polycost

POLYCOST  Evaluates polynomial generator cost & derivatives.
   F = POLYCOST(GENCOST, PG) returns the vector of costs evaluated at PG

   DF = POLYCOST(GENCOST, PG, 1) returns the vector of first derivatives
   of costs evaluated at PG

   D2F = POLYCOST(GENCOST, PG, 2) returns the vector of second derivatives
   of costs evaluated at PG

   GENCOST must contain only polynomial costs
   PG is in MW, not p.u. (works for QG too)

   This is a more effecient implementation that what can be done with
   MATLAB's built-in POLYVAL and POLYDER functions.

0001 function f = polycost(gencost, Pg, der)
0002 %POLYCOST  Evaluates polynomial generator cost & derivatives.
0003 %   F = POLYCOST(GENCOST, PG) returns the vector of costs evaluated at PG
0004 %
0005 %   DF = POLYCOST(GENCOST, PG, 1) returns the vector of first derivatives
0006 %   of costs evaluated at PG
0007 %
0008 %   D2F = POLYCOST(GENCOST, PG, 2) returns the vector of second derivatives
0009 %   of costs evaluated at PG
0010 %
0011 %   GENCOST must contain only polynomial costs
0012 %   PG is in MW, not p.u. (works for QG too)
0013 %
0014 %   This is a more effecient implementation that what can be done with
0015 %   MATLAB's built-in POLYVAL and POLYDER functions.
0016 
0017 %   MATPOWER
0018 %   Copyright (c) 2009-2016, Power Systems Engineering Research Center (PSERC)
0019 %   by Ray Zimmerman, PSERC Cornell
0020 %
0021 %   This file is part of MATPOWER.
0022 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0023 %   See https://matpower.org for more info.
0024 
0025 %%----- initialize -----
0026 %% define named indices into data matrices
0027 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0028 
0029 if nargin < 3
0030     der = 0;
0031 end
0032 
0033 if any(gencost(:, MODEL) == PW_LINEAR)
0034     error('polycost: all costs must be polynomial');
0035 end
0036 
0037 ng = length(Pg);
0038 maxN = max(gencost(:, NCOST));
0039 minN = min(gencost(:, NCOST));
0040 
0041 %% form coefficient matrix where 1st column is constant term, 2nd linear, etc.
0042 c = zeros(ng, maxN);
0043 for n = minN:maxN
0044     k = find(gencost(:, NCOST) == n);   %% cost with n coefficients
0045     c(k, 1:n) = gencost(k, (COST+n-1):-1:COST);
0046 end
0047 
0048 %% do derivatives
0049 for d = 1:der
0050     if size(c, 2) >= 2
0051         c = c(:, 2:maxN-d+1);
0052     else
0053         c = zeros(ng, 1);
0054         break;
0055     end
0056     for k = 2:maxN-d
0057         c(:, k) = k * c(:, k);
0058     end
0059 end
0060 
0061 %% evaluate polynomial
0062 if isempty(c)
0063     f = zeros(size(Pg));
0064 else
0065     f = c(:, 1);        %% constant term
0066     for k = 2:size(c, 2)
0067         f = f + c(:, k) .* Pg .^ (k-1);
0068     end
0069 end