CN104091092B - Feature value analysis system for small-interference stability of large-scale power system - Google Patents
Feature value analysis system for small-interference stability of large-scale power system Download PDFInfo
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Abstract
The invention provides a feature value analysis system for small-interference stability of a large-scale power system, and belongs to the technical field of power system simulation and analysis. The feature value analysis system comprises a BPA data interface module for achieving seamless read-write operation of a BPA data file, a sparse matrix calculation module for achieving relevant sparse matrix processing in small-interference stability feature value analysis, a power flow calculation module, a system modeling and linearization module, a state matrix calculation module, an all feature value calculation engine module, a partial feature value calculation engine module and an oscillation mode extraction and analysis module. Omni-bearing and missing-free feature value simulation analysis for small-interference stability of an actual large-scale power grid is achieved by the adoption of TTQRE and IRAM and JDM with multiple calculation schemes.
Description
Technical field
The present invention relates to the system of a kind of electric system simulation and analysis technical field, specifically a kind of to adopt three kinds
The Eigenvalues analysis system of the large-scale electrical power system small signal stability of different characteristic value-based algorithm.
Background technology
Power system small signal stability is referred to after electrical network experiences small sample perturbations, continues the energy for keeping synchronous operation
Power.Power system small signal stability is typically using the method for Liapunov first as criterion.The method of Liapunov first
Point out, if the eigenvalue of zero or positive real part does not occur in the state matrix after system linearization, then it is determined that working as
Front system is small interference stability.Therefore, in power system, eigenvalue calculation is all the time to realize low frequency power oscillation
The identification of pattern, the assembling addressing of all kinds of stability controllers and parameter optimization, operational factor to the sensitive analysis of control parameter,
The important prerequisite and basic guarantee of the functions such as the modal information extraction of on-line checking oscillation data.
Due to the continuous expansion of electrical network scale, from eighties of last century eighties, the research worker of power industry has just been thrown
Enter substantial amounts of energy in eigenvalue calculation method and analysis on Small Disturbance Stability systematic research and exploitation.Up to now, generation
All Eigenvalues analysis systems for being used for large-scale electrical power system small signal stability are occurred in that in the range of boundary, for example：The U.S.
EISEMAN that Pacific Ocean gas is developed with Utilities Electric Co., U.S.'s DianKeYuan combine Ontario, Canada hydroelectric board joint development
SSSP, the SSAT of Canadian power technology development in laboratory, the NEVA of Siemens exploitation, Brazilian power science research
PacDyn, PSASP and PSD-SSAP of China Electric Power Research Institute's exploitation of center exploitation etc..
Quantity according to eigenvalue to be asked is sorted out, and the Eigenvalues analysis method of power system small signal stability is divided into
All Eigenvalues analytic process and partial feature value analytic process.Although almost all of large-scale electrical power system small signal stability point
Analysis system analyzes two aspects comprising All Eigenvalues analysis and partial feature value, but still there is problem below and not
Foot：
1) nucleus module of All Eigenvalues analytic process still use the eighties of last century Kublanovskay sixties and
The dual step displacement implicit expression QR algorithm that Francis is proposed, so as to cause domestic electrical industry personage to generally believe：For large-scale electricity
For the analysis on Small Disturbance Stability of Force system, there is low memory in QR algorithms, the calculating time is very long, the eigenvalue that calculates is missed
The problems such as difference is very big, algorithm may not restrain [Wang Kang, Jin Yuqing, Gande is strong, etc. the stability analysis of power system small-signal and control
System summary [J]. Electric Power Automation Equipment, 2009 (5):10-19. Xue Yu win, Hao Sipeng, Liu Junyong. with regard to Low Frequency Oscillation Analysis
The commentary [J] of method. Automation of Electric Systems, 2009,33 (3):1-8. China Electric Power Research Institutes, PSASP7.0 versions are little dry
Disturb calculating user's manual [R], Beijing:China Electric Power Research Institute, 2010. China Electric Power Research Institutes, PSD-SSAP is little
Interference stability analysis program user's manual (2.5.2 versions) [R], Beijing:China Electric Power Research Institute, 2012.].Could not
Recognize, the dual step displacement implicit expression QR algorithm of early stage has above-described variety of problems really.However, with numerical computation method
And the continuous progress of computer hardware technique, QR algorithms complete already step multiple from dual step displacement-bulk
The differentiation of the multiple step displacement of shifting-chain type fritter-multiple step displacement of two step fritters with positive early-age shrinkage strategy
[Francis J G F.The QR transformation a unitary analogue to the LR
Transformation-Part 1 [J] .The Computer Journal, 1961,4 (3):265‐271.Francis J G
F.The QR transformation-part 2 [J] .The Computer Journal, 1962,4 (4):332‐345.Bai
Z, Demmel J.On a Block Implementation of Hessenberg Multishift QR Iteration
[J] .International Journal of High Speed Computing, 1989,1 (1):97-112.Braman K,
Byers R, Mathias R.The multishift QR algorithm.part I:Maintaining well‐focused
shifts and level 3 performance[J].SIAM Journal on Matrix Analysis and
Applications, 2002,23 (4):929-947.Braman K, Byers R, Mathias R.The multishift QR
algorithm.Part II:Aggressive early deflation[J].SIAM Journal on Matrix
Analysis and Applications, 2002,23 (4):948-973.], personal computer also already from be only capable of support 4GB
32 of addressing, becoming can support 16EB (1EB=230GB) 64 of addressing.Therefore, based on dual step displacement implicit expression QR
The All Eigenvalues analytic process of algorithm and 32 personal computers, it is clear that can not meet current large-scale electrical power system little dry
Disturb the calculating demand of stability analyses；
2) partial feature value analytic process is the main stream approach of present analysis large-scale electrical power system small signal stability.Part
The nucleus module of eigenvalue Method be a class iterative projection method (Iterative projection methods) [Bai Z J,
et al.Templates for the solution of algebraic eigenvalue problems:a practical
Guide [M] .Siam, 2000.].Grind in the feature value-based algorithm of the large-scale electrical power system analysis on Small Disturbance Stability over nearly 10 years
In studying carefully, the most iterative projection method of the frequency of occurrences has two, and one is the IRAM (Implicitly under Krylov subspace
Restarted Arnoldi Method, implicit restarted Arnoldi algorithm) [Kim D J, Moon Y H.Application
of the implicit restarted Arnoldi method to the small‐signal stability of
Power systems [J] .Journal of Electrical Engineering＆Technology, 2007,2 (4):428‐
433. it is secondary realize it, Song Xinli, Tang Yong, etc. power system frequency domain character value parallel search algorithm [J] based on multi-process. electric power
System automation, 2010 (21):11-16.], another is then the Jacobi-Davidson methods under non-Krylov subspace
(JDM) [Du Zhengchun, Liu Wei, Fang Wanliang, etc. it is crucial special in the analysis on Small Disturbance Stability based on Jacobi-Davidson methods
Value indicative calculates [J]. Proceedings of the CSEE, 2005,25 (14):19-24.Tsai S H, Lee C Y, Wu Y
K.Efficient calculation of critical eigenvalues in large power systems using
The real variant of the Jacobi-Davidson QR method [J] .IET generation,
Transmission＆distribution, 2010,4 (4):467‐478.].
Although IRAM has extensively been integrated in each power system small signal stability analysis system, its algorithm tool itself
Standby function but could not be played farthest, for example：PSD-SSAP and PSASP are only provided based on translation-inverse transformation
Frequency sweep IRAM, and be very suitable for calculating the Cayley conversion IRAM of crucial oscillation mode, without body in two methods
It is existing.Although frequency sweep IRAM has linear convergence rate for pole eigenvalue, its search behavior has randomness, in parameter
In the case of unreasonable allocation, easily there is " leakage root ", that is, miss some particularly critical oscillation modes.When accurate solution is repaiied
During positive equation, JDM has the convergence rate of progressive second order, even if but importantly, not using spectral transformation, JDM to remain able to
The rule (real part is maximum, damping ratio is minimum) specified according to certain, sequentially restrains impact power system small signal stability
Those crucial oscillation modes.
However, unlike IRAM has math library ARPACK increased income, only have the example procedure under Matlab due to JDM, because
This, JDM is common in always academic research, without being integrated into any large-scale electrical power system small signal stability eigenvalue point
In analysis system.
The interconnection of " three is magnificent " (Central China-East China-North China) extra-high voltage AC/DC electrical network, necessarily occurs newly-increased low frequency work(
Rate oscillation mode, " the tetanic weak friendship " electrical network of now in first stage of construction, it is most likely that so that some patterns therein will
Or unsure state has been presented, therefore, analyzed using the diverse feature value-based algorithm of three kinds of Numerical Principles big
The small signal stability of scale power system, not only with theory value, with more realistic meaning.
The content of the invention
The present invention is directed to deficiencies of the prior art, proposes a kind of large-scale electrical power system small signal stability
Eigenvalues analysis system, according to the electric network data file (* .dat and * .swi) of PSD-BPA forms, using TTQRE (Two-tone
Small-bulge multishift QR algorithm with aggressive early deflation, with positive
The multiple step displacement QR algorithms of two step fritters of early-age shrinkage strategy), fast and accurately identifying affects the complete of power system dynamic stability
Portion's electromechanic oscillation mode；Using the IRAM with various computing schemes, extract and the part of analyzing influence power system dynamic stability is closed
Key electromechanic oscillation mode；Using the JDM with various computing schemes, the Partial key with analyzing influence power system dynamic stability is extracted
Electromechanic oscillation mode, it is final to realize to actual extensive electricity by matching and comparing the electromechanic oscillation mode that three kinds of algorithms are obtained
Net carries out comprehensive, exhaustively little interference dynamic stability oscillation mode identification and model analyses.
The present invention is achieved by the following technical solutions：
The present invention relates to a kind of Eigenvalues analysis system of large-scale electrical power system small signal stability, including：BPA data
Interface module, for realizing small signal stability Eigenvalues analysis in sparse matrix relevant treatment sparse matrix calculate mould
Block, Load flow calculation module, system modelling and its linearization block, state matrix computing module, All Eigenvalues computing engines mould
Block, partial feature value computing engines module and oscillation mode are extracted and analysis module, wherein：BPA data interface modules receive electricity
Network data file, and be connected with Load flow calculation module and system modelling and its linearization block respectively and API is provided
(Application Program Interface, application programming interfaces)；Sparse matrix computing module respectively with Load flow calculation mould
Block, system modelling and its linearization block, state matrix computing module are connected and provide with partial feature value computing engines module
API；The API that Load flow calculation module is provided according to BPA data interface modules and sparse matrix computing module, realizes extensive electricity
The Load flow calculation of Force system simultaneously exports calculation of tidal current to system modelling and its linearization block；System modelling and its linearisation
The calculation of tidal current that the API and Load flow calculation module that module is provided according to BPA data interface modules is provided, realizes extensive electricity
The linearisation modeling of Force system, that is, generate the systematic observation matrix of augmentation and export respectively to state matrix computing module and part
Eigenvalue calculation engine modules；API that state matrix computing module is provided according to sparse matrix computing module and system modelling and
The systematic observation matrix of the augmentation that its linearization block is provided, obtain systematic observation matrix and export to All Eigenvalues to calculate and draw
Hold up module；All Eigenvalues computing engines module obtains the whole of systematic observation matrix according to TTQRE from systematic observation matrix
Eigenvalue and part left/right characteristic vector and exporting to oscillation mode is extracted and analysis module；Partial feature value computing engines
The API that module is provided according to sparse matrix computing module, with RCI (Reverse Communication Interface, it is inverse logical
Letter interface) mode perform the iterative numerical process of IRAM or JDM, obtain partial feature value and the part of systematic observation matrix
Left/right characteristic vector is simultaneously exported to oscillation mode extraction and analysis module；Oscillation mode is extracted and analysis module refers to according to user
Merge from All Eigenvalues computing engines module or the spy of the systematic observation matrix of partial feature value computing engines module calmly
Value indicative and left/right characteristic vector, realize the identification and model analyses of electromechanic oscillation mode, and by the pattern information and mode of gained
Analysis result is exported to user in the way of Excel forms.
Systematic observation matrix J of described augmentationaugMeet：Wherein：JAFor dynamic element linearisation
The block diagonal matrix of model splicing, JBFor dynamic element and the relational matrix of static cell, JCFor static cell and dynamic
The relational matrix of element, JDFor the system admittance matrix of amendment.
Described systematic observation matrix S are referred to：
Include TTQRE units, the unit and state matrix computing module in described All Eigenvalues computing engines module
It is connected, and is obtained according to systematic observation matrix after the All Eigenvalues and part left/right characteristic vector of systematic observation matrix, output
Extract to oscillation mode and analysis module.
Described partial feature value computing engines module includes：IRAM units and JDM units, wherein：IRAM units be
Construction in a systematic way mould and its linearization block are connected, and to be determined according to the selection of user and combine mould maximum Ritz values using translation-inverse transformation
Selection strategy or Cayley conversion combine the numerical procedure of mould maximum Ritz value selection strategyes, and according to the system mode of augmentation
Matrix is obtained after the partial feature value and part left/right characteristic vector of systematic observation matrix, is exported to oscillation mode and is extracted and divide
Analysis module；JDM units are connected with system modelling and its linearization block, are determined according to the selection of user using translation-inversion
Change and combine mould maximum Ritz value selection strategyes, original matrix and combine in fact with reference to mould maximum Ritz value selection strategyes, Cayley conversion
Portion's maximum Ritz values selection strategy or original matrix combine the numerical procedure of damping ratio minimum Ritz value selection strategyes, and according to
The systematic observation matrix of augmentation are obtained after the partial feature value and part left/right characteristic vector of systematic observation matrix, are exported to shaking
Swing schema extraction and analysis module.
Described oscillation mode identification and model analyses is referred to：Individual features are obtained according to every a pair of left/right characteristic vector
The correlation factor of value, according to correlation factor the electromechanical circuit correlation ratio of this feature value is obtained, if electromechanical circuit correlation ratio more than 1 and
This feature value is plural number, then judge this feature value as electromechanic oscillation mode, and corresponding right characteristic vector is Oscillatory mode shape；It is related because
The size of submodule value has reacted the degree of coupling between Electrical Power System Dynamic element and oscillation mode, in the machine that degree of coupling is maximum
Install power system stabilizer, PSS in group additional, be to suppress always doing for the power system low frequency power oscillation induced by the oscillation mode
Method；What the amplitude of Oscillatory mode shape determined unit under the oscillation mode waves degree, and angle determines unit under the oscillation mode
Relative between unit waves relation, Oscillatory mode shape be judge oscillation mode to the influence degree of unit, judge multiple units
Whether the important indicator of dynamic equivalent can be carried out.
Technique effect
Compared with prior art means, beneficial effects of the present invention include：
1. employing can represent the TTQRE of the present art to realize large-scale electrical power system small signal stability
All Eigenvalues analysis.The algorithm pursues technology in eigenvalue iterative link using chain type fritter, eliminates multiple step
The displacement blooming of displacement QR blocks pursuit, solves the problems, such as that algorithm is not restrained；Using positive early-age shrinkage strategy, reduce
The number of times of QR iteration, improves the computational accuracy of algorithm；Using the high level operations of matrix-matrix, the utilization of cpu cache is improve
Rate, saves the calculating time of algorithm.From the angle of Practical, QR algorithms are demonstrated little for large-scale power system dry
Disturb the feasibility of stability All Eigenvalues analysis；
2. it is operational form by the spectral transformation Unify legislation of IRAM, realizes and combine mould maximum with translation-inverse transformation
Ritz value selection strategyes, Cayley conversion combine the IRAM of mould maximum Ritz values two kinds of numerical procedure of selection strategy.Cayley becomes
The great advantage for changing IRAM is that it is possible to effectively recognize some keys of damping ratio less than or equal to certain designated value in power system
Oscillation mode, compares translation-inverse transformation IRAM, and the search behavior of Cayley conversion IRAM is substantially not present randomness, therefore, i.e.,
It is that in the case of parameter configuration is not exclusively rational, Cayley conversion IRAM can still identify the crucial vibration of the overwhelming majority
Pattern, largely reduce with IRAM analyze large-scale electrical power system small signal stability when, occur " leakage root " can
Can property；
3. JDM is at home and abroad realized in the way of RCI first.Not only feature value-based algorithm and electric power have been annotated in perfection to RCI
Separation between system application, RCI also causes iterative projection method to possess consistent calling rule.Compare Krylov subspace
Under iterative projection method, the JDM under non-Krylov subspace not only has faster convergence rate, and do not using spectral transformation
In the case of, the Ritz value selection strategyes (damping ratio is minimum, real part is maximum) that JDM still can be specified according to certain are restrained successively
Go out the eigenvalue wanted.Realize the JDM with 4 kinds of numerical procedure, and it has been integrated into together with IRAM extensive electric power
In system small signal stability Eigenvalues analysis system, the effect of promotion is served to the practical application of JDM.
Description of the drawings
The technical scheme enforcement figure that Fig. 1 is provided for the present invention；
Fig. 2 a and Fig. 2 b are respectively the left-half and right half part of the iterative numerical process schematic of IRAM and JDM；
Fig. 3 is the application effect figure of translation-inverse transformation frequency sweep IRAM；
Fig. 4 is application effect figure of the Cayley conversion with reference to mould maximum Ritz value selection strategy IRAM；
Fig. 5 is the application effect figure that original matrix combines damping ratio minimum Ritz value selection strategy JDM；
Fig. 6 is the convergence process figure that original matrix combines damping ratio minimum Ritz value selection strategy JDM；
Fig. 7 is the model analyses figure of a certain inter-area oscillation mode in HD8241 systems.
Specific embodiment
Embodiments of the invention are elaborated below, the present embodiment is carried out under premised on technical solution of the present invention
Implement, give detailed embodiment and specific operating process, but protection scope of the present invention is not limited to following enforcements
Example.
Embodiment 1
As shown in figure 1, the present embodiment includes：For realizing the BPA data-interfaces of the seamless read-write operation of BPA data files
Module, for realizing small signal stability Eigenvalues analysis in sparse matrix relevant treatment sparse matrix computing module, tide
Stream calculation module, system modelling and its linearization block, state matrix computing module, All Eigenvalues computing engines module, portion
Dtex value indicative computing engines module and oscillation mode are extracted and analysis module, wherein：
Described BPA data interface modules：Because domestic power grid enterprises are partial to be deposited using the file format of BPA
Actual electric network data, for this purpose, being based on OOP thought, using C++ the BPA numbers with dynamic link library form are developed
According to interface module.The module not only has the seamless read-write capability of BPA data files, can also provide API for other modules.Should
The specific embodiment of module includes following 3 key steps：
<1>The Analysis of Hierarchy Structure of BPA data files, for determining the static state/dynamic element parameter of electrical network in BPA data
Deposit position in file and storage order, realize efficiently separating for data card and control card；
<2>The design of class formation framework, according to the requirement of OOP, designs a set of and BPA program user handbooks
Class formation framework with identical hierarchical relationship, maintenance and the extension of Convenient interface module；
<3>The generation of BPA data-interfaces, realization, the number of generation are programmed using C++ to designed class formation framework
API not only can be provided according to interface, independent application program more can be provided.
Described sparse matrix computing module：The simulation analysis of any large-scale electrical power system and calculating, all be unable to do without dilute
Thin technology.The module employs the SuiteSparse that Florida State University Timothy professors A.Davis provide, and comes real
Now related to sparse matrix all computings, API is provided in the form of dynamic link library as other modules.The module is mainly by 5
Part is constituted：
<1>Data input/output, realizes bidirectional data transfers of the sparse matrix between hard disk to internal memory, and the part was both
The sparse matrix for supporting 2 system forms to preserve, while and the demand of 32/64 bit addressing of satisfaction；
<2>Fundamental matrix computing, realizes some conventionally calculations of sparse matrix, for example：Transposition, rearrangement, Matrix-Vector are taken advantage of
Method, matrix-matrix addition, matrix-matrix multiplication etc.；
<3>Sparse LU decomposes, and realizes symbolic analysis and the LU value decompositions of sparse matrix；
<4>Sparse former generation/back substitution, realizes the quick former generation/back substitution of sparse matrix；
<5>Extended matrix computing, realizes the sparse matrix computing of some extensions, for example：Sparse matrix is calculated with regard to certain
The Schur benefits of sub-block, the sparse matrix-vector multiplication blocked etc..
SuiteSparse is the sparse matrix solver equally celebrated for their achievements with SuperLU, PARDISO, TAUCS etc. in prior art,
Importantly, on the basis of SuiteSparse source codes, can develop and be exclusively used in power system small signal stability feature
The sparse matrix computing function of value analysis, for example, the of sparse matrix computing module<4>With<5>Function shown in part.This
The practical application effect of a little extension sparse matrix computing functions, will hereinafter be provided.
Described Load flow calculation module：The API provided using BPA data interface modules and sparse matrix computing module,
The Load flow calculation of large-scale electrical power system is realized, is that system modelling and its linearization block provide calculation of tidal current.
API and Load flow calculation mould that described system modelling and its linearization block is provided according to BPA data interface modules
The calculation of tidal current that block is provided, and with reference to document [encourage just, Chen Chen. Application Design mode development analysis on Small Disturbance Stability side
Method [J]. Proceedings of the CSEE, 2002,22 (1):12-16.] propose unified element connection modeling method, to it is little do
Disturbing stability analyses carries out system linearization modeling, while generating systematic observation matrix J of augmentationaugMeet：Wherein：JAFor the block diagonal matrix that dynamic element inearized model is spliced, JBFor dynamic element with
The relational matrix of static cell, JCFor static cell and the relational matrix of dynamic element, JDFor the system admittance matrix of amendment.
Described state matrix computing module：The API provided using sparse matrix computing module and system modelling and its line
Property module provide sparse matrix JA、JB、JCAnd JD, realize the sparse solution of systematic observation matrix S：
Because S is dense matrix, and JA、JB、JC、JDIt is sparse matrix, S is solved according to the computational methods of dense matrix, on the one hand counts
Evaluation time can be very long, and another aspect memory cost also can be very big, and then, the module solves S using following steps：
<1>To JDCarry out symbolic analysis and sparse LU decomposes：PDJDQD=LDUD；Wherein：PDAnd QDRespectively realize column selection
Pivot and the reorder matrix of approximate minimum degree sequence.
<2>Use JATo initialize the S of dense storage：S=full (JA)
<3>The extended matrix calculation function provided using sparse matrix computing module, calculates sparse matrix JaugWith regard to sub-block
JDSchur mend：Due to the J in power system small signal stability analysisBAnd JCTool
There is a very special sparsity structure, and cause the<3>The right-hand vector of step formula simultaneously need not perform whole numerical computations, because
This, sparse matrix computing module just can be realized and " calculate sparse matrix with regard to certain on the basis of the source code of SuiteSparse
The extended matrix calculation function of the Schur benefits of sub-block ".The practical application effect of the function will hereinafter be provided.
Described All Eigenvalues computing engines module：Using TTQRE, All Eigenvalues, the portion to state matrix S is realized
Divide the solution of left/right characteristic vector, including following 6 key steps：
<1>Matrix equilibrium, is reset using matrix and isolates the part factual investigation being exposed on S diagonal, is adopted
Circulation scaling reduces 2 norms of matrix A after balance：A=(PD)-1S(PD)；Wherein：P is reorder matrix, and D is diagonal matrix.
<2>Hessenberg reduction, is reflected using a series of Householder, and A is about turned to upper Hessenberg forms
H：H=QTAQ；Wherein：Q is a series of orthogonal matrix of Householder reflections accumulations.
<3>Chain type fritter pursuit multiple step displacement implicit expression QR iteration, using a series of Householder reflection and
Givens rotations perform the pursuit of chain type QR block, and using contraction window multiple eigenvalues are restrained, and are to intend upper triangular matrix by H similarity transformations
The All Eigenvalues result of calculation of T, S is all diagonal elements of T：T=QTAQ；Wherein：Q is further to accumulate just
Matrix is handed over, comprising a series of Householder reflections and Givens rotations.
<4>The solution of standard Schur type Partial Feature vector, after determining the eigenvalue Λ wanted in T, calculates T with regard to Λ
Left eigenvector V and right characteristic vector U：
<5>The solution of state matrix Partial Feature vector is according to step<1>The P for obtaining and D, step<3>Q, the step for obtaining
Suddenly<4>The V for obtaining and U, pushes back the left eigenvector V and right characteristic vector U for calculating S with regard to Λ：
<6>By calculated All Eigenvalues and part left/right characteristic vector, in the form of 2 systems text is input to
In file.
The numerical computations storehouse that above-mentioned calculation procedure can be completed in prior art is very more, for example：MKL, AMD of Intel
ATLAS/LAPACK, Matlab of reference BLAS/LAPACK, SourceForge of ACML, Netlib etc..To cause TTQRE
Algorithm can give play to optimal calculating performance on the computer disposed, and the present embodiment is opened using Chinese Academy of Sciences's software
The OpenBLAS v0.2.8 that Xian Yi team provides, and the reference LAPACK v3.5.0 that Netlib is provided.The reality of the module
Application effect will be given in the above-described embodiments.
OpenBLAS is a set of optimization BLAS subroutine librarys for being directed to different CPU core frameworks.Its Shi Zhangxianyi team
On the basis of the GotoBLAS2 of Hou rattan and cyclopentadienyl exploitation, gradually develop and the perfect multi-threaded parallel BLAS subroutine librarys.For
Different CPU micro-architectures, for example：Penryn, Athlon, SandyBridge etc., the calculating speed of OpenBLAS than MKL,
ACML, ATLAS, Matlab etc. are fast, and matrix size is bigger, and the acceleration effect of OpenBLAS is more obvious.
LAPACK is that on the basis of the BLAS subroutine librarys, a set of using Fortran77 exploitations is exclusively used in dense matrix
The linear algebra approach of numerical computations.LAPACK is the linear algebra approach LINPACK and eigenvalue method EISPACK of early stage
Aggregation, cover the Solving Linear in LINPACK, linear least-squares approach and EISPACK in feature
The functions such as value calculating.In addition, the LAPACK of 3.1.0 and its later version, encapsulation is exactly TTQRE.
Described partial feature value computing engines module：In the way of RCI functions readjustment, the number of IRAM or JDM is performed
The API that value iterative process is provided according to sparse matrix computing module, realizes all computings related to sparse matrix.The module bag
Containing following 11 key steps：
<1>Read in the J that system modelling and its linearization block are generatedA、JB、JCAnd JD；
<2>Splicing JaugAnd carry out symbolic analysis, reorder matrix Q of stet analysisaug；
<3>To JDCarry out symbolic analysis and LU value decompositions；
<4>The configuration information of partial feature value computing engines is read in from * .cfg files, including：Selected algorithm, spectral transformation
Type, Ritz value selection strategyes, eigenvalue number, the dimension of min/max search subspace, convergence precision, the maximum of search
Iterationses, translation point σ and anti-translation point μ；
<5>J is corrected using translation point σaugPart diagonal element, and to revised Jaug- σ I carry out LU value decompositions：
Paug(Jaug-σI)Qaug=LaugUaug；Wherein：PaugAnd QaugRespectively realize the rearrangement of column selection pivot and the sequence of approximate minimum degree
Matrix.
<6>If selected algorithm is IRAM, step is proceeded to<7>, otherwise selected algorithm is JDM, proceeds to step<8>；
<7>The RCI functions of IRAM are called, the iterative numerical of IRAM is performed, step is proceeded to<9>；
<8>The RCI functions of JDM are called, the iterative numerical of JDM is performed, step is proceeded to<9>；
<9>Judge whether iterative numerical terminates, if so, then proceed to step<11>, if it is not, then proceeding to step<10>；
<10>According to the type of spectral transformation operator Op according to the intermediate variable preserved in abovementioned steps, realize that RCI functions are returned
The sparse solution of the implicit expression of two matroids-vector multiplication during tune, solution returns to step after finishing<6>；
Two described matroids-vector multiplication is referred to：Wherein：S is system
State matrix, the RCI readjustment vectors that x is provided for IRAM or JDM, θ is the RCI readjustment scalars that JDM is provided, and y is to be supplied to
The waiting of IRAM or JDM seeks vector.
<11>If algorithmic statement has obtained a part of eigenvalue and its right characteristic vector, solved using inverse power method twice
The corresponding left eigenvector of the partial feature value, and all of result of calculation is input in text in the form of 2 systems.
As Fig. 2 a and Fig. 2 b (left-half and right half part of the iterative numerical process schematic of IRAM and JDM) give
Above-mentioned steps<6>～step<10>Specific implementation process, by Fig. 2 a and Fig. 2 b can be seen that RCI functions readjustment execution
Journey is extremely complex, but as Jack Dongarra are taught in document [Dongarra J, Eijkhout V, Kalhan
A.Reverse communication interface for linear algebra templates for iterative
Methods [J] .UT, CS-95-291, May, 1995.] introduction described in：" inverse communication is a technology, and by it, we can
To realize the details to stashing various operations in iterative algorithm.On the one hand, algorithm development person can consider user
It is which type of data structure to preserve the matrix needed for iterative device using, on the other hand, user can think according to oneself
The mode wanted is realizing the computing required by iterative device ".Although the present embodiment provide only two kinds of features of IRAM and JDM
The specific embodiment of value-based algorithm, it can be seen that for other iterative projection methods, as long as being modified slightly being deployed as
RCI forms, it is possible in being directly appended to partial feature value computing engines module, therefore, the present embodiment have it is very strong can
Autgmentability.
The step<10>In, the sparse solution of implicit expression of two matroids-vector multiplication is calculated by calling sparse matrix
" sparse matrix-vector multiplication blocked " this extended matrix calculation function is realizing in module.
By taking Cayley conversion as an example, i.e. Op (S)=(S-μ I) × (S-σ I)‐1, IRAM and JDM using below step come
Realize the sparse solution of implicit expression of 1 matroid-vector multiplication.
<a>Initialized with x and JaugWith the column vector z=[x of dimension；0]；
<b>Sparse former generation/back substitution is performed to z：Z=Qaug×(Uaug\(Laug\(Paug×z)))
<c>Note n is the exponent number of S, takes out the front n rows of z, generates column vector y=z (1:n)；
<d>2 grades of BLAS subprogram gemv are called, y=x+ (σ-μ) × y is calculated.
By taking translation-inverse transformation as an example, i.e. Op (S)=(S-σ I)‐1, JDM realized using below step the 2nd matroid-
The sparse solution of implicit expression of vector multiplication.
<e>Calculate interim vector v：V=QD×(UD\(LD\(PD×(-JC×x))))
<f>Calculate interim vector u：
<g>Using interim translation point α=(1+ θ × σ)/θ amendment JaugPart diagonal element, and to revised Jaug–αI
Carry out LU value decompositions：
<h>Initialized with u and JaugWith the column vector z=[u of dimension；0]；
<i>Sparse former generation/back substitution is performed to z：
<j>Note n is the exponent number of S, takes out the front n rows of z, generates column vector y=z (1:n).
Described oscillation mode is extracted and analysis module：Read All Eigenvalues computing engines module or partial feature value
The result of calculation of computing engines module, realizes identification and the model analyses function of electromechanic oscillation mode, most at last obtained by calculating
Pattern and modal information, are exported in the form of Excel forms.
In order to further illustrate the correctness and effectiveness of the present embodiment system, respectively to 3 ieee standard systems and 3
The small signal stability of real system has carried out simulation analysis and has calculated.Wherein, 3 real systems are taken respectively from East China Power Grid
05th, the high layout data of the summer of 09 and 15 year.The details of this 6 test systems are as shown in table 1.
The test system of table 1 is described
| Test system | Node number | Branch road number | Electromotor number | State variable number | Algebraic variable number |
| IEEE118 | 118 | 186 | 34 | 340 | 236 |
| IEEE300 | 300 | 411 | 69 | 690 | 600 |
| IEEE600 | 600 | 823 | 139 | 1390 | 1200 |
| HD4171 | 4171 | 5318 | 375 | 3750 | 8342 |
| HD5473 | 5473 | 7440 | 472 | 4720 | 10946 |
| HD8241 | 8241 | 11657 | 500 | 3000 | 16482 |
Because the data of test system are stored as the file format of PSD-BPA, therefore, by PSD-SSAP v2.5.2
As the canonical reference of precision, by Matlab R2012a as the canonical reference of speed, the little dry of the present embodiment offer is verified
Disturb the correctness and effectiveness of stability features value analysis system.All tests are carried out under same computing environment：
Windows XP operating systems, 4GB internal memories, the double-core CPU E5200 of Intel 2.5GHz.Because the CPU is the micro- framves of Penryn
Structure, therefore, in the makefile.rule files of OpenBLAS, it is intended that TARGET=PENRYN.Because PSD-SSAP is serial
Computation schema, to even things up, the present embodiment and Matlab are also appointed as the serial computing pattern of single core CPU.
Verification of correctness includes following 2 aspects：
1) the QR methods of the TTQRE and PSD-SSAP of the present embodiment are respectively adopted, the All Eigenvalues of 6 test systems are calculated
With left/right characteristic vector, after the electromechanic oscillation mode that identification is obtained is matched two-by-two, compare the maximum of result of calculation definitely
Deviation, as a result as shown in table 2；
2) translation-inverse transformation IRAM of the translation of the present embodiment-inverse transformation IRAM and PSD-SSAP is respectively adopted, 6 are calculated
The partial feature value and left/right characteristic vector of individual test system, after the electromechanic oscillation mode that identification is obtained is matched two-by-two,
Compare the absolute deviation of result of calculation, as a result as shown in table 3.The parameter configuration that frequency sweep IRAM is given tacit consent to using PSD-SSAP.
The verification of correctness of the All Eigenvalues of table 2 analysis
Verification of correctness of the table 3 based on the analysis of translation-inverse transformation frequency sweep IRAM partial feature value
By table 2 and table 3 as can be seen that the present embodiment is correct.The reason for deviation occurs in generation oscillation mode number exists
In,
The present embodiment and PSD-SSAP employ different methods to calculate correlation factor.
Validation verification includes following 3 aspects：
1) the state matrix computing module of the present embodiment, the sparse matrix of PSD-SSAP, Matlab is respectively adopted and calculates work(
Can, the state matrix for calculating 6 test systems is shown, the calculating time of three is as shown in table 4；
2) QR methods, the eig functions of Matlab of TTQRE, PSD-SSAP of the present embodiment are respectively adopted, 6 tests are calculated
The All Eigenvalues and left/right characteristic vector of system, the calculating time of three is as shown in table 5；
3) translation-inverse transformation IRAM of the translation of the present embodiment-inverse transformation IRAM and PSD-SSAP is respectively adopted, 6 are calculated
The partial feature value and left/right characteristic vector of individual test system, both calculating time is as shown in table 6.Similarly, frequency sweep IRAM
The parameter configuration given tacit consent to using PSD-SSAP.
The validation verification that the state matrix of table 4 is calculated
The validation verification that the All Eigenvalues of table 5 and characteristic vector are calculated
| Test system | The TTQRE/s of the present embodiment | QR methods/the s of PSD-SSAP | Eig functions/the s of Matlab |
| IEEE118 | 0.203 | 0.540 | 0.408 |
| IEEE300 | 1.705 | 4.190 | 2.029 |
| IEEE600 | 13.144 | 31.115 | 14.371 |
| HD4171 | 236.007 | 694.957 | 253.122 |
| HD5473 | 450.542 | 1812.102 | 482.496 |
| HD8241 | 128.400 | 376.078 | 139.143 |
Validation verification of the table 6 based on the analysis of translation-inverse transformation frequency sweep IRAM partial feature value
| Test system | The translation of the present embodiment-inverse transformation frequency sweep IRAM/s | The translation of PSD-SSAP-inverse transformation frequency sweep IRAM/s |
| IEEE118 | 1.058 | 1.206 |
| IEEE300 | 1.523 | 1.618 |
| IEEE600 | 3.224 | 3.388 |
| HD4171 | 63.072 | 76.291 |
| HD5473 | 72.184 | 85.682 |
| HD8241 | 24.825 | 27.071 |
Table 4 is fully demonstrated in the sparse matrix computing module of the present embodiment, " calculates sparse matrix with regard to certain sub-block
Schur is mended " effectiveness of this extended matrix calculation function.Table 5 fully demonstrates the All Eigenvalues of the present embodiment and calculates and draws
In holding up module, the effectiveness of TTQRE algorithms.Table 6 is fully demonstrated in sparse matrix computing module, " sparse matrix for blocking-to
Amount multiplication " this extended matrix calculation function effectiveness.
In in order to investigate the present embodiment provide Cayley conversion with reference to mould maximum Ritz value selection strategyes IRAM units,
Original matrix combines the JDM units of damping ratio minimum Ritz value selection strategyes, for the crucial vibration of identification large-scale electrical power system
The practical application effect of pattern, the HD8241 systems taken in above-described embodiment carry out emulation testing.Crucial oscillation mode is referred to
Damping ratio is not more than 5% eigenvalue.
Fig. 3 show the electromechanic oscillation mode that translation-inverse transformation frequency sweep IRAM is identified.Frequency sweep IRA identifies 115 moulds
Formula, wherein 72 is critical mode of the damping ratio less than 5%, and all mode has 499, wherein 87 is critical mode, because
This, frequency sweep IRA method occurs in that " leakage root ", particularly near 1.2Hz.
Fig. 4 show the electromechanic oscillation mode that Cayley conversion is identified with reference to mould maximum Ritz value selection strategy IRAM.
Cayley conversion IRAM have iteration 70 times altogether, take 60.058 seconds, have identified all crucial machine of 87 damping ratios less than 5%
Electric oscillation pattern, therefore, without appearance " leakage root ".
Fig. 5 show the electromechanic oscillation mode that original matrix is identified with reference to damping ratio minimum Ritz value selection strategy JDM.
The JDM of the numerical procedure has iteration 109 times altogether, takes 208.007 seconds, have identified all pass of 87 damping ratios less than 5%
Key electromechanic oscillation mode, therefore, without appearance " leakage root ".
Fig. 6 show iterative numerical convergence process of the original matrix with reference to damping ratio minimum Ritz value selection strategy JDM.Though
The computational efficiency of JDM is not as good as IRAM in right the present embodiment, but from this figure, it can be seen that JDM can be ascending according to damping ratio
Order, restrain crucial oscillation mode successively.
The electromechanic oscillation mode identified due to the system and modal information are exported in the form of Excel forms, therefore,
The function that user both can have been carried using Excel, again can be using result of calculation using other modes.
Still by taking HD8241 systems as an example, two kinds of application scenarios of the system simulation analysis result are given：
1) original matrix is combined into damping ratio minimum Ritz value selection strategy JDM and translation-inverse transformation frequency sweep in Excel
After the electromechanic oscillation mode that IRAM is obtained is according to the arrangement of damping ratio ascending order, it is found that IRAM miss out a damping ratio and be
0.04303542nd, frequency is the crucial oscillation mode of 1.19297526Hz, and the correlation factor of the oscillation mode is dropped according to modulus value
After sequence arrangement, find and the maximally related unit of the oscillation mode be " ZCN_1 " and " ZCN_2 ", then, divide on this two units
Do not install power system stabilizer, PSS additional, the dynamic stability of HD8241 systems can be effectively improved；
2) the calculated modal informations of JDM of the reading and saving in Excel file in Matlab, finding damping ratio is
0.02234904th, frequency for 0.62502012Hz crucial oscillation mode, due to the frequency of oscillation of the pattern it is relatively low, it can be determined that
It is inter-area oscillation mode, in order to find out the pattern under oscillation area, mapping results are carried out to the modal information of the pattern
As shown in fig. 7, as seen from Figure 7 in this mode, carry out between the unit of " oscillation area 1 " and " oscillation area 2 " relative
Wave, therefore, analysis result shows that all units in the two oscillation areas can carry out dynamic equivalent.
Claims (5)
1. a kind of Eigenvalues analysis system of large-scale electrical power system small signal stability, it is characterised in that include：BPA data
Interface module, for realizing small signal stability Eigenvalues analysis in sparse matrix relevant treatment sparse matrix calculate mould
Block, Load flow calculation module, system modelling and its linearization block, state matrix computing module, All Eigenvalues computing engines mould
Block, partial feature value computing engines module and oscillation mode are extracted and analysis module, wherein：BPA data interface modules receive electricity
Network data file, and be connected and application program is provided with Load flow calculation module and system modelling and its linearization block respectively and connect
Mouthful；Sparse matrix computing module respectively with Load flow calculation module, system modelling and its linearization block, state matrix computing module
It is connected and provides application programming interfaces with partial feature value computing engines module；Load flow calculation module is according to BPA data-interface moulds
The application programming interfaces that block and sparse matrix computing module are provided, realize the Load flow calculation of large-scale electrical power system and export tide
Stream calculation result is to system modelling and its linearization block；System modelling and its linearization block are according to BPA data interface modules
The calculation of tidal current that the application programming interfaces of offer and Load flow calculation module are provided, realizes the linearisation of large-scale electrical power system
Modeling, that is, generate the systematic observation matrix of augmentation and export respectively to state matrix computing module and partial feature value computing engines
Module；Application programming interfaces that state matrix computing module is provided according to sparse matrix computing module and system modelling and its linear
Change the systematic observation matrix of the augmentation that module is provided, obtain systematic observation matrix and export to All Eigenvalues computing engines mould
Block；All Eigenvalues computing engines module according to positive early-age shrinkage strategy the multiple step displacement QR algorithms of two step fritters from
The All Eigenvalues and part left/right characteristic vector of systematic observation matrix are obtained in systematic observation matrix and is exported to oscillation mode
Formula is extracted and analysis module；Partial feature value computing engines module connects according to the application program that sparse matrix computing module is provided
Mouthful, perform that implicit expression restarts ARNOLDI algorithms or the numerical value of JACOBI-DAVIDSON methods changes in the way of inverse communication interface
For process, obtain the partial feature value and part left/right characteristic vector of systematic observation matrix and export to oscillation mode extract and
Analysis module；Oscillation mode is extracted and analysis module specified according to user merge from All Eigenvalues computing engines module or
The eigenvalue and left/right characteristic vector of the systematic observation matrix of partial feature value computing engines module, realizes electromechanical oscillation mode
Formula is recognized and model analyses, and the pattern information and modal analysis result of gained are exported to user in the way of Excel forms.
2. system according to claim 1, is characterized in that, the systematic observation matrix of described augmentation, i.e. JaugMeet：Wherein：JAFor the block diagonal matrix that dynamic element inearized model is spliced, JBFor dynamic element with
The relational matrix of static cell, JCFor static cell and the relational matrix of dynamic element, JDFor the system admittance matrix of amendment.
3. system according to claim 1, is characterized in that, described systematic observation matrix, i.e. S are referred to：
Wherein：JAFor the block diagonal matrix that dynamic element inearized model is spliced, JBFor dynamic unit
The relational matrix of part and static cell, JCFor static cell and the relational matrix of dynamic element, JDFor the system admittance square of amendment
Battle array.
4. system according to claim 1, is characterized in that, described partial feature value computing engines module includes：Implicit expression
ARNOLDI algorithm units and JACOBI-DAVIDSON method units are restarted, wherein：Implicit expression restarts ARNOLDI algorithm units
It is connected with system modelling and its linearization block, is determined according to the selection of user and combine mould maximum using translation-inverse transformation
Ritz values selection strategy or Cayley conversion combine the numerical procedure of mould maximum Ritz value selection strategyes, and are according to augmentation
System state matrix is obtained after the partial feature value and part left/right characteristic vector of systematic observation matrix, is exported to oscillation mode and is carried
Take and analysis module；JACOBI-DAVIDSON methods unit is connected with system modelling and its linearization block, according to the choosing of user
Select and combine mould maximum Ritz value selection strategyes, Cayley conversion with reference to the choosing of mould maximum Ritz values using translation-inverse transformation to determine
Select strategy, original matrix to select with reference to damping ratio minimum Ritz values with reference to real part maximum Ritz values selection strategy or original matrix
The numerical procedure of strategy, and according to the systematic observation matrix of augmentation obtain systematic observation matrix partial feature value and part it is left/
After right characteristic vector, export to oscillation mode and extract and analysis module.
5. system according to claim 1, is characterized in that, described oscillation mode identification and model analyses is referred to：According to
Every a pair of left/right characteristic vector obtains the correlation factor of individual features value, is returned according to the electromechanics that correlation factor obtains this feature value
Road correlation ratio, if electromechanical circuit correlation ratio is more than 1 and this feature value is plural number, judges this feature value as electromechanic oscillation mode,
Corresponding right characteristic vector is Oscillatory mode shape；The size of correlation factor modulus value reflects Electrical Power System Dynamic element and oscillation mode
Between degree of coupling, install power system stabilizer, PSS additional on the maximum unit of degree of coupling, be to suppress to be lured by the oscillation mode
The customary practice of electricity Force system low frequency power oscillation；The amplitude of Oscillatory mode shape determines waving for unit under the oscillation mode
Degree, angle determine under the oscillation mode between unit and unit it is relative wave relation, Oscillatory mode shape is to judge oscillation mode
Formula to the influence degree of unit, judge whether multiple units can carry out the important indicator of dynamic equivalent.
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| CN105375468B (en) * | 2015-11-12 | 2017-12-29 | 南昌大学 | A kind of method that rectangular co-ordinate Newton-Laphson method trend is quickly asked for based on symmetrical and sparse technology |
| CN108471131B (en) * | 2018-03-21 | 2020-02-07 | 华北电力大学 | Method and system for evaluating stability of flexible direct current transmission system |
| CN109101464A (en) * | 2018-07-13 | 2018-12-28 | 清华大学 | Based on the modified electric system sparse matrix Parallel implementation method and system of matrix |
| CN110456188B (en) * | 2019-07-23 | 2021-12-28 | 上海交通大学 | Power system stability detection system and method based on sparse polynomial chaos expansion |
| CN110350529B (en) * | 2019-07-30 | 2021-01-19 | 南方电网科学研究院有限责任公司 | Small interference stabilizing method, device, equipment and storage medium for power system |
| CN111310326B (en) * | 2020-02-10 | 2021-12-28 | 西安交通大学 | Method for analyzing influence of dynamic elements of power system on damping of system oscillation mode |
| CN111614078B (en) * | 2020-04-28 | 2021-12-14 | 南方电网科学研究院有限责任公司 | Method, device, equipment and storage medium for analyzing small interference stability of power system |
| CN112003317B (en) * | 2020-06-05 | 2022-01-25 | 国电南瑞科技股份有限公司 | Method and device for optimizing power regulation input and output of hydroelectric generating set |
| CN112165085B (en) * | 2020-07-31 | 2022-05-17 | 山东大学 | Time-lag power system efficient characteristic value analysis method and system based on PSOD |
| CN113517686B (en) * | 2021-05-06 | 2022-09-20 | 东方电子股份有限公司 | Low-frequency oscillation analysis method based on Givens orthogonal similarity transformation |
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101630273A (en) * | 2009-08-06 | 2010-01-20 | 中国电力科学研究院 | Small interference stability simulation method of electric power system |
| CN101917003A (en) * | 2010-07-29 | 2010-12-15 | 东南大学 | Small interference oscillatory stability decomposed model analysis method for electric power system |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9640994B2 (en) * | 2012-02-24 | 2017-05-02 | Mitsubishi Electric Research Laboratories, Inc. | Decoupled three-phase power flow analysis method for unbalanced power distribution systems |
-
2014
- 2014-07-29 CN CN201410366590.XA patent/CN104091092B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101630273A (en) * | 2009-08-06 | 2010-01-20 | 中国电力科学研究院 | Small interference stability simulation method of electric power system |
| CN101917003A (en) * | 2010-07-29 | 2010-12-15 | 东南大学 | Small interference oscillatory stability decomposed model analysis method for electric power system |
Non-Patent Citations (2)
| Title |
|---|
| 电力系统小信号稳定全特征值分析的改进BR算法;赵文恺等;《中国电机工程学报》;20140405;第34卷(第10期);第1599-1608页 * |
| 电力系统并行计算的嵌套分块对角加边形式划分算法;赵文恺等;《中国电机工程学报》;20100905;第30卷(第25期);第66-73页 * |
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