I corresponding to the ith nonzero element in the lower triangle of the Y array_{p,ai}、ΔI_{p,bi}、ΔI_{p,ci}And Δ I_{q,ai}、ΔI_{q,bi}、ΔI_{q,ci}And (4) partial. When I is circulated from 1 to n in sequence and each part of all node currents is calculated in a segmentation mode according to symmetry, the complete form I of all node currents can be obtained_{pi}、I_{qi}. The random sectional calculation method of the node current can better solve the problem of calculating the node current according to the triangular elements on the Y array.
And 5: according to the element structure of the Y array and J in the J array_{ij}And J_{ji}The corresponding relation of the positions of the nonzero elements of the subarrays uses triangular nonzero elements on the Y (n, d) array to quickly form a J array in a mode of two rows and two columns/power;
y array is symmetrical and J array is asymmetrical in power system load flow calculation, but if J array is used as J array_{ij}The submatrix represents that except the balanced nodes, the structure of the Ymatrix elements and J_{ij}The subarrays are identical in structure. At this time, although the J array is still asymmetric, J_{ij}Subarrays and J_{ji}The nonzero position of the subarray is symmetrical, and by utilizing the characteristic, the J can be calculated according to the symmetry of the Y array element_{ij}Subarrays and J_{ji}Subarrays ofAnd forming a J matrix rapidly.
To use Y array elements and J_{ij}、J_{ji}The invention provides a novel method for calculating elements of a J array, and the J array is quickly formed by static corresponding relations of nonzero elements of a sub array. Firstly, dividing the rectangular coordinate Newton method correction equation (3) into an upper left area A, an upper right area B, a lower left area C and a lower right area D according to a dotted line, and marking the serial number of the subarray on the subarray.
In the Y matrix, e.g. b_{ij}Not equal to 0 can determine y_{ij}Not equal to 0, and b is obtained due to the symmetry of the Yarray elements_{ji}Not equal to 0 and y_{ji}Not equal to 0. Then according to the Y array element structure and J_{ij}And J_{ji}The corresponding relation of the positions of the nonzero elements of the subarrays can be deduced_{ij}Element and J_{ij}Subarrays, y_{ji}Element and J_{ji}The subarrays having a static correspondence of nonzero elements, i.e. J_{ij}And J_{ji}The subarrays also have a nonzero element position symmetry relationship. Thus, b_{ij}≠0→b_{ji}≠0→y_{ij}≠0→y_{ji}≠0→J_{ij}≠0→J_{ji}Not equal to 0, thus obtaining J_{ij}And J_{ji}The element H, N, M, L in the subarray is also a nonzero element, but does not include the R, S element. The partitioning of the elements in the Jarray of equation (3) is calculated as follows:
(1) region A2 and 2' subarrays, b_{1m}≠0→J_{1m}≠0→J_{m1}≠0→(H_{1m}、N_{1m}、M_{1m}、L_{1m}) Not equal to 0 and (H)_{m1}、N_{m1}、M_{m1}、L_{m1}) Not equal to 0, i.e. according to b in the Y matrix_{1m}One element, eight elements in the Jmatrix can be calculated as "8 out of 1". But also in the calculation process (H)_{1m}＝L_{1m}、N_{1m}＝M_{1m})、(H_{m1}＝L_{m1}、N_{m1}＝M_{m1}) These relationships.
(2) B, C areas 3 and 3' subarrays, b_{1,m+1}≠0→J_{1,m+1}≠0→J_{m+1,1}Not equal to 0 → in region B (H)_{1,m+1}、N_{1,m+1}、M_{1,m+1}、L_{1,m+1}) Not equal to 0 and in region C (H)_{m+1,1}、N_{m+1,1}) Not equal to 0, but (R)_{m+1,1}、S_{m+1,1}) 0, i.e. according to b in the Y matrix_{1,m+1}One element, six elements in the Jmatrix can be calculated as "6 out of 1".
(3) D regions 9 and 9' subarrays, b_{m+1,n1}≠0→J_{m+1,n1}≠0→J_{n1,m+1}≠0→(H_{m+1,n1}、N_{m+1,n1}) Not equal to 0 and (H)_{n1,m+1}、N_{n1,m+1}) Not equal to 0, but (R)_{m+1,n1}、S_{m+1,n1}) And (R)_{n1,m+1}、S_{n1,m+1}) 0, i.e. according to b in the Y matrix_{m+1,n1}One element, four elements in the Jmatrix can be calculated as "4 out of 1".
The calculation process shows that the nonzero elements of the triangles on the 2 i1 th row and the 2 ith row in the J array can be calculated according to the corresponding relation between the nonzero elements of the ith row in the Y (n, d) array and the elements of the J array, the nonzero elements of the triangles under the ith row of the Y array can be obtained according to the symmetry of the elements of the Y array, and then the nonzero elements of the triangles under the 2 i1 th row and the 2 ith row of the J array can be directly calculated. Thus, the calculation of (two rows + two columns) elements in the J array can be completed simultaneously according to one row of nonzero elements in the Y (n, d) array. Or according to a nonzero element of a triangle on the Y (n, d) array, taking four diagonal elements in the J array as starting points, respectively calculating 8 or 6 or 4J array elements in A, B and C, D areas of the J array in a (tworow + twocolumn)/secondary symmetrical calculation mode, thereby randomly and quickly forming the J array.
Step 6: according to the calculated I_{pi}、I_{qi}And correcting all diagonal elements in the J array to form a complete J array.
In the load flow calculation method of the traditional power system, the general formula (4) for Jarray diagonal element calculation is adopted, and I is not utilized_{pi}、I_{qi}The repeated calculation of a plurality of Σ greatly affects the calculation efficiency, and the H, N, M, L elements must be calculated separately.
Therefore, the invention provides a novel method for calculating the diagonal elements of the J array, and the formula (5) can be obtained by transforming the formula (4).
When the equation (5) replaces the calculation of Σ in the equation (4) with I including the node current_{pi}、I_{qi}Computing, whereby I is computed before diagonal is computed_{pi}、I_{qi}Sigma calculation in diagonal elements can be omitted; and may find that the computation of a diagonal is actually a fraction of it computed as a nondiagonal, plus I_{pi}Or I_{qi}. Therefore, the diagonal elements can be calculated according to the calculation formula of the nondiagonal elements, and I is used after the calculation is finished_{pi}、I_{qi}It is corrected. In addition, there is H in the conventional method_{ii}≠L_{ii}、N_{ii}≠M_{ii}However, in formula (5), it can be found that I is not counted_{pi}、I_{qi}When there is L_{ijj＝i}＝H_{ijj＝i}And M_{ijj＝i}＝N_{ijj＝i}This is true. Therefore, the relationship between H and L, N and M elements can be used to calculate all diagonal elements and nonzero nondiagonal elements in the J matrix simultaneously, and then add I to all diagonal elements_{pi}、I_{qi}And partial operation is required, so that the calculation speed of the diagonal elements is greatly improved.
The main innovation points of the invention are as follows:
(1) compared with the storage scheme of the traditional method without considering element sparsity and considering element sparsity, the random storage mode of the upper triangular nonzero element Y (n, d) can greatly reduce storage units, improve the forming speed of the Y array and the reading and writing speed of the Y array data file, and is convenient for the application of calculation, retrieval, modification and the like of stored data. Compared with the sequential storage mode of the upper triangle nonzero elements, a large amount of judgment in the loop statement can be omitted, and therefore the forming speed of the Y (n, d) array is greatly improved.
(2) Providing Y array elements and J_{ij}And J_{ji}The subarray elements have similar structures,Nonzero elements have a static correspondence, J_{ij}And J_{ji}The subarrays also have a nonzero element position symmetry relationship, and a new method for calculating elements of the J array is further provided, namely 8 or 6 or 4 elements in A, B and C, D four areas in the J array can be respectively calculated according to an imaginary element of the Y array in a (tworow + twocolumn)/secondary symmetry calculation mode, and the J array is quickly formed. Also because of J_{ij}And J_{ji}The position of the nonzero elements of the subarray is symmetrical, so that the Y (n, d) array of the upper triangular nonzero elements can be randomly stored, and the J array can be quickly formed according to a (two rows + two columns)/secondary random symmetrical calculation mode.
(3) Provides a random segmentation calculation I by using the symmetry of Y array elements_{pi}、I_{qi}By the new method, I can be greatly accelerated_{pi}、I_{qi}And calculating the power of the nodes in the Jarray diagonal elements and the subsequent load flow calculation.
(4) A new method for calculating the diagonal elements of the J array is provided, and the calculation speed of the diagonal elements of the J array is further improved.
Drawings
FIG. 1 is a flow chart of a conventional method for forming a Y (n,2n) array without considering element sparsity and symmetry.
FIG. 2 is a flow chart for forming a Y (n, d) array in consideration of element sparsity and symmetry according to the present invention.
FIG. 3 is a flow chart of a conventional method for forming a Jmatrix from Y (n,2n) arrays.
FIG. 4 is a flow chart of the present invention for forming Jmatrix with Y (n, d) array.
Detailed Description
The invention will be further illustrated by the following examples.
Example 1.
For the IEEE30, 57, 118 systems, the comparison of the time for forming and storing Ymatrix data files using the conventional method without considering sparsity and the Y (n,2n) method of the present invention is shown in Table 2.
Table 2 shows a comparison of time for forming and storing Ymatrix data files for the IEEE system in accordance with the conventional method and the present invention.
t_{11}、t_{21}: the time for forming and storing Yarray data files is respectively the traditional method and the invention.
t_{21}/t_{11}(%): the present invention forms and stores the Yarray data file in percentage of time as compared to the conventional method.
Example 2.
For the IEEE30, 57, 118 systems, a comparison of the time to read Ymatrix data files and form Jmatrix data files using the conventional method and the present invention, respectively, is shown in Table 3.
Table 3 shows a comparison of the time to read the Ymatrix data file of the IEEE system and to form the Jmatrix according to the conventional method and the present invention.
t_{12}、t_{22}: the time for reading the Yarray data file by the traditional method and the time for reading the Yarray data file by the invention are respectively.
t_{22}/t_{12}(%): the invention is compared with the traditional method to read the percentage of time of the Yarray data file.
t_{13}、t_{23}: respectively the time for forming the Jarray by the traditional method and the invention.
t_{23}/t_{13}(%): the percentage of time for forming the Jarray by the method is compared with that of the conventional method.
As can be seen from tables 2 and 3:
1. the calculation speed of the invention is much better than that of the traditional method no matter in the process of forming and storing the Yarray data file, reading the Yarray data file and forming the Jarray.
Taking an IEEE118 system as an example, the time for forming and storing the Yarray data file is only 13.92% of the time for not considering the sparsity of the elements in the traditional method; the time for reading the Yarray data file is only 12.49% of the time of the traditional method; the time for forming the Jarray is only 11.05 percent of the time of the traditional method.
2. The larger the number of nodes of the power system is, the faster the data file is read and written and the Jarray is formed.
The invention determines d in the Y array according to the maximum branch number of the network, and only operates on the diagonal elements of the Y array and the nonzero nondiagonal elements in the upper triangle. Therefore, the storage units cannot be obviously increased along with the increase of the number of the system nodes, and the time for reading and writing the data file and forming the J array cannot be obviously increased. The larger the number of nodes, the higher the calculation efficiency.
The invention can be realized by adopting any programming language and programming environment, wherein the C + + programming language is adopted, the development environment is Visual C + +, and the computer model is the associative restart M4500.
Claims (1)
1. A method for quickly forming a Jacobian matrix in power flow calculation of an electric power system is characterized by comprising the following steps:
step 1: establishing an array Y (n, d) for only storing triangular nonzero elements on the Y array according to a random sequence;
defining the number of ungrounded branches of the maximum triangular connection on each node in the system as l_{max}Creating an array that stores only the triangular nonzero elements on the array of Y's as Y (n, d), where d is 3 x l_{max}+4, divide the Y (n, d) array into 3 groups, as follows:
group 1: number of nonzero elements S_{i}Storing the sum S of the number of nondiagonal elements of the upper triangle which is connected with the diagonal elements but does not include the diagonal elements in the Y matrix and is not zero_{i}；
Group 2: the diagonal element group respectively stores the line number i and the parameter g of the diagonal element_{ii}、b_{ii}；
Group 3: three rows and one group of nonzero nondiagonal tuples, 3l_{i}Column, l_{i}Respectively and randomly storing the column number j and the parameter g of all nonzero nondiagonal elements of the upper triangle connected with the diagonal element i for the actual connection branch number of the triangle on each node_{ij}、b_{ij}；
Step 2: reading data i, j, r, x and k of each line branch of the system, and accumulating and calculating the selfadmittance of the nodes i and j; respectively calculating the mutual admittance between the i and j nodes, and according to the number of the triangle mutual admittance on each nodeCumulative calculation S_{i}；
(1) Selfadmittance of the i and j nodes is respectively stored in a line number column i and a parameter column g 'of the diagonal tuple of the ith line'_{ii}、b′_{ii}And row number column j and parameter column g 'of jth row diagonal tuple'_{jj}、b′_{jj}And respectively comparing the selfadmittance of the subsequently increased i and j nodes with g'_{ii}、b′_{ii}Or g'_{jj}、b′_{jj}Accumulating until the completion;
(2) if i<j, S of the ith row can be directly connected_{i}The value is added by 1, the mutual admittance of the i and j nodes is calculated and stored in the S th row of the nonzero offdiagonal tuple_{i}In the subgroup, the initial column number is T3 (S)_{i}+1) 1, respectively storing its column number j and parameter g_{ij}、b_{ij}In the T th to T +2 th columns;
(3) if i>j, S of the jth row_{j}The value is added by 1, the mutual admittance of the i and j nodes is calculated and stored in the S th row of the nonzero and diagonal tuple_{j}In the subgroup, the starting sequence is T3 (S)_{j}+1) 1, respectively storing its column number i and parameter g_{ji}、b_{ji}In the T th to T +2 th columns;
(4) the whole Y (n, d) array can be obtained by the circulation;
and step 3: writing the Y (n, d) array into a data file;
and 4, step 4: reading a Y (n, d) data file and randomly and sectionally calculating the active current I of the node according to the parameters of the Y (n, d) array_{pi}And node reactive current I_{qi}；
(1) Will be conventional I_{pi}、I_{qi}The formula (c) is rewritten as follows:
(2) if only the ith row element of the Y array is nonzero in the a, b and c columns_{pi}＝ΔI_{p,ia}+ΔI_{p,ib}+ΔI_{p,ic}And I_{qi}＝ΔI_{q,ia}+ΔI_{q,ib}+ΔI_{q,ic}While randomly calculating I of the a, b and c lines_{pa}、I_{pb}、I_{pc}And I_{qa}、I_{qb}、I_{qc}In delta I corresponding to the ith nonzero element in the lower triangle of the Y array_{p,ai}、ΔI_{p,bi}、ΔI_{p,ci}And Δ I_{q,ai}、ΔI_{q,bi}、ΔI_{q,ci}A moiety; when I is circulated from 1 to n in sequence and each part of all node currents is calculated in a segmentation mode according to symmetry, all node currents I can be obtained_{pi}、I_{qi}；
And 5: according to the element structure of the Y array and J in the J array_{ij}And J_{ji}The corresponding relation of the positions of the nonzero elements of the subarrays uses triangular nonzero elements on the Y (n, d) array to quickly form a J array in a tworow + twocolumn mode;
(1) according to the structure of Y array element and J_{ij}And J_{ji}The corresponding relationship of the position of the nonzero elements of the subarray can obtain b_{ij}≠0→b_{ji}≠0→y_{ij}≠0→y_{ji}≠0→J_{ij}≠0→J_{ji}Not equal to 0, and can obtain J_{ij}And J_{ji}The H, N, M, L elements in the subarray are also nonzero;
(2) calculating nonzero elements of triangles on the 2 i1 th row and the 2 i2 th row in the J array according to the nonzero elements of the ith row in the Y (n, d) array, and simultaneously calculating nonzero elements of triangles under the 2 i1 th column and the 2 i2 th column in the J array, thereby simultaneously completing the calculation of elements of two rows and two columns in the J array according to one row of nonzero elements in the Y (n, d) array;
step 6: according to calculated I_{pi}、I_{qi}Correcting all diagonal elements in the J array to form a complete J array;
(1) the traditional calculation of sigma contained in the diagonal element of the J array is replaced by the current I containing the node_{pi}、I_{qi}Is calculated as follows;
(2) using the relationship of H and L, N to the M element, the diagonal elements are calculated as nondiagonal elements, plus I_{pi}Or I_{qi}。
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