Source Code for Module pypower.d2Ibr_dV2

 1  # Copyright (C) 2008-2011 Power System Engineering Research Center (PSERC) 
 2  # Copyright (C) 2011 Richard Lincoln 
 3  # 
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 5  # it under the terms of the GNU General Public License as published 
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 7  # or (at your option) any later version. 
 8  # 
 9  # PYPOWER is distributed in the hope that it will be useful, 
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12  # GNU General Public License for more details. 
13  # 
14  # You should have received a copy of the GNU General Public License 
15  # along with PYPOWER. If not, see <http://www.gnu.org/licenses/>. 
16   
17  """Computes 2nd derivatives of complex branch current w.r.t. voltage. 
18  """ 
19   
20  from numpy import ones, arange 
21  from scipy.sparse import csr_matrix as sparse 
22   
23   
24 -def d2Ibr_dV2(Ybr, V, lam): 
25      """Computes 2nd derivatives of complex branch current w.r.t. voltage. 
26   
27      Returns 4 matrices containing the partial derivatives w.r.t. voltage 
28      angle and magnitude of the product of a vector LAM with the 1st partial 
29      derivatives of the complex branch currents. Takes sparse branch admittance 
30      matrix C{Ybr}, voltage vector C{V} and C{nl x 1} vector of multipliers 
31      C{lam}. Output matrices are sparse. 
32   
33      For more details on the derivations behind the derivative code used 
34      in PYPOWER information, see: 
35   
36      [TN2]  R. D. Zimmerman, I{"AC Power Flows, Generalized OPF Costs and 
37      their Derivatives using Complex Matrix Notation"}, MATPOWER 
38      Technical Note 2, February 2010. 
39      U{http://www.pserc.cornell.edu/matpower/TN2-OPF-Derivatives.pdf} 
40   
41      @author: Ray Zimmerman (PSERC Cornell) 
42      @author: Richard Lincoln 
43      """ 
44      nb = len(V) 
45      ib = arange(nb) 
46      diaginvVm = sparse((ones(nb) / abs(V), (ib, ib))) 
47   
48      Haa = sparse((-(Ybr.T * lam) * V, (ib, ib))) 
49      Hva = -1j * Haa * diaginvVm 
50      Hav = Hva.copy() 
51      Hvv = sparse((nb, nb)) 
52   
53      return Haa, Hav, Hva, Hvv 
54