Source Code for Module pypower.d2AIbr_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  # 
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13  # 
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15  # along with PYPOWER. If not, see <http://www.gnu.org/licenses/>. 
16   
17  """Computes 2nd derivatives of |complex current|**2 w.r.t. V. 
18  """ 
19   
20  from scipy.sparse import csr_matrix as sparse 
21   
22  from d2Ibr_dV2 import d2Ibr_dV2 
23   
24   
25 -def d2AIbr_dV2(dIbr_dVa, dIbr_dVm, Ibr, Ybr, V, lam): 
26      """Computes 2nd derivatives of |complex current|**2 w.r.t. V. 
27   
28      Returns 4 matrices containing the partial derivatives w.r.t. voltage 
29      angle and magnitude of the product of a vector C{lam} with the 1st partial 
30      derivatives of the square of the magnitude of the branch currents. 
31      Takes sparse first derivative matrices of complex flow, complex flow 
32      vector, sparse branch admittance matrix C{Ybr}, voltage vector C{V} and 
33      C{nl x 1} vector of multipliers C{lam}. Output matrices are sparse. 
34   
35      For more details on the derivations behind the derivative code used 
36      in PYPOWER information, see: 
37   
38      [TN2]  R. D. Zimmerman, I{"AC Power Flows, Generalized OPF Costs and 
39      their Derivatives using Complex Matrix Notation"}, MATPOWER 
40      Technical Note 2, February 2010. 
41      U{http://www.pserc.cornell.edu/matpower/TN2-OPF-Derivatives.pdf} 
42   
43      @see: L{dIbr_dV}. 
44   
45      @author: Ray Zimmerman (PSERC Cornell) 
46      @author: Richard Lincoln 
47      """ 
48      # define 
49      il = range(len(lam)) 
50   
51      diaglam = sparse((lam, (il, il))) 
52      diagIbr_conj = sparse((Ibr.conj(), (il, il))) 
53   
54      Iaa, Iav, Iva, Ivv = d2Ibr_dV2(Ybr, V, diagIbr_conj * lam) 
55   
56      Haa = 2 * ( Iaa + dIbr_dVa.T * diaglam * dIbr_dVa.conj() ).real 
57      Hva = 2 * ( Iva + dIbr_dVm.T * diaglam * dIbr_dVa.conj() ).real 
58      Hav = 2 * ( Iav + dIbr_dVa.T * diaglam * dIbr_dVm.conj() ).real 
59      Hvv = 2 * ( Ivv + dIbr_dVm.T * diaglam * dIbr_dVm.conj() ).real 
60   
61      return Haa, Hav, Hva, Hvv 
62