Source Code for Module pypower.makeAy

  1  # Copyright (C) 1996-2011 Power System Engineering Research Center (PSERC) 
  2  # Copyright (C) 2011 Richard Lincoln 
  3  # 
  4  # PYPOWER is free software: you can redistribute it and/or modify 
  5  # it under the terms of the GNU General Public License as published 
  6  # by the Free Software Foundation, either version 3 of the License, 
  7  # or (at your option) any later version. 
  8  # 
  9  # PYPOWER is distributed in the hope that it will be useful, 
 10  # but WITHOUT ANY WARRANTY; without even the implied warranty of 
 11  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 
 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  """Make the A matrix and RHS for the CCV formulation. 
 18  """ 
 19   
 20  from numpy import array, diff, any, zeros, r_, flatnonzero as find 
 21  #from scipy.sparse import csr_matrix as sparse 
 22  from scipy.sparse import lil_matrix as sparse 
 23   
 24  from idx_cost import MODEL, PW_LINEAR, NCOST, COST 
 25   
 26   
 27 -def makeAy(baseMVA, ng, gencost, pgbas, qgbas, ybas): 
 28      """Make the A matrix and RHS for the CCV formulation. 
 29   
 30      Constructs the parameters for linear "basin constraints" on C{Pg}, C{Qg} 
 31      and C{Y} used by the CCV cost formulation, expressed as:: 
 32   
 33           Ay * x <= by 
 34   
 35      where C{x} is the vector of optimization variables. The starting index 
 36      within the C{x} vector for the active, reactive sources and the C{y} 
 37      variables should be provided in arguments C{pgbas}, C{qgbas}, C{ybas}. 
 38      The number of generators is C{ng}. 
 39   
 40      Assumptions: All generators are in-service.  Filter any generators 
 41      that are offline from the C{gencost} matrix before calling L{makeAy}. 
 42      Efficiency depends on C{Qg} variables being after C{Pg} variables, and 
 43      the C{y} variables must be the last variables within the vector C{x} for 
 44      the dimensions of the resulting C{Ay} to be conformable with C{x}. 
 45   
 46      @author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad 
 47      Autonoma de Manizales) 
 48      @author: Richard Lincoln 
 49      """ 
 50      ## find all pwl cost rows in gencost, either real or reactive 
 51      iycost = find(gencost[:, MODEL] == PW_LINEAR) 
 52   
 53      ## this is the number of extra "y" variables needed to model those costs 
 54      ny = iycost.shape[0] 
 55   
 56      if ny == 0: 
 57          Ay = zeros((0, ybas + ny - 1))  ## TODO: Check size (- 1) 
 58          by = array([]) 
 59          return Ay, by 
 60   
 61      ## if p(i),p(i+1),c(i),c(i+1) define one of the cost segments, then 
 62      ## the corresponding constraint on Pg (or Qg) and Y is 
 63      ##                                             c(i+1) - c(i) 
 64      ##  Y   >=   c(i) + m * (Pg - p(i)),      m = --------------- 
 65      ##                                             p(i+1) - p(i) 
 66      ## 
 67      ## this becomes   m * Pg - Y   <=   m*p(i) - c(i) 
 68   
 69      ## Form A matrix.  Use two different loops, one for the PG/Qg coefs, 
 70      ## then another for the y coefs so that everything is filled in the 
 71      ## same order as the compressed column sparse format used by matlab 
 72      ## this should be the quickest. 
 73   
 74      m = sum( gencost[iycost, NCOST].astype(int) )  ## total number of cost points 
 75      Ay = sparse((m - ny, ybas + ny - 1)) 
 76      by = array([]) 
 77      ## First fill the Pg or Qg coefficients (since their columns come first) 
 78      ## and the rhs 
 79      k = 0 
 80      for i in iycost: 
 81          ns = gencost[i, NCOST].astype(int)         ## # of cost points segments = ns-1 
 82          p = gencost[i, COST:COST + 2 * ns - 1:2] / baseMVA 
 83          c = gencost[i, COST + 1:COST + 2 * ns:2] 
 84          m = diff(c) / diff(p)               ## slopes for Pg (or Qg) 
 85          if any(diff(p) == 0): 
 86              print 'makeAy: bad x axis data in row ##i of gencost matrix' % i 
 87          b = m * p[:ns - 1] - c[:ns - 1]        ## and rhs 
 88          by = r_[by,  b] 
 89          if i > ng: 
 90              sidx = qgbas + (i - ng) - 1        ## this was for a q cost 
 91          else: 
 92              sidx = pgbas + i - 1               ## this was for a p cost 
 93   
 94          ## FIXME: Bug in SciPy 0.7.2 prevents setting with a sequence 
 95  #        Ay[k:k + ns - 1, sidx] = m 
 96          for ii, kk in enumerate(range(k, k + ns - 1)): 
 97              Ay[kk, sidx] = m[ii] 
 98   
 99          k = k + ns - 1 
100      ## Now fill the y columns with -1's 
101      k = 0 
102      j = 0 
103      for i in iycost: 
104          ns = gencost[i, NCOST].astype(int) 
105          ## FIXME: Bug in SciPy 0.7.2 prevents setting with a sequence 
106  #        Ay[k:k + ns - 1, ybas + j - 1] = -ones(ns - 1) 
107          for kk in range(k, k + ns - 1): 
108              Ay[kk, ybas + j - 1] = -1 
109          k = k + ns - 1 
110          j = j + 1 
111   
112      return Ay.tocsr(), by 
113