CN109344361B - Method for quickly forming Jacobian matrix in power system load flow calculation - Google Patents

Method for quickly forming Jacobian matrix in power system load flow calculation Download PDF

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CN109344361B
CN109344361B CN201810977510.2A CN201810977510A CN109344361B CN 109344361 B CN109344361 B CN 109344361B CN 201810977510 A CN201810977510 A CN 201810977510A CN 109344361 B CN109344361 B CN 109344361B
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陈恳
彭丽君
丁戈
文祥
郭甲宝
宫嘉炜
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Nanchang University
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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 non-zero elements on the Y array according to a random sequence, and controlling the reading and application of the non-zero elements by using the non-zero element number; accumulating and calculating the self-admittance 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 admittancei(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) arraypiAnd a reactive current Iqi(ii) a According to Y array elements and JijAnd JjiCalculating the elements of the J array by using Y (n, d) array elements and simultaneously according to a two-row + two-column mode according to the corresponding relation of the positions of the non-zero elements of the sub-arrays; according to Ipi、IqiAnd correcting all diagonal elements to form a complete J array. The calculation speed of forming and storing the Y-array data file, reading the Y-array data file and forming the J-array is greatly superior to that of the traditional method, and the advantages are more obvious along with the increase of the system scale.

Description

Method for quickly forming Jacobian matrix in power system load flow calculation
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 non-zero 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 JijThe submatrix represents that the structure of Y matrix elements and J in the J matrix except the balanced nodesijThe sub-arrays are identical in structure. It can also be seen at this point that, although the J-array is asymmetric, in the J-array, JijSubarrays and JjiThe non-zero positions of the sub-arrays are almost symmetrical, and the characteristic causes the elements of the Y array and the J in the J arrayijSubarrays and JjiThe 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 Y-array 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 usedijSubarrays and JjiThe relationship of the sub-array elements makes the formation of a J-array inefficient.
Although storage units of a coordinate method, a sequence method and a linked list method considering sparsity of Y-array elements in the traditional method are greatly reduced, diagonal elements and non-zero non-diagonal 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 Y-array and the J-array, and the Y-array elements and the J-array cannot be reflectedijSubarrays and JjiThe relationship of the sub-array 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 non-zero elements is provided, and the storage method of the upper triangular non-zero 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 matrix1<j2<j3<j4<j5<j6The 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 non-zero elements are inconvenient to obtainpiAnd IqiNode active and reactive power PiAnd QiDiagonal element H in J matrixii、Nii、Mii、LiiIt also causes inconvenience in calculation; the method also does not utilize the structure of the Y-array element and JijAnd JjiThe corresponding relation of the positions of the non-zero elements of the sub-array forms a J-array.
Disclosure of Invention
The invention provides a method for randomly storing triangular non-zero 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 non-zero 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 lmaxCreating an array that stores only the triangular non-zero elements on the array of Y's as Y (n, d), where d is 3 x lmax+4, divide the Y (n, d) array into 3 groups, as follows:
group 1: number of non-zero elements SiOnly 1 row, storing the sum S of the non-diagonal elements of the upper triangle which is connected with the diagonal elements but does not include the diagonal elements in the Y arrayi(ii) a Form Y matrix SiGenerated by program accumulation, SiThe method can ensure that the Y-array parameters can be accurately and quickly read and the J-array 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 elementii、bii；
Group 3: there may be at most l in non-zero non-diagonal tuplesmaxIn small groups, maximum number of columns is 3lmaxAnd (4) columns. But the actual number of the connecting branches of the triangle on each node is liThus, there is l in the non-zero off-diagonal tuples in each rowiSmall group with 3l of actual columnsiAnd (4) columns. Therefore, the non-zero non-diagonal tuple is three rows and one group which respectively and randomly stores the row number j and the parameter g of all non-zero non-diagonal elements of the upper triangle connected with the diagonal element iij、bijThat is, the column numbers and their corresponding parameters of each subgroup in the non-zero non-diagonal tuple can be stored in random order without requiring j1<j2<j3<j4<j5<j6And 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).
Figure GDA0003540090480000021
Step 2: reading data i, j, r, x and k of each line branch of the system, and accumulating and calculating the self-admittance 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 nodei；
(1) Self-admittance 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′iiAnd row number column j and parameter column g 'of j-th row diagonal tuple'jj、b′jjAnd respectively comparing the self-admittance of the subsequently increased i and j nodes with g'ii、b′iiOr g'jj、b′jjAccumulating until the completion;
(2) if i<j, then is the upper triangle element, can directly connect the I-th row SiThe 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 off-diagonal tupleiIn the subgroup, the initial column number is T-3 (S)i+1) -1, i.e. storing its column number j and parameter g, respectivelyij、bijIn the T-th columnColumn T + 2;
(3) if i>j, then is the lower triangle element, the S of the j rowjThe 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 tuplejIn the subgroup, the initial column number is T-3 (S)j+1) -1, i.e. storing its column number i and parameter g, respectivelyji、bjiIn the T-th column to the T + 2-th 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 non-zero elements in the upper triangle is determined by the node number of the read-in 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 arrayijAnd JjiAnd the corresponding relation of the positions of the non-zero elements of the sub-arrays quickly forms a J-array.
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) arraypiAnd node reactive current Iqi；
In the conventional calculation method of the power system IpiAnd IqiThe calculation formula of (a) is as follows:
Figure GDA0003540090480000031
as can be seen from equation (1), I is calculatedpi、IqiThe invention only stores diagonal elements of Y array and non-zero elements of upper triangle, and has no non-zero elements of lower trianglepi、IqiA new method. At this time, the formula(1) The formula (2) is rewritten.
Figure GDA0003540090480000032
Wherein, Delta Ip,ij、ΔIq,ijIs represented bypi、IqiThe j-th of the summation terms, i.e. Δ Ip,ij＝gijej-bijfj、ΔIq,ij＝gijfj+bijej. If only the ith row element of the Y array is nonzero in the a, b and c columnspi＝ΔIp,ia+ΔIp,ib+ΔIp,icAnd Iqi＝ΔIq,ia+ΔIq,ib+ΔIq,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 mannerpa、Ipb、IpcAnd Iqa、Iqb、IqcIn delta I corresponding to the ith non-zero element in the lower triangle of the Y arrayp,ai、ΔIp,bi、ΔIp,ciAnd Δ Iq,ai、ΔIq,bi、ΔIq,ciAnd (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 obtainedpi、Iqi. 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 arrayijAnd JjiThe corresponding relation of the positions of the non-zero elements of the sub-arrays uses triangular non-zero 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 arrayijThe submatrix represents that except the balanced nodes, the structure of the Y-matrix elements and JijThe sub-arrays are identical in structure. At this time, although the J array is still asymmetric, JijSubarrays and JjiThe non-zero position of the subarray is symmetrical, and by utilizing the characteristic, the J can be calculated according to the symmetry of the Y array elementijSubarrays and JjiSub-arrays ofAnd forming a J matrix rapidly.
To use Y array elements and Jij、JjiThe invention provides a novel method for calculating elements of a J array, and the J array is quickly formed by static corresponding relations of non-zero 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.
Figure GDA0003540090480000041
In the Y matrix, e.g. bijNot equal to 0 can determine yijNot equal to 0, and b is obtained due to the symmetry of the Y-array elementsjiNot equal to 0 and yjiNot equal to 0. Then according to the Y array element structure and JijAnd JjiThe corresponding relation of the positions of the non-zero elements of the subarrays can be deducedijElement and JijSubarrays, yjiElement and JjiThe subarrays having a static correspondence of non-zero elements, i.e. JijAnd JjiThe subarrays also have a non-zero element position symmetry relationship. Thus, bij≠0→bji≠0→yij≠0→yji≠0→Jij≠0→JjiNot equal to 0, thus obtaining JijAnd JjiThe element H, N, M, L in the sub-array is also a non-zero element, but does not include the R, S element. The partitioning of the elements in the J-array of equation (3) is calculated as follows:
(1) region A2 and 2' subarrays, b1m≠0→J1m≠0→Jm1≠0→(H1m、N1m、M1m、L1m) Not equal to 0 and (H)m1、Nm1、Mm1、Lm1) Not equal to 0, i.e. according to b in the Y matrix1mOne element, eight elements in the J-matrix can be calculated as "8 out of 1". But also in the calculation process (H)1m＝L1m、N1m＝-M1m)、(Hm1＝Lm1、Nm1＝-Mm1) These relationships.
(2) B, C areas 3 and 3' subarrays, b1,m+1≠0→J1,m+1≠0→Jm+1,1Not equal to 0 → in region B (H)1,m+1、N1,m+1、M1,m+1、L1,m+1) Not equal to 0 and in region C (H)m+1,1、Nm+1,1) Not equal to 0, but (R)m+1,1、Sm+1,1) 0, i.e. according to b in the Y matrix1,m+1One element, six elements in the J-matrix can be calculated as "6 out of 1".
(3) D regions 9 and 9' subarrays, bm+1,n-1≠0→Jm+1,n-1≠0→Jn-1,m+1≠0→(Hm+1,n-1、Nm+1,n-1) Not equal to 0 and (H)n-1,m+1、Nn-1,m+1) Not equal to 0, but (R)m+1,n-1、Sm+1,n-1) And (R)n-1,m+1、Sn-1,m+1) 0, i.e. according to b in the Y matrixm+1,n-1One element, four elements in the J-matrix can be calculated as "4 out of 1".
The calculation process shows that the non-zero elements of the triangles on the 2 i-1 th row and the 2 i-th row in the J array can be calculated according to the corresponding relation between the non-zero elements of the i-th row in the Y (n, d) array and the elements of the J array, the non-zero elements of the triangles under the i-th row of the Y array can be obtained according to the symmetry of the elements of the Y array, and then the non-zero elements of the triangles under the 2 i-1 th row and the 2 i-th 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 non-zero elements in the Y (n, d) array. Or according to a non-zero 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 (two-row + two-column)/secondary symmetrical calculation mode, thereby randomly and quickly forming the J array.
Step 6: according to the calculated Ipi、IqiAnd 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 J-array diagonal element calculation is adopted, and I is not utilizedpi、IqiThe repeated calculation of a plurality of Σ greatly affects the calculation efficiency, and the H, N, M, L elements must be calculated separately.
Figure GDA0003540090480000051
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).
Figure GDA0003540090480000052
When the equation (5) replaces the calculation of Σ in the equation (4) with I including the node currentpi、IqiComputing, whereby I is computed before diagonal is computedpi、IqiSigma 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 non-diagonal, plus IpiOr Iqi. Therefore, the diagonal elements can be calculated according to the calculation formula of the non-diagonal elements, and I is used after the calculation is finishedpi、IqiIt is corrected. In addition, there is H in the conventional methodii≠Lii、Nii≠-MiiHowever, in formula (5), it can be found that I is not countedpi、IqiWhen there is Lij|j＝i＝Hij|j＝iAnd Mij|j＝i＝-Nij|j＝iThis is true. Therefore, the relationship between H and L, N and M elements can be used to calculate all diagonal elements and non-zero non-diagonal elements in the J matrix simultaneously, and then add I to all diagonal elementspi、IqiAnd 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 non-zero 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 non-zero 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 JijAnd JjiThe sub-array elements have similar structures,Non-zero elements have a static correspondence, JijAnd JjiThe subarrays also have a non-zero 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 (two-row + two-column)/secondary symmetry calculation mode, and the J array is quickly formed. Also because of JijAnd JjiThe position of the non-zero elements of the subarray is symmetrical, so that the Y (n, d) array of the upper triangular non-zero 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 elementspi、IqiBy the new method, I can be greatly acceleratedpi、IqiAnd calculating the power of the nodes in the J-array 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 J-matrix from Y (n,2n) arrays.
FIG. 4 is a flow chart of the present invention for forming J-matrix with Y (n, d) array.
Detailed Description
The invention will be further illustrated by the following examples.
Example 1.
For the IEEE-30, -57, -118 systems, the comparison of the time for forming and storing Y-matrix 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 Y-matrix data files for the IEEE system in accordance with the conventional method and the present invention.
Figure GDA0003540090480000061
t11、t21: the time for forming and storing Y-array data files is respectively the traditional method and the invention.
t21/t11(%): the present invention forms and stores the Y-array data file in percentage of time as compared to the conventional method.
Example 2.
For the IEEE-30, -57, -118 systems, a comparison of the time to read Y-matrix data files and form J-matrix 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 Y-matrix data file of the IEEE system and to form the J-matrix according to the conventional method and the present invention.
Figure GDA0003540090480000062
t12、t22: the time for reading the Y-array data file by the traditional method and the time for reading the Y-array data file by the invention are respectively.
t22/t12(%): the invention is compared with the traditional method to read the percentage of time of the Y-array data file.
t13、t23: respectively the time for forming the J-array by the traditional method and the invention.
t23/t13(%): the percentage of time for forming the J-array 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 Y-array data file, reading the Y-array data file and forming the J-array.
Taking an IEEE-118 system as an example, the time for forming and storing the Y-array 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 Y-array data file is only 12.49% of the time of the traditional method; the time for forming the J-array 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 J-array 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 non-zero non-diagonal 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 non-zero 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 lmaxCreating an array that stores only the triangular non-zero elements on the array of Y's as Y (n, d), where d is 3 x lmax+4, divide the Y (n, d) array into 3 groups, as follows:
group 1: number of non-zero elements SiStoring the sum S of the number of non-diagonal 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 zeroi；
Group 2: the diagonal element group respectively stores the line number i and the parameter g of the diagonal elementii、bii；
Group 3: three rows and one group of non-zero non-diagonal tuples, 3liColumn, liRespectively and randomly storing the column number j and the parameter g of all non-zero non-diagonal elements of the upper triangle connected with the diagonal element i for the actual connection branch number of the triangle on each nodeij、bij；
Step 2: reading data i, j, r, x and k of each line branch of the system, and accumulating and calculating the self-admittance 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 Si；
(1) Self-admittance 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′iiAnd row number column j and parameter column g 'of j-th row diagonal tuple'jj、b′jjAnd respectively comparing the self-admittance of the subsequently increased i and j nodes with g'ii、b′iiOr g'jj、b′jjAccumulating until the completion;
(2) if i<j, S of the ith row can be directly connectediThe 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 off-diagonal tupleiIn the subgroup, the initial column number is T-3 (S)i+1) -1, respectively storing its column number j and parameter gij、bijIn the T th to T +2 th columns;
(3) if i>j, S of the jth rowjThe 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 tuplejIn the subgroup, the starting sequence is T-3 (S)j+1) -1, respectively storing its column number i and parameter gji、bjiIn 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) arraypiAnd node reactive current Iqi；
(1) Will be conventional Ipi、IqiThe formula (c) is rewritten as follows:
Figure FDA0001777774650000011
(2) if only the ith row element of the Y array is nonzero in the a, b and c columnspi＝ΔIp,ia+ΔIp,ib+ΔIp,icAnd Iqi＝ΔIq,ia+ΔIq,ib+ΔIq,icWhile randomly calculating I of the a, b and c linespa、Ipb、IpcAnd Iqa、Iqb、IqcIn delta I corresponding to the ith non-zero element in the lower triangle of the Y arrayp,ai、ΔIp,bi、ΔIp,ciAnd Δ Iq,ai、ΔIq,bi、ΔIq,ciA 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 obtainedpi、Iqi；
And 5: according to the element structure of the Y array and J in the J arrayijAnd JjiThe corresponding relation of the positions of the non-zero elements of the sub-arrays uses triangular non-zero elements on the Y (n, d) array to quickly form a J array in a two-row + two-column mode;
(1) according to the structure of Y array element and JijAnd JjiThe corresponding relationship of the position of the non-zero elements of the subarray can obtain bij≠0→bji≠0→yij≠0→yji≠0→Jij≠0→JjiNot equal to 0, and can obtain JijAnd JjiThe H, N, M, L elements in the sub-array are also non-zero;
(2) calculating non-zero elements of triangles on the 2 i-1 th row and the 2 i-2 th row in the J array according to the non-zero elements of the i-th row in the Y (n, d) array, and simultaneously calculating non-zero elements of triangles under the 2 i-1 th column and the 2 i-2 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 non-zero elements in the Y (n, d) array;
step 6: according to calculated Ipi、IqiCorrecting 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 nodepi、IqiIs calculated as follows;
Figure FDA0001777774650000021
(2) using the relationship of H and L, N to the M element, the diagonal elements are calculated as non-diagonal elements, plus IpiOr Iqi。
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