Source Code for Module pypower.dIbr_dV

 1  # Copyright (C) 1996-2011 Power System Engineering Research Center (PSERC) 
 2  # Copyright (C) 2011 Richard Lincoln 
 3  # 
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 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 partial derivatives of branch currents w.r.t. voltage. 
18  """ 
19   
20  from numpy import diag, asmatrix, asarray 
21  from scipy.sparse import issparse, csr_matrix as sparse 
22   
23   
24 -def dIbr_dV(branch, Yf, Yt, V): 
25      """Computes partial derivatives of branch currents w.r.t. voltage. 
26   
27      Returns four matrices containing partial derivatives of the complex 
28      branch currents at "from" and "to" ends of each branch w.r.t voltage 
29      magnitude and voltage angle respectively (for all buses). If C{Yf} is a 
30      sparse matrix, the partial derivative matrices will be as well. Optionally 
31      returns vectors containing the currents themselves. The following 
32      explains the expressions used to form the matrices:: 
33   
34          If = Yf * V 
35   
36      Partials of V, Vf & If w.r.t. voltage angles:: 
37          dV/dVa  = j * diag(V) 
38          dVf/dVa = sparse(range(nl), f, j*V(f)) = j * sparse(range(nl), f, V(f)) 
39          dIf/dVa = Yf * dV/dVa = Yf * j * diag(V) 
40   
41      Partials of V, Vf & If w.r.t. voltage magnitudes:: 
42          dV/dVm  = diag(V / abs(V)) 
43          dVf/dVm = sparse(range(nl), f, V(f) / abs(V(f)) 
44          dIf/dVm = Yf * dV/dVm = Yf * diag(V / abs(V)) 
45   
46      Derivations for "to" bus are similar. 
47   
48      @author: Ray Zimmerman (PSERC Cornell) 
49      @author: Richard Lincoln 
50      """ 
51      i = range(len(V)) 
52   
53      Vnorm = V / abs(V) 
54   
55      if issparse(Yf): 
56          diagV = sparse((V, (i, i))) 
57          diagVnorm = sparse((Vnorm, (i, i))) 
58      else: 
59          diagV       = asmatrix( diag(V) ) 
60          diagVnorm   = asmatrix( diag(Vnorm) ) 
61   
62      dIf_dVa = Yf * 1j * diagV 
63      dIf_dVm = Yf * diagVnorm 
64      dIt_dVa = Yt * 1j * diagV 
65      dIt_dVm = Yt * diagVnorm 
66   
67      # Compute currents. 
68      if issparse(Yf): 
69          If = Yf * V 
70          It = Yt * V 
71      else: 
72          If = asarray( Yf * asmatrix(V).T ).flatten() 
73          It = asarray( Yt * asmatrix(V).T ).flatten() 
74   
75      return dIf_dVa, dIf_dVm, dIt_dVa, dIt_dVm, If, It 
76