CN105591388B - A kind of electric system rectangular co-ordinate PQ decomposition method flow data memory methods based on Sparse technology - Google Patents

A kind of electric system rectangular co-ordinate PQ decomposition method flow data memory methods based on Sparse technology Download PDF

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CN105591388B
CN105591388B CN201610130999.0A CN201610130999A CN105591388B CN 105591388 B CN105591388 B CN 105591388B CN 201610130999 A CN201610130999 A CN 201610130999A CN 105591388 B CN105591388 B CN 105591388B
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CN105591388A (en
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陈恳
席小青
万新儒
陆节涣
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Nanchang University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

A kind of electric system rectangular co-ordinate PQ decomposition method flow data memory methods based on Sparse technology, the method of the present invention is by Y (n in conventional method, 2n), B ' (n 1, n 1), three arrays of B " (n 1; n 1) up and down triangle nonzero element be stored in A (n; d) in array, greatly reduce memory cell number and improve data file read or write speed and PQ decomposition method trends in Ipi、IqiOr Δ Pi、ΔQiCalculating speed, and using the almost the same relationship of Y, B ', B " battle array three's nonzero element position, be further reduced memory cell.Compared with the methods of chain technique, the quantity of memory cell is greatly reduced.Such as to 118 node systems of IEEE, the present invention is compared with conventional method, and maximum storage unit number and practical memory cell number are respectively the 10.00% of the latter, 4.48%, and the time of write-read data file is respectively the 11.45% and 6.20% of the latter.Number of nodes is more, and advantage of the present invention is more apparent.

Description

A kind of electric system rectangular co-ordinate PQ decomposition method flow datas based on Sparse technology are deposited Storage method
Technical field
The invention belongs to electrical power system analysis and computing fields.
Background technology
Newton-Raphson approach (Newton method) is most common method during electric power system tide calculates, and can be incited somebody to action by calculating process It is divided into rectangular co-ordinate Newton method and polar coordinates Newton method, and polar coordinates PQ decomposition methods can be derived respectively according to the two characteristics simplified With rectangular co-ordinate PQ decomposition methods.In general rectangular co-ordinate Newton method illustrates and calculation and programming side than polar coordinates Newton method in principle Face is best understood from, but from calculating process, equation number of the polar coordinates Newton method than rectangular co-ordinate Newton method update equation formula Lack, the type and quantity of Jacobian matrix element are also few, and trend iterations also lack 1 time or identical sometimes, therefore polar coordinates Newton method seems more extensive than rectangular co-ordinate Newton method application.By the same token, polar coordinates PQ decomposition methods have become PQ points The synonym of solution introduces rectangular co-ordinate PQ decomposition methods almost without document.In fact, due to not related in rectangular co-ordinate Load flow calculation And trigonometric function, this is especially considering sparsity and the case where rectangular co-ordinate Load flow calculation coefficient matrix feature to many systems Lower its memory cell number, trend iteration speed etc. are simultaneously no less than polar index.
To multiple symmetrical, extremely sparse coefficient matrix applications involved in PQ decomposition methods Load flow calculation in electric system. If not considering the sparsity of these coefficient matrixes, the data of a large amount of neutral elements can cause to deposit in storage, reading and calculating process Significant wastage, read-write data file and the calculating process overlong time of receptacle space.Therefore, in conjunction with rectangular co-ordinate PQ decomposition method coefficients The characteristics of matrix, simultaneously considers that Sparse technology not only can largely save memory cell to the storage mode of element, can also greatly reduce The time of the storage of data file, reading and calculating process.
It needs to use 3 arrays in rectangular co-ordinate PQ decomposition method Load flow calculations, wherein admittance matrix Y is used for calculate node electric current (Ipi、Iqi) and node power (Δ Pi、ΔQi), coefficient matrix B ' is for calculating voltage imaginary part increment Delta fi, coefficient matrix B " use In calculating voltage real part increment Delta ei.In traditional PQ decomposition methods to the storage of this 3 coefficient matrix data, reading, using etc. deposit In following deficiency:
(1) acquisition modes of B ', B " array element element are unreasonable.
Due to Y, B ', B, " composition of array element element is affected to trend convergence or convergence rate, its general element is constituted It answers different.Simplest B ', B " array element element acquisition modes are directly to be derived from the imaginary part of Y array element elements, as long as storing 1 in this way Y array element elements.But if B ', B " array element element take the imaginary part of Y array element elements completely, or if only B ', B " array element element it is identical and Different from the imaginary part of Y array element elements, the iterations or convergence of PQ decomposition method trends may be all influenced.
(2) storage mode of Y, B ', B " array element element is unreasonable.
If n is the number of nodes of system, m is the PQ number of nodes of system, corresponding number in traditional rectangular co-ordinate PQ decomposition methods Group is respectively Y (n, 2n), B ' (n-1, n-1), B " (n-1, n-1), corresponds to extremely sparse Y, B ', B " the array element element of storage respectively. This storage mode can cause the significant wastage of memory space and read-write data file and calculate overlong time, and with Y (n, 2n) Array calculates Ipi、IqiOr Δ Pi、ΔQiEfficiency is extremely inefficient.If with the methods of coordinate storage, sequential storing, chained list storage, Although many memory cells can be saved, make the reading process of data cumbersome since diagonal element separately stores with nondiagonal element, It is unfavorable for it to calculate and handle, calculates Ipi、IqiOr Δ Pi、ΔQiWhen efficiency it is also not high.
(3) the storage number of Y, B ', B " battle array data file is more, access time is longer.
If do not considered, sparsity traditionally stores three data files of Y, B ', B " battle array respectively, then in Load flow calculation Three data files are opened in program respectively and read data;Such as consider sparsity by chained list memory method respectively to Y, B ', B " is stored by battle array, then the number for storing file is up to 9.The data file number of storage is more, then writes data file Time is longer, and also resulting in needs the open data file number more and read data file in PQ decomposition method flow calculation programs Time is longer, is unfavorable for the real-time calculating of PQ decomposition methods.
(4) relationship between Y, B ', B " battle array nonzero element position is underused.
Y, the corresponding array of B ', B " battle array is respectively Y (n, 2n), B ' (n-1, n-1), B " (n-1, n-1).Y gusts of exponent number is N, and B ', B " order of matrix number are (n-1).In 1~(n-1) order range, during forming Y, B ' battle arrays, its is quiet when exponent number is identical The position of the nonzero element of state and number are just the same;And in the forward steps of Y, B ' battle array, it is dynamic non-when exponent number is identical The position of neutral element and number are also just the same.In 1~m line ranges, the position of each row nonzero element of B ', B " battle array and number It is identical under current intelligence in static state, and in (m+1)~(n-1) rows, for B " in battle array in addition to diagonal element is -2, remaining is first Element is zero, and the position of nonzero element and number are different under static and current intelligence in going from B ' battle arrays (m+1)~(n-1). Due to not utilizing the two characteristics in conventional method, not so as to cause some in the waste of memory cell and factor table forming process Necessary calculating.
Invention content
In order to overcome the above-mentioned deficiencies of the prior art, a kind of PQ points of electric system rectangular co-ordinate based on Sparse technology is proposed Solution flow data memory method.
Array Y (n, 2n) that the present invention separately stores three in traditional PQ decomposition methods Load flow calculation, B ' (n-1, n-1), B " (n-1, n-1) is respectively with three virtual array Y (n, 3d1)、B′(n-1,d2)、B″(m,d2) replacement is corresponded to, number is deposited in merging In group A (n, d).The sum of line number, each host node and nonzero element child node in A (n, d) containing host node, Y (n, 3d1) correspond to and deposit Y gusts of information are store, for calculating Ipi、IqiOr Δ Pi、ΔQi, row number and parameter containing host node Yu nonzero element child node;B′(n- 1,d2)、B″(m,d2) storage B ', B " battle array information are corresponded to, for completing PQ decomposition method Load flow calculations, wherein B ' (n-1, d2) in contain The parameter of host node and nonzero element child node, and B " (m, d2) in contain only 1~m rows host node and nonzero element child node Parameter.
The present invention is achieved by the following technical solutions.
A kind of electric system rectangular co-ordinate PQ decomposition method flow datas storage side based on Sparse technology of the present invention Method includes the following steps:
Step 1:Define data file array A (n, d);
(1) node corresponding with line number i is father node, and coupled nonzero element node is child node, neutral element Child node does not occur;
(2) three virtual arrays of storage Y, B ', B " array element element are Y (n, 3d1)、B′(n-1,d2)、B″(m,d2)。Y(n, 3d1) store in array the row number j of all father nodes and nonzero element child node and the real part of corresponding self-admittance and transadmittance and Imaginary values, since the maximum non-zero entry prime number of the sum of each row father node and nonzero element child node is S1max=d1, therefore it is maximum Columns is 3 × d1。B′(n-1,d2)、B″(m,d2) all father nodes are only stored in array and nonzero element child node is corresponding The imaginary values of self-admittance and transadmittance, and B " (m, d2) in only store the corresponding parameter of PQ nodes, each row father node and non-at this time The maximum non-zero entry prime number of the sum of neutral element child node is S2max=d2, therefore its maximum number of column is d2, and its nonzero element Row number j can be by Y (n, 3d1) in obtain;
(3) by Y (n, 3d1)、B′(n-1,d2)、B″(m,d2) data of three arrays coexist in A (n, d) array, wherein D=3d1+2d2+3."+3 " are respectively line number row and S1max、S2maxThe count column at place, i.e., the 1st~3 row in table 1;
(4) the maximum storage unit number U of this methodmax.newIt is calculated by maximum non-zero entry prime number in each row:
Umax.new=U1max+U2max+U3max=Y (n, 3d1)+B′(n-1,d2)+B″(m,d2)
=n × (d1+2)+(n-1)×(d2+1)+m×d2
Note:"+2 " correspond to line number row and Y gusts of count columns;"+1 " corresponds to the count column of B ' battle arrays and B " battle array;
(5) the practical memory cell number U of this methodact.newBy each row SiThe sum of non-zero entry prime number of actual count calculates, Uact.new=Y (n, 3d '1)+B′(n-1,d′2)+B″(m,d′2).Calculate analysis shows, the practical memory cell number of new method is about 50% or so of new method maximum storage unit number is accounted for, and percentage is reduced with the increase of number of nodes;
(6) A (n, d) array is divided into " line number group ", " node array ", " Y gusts of groups ", " B ' battle arrays group ", " B " battle array group ", storage Format is as follows:
Line number group i:Storage line number corresponding with father node is located at the 1st row;
Node array Si1、Si2:The sum of each row father node and nonzero element son node number in Y, B ' (B ") battle array are stored, is located at 2nd, 3 row, Si1、Si2Value is added up by program automatically to ensure quickly and efficiently to read corresponding father node and non-zero entry sub-prime section The parameter of point, to make the practical memory cell number of the present invention be much smaller than its maximum storage unit number;
Y gusts of groups:Storage and Y (n, 3d1) the corresponding Y gusts of data of array, it is located at the 4th~(3d1+ 3) it arranges, is incremented by by row number suitable Sequence stores the row number j and corresponding self-admittance, the real part of transadmittance, imaginary values of father node and nonzero element child node;
B ' battle array groups:Storage and B ' (n-1, d2) the corresponding B ' battle arrays data of array, it is located at (3d1+ 4)~(3d1+d2+ 3) it arranges, Store the imaginary values of father node and the corresponding self-admittance of nonzero element child node, transadmittance, non-zero entry by row number incremental order The row number j of element can be by Y (n, 3d1) in obtain;
B " battle array groups:Storage and B " (m, d2) array corresponding B " battle array data, it is located at (3d1+d2+ 4)~(3d1+2d2+3) Row are stored the imaginary values of father node and the corresponding self-admittance of nonzero element child node, transadmittance, non-zero by row number incremental order The row number j of element can be by Y (n, 3d1) in obtain.
The storage mode of A (n, d) array element is as shown in table 1.
The storage mode of table 1 A (n, d) array element
Note:In table 1 in addition to containing the corresponding row of maximum nonzero element node, and not all memory cell has data, and Use Si1、Si2It can guarantee that practical memory cell number is far smaller than maximum storage unit number, further increase the read-write efficiency of data.
Step 2:All branches data are read in from data file;
Step 3:It calculates all elements of Y, B ', B " battle array and data is stored in A (n, d) array;
Y array element elements generally include the real and imaginary parts that all branch parameters are formed by Y array element elements, are only used for follow-up PQ points I in solution Load Flow Programpi、IqiOr Δ Pi、ΔQiCalculating;B ', B " array element element are used to solve Δ f in down-streami、Δei;One As remove line mutual-ground capacitor c during calculating B ' array element elements and remove line electricity during calculating B " array element elements Hinder r;
Step 4:Data file is written into the data of A (n, d) array in case down-stream uses.
In view of the modularization of program, the program for forming A (n, d) array leaves it at that, and A (n, d) array data file Calling then by PQ decomposition method flow calculation programs execute.
The data file that A (n, d) array is opened in PQ decomposition method flow calculation programs, by Y gust data reading Y (n, 3d1) array to be quickly to calculate Ipi、IqiOr Δ Pi、ΔQi;By B ', B " battle array data read in respectively B ' (n-1, n-1) and B " (n-1, N-1) array is to solve Δ fi、Δei.The data of A (n, d) data file are read in than reading in Y (n, 2n), B ' (n-1, n-1) respectively " much less is wanted with B the time required to the data of (n-1, n-1) data file.
The present invention is compared with the storage mode of traditional Y, B ', B for not considering element openness " array element elements, by multiple numbers It is simplified to the storage of 1 data file according to the storage of file, the storage of all data will be simplified to only deposit nonzero element Storage, the relationship for utilizing Y, B ', B " battle array nonzero element position almost the same are saved and arrange lower target storage to B ', B " battle array nonzero element With the storage to B " battle array PV node corresponding datas, the memory cell of data and the access time to data file are greatly reduced With calculating Ipi、IqiOr Δ Pi、ΔQiTime.The present invention with store by coordinate, be stored in order, by the methods of chained list storage phase Than still can more reduce the memory cell of data and the storage quantity of data file, improve the read-write speed to data file Degree, and storage mode is more simple, calculation processing of follow-up data etc. is more convenient, quick.
Description of the drawings
Fig. 1 is the flow chart that the present invention forms rectangular co-ordinate PQ decomposition method flow data files.
Fig. 2 is the flow chart that conventional method forms rectangular co-ordinate PQ decomposition method flow data files.
Specific implementation mode
The present invention will be described further by following embodiment.
Embodiment.It is respectively compared traditional memory method for not considering sparsity and considers the chained list memory method of sparsity And the plain required data file number of the method for the present invention storage IEEE-30, -57, -118 node system Y, B ', B " array element, storage The average time of unit number, data file read-write process.Table 2 gives the comparison result of various methods.
(1) comparison of data file number.
1) respectively by Y, B ', B, " array element element is stored in Y (n, 2n), B ' (n-1, n-1) and B " (n- to traditional memory method respectively 1, n-1) in 3 arrays, 3 data files are needed;
2) chained list memory method respectively stores 3 diagonal element, off-diagonal element, line number (chained list) arrays, therefore Storing corresponding Y, B ', B " array element element respectively needs 9 arrays, needs 9 data files;
3) Y, B ', B " array element element are stored in A (n, d) array by the present invention jointly, it is only necessary to 1 data file;
(2) store the comparison of Y, B ', B " array element element unit number.
If n is the number of nodes of system, m is the PQ number of nodes of system;Per node on average is connected with 4 branches;Due to being Complex matrix, Y array elements element × 2.To IEEE-118 node systems, n=118, m=64,3d1=3 × S1max=30, d2=S2max =9.
1) Traditional Method memory cell number:Uc=n × 2 × n+2 (n-1) × (n-1)=55226;
2) chain technique memory cell number:Ut=(2n+2N+N)=(2n+3N)=(14 × n)=6580;
To simplify the calculation, the exponent number for being approximately considered B ', B " battle array herein is (n-1).Since the calculating of above-mentioned chain technique is public Formula is suitable for real number matrix, considers Y array elements element × 2, therefore the simplification calculates the storage lists for calculating chain technique not more First number.
3) maximum storage unit number of the present invention:It is calculated by maximum non-zero entry prime number in each row:
Umax.new=U1max+U2max+U3max=n × (3d1+2)+(n-1)×(d2+1)+m×d2=5522.
Due to d=3d1+2d2+ 3, therefore to IEEE-118 node systems, all information can be stored with A (118,51) array.
4) the practical memory cell number of the present invention:By S in each rowiThe sum of non-zero entry prime number of actual count calculates:
Uact.new=Y (n, 3d '1)+B′(n-1,d′2)+B″(m,d′2)=2474.
The maximum storage unit number that above-mentioned comparison can be seen that the present invention accounts for the 10.00% of conventional method memory cell number, And it is reduced with the increase of number of nodes;The practical memory cell number of the present invention accounts for new method maximum storage unit number 44.80%, it is reduced also with the increase of number of nodes;And the practical memory cell number of the present invention accounts for conventional method memory cell number 4.48%, substantially reduced likewise as the increase of number of nodes;It is single that the practical memory cell number of the present invention accounts for chain technique storage The 37.60% of first number, is reduced likewise as the increase of number of nodes.Therefore number of nodes is bigger, the memory cell that the present invention saves It is more, and to Ipi、IqiOr Δ Pi、ΔQiComputational efficiency it is high.
Comparison of the 2 various methods of table to IEEE system data files access time and memory cell number
tw.c、tr.c、Uc:Conventional method is averaged write-read time, required memory cell number to Y, B ', B " battle array data file;
tw.new、tr.new、Umax.new、Uact.new:The present invention is averaged write-read time, required to Y, B ', B " battle array data file Maximum, practical memory cell number;
tw.new/tw.c、tr.new/tr.c、Umax.new/Uc、Uact.new/Uc:The average write-read time of the present invention and conventional method, The percentage of the percentage of maximum storage unit number, actually required memory cell number.
Ut、Uact.new/Ut:Memory cell number needed for chain technique is deposited needed for practical memory cell number and chain technique of the invention The percentage of storage unit number.
Above-mentioned calculating analysis shows:
1. the memory cell number of the present invention and the speed of write-read data file are significantly better than conventional method.
The present invention by 3 data file coexistences needed for PQ decomposition methods in 1 array, with conventional method by 3 data File separates storage mode and compares, when greatly reducing the write-read of the number of required data file, memory cell and data file Between.Such as to IEEE-118 node systems, the time that the present invention writes data file is only the 11.45% of conventional method, reads data text The time of part is only the 6.20% of conventional method, and maximum storage unit number is only the 10.00% of conventional method, and actual storage list Member is only the 4.48% of conventional method.
2. the memory cell number of the present invention is equally better than considering the chained list storage mode of sparsity.
The present invention only stores 1 data file, chain technique need to store 9 data files;The maximum storage of the method for the present invention Unit number is about the 60%~80% of chain technique, but the practical memory cell number of the method for the present invention is about the 40% of chain technique.
3. electric system number of nodes is more, the advantage of data-storing of the present invention and reading process is bigger.
The present invention can't be dramatically increased with the increase memory cell of system node number, the time of write-read data file It will not dramatically increase.
4. due to simultaneously store Y, B ', B " battle array up and down triangle nonzero element, formed B ', B " factor table battle array, Calculate Ii、ΔPi、ΔQiWhen will be extremely convenient, and reading and writing data time or memory cell number with only store upper triangle nonzero element Mode compare almost without difference.
5. the present invention is according to the almost the same relationship of Y, B ', B " battle array nonzero element position, to B ', B, " battle array only stores non-zero entry Plain parameter, and the row subscript of nonzero element directly uses Y (n, 3d1) in the row subscript stored.
6. in view of the particularity of B " PV node data in battle array, B " (m, d of the present invention2) in only store PQ node datas, and Assignment directly is carried out to PV node data again after the data file that PQ decomposition method Load Flow Programs call A (n, d) array, further Reduce the storage capability of element.
7. read-write and application for the multiple asymmetric data files of various engineering fields, the present invention has same excellent Gesture.
Any type programming language may be used in the present invention and programmed environment is realized, uses C++ programming languages, exploitation here Environment is Visual C++, and operation platform is Intel (R) Core i7-4790CPU@3.60GHZ, memory 8.00GB.

Claims (1)

1. a kind of electric system rectangular co-ordinate PQ decomposition method flow data memory methods based on Sparse technology, feature include with Lower step:
Step 1:Define data file array A (n, d);
(1) it is father node to define node corresponding with line number i, and coupled nonzero element node is child node, neutral element Child node and parameter are not present in memory cell;
(2) three virtual arrays of definition storage Y, B ', B " array element element are Y (n, 3d1)、B′(n-1,d2)、B″(m,d2);Y(n, 3d1) the row number j of all father nodes and nonzero element child node and corresponding parameter, corresponding maximum non-zero entry are stored in array Prime number is S1max;And B ' (n-1, d2)、B″(m,d2) all father nodes are only stored in array and nonzero element child node is corresponding The row number j of parameter, nonzero element can be by Y (n, 3d1) in obtain, it is corresponding maximum non-zero entry prime number be S2max, and B " (m,d2) in only store the corresponding parameter of PQ nodes;
(3) by Y (n, 3d1)、B′(n-1,d2)、B″(m,d2) data of three arrays coexist in A (n, d) array;
(4) it is defined as maximum storage unit number U by maximum non-zero entry prime number in each rowmax.new
(5) each row S is pressediThe non-zero entry prime number of actual count is defined as practical memory cell number Uact.new
(6) A (n, d) array is divided into " line number group ", " node array ", " Y gusts of groups ", " B ' battle arrays group ", " B " battle array group ", Store form It is as follows:
Line number group i:It is used for inspection data, stores line number corresponding with father node;
Node array Si1、Si2:It is used efficiently to read and write data, Si1Each row father node and nonzero element son node number in Y gusts of storage The sum of, Si2Storage B ' and/or B " the sum of each row father node and nonzero element son node number, S in battle arrayi1、Si2Value is automatic by program It is cumulative;
Y gusts of groups:Storage and Y (n, 3d1) the corresponding Y gusts of data of array, store father node and non-zero entry sub-prime by row number incremental order The row number j of node and corresponding self-admittance, the real part of transadmittance, imaginary values;
B ' battle array groups:Storage and B ' (n-1, d2) the corresponding B ' battle arrays data of array, store father node and non-zero entry by row number incremental order The corresponding self-admittance of sub-prime node, transadmittance imaginary values, nonzero element row number j is by Y (n, 3d1) in obtain;
B " battle array groups:Storage and B " (m, d2) array corresponding B " battle array data, store father node and nonzero element by row number incremental order The corresponding self-admittance of child node, transadmittance imaginary values, nonzero element row number j is by Y (n, 3d1) in obtain;
Step 2:All branches data are read in from data file;
Step 3:It calculates all elements of Y, B ', B " battle array and data is stored in A (n, d) array;
Y array element elements generally include the real and imaginary parts element that all branch parameters are formed by Y gusts, are only used for follow-up PQ decomposition methods I in Load Flow Programpi、IqiOr Δ Pi、ΔQiCalculating;B ', B " array element element are used to solve Δ f in down-streami、Δei, calculating Remove line mutual-ground capacitor c during B ' array element elements and remove line resistance r during calculating B " array element elements;
Step 4:Data file is written into the data of A (n, d) array in case down-stream uses.
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