modcost

MODCOST  Modifies generator costs by shifting or scaling (F or X).
   NEWGENCOST = MODCOST(GENCOST, ALPHA)
   NEWGENCOST = MODCOST(GENCOST, ALPHA, MODTYPE)

   For each generator cost F(X) (for real or reactive power) in
   GENCOST, this function modifies the cost by scaling or shifting
   the function by ALPHA, depending on the value of MODTYPE, and
   and returns the modified GENCOST. Rows of GENCOST can be a mix
   of polynomial or piecewise linear costs. ALPHA can be a scalar,
   applied to each row of GENCOST, or an NG x 1 vector, where each
   element is applied to the corresponding row of GENCOST.

   MODTYPE takes one of the 4 possible values (let F_alpha(X) denote the
   the modified function):
       'SCALE_F' (default) : F_alpha(X)         == F(X) * ALPHA
       'SCALE_X'           : F_alpha(X * ALPHA) == F(X)
       'SHIFT_F'           : F_alpha(X)         == F(X) + ALPHA
       'SHIFT_X'           : F_alpha(X + ALPHA) == F(X)

0001 function gencost = modcost(gencost, alpha, modtype)
0002 %MODCOST  Modifies generator costs by shifting or scaling (F or X).
0003 %   NEWGENCOST = MODCOST(GENCOST, ALPHA)
0004 %   NEWGENCOST = MODCOST(GENCOST, ALPHA, MODTYPE)
0005 %
0006 %   For each generator cost F(X) (for real or reactive power) in
0007 %   GENCOST, this function modifies the cost by scaling or shifting
0008 %   the function by ALPHA, depending on the value of MODTYPE, and
0009 %   and returns the modified GENCOST. Rows of GENCOST can be a mix
0010 %   of polynomial or piecewise linear costs. ALPHA can be a scalar,
0011 %   applied to each row of GENCOST, or an NG x 1 vector, where each
0012 %   element is applied to the corresponding row of GENCOST.
0013 %
0014 %   MODTYPE takes one of the 4 possible values (let F_alpha(X) denote the
0015 %   the modified function):
0016 %       'SCALE_F' (default) : F_alpha(X)         == F(X) * ALPHA
0017 %       'SCALE_X'           : F_alpha(X * ALPHA) == F(X)
0018 %       'SHIFT_F'           : F_alpha(X)         == F(X) + ALPHA
0019 %       'SHIFT_X'           : F_alpha(X + ALPHA) == F(X)
0020 
0021 %   MATPOWER
0022 %   Copyright (c) 2010-2016, Power Systems Engineering Research Center (PSERC)
0023 %   by Ray Zimmerman, PSERC Cornell
0024 %
0025 %   This file is part of MATPOWER.
0026 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0027 %   See https://matpower.org for more info.
0028 
0029 %% define named indices into data matrices
0030 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0031 
0032 if nargin < 3
0033     modtype = 'SCALE_F';
0034 end
0035 
0036 [ng, m] = size(gencost);
0037 
0038 if ng ~= 0
0039     if length(alpha) ~= ng
0040         if length(alpha) == 1 && ng > 1     %% scalar, make it a col vector
0041             alpha = alpha * ones(ng, 1);
0042         else
0043             error('modcost: ALPHA must be a scalar or col vector with NG rows');
0044         end
0045     elseif size(alpha, 2) ~= 1
0046         alpha = alpha';                     %% convert row vector to col vector
0047     end
0048 
0049     ipwl = find(gencost(:, MODEL) == PW_LINEAR);
0050     ipol = find(gencost(:, MODEL) == POLYNOMIAL);
0051     c = gencost(ipol, COST:m);
0052 
0053     switch modtype
0054         case 'SCALE_F',
0055             gencost(ipol, COST:m)       = diag(alpha(ipol)) * c;
0056             gencost(ipwl, COST+1:2:m)   = diag(alpha(ipwl)) * gencost(ipwl, COST+1:2:m);
0057         case 'SCALE_X',
0058             for k = 1:length(ipol)
0059                 n = gencost(ipol(k), NCOST);
0060                 for i = 1:n
0061                     gencost(ipol(k), COST+i-1) = c(k, i) / alpha(ipol(k))^(n-i);
0062                 end
0063             end
0064             gencost(ipwl, COST:2:m-1)   = diag(alpha(ipwl)) * gencost(ipwl, COST:2:m-1);
0065         case 'SHIFT_F',
0066             for k = 1:length(ipol)
0067                 n = gencost(ipol(k), NCOST);
0068                 gencost(ipol(k), COST+n-1) = alpha(ipol(k)) + c(k, n);
0069             end
0070             gencost(ipwl, COST+1:2:m)   = ...
0071                 diag(alpha(ipwl)) * ones(length(ipwl), (m+1-COST)/2) + ...
0072                     gencost(ipwl, COST+1:2:m);
0073         case 'SHIFT_X',
0074             for k = 1:length(ipol)
0075                 n = gencost(ipol(k), NCOST);
0076                 gencost(ipol(k), COST:COST+n-1) = polyshift(c(k, 1:n)', alpha(ipol(k)))';
0077             end
0078             gencost(ipwl, COST:2:m-1)   = ...
0079                 diag(alpha(ipwl)) * ones(length(ipwl), (m+1-COST)/2) + ...
0080                     gencost(ipwl, COST:2:m-1);
0081         otherwise
0082             error('modcost: ''%s'' is not a valid modtype\n', modtype);
0083     end
0084 end
0085 
0086 
0087 %%-----  POLYSHIFT  -----
0088 function d = polyshift(c, a)
0089 %POLYSHIFT  Returns the coefficients of a horizontally shifted polynomial.
0090 %
0091 %   D = POLYSHIFT(C, A) shifts to the right by A, the polynomial whose
0092 %   coefficients are given in the column vector C.
0093 %
0094 %   Example: For any polynomial with n coefficients in c, and any values
0095 %   for x and shift a, the f - f0 should be zero.
0096 %       x = rand;
0097 %       a = rand;
0098 %       c = rand(n, 1);
0099 %       f0 = polyval(c, x)
0100 %       f  = polyval(polyshift(c, a), x+a)
0101 
0102 n = length(c);
0103 d = zeros(size(c));
0104 A = (-a * ones(n, 1)) .^ ((0:n-1)');
0105 b = ones(n, 1);
0106 for k = 1:n
0107     d(n-k+1) = b' * ( c(n-k+1:-1:1) .* A(1:n-k+1) );
0108     b = cumsum(b(1:n-k));
0109 end