CN105786769B - Application of method based on rapid data reading and symmetric sparse factor table in polar coordinate PQ decomposition method trend - Google Patents
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Abstract
Base of a fuel cellIn the application of the rapid data reading and the symmetrical sparse factor table method in the trend of the polar coordinate PQ decomposition method, the symmetrical sparse matrix technology is utilized to rapidly form the factor table; recording the column corner marks of the triangular non-zero elements on the column corner marks and the number of the column corner marks; using a symmetric sparse matrix technique for subsequent fast forward and backward calculations; and a Seidel mode is introduced into active and reactive iterations to accelerate the load flow calculation speed. The invention reads data from the data file with a given structure, greatly improves the data reading speed and Ipi、IqiOr Δ Pi、ΔQiThe calculated speed of (2); for example, for an IEEE-118 system, compared with the traditional method, the total time for reading the data file, forming the factor table, the active iteration time and the reactive iteration time and the total time for load flow calculation are respectively 7.31%, 3.17%, 7.51% and 7.29% of the latter. And the more the number of system nodes is, the greater the advantages of the invention are.
Description
Technical Field
The invention belongs to the field of electric power system analysis and calculation.
Background
The load flow calculation is a basic calculation in the power system and is a basis for carrying out steady-state analysis on the power system and determining the operation mode of the system. A PQ decomposition method (rapid decoupling method) derived from a Newton-Raphson method is an important method for power flow calculation of a power system, and the PQ decomposition method is high in convergence speed and small in occupied memory due to a series of simplification on the basis of the Newton method, and is more suitable for real-time power flow calculation of the power system. Therefore, it is a continuous pursuit to further increase the flow calculation speed of the PQ decomposition method.
The PQ decomposition method flow calculation needs 3 matrixes Y, B 'and B' in which an admittance matrix Y is used for calculating node current (I)pi、Iqi) Or node power (Δ P)i、ΔQi) Coefficient matrix B' matrix for calculating voltage phase angle deltaiCoefficient matrix B' array for calculating voltage amplitude increment DeltaVi. The traditional PQ decomposition method has the following defects in the reading and application of Y, B 'and B' array data:
(1) y, B 'and B' array data files have more storage number and longer read-write time.
If 3 data files of Y, B 'and B' arrays are stored respectively without considering element sparsity, opening and reading the 3 data files in the trend program; if Y, B 'and B' arrays are stored by methods such as link list storage considering element sparsity, the number of stored files is about 9. The storage of more data files makes the writing and reading time of the data files and the opening of the data files in the trend program longer, which is not beneficial to real-time calculation.
(2) Y, B 'and B' array elements are stored and read in unreasonable ways.
Because the Y, B 'and B' arrays are extremely sparse arrays, the corresponding arrays in the traditional PQ decomposition method are Y (n,2n), B '(n-1 ) and B' (m, m), wherein n is the number of nodes of the system, and m is the number of PQ nodes of the system. This storage method is simple, but its storage space is greatly wasted, and the time for reading and writing data file and subsequent calculation is too long, and Y (n,2n) is used to calculate Ipi、IqiOr Δ Pi、ΔQiIs extremely inefficient. If the sparsity of elements is considered, Y, B 'and B' array elements are stored by coordinate storage, sequential storage, linked list storage and other methods, although the storage unit can be saved, the number of data files is large, and the diagonal elements and the non-diagonal elements are stored separately, so that the reading process of the data is complicated, the calculation and the processing of the data are not facilitated, and the calculation Ipi、IqiOr Pi、QiThe efficiency is also not high. If the symmetry of the Y, B 'and B' array elements is considered, only the non-zero elements of the upper triangle are stored, and when the non-zero elements of the lower triangle are obtained according to the symmetry, the time for the transformation of the angle marks and the assignment of the elements also takes much time, and the advantages are not great.
(3) The way of forming factor arrays for B', B "arrays is not appropriate.
1) The method of forming the factor array is not suitable. Because the P-delta and Q-V iterative equations are constant coefficient linear equations, the method can be solved by a factor table method or LR, LDU, CU trigonometric decomposition method, and the like, and the LDU trigonometric decomposition method is generally used. However, the LDU trigonometric decomposition method needs to form and solve L, D, U three factor arrays, and the factor table method only needs two, and the calculation process is simple. Therefore, the factor table method is faster in calculation than the LDU triangulation method.
2) The sparse matrix technique is not sufficiently applied when forming the factor table. The B ', B' array and the Y array elements have almost the same structure, and the Y array elements have extreme sparsity, so that the calculation efficiency is extremely low if a sparse matrix technology is not used for forming the factor table. The application of the sparse matrix technology in the triangular decomposition method is rare, while the application of the sparse matrix technology in the traditional factor table method is extremely wide but not completely in place.
(4) The sparse matrix technique is not applied well in the process of carrying out the previous generation and the next generation by using the factor table.
After the factor table is formed in the traditional method, the delta can be obtained by utilizing the quick back substitution of the non-zero elements of the triangle on the factor tablei、ΔViHowever, the column corner mark of the non-zero element and the number of the non-zero elements in each row are stored separately, so that the calculation speed is not optimal, and sparse matrix technology is not utilized for the prior generation calculation of delta P/V and delta Q/V.
(5) The active and reactive iteration process does not introduce a Seidel iteration mode.
The introduction of the seidel iteration mode not only has a great influence on the calculation speed of the PQ decomposition method, but also may influence the convergence of the PQ decomposition method, and the introduction of the seidel iteration mode in the traditional PQ decomposition method is less.
For the above reasons, the computation speed of the conventional PQ decomposition method is far from optimal.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an application of a method based on rapid data reading and a symmetric sparse factor table in the trend of a polar coordinate PQ decomposition method.
The data file read by the method is three virtual arrays Y (n,3 d) only composed of non-zero elements1)、B′(n-1,2d2)、B″(m,2d3) The formed A (n, d) data file improves the reading speed and I of the data filepi、IqiOr Δ Pi、ΔQiThe calculated speed of (2); accelerating the formation of a factor table by using a symmetric sparse matrix technology; recording the position of upper triangular non-zero element in the formation process of factor table, and using the symmetric sparse matrix techniqueAccelerating subsequent calculation of the previous generation and the next generation; and a Seidel iteration mode is introduced in the iteration process, so that the active and reactive iteration speeds are accelerated.
The invention is realized by the following technical scheme.
The invention relates to an application of a method based on rapid data reading and a symmetric sparse factor table in a polar coordinate PQ decomposition method trend, which comprises the following steps:
step 1: define array Y (n,3 d)1)、B′(n-1,n-1)、B″(m,m)；
Step 2: virtual array Y (n,3 d) is extracted from A (n, d) data file1)、B′(n-1,2d2)、B″(m,2d3) Respectively read in Y (n,3 d)1) Arrays of B '(n-1 ), B' (m, m);
(1) before applying PQ decomposition method trend program, firstly establishing A (n, d) data file without non-zero elements, and making virtual array Y (n,3 d)1)、B′(n-1,2d2)、B″(m,2d3) Corresponding data are all stored in an A (n, d) array to reduce the number of writing and reading data files, wherein d is 3 × d1+2×d2+2×d3+4. Array Y (n,3 d)1)、B′(n-1,2d2)、B″(m,2d3) The sum of the corresponding father node and the non-zero element child node in each row is S1max、S2max、S3maxAnd according to the array structure has d1＝S1max，d2＝S2max，d3＝S3max。
(2) The A (n, d) array is divided into a row number group, a node array group, a Y array group, a B 'array group and a B' array group, and the storage modes are shown in Table 1.
TABLE 1A (n, d) storage of array elements
Note: in Table 1, not all memory cells have data except the row corresponding to the node containing the largest non-zero element, and Si1、Si2、Si3The actual number of storage units is far less than the maximum number of storage units, and the storage and read-write efficiency of data is further improved.
(3) Virtual array Y (n,3 d) is extracted from A (n, d) data file1)、B′(n-1,2d2)、B″(m,2d3) Corresponding data are read in Y (n,3 d) respectively1) B '(n-1 ), B' (m, m) arrays, Y (n,3 d)1) For fast calculation of Ipi、IqiOr Δ Pi、ΔQiB '(n-1 ), B' (m, m) is used to solve for Δ δi、ΔVi。
And step 3: factor table B 'of B' (n-1 ), B '(m, m) is quickly formed according to a symmetric sparse matrix technology'(n-2)、B″(m-1)Recording the number and column corner mark of triangle non-zero elements on each line in each factor table;
(1) fast formation of factor table B ' of B ' (n-1 ) by symmetric sparse matrix technique '(n-2)Automatically and statistically recording triangular non-zero elements u 'on each line in the factor table'ijOf S'iAnd column corner marks, and the calculation points are as follows.
1) Non-zero elements and calculation elements are quickly determined. And obtaining the value and the position of the nonzero element below the diagonal element by symmetry according to the value and the position of the right nonzero element of the diagonal element, and only calculating the elements on the interaction points of the rows and the columns of the nonzero elements.
Due to B ' in the process of ' normalization by line, elimination by column '(n-2)Before normalization, the nonzero elements of the right element and the right element of the diagonal element of each row of elements are equal in numerical value and symmetrical in position with the nonzero elements below the diagonal element; after normalization, the values of the nonzero elements to the right of the diagonal elements are not equal to the values of the nonzero elements below the diagonal elements (only the values of the diagonal elements are different), but the positions are still symmetrical. Therefore, the values and positions of the nonzero elements below the diagonal elements can be obtained according to the values and positions of the nonzero elements on the right side of the diagonal elements and the symmetry, and the elements to be calculated are determined by utilizing the interaction points of the rows where the nonzero elements are located and the columns where the corresponding nonzero elements are located. This can greatly improve the efficiency of judging non-zero elements and ensure that all element calculations are valid calculations.
2) The calculation of the lower triangular non-zero elements is omitted. According to the above analysis, before normalizing the elements to the right of the diagonal element, the elements to the diagonal element or less at the corresponding position may be assigned. Therefore, only the diagonal elements and the elements on the right and non-zero element row-column interaction points need to be calculated in the process of forming the factor table, and the calculation of the non-zero non-diagonal elements can be reduced by 50%.
3) And automatically counting and recording the number of the non-zero elements of the upper triangle and the column corner mark. Record B 'automatically'(n-2)Middle per-row upper triangular non-zero element u'ijOf S'iAnd corresponding column corner mark, and storing in a designated array for subsequent calculation according to S'iAnd corresponding column corner mark direct taking B'(n-2)The non-zero elements are repeatedly and rapidly subjected to forward generation and backward generation, so that the invalid calculation of a large number of zero elements in the process is avoided.
(2) Fast forming B '(m, m) factor table B' by using symmetric sparse matrix technology(m-1)Automatically counting and recording triangular non-zero element u' on each line in the factor tableijNumber of (1) < SiAnd a corner mark, and stores in a designated array for subsequent calculation according to S ″)iAnd the corresponding corner mark is directly marked with B(m-1)The fast forward and backward generations are repeated.
And 4, step 4: utilizing factor table B 'according to symmetric sparse matrix technique'(n-2)、B″(m-1)Non-zero element l 'of middle and lower triangles'ji、l″jiAnd S'i、S″iRapidly calculating delta P/V and delta Q/V by the previous generation; non-zero element u 'of upper triangle using factor table'ij、u″ijAnd S'i、S″iFast back substitution to obtain deltai、ΔViIntroducing a Seidel mode in the active and reactive iterative process;
(1) by upper triangular non-zero element u 'recorded during factor Table formation'ij、u″ijThe corner mark of (1) is a lower triangular non-zero element l 'obtained according to symmetry'ji、l″jiIs a symbol of l'ji、l″jiElement and S'i、S″iCan be used as a fast generationCalculating delta P/V and delta Q/V; from u'ij、u″ijElement and S'i、S″iCan be quickly substituted to obtain deltai、ΔViAnd a large amount of invalid calculation of zero elements is avoided, and the previous generation and the next generation processes are greatly accelerated.
(2) After introducing the Sedel iteration mode, the iteration process of the PQ decomposition method is as follows: delta Pi→Δδi→δi+1＝δi+Δδi，ΔQi→ΔVi→Vi+1＝Vi+ΔViThe active power is calculated, then the active power is iterated to calculate the correction quantity and the new value of the voltage phase angle, then the phase angle new value is used for calculating the reactive power, and then the reactive power is iterated to calculate the correction quantity of the voltage amplitude, so that the convergence speed is accelerated.
And 5: judging whether a convergence condition is met;
if the convergence condition is not satisfied, delta obtained by the iteration is utilizedi、ViContinuing to perform next previous generation and next generation calculation; if the convergence condition is satisfied, step 6 is performed.
Step 6: and calculating the power of the balance node and the branch power and outputting a calculation result.
The method of the present invention has the following advantages compared to the conventional PQ decomposition method.
(1) Only 1 data file of the A (n, d) array is read, only corresponding non-zero elements are stored in the A (n, d) array, and the number of storage units and the reading time are greatly reduced.
(2) Can be directly based on Y (n,3 d)1) Array calculation Ipi、IqiOr Δ Pi、ΔQiNo judgment or invalid computation of non-zero elements is required.
(3) Rapidly obtaining a factor table of the B 'and B' array according to the symmetry sparsity, and recording the upper triangular non-zero element u 'in each factor table'ij、u″ijOf S'i、S″iAnd column corner mark for direct taking of B 'in subsequent calculations'(n-2)、B″(m-1)The non-zero elements of the array are repeatedly subjected to rapid generation and generation.
(4) Non-zero element l 'by bottom triangle'ji、l″jiAnd S'i、S″iThe method can quickly calculate delta P/V and delta Q/V of the previous generation, and greatly improve the calculation efficiency of the previous generation.
(5) Using non-zero elements u 'of the upper triangle'ij、u″ijAnd S'i、S″iThe method can quickly back-substitute to obtain delta and delta V, and greatly improves the back-substitution calculation efficiency.
(6) And a Seidel iteration mode is introduced in the active and reactive iteration processes, so that the power flow convergence speed is further accelerated.
Drawings
FIG. 1 is a flow chart of flow calculation in a conventional polar PQ decomposition method.
FIG. 2 is a flow chart of the present invention for polar PQ decomposition flow calculation.
Detailed Description
The invention will be further illustrated by the following examples.
Examples are given. The traditional polar coordinate PQ decomposition method and the polar coordinate PQ decomposition method used by the invention are respectively used for carrying out load flow calculation on an IEEE-30, -57, -118 node system, and the read data files are compared to form a factor table, and the average calculation time of active and reactive iteration and load flow calculation (total) is compared. The calculation results are shown in table 2.
TABLE 2 comparison of time required for PQ decomposition of IEEE System nodes by the factor Table method
tr.c、tf.c、ti.c、tp.c: when sparsity is not considered in the traditional PQ decomposition method, a data file is read, a factor table is formed, and the average calculation time of active and reactive iterations and the (total) time of load flow calculation are calculated.
tf.s.c、tp.s.c: in the traditional PQ decomposition method, only the average calculation time of a nonzero element formation factor table below a diagonal element and the load flow calculation (total) time are judged (except for the formation factor table, element sparsity is not considered in other traditional methods).
tr.new、tf.new、ti.new、tp.new: the invention reads the time of a data file, forms a factor table, and calculates the average time of active and reactive iterations and the (total) time of load flow calculation by a PQ decomposition method.
tr.new/tr.c、tf.new/tf.c、ti.new/ti.c、tp.new/tp.c: compared with the traditional method, the method does not consider the sparsity, reads the data file time, forms the percentage of the factor table time, the active and reactive iteration time and the load flow calculation (total) time.
tf.s.c/tx.c、tp.s.c/tp.c: the percentage of the time of forming the factor table by the non-zero elements below the diagonal elements and the PQ decomposition method load flow calculation (total) time in the traditional method is only judged compared with the percentage of the traditional method when any sparsity is not considered.
Taking the IEEE-118 node system as an example, the calculation results are analyzed as follows:
(1) and reading the comparison of the number of the data files and the time.
In the traditional factor table method, Y, B 'and B' array elements are respectively stored in Y (n,2n), B '(n-1 ) and B' (m, m) arrays, 3 data files need to be read, while the method of the invention is stored in A (n, d) array, and only 1 data file needs to be read. The time for reading the data file is only 7.31 percent of that of the traditional method.
(2) A comparison of the factor table times is made.
The time for forming the factor table is only 3.17 percent of that of the traditional method; if it is judged in the conventional method that the nonzero elements below the diagonal element form a factor table, it is 9.28% of that in the conventional method when the sparsity is not considered.
(3) The active and reactive iteration time of the method is only 7.51 percent of that of the traditional method.
(4) Comparison of load flow calculation (total) time.
The (total) time of the load flow calculation of the invention is only 7.29 percent of that of the traditional method. Compared with the traditional method which does not consider the sparsity, the speed of forming the factor table by judging the nonzero element below the diagonal element in the traditional method is greatly improved, but the time of load flow calculation in the former method is almost unchanged compared with that in the latter method.
The calculation result shows that compared with the traditional PQ decomposition method, the calculation speed is greatly accelerated in the aspects of reading data files, forming factor tables, active and reactive iteration and load flow calculation, and the calculation efficiency of the method is extremely high. And the more the number of nodes of the power system is, the greater the advantages of the invention are.
The method can be realized by any programming language and programming environment, wherein the Visual C + + language is adopted, the development environment is Visual C + +, and the operation platform is Intel (R) Core i7-4790CPU@3.60GHZAnd 8.00GB of memory.
Claims (1)
1. An application of a method based on rapid data reading and a symmetric sparse factor table in power system power flow of a polar coordinate PQ decomposition method is characterized by comprising the following steps:
step 1: define array Y (n,3 d)1)、B′(n-1,n-1)、B″(m,m)；
Step 2: virtual array Y (n,3 d) is extracted from A (n, d) data file1)、B′(n-1,2d2)、B″(m,2d3) Respectively read into Y (n,3 d)1) B '(n-1 ), B' (m, m) arrays, where Y (n,3 d)1) For fast calculation of Ipi、IqiOr Δ Pi、ΔQiThe B '(n-1 ), B' (m, m) arrays are used to solve for Δ δi、ΔVi；
And step 3: factor table B 'of B' (n-1 ), B '(m, m) is quickly formed according to a symmetric sparse matrix technology'(n-2)、B″(m-1)Recording the number and column corner mark of triangle non-zero elements on each line in each factor table;
(1) fast formation of factor table B ' of B ' (n-1 ) by symmetric sparse matrix technique '(n-2)Automatically and statistically recording triangular non-zero elements u 'on each line in the factor table'ijOf S'iAnd column corner marks for accelerating subsequent calculation of the previous generation and the next generation; the main contents comprise: quickly determining non-zero elements according to symmetry and crossMutually and rapidly determining a calculation element; according to the symmetry, the calculation of the lower triangular non-zero element is omitted; automatically counting and recording the number of upper triangle non-zero elements and column corner marks; accelerating subsequent previous generation and back generation calculation by using the number of non-zero elements and a column corner mark;
(2) fast forming B '(m, m) factor table B' by using symmetric sparse matrix technology(m-1)Automatically counting and recording triangular non-zero element u' on each line in the factor tableijNumber of (1) < SiAnd column corner marks for accelerating subsequent calculation of the previous generation and the next generation;
and 4, step 4: utilizing factor table B 'according to symmetric sparse matrix technique'(n-2)、B″(m-1)Middle and lower triangular non-zero element l'ji、l″jiAnd S'i、S″iRapidly calculating delta P/V and delta Q/V by the previous generation; utilizing a factor-based upper triangular non-zero element u'ij、u″ijAnd S'i、S″iFast back substitution to obtain deltai、ΔViIntroducing a Seidel mode in the active and reactive iterative process;
and 5: judging whether a convergence condition is met;
if the convergence condition is not satisfied, delta obtained by the iteration is utilizedi、ViContinuing to jump to step 4; if the convergence condition is satisfied, executing step 6;
step 6: and calculating the power of the balance node and the branch power and outputting a calculation result.
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