S40PI_n.mtx

%%MatrixMarket matrix coordinate real general
%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/Rommes/S40PI_n
% name: Rommes/S40PI_n
% [Transmission line, 40 sections, SISO, index-2 DAE (CEPEL, Brazil)]
% id: 2371
% date: 2010
% author: F. Freitas
% ed: J. Rommes
% fields: name title A id date author ed kind notes aux
% aux: B C E
% kind: eigenvalue/model reduction problem
%-------------------------------------------------------------------------------
% notes:
% 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 http://sites.google.com/site/rommes/software       
%                                                                                
% 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 ( http://www.cepel.br/ )          
%                                                                                
% 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.                  
%    PIsections10to80.zip            [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]  
%                                                                                
% References:                                                                    
%                                                                                
% [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             
%-------------------------------------------------------------------------------
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