Matrix: Rommes/M10PI_n

Description: Transmission line, 10 sections, MIMO, index-2 DAE (CEPEL, Brazil)

Rommes/M10PI_n graph
(undirected graph drawing)

Rommes/M10PI_n dmperm of Rommes/M10PI_n

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  • download as a MATLAB mat-file, file size: 10 KB. Use UFget(2361) or UFget('Rommes/M10PI_n') in MATLAB.
  • download in Matrix Market format, file size: 12 KB.
  • download in Rutherford/Boeing format, file size: 11 KB.

    Matrix properties
    number of rows682
    number of columns682
    structural full rank?no
    structural rank679
    # of blocks from dmperm96
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 11%
    Cholesky candidate?no
    positive definite?no

    authorF. Freitas
    editorJ. Rommes
    kindeigenvalue/model reduction problem
    2D/3D problem?yes

    Additional fieldssize and type
    Bsparse 682-by-3
    Csparse 3-by-682
    Esparse 682-by-682


    Power system models from Joost Rommes, Nelson Martins, Francisco Freitas       
    This collection of power system models originates from real power systems,     
    mostly based on Brazilian interconection power systems (BIPS) models (the file 
    names refer to the actual power system related to a given year electric load   
    scenario).  These systems [E dx/dt = Ax + Bu ; y=Cx + Du] are interesting      
    benchmarks for several numerical algorithms, including eigenvalue algorithms   
    (dominant modes/poles/zeros, stability analysis, computing rightmost           
    eigenvalues and/or with smallest damping ratio, eigenvalue parameter           
    sensitivity) and model order reduction (large-scale DAEs ). Refer to the       
    corresponding publications for more details on the systems and numerical       
    results of several eigenvalue/model order reduction algorithms. For            
    corresponding software, see       
    If E is not present in the problem, then E=I should be assumed.                
    If D is not present, D=0 should be assumed.  (Note that as of Jan 2011,        
    no problem has a nonzero D).                                                   
    The iv vector in some of the files is a vector with nonzeros (ones) at indices 
    that represent state-variables (the zeros are algebraic variables). One can    
    construct the descriptor matrix E by E=spdiags(iv,0,n,n). This iv vector is    
    generated by the Brazilian power system simulation software, and can be more   
    efficient to compute with.                                                     
    Test systems:                                                                  
    All power system models originate from CEPEL ( )          
    power system    file                    n  #inputs #outputs  references        
    ------------    ----               ------  ------- --------  --                
    New England     ww_36_pmec_36          66   1       1        [1]               
    BIPS/97         ww_vref_6405        13251   1       1        [1]               
    BIPS/2007       xingo_afonso_itaipu 13250   1       1        [2]               
    BIPS/97         mimo8x8_system      13309   8       8        [3]               
    BIPS/97         mimo28x28_system    13251  28      28        [3]               
    BIPS/97         mimo46x46_system    13250  46      46        [4]               
    Juba5723        juba40k             40337   2       1        [5]               
    Bauru5727       bauru5727           40366   2       2        [5]               
    zeros_nopss     zeros_nopss_13k     13296  46      46        [5]               
    xingo6u         descriptor_xingo6u  20738   1       6        [5]               
    nopss           nopss_11k           11685   1       1        [5]               
    xingo3012       xingo3012           20944   2       2        [5]               
    bips98_606      bips98_606           7135   4       4        [6]               
    bips98_1142     bips98_1142          9735   4       4        [6]               
    bips98_1450     bips98_1450         11305   4       4        [6]               
    bips07_1693     bips07_1693         13275   4       4        [6]               
    bips07_1998     bips07_1998         15066   4       4        [6]               
    bips07_2476     bips07_2476         16861   4       4        [6]               
    bips07_3078     bips07_3078         21128   4       4        [6]               
    Several SISO/MIMO test systems, whose main components are transmission lines   
    (TL) are available.  TLs are modeled by ladder networks, comprised of cascaded 
    RLC PI-circuits, having fixed parameters.                                      
       Transmission lines with 10--80 PI Sections are considered.                            [Submitted]                                 
       There are two kinds of files for representing a same system: the file with  
       termination _n refers to an index-2 system DAE model, while _n1 means       
       a model of the same system, but for an index-1 DAE representation.  The     
       representation of each test system has the form [E dx/dt = Ax + Bu ; y=Cx]  
    [1] ROMMES, J., MARTINS, N., Efficient computation of transfer function        
        dominant poles using subspace acceleration.  IEEE Trans. on Power Systems, 
        Vol.  21, Issue 3, Aug. 2006, pp. 1218-1226                                
    [2] ROMMES, J., MARTINS, N., Computing large-scale system eigenvalues most     
        sensitive to parameter changes, with applications to power system          
        small-signal stability , IEEE Transactions on Power Systems, Vol. 23, Issue
        2, May 2008, pp.  434-442                                                  
    [3] ROMMES, J., MARTINS, N., Efficient computation of multivariable transfer   
        function dominant poles using subspace acceleration.  2006, IEEE Trans. on,
        Power Systems, Vol. 21, Issue 4, Nov. 2006, pp.  1471-1483.                
    [4] MARTINS, N., PELLANDA, P.C.,ROMMES, J., Computation of transfer function   
        dominant zeros with applications to oscillation damping control of large   
        power systems, IEEE Trans. on Power Systems, Vol. 22, Issue 4, Nov. 2007,  
        pp.  1657-1664                                                             
    [5] ROMMES, J., MARTINS, N., FREITAS, F., Computing Rightmost Eigenvalues for  
        Small-Signal Stability Assessment of Large-Scale Power Systems, IEEE       
        Transactions on Power Systems, Vol. 25, Issue 2, May 2010, pp.929-938      
    [6] FREITAS, F., ROMMES, J., MARTINS, N., Gramian-Based Reduction Method       
        Applied to Large Sparse Power System Descriptor Models, IEEE Transactions  
        on Power Systems, Vol. 23, Issue 3, August 2008, pp. 1258-1270             

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD1,849
    Cholesky flop count5.2e+03
    nnz(L+U), no partial pivoting, with AMD3,016
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD1,802
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD2,937

    SVD-based statistics:
    null space dimension3
    full numerical rank?no
    singular value gap7.59205e+09

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    Rommes/M10PI_n svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.