genform.m

以上所传的内容为电力系统比较全面的分析程序,才用的是matlab编写m的文件

% In the generalized OPF formulation, the capability to accept
% general linear constraints is used to introduce new variables "y"
% (one for each piecewise-linear cost in the problem) and constraints
% (one for each cost segment in the problem).  The function that
% builds the coefficient matrix for the restrictions is makeAy.m .
% Because a linear cost on the y variables is also required, the
% last row of the matrix that is actually passed on to the solver
% is expected to contain not some linear restriction coefficients
% but a linear cost vector on [x;y] .  In normal use this is done
% automatically inside fmincopf.m (or mopf.m when using MINOS) and
% the users need not worry about this.  If the user wants to add
% linear constraints of his or her own, however, it is necessary
% to know in advance how many y variables there are so that
% the coefficient matrix for the user's constraints have a matching
% number of columns to multiply [x;y].  In that case it is necessary to
% know how many piece wise linear cost curves (both active and reactive)
% there are for the generators that are online.  That is equal to the
% number of "y" variables.
%
% *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
% 4.0 CURTAILABLE AND PRICE-SENSITIVE LOADS
% *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
%
% In general, price-sensitive loads can be modeled as negative
% real power injections with associated costs.  The current test
% is that if PMIN <  PMAX <= 0 for a generator, then
% it is really a price-sensitive load.  If a load has a demand
% curve like the following
%
%  quantity
%     ^
%     |
%     |
% P2  |-------------
%     |             |
%     |             |
% P1  |____________ |_____________
%     |                           |
%     |                           |
%     |-------------------------------->   price
%                 price1        price2
%
% so that it will consume zero if the price is higher than price2,
% P1 if the price is less than price2 but higher than price1, and P2
% if the price is equal or lower than price1. Then, when the load is
% is considered as a negative injection what is wanted is that it is 
% dispatched at zero if the price is greater than price2,
% at -P1 if the price is higher than price1 but lower than price2,
% and at -P2 if the price is equal to or lower than price1.
% This suggests the following piece wise-linear cost curve:
%
%                                       cost
%                                        ^
%          -P2              -P1         0|
% ---------------------------------------*-->  power
%                                      * |0
%                       slope=price2 *   |
%                                  *     |
%                                *       |
%                              *         |
%                            *           |
%                       *                |
%                  *                     |
%             * slope=price1             |
%        *                               |
%
%
% Note that this assumes that the demand blocks can be "split";
% if the price trigger is reached half-way through the block, the load
% must accept the partial block.  Otherwise, accepting or rejecting
% whole blocks really poses a mixed-integer problem, which is not
% inside the scope of MATPOWER at this time.
%
% When there are price-sensitive loads, the issue of reactive
% dispatch arises.  If the QMIN/QMAX generation limits for the
% generator (really a load) in question are not set to zero,
% then the algorithm will actually dispatch the reactive injection
% to the most convenient value.  This is not normal load behavior
% and therefore in the generalized formulation it is assumed that
% variable loads maintain a constant power factor.  The mechanism
% for posing additional general linear constraints is employed to
% automatically include restrictions for these injections to
% keep the ratio of Pg and Qg constant.  This ratio is inferred
% from the initial values of PG and QG in the gen() table;
% thus, it is important to set these appropriately, keeping in mind
% that PG is negative and that for normal inductive loads
% QG should also be negative (a positive reactive load is a
% negative reactive injection).
%
% *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
% 5. ADDITIONAL STRUCTURE INFORMATION
% *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
%
% The advanced user may need to add linear constraints to the
% problem and/or linear costs.  Sometimes new state variables
% may need to be defined (in addition to x and y discussed
% before).  And, sometimes the user may also need to include
% additional linear costs on some or all of the variables, but
% in most cases fmincopf (or mopf) hide these steps from
% the user and create certain costs and restrictions automatically.
% This creates a conflict between ease of use and generality
% of the software.  In this section we explain the behavior
% adopted by fmincopf.m and mopf.m when the following factors
% interact:
%
% a) existence of y variables because of piece wise-linear costs
% b) User-provided linear restrictions
%   b1) on whatever the existing variables [x;y] are;
%   b2) with A having more columns than there are elements
%       in [x;y], thus creating extra variables z and an overall
%       optimization vector [x;y;z].
%
% If the user does not provide any additional linear restrictions
% via the A, l, u parameters, then internally there are only
% x and y-type variables; if there are y-type variables for modeling
% piece wise-linear costs, then some additional constraints will
% be constructed to model the cost segments.  If there are
% price-sensitive loads (with either polynomial or piece wise-linear costs)
% then some more constraints will be added to maintain a constant power
% factor.
%
% If a user does provide A, l, u parameters to add general linear
% constraints, then
%
%   a) if the number of columns in A is the same as the number
%      of variables in [x;y], the software takes charge of constructing
%      any linear cost vector needed for modeling of the piece wise-linear
%      costs and it does not expect any user-provided cost row
%      in A.
%
%   b) If the number of columns in A is greater than the number of
%      elements in [x;y], then it becomes the user's responsibility to
%      provide 
%
%      b1) the appropriate linear restrictions on y and the Pg, Qg
%          sections of the x vector to model each of the segments
%          of the piece wise-linear costs as described in section 2;
%          this includes both the coefficient matrix and the left
%          and right hand sides of the restrictions.
%          The function makeAy.m can be used for this, but keep in mind
%          that it will return a coefficient matrix that has only
%          as many columns as elements in [x;y].  It must be padded
%          with enough sparse zero columns on the right to make it
%          conformable with [x;y;z] if there are any z variables.
%
%      b2) the appropriate linear cost in the last row of A
%          and this includes ANY NECESSARY COST COEFFICIENTS ON THE "y" 
%          SECTION OF THE COST VECTOR. Note that l and u must still have 
%          the same number of elements as A has rows but the last elements 
%          in l and u are meaningless; set them to (-large, +large).
%
% Note that this means that if the user wants to add linear costs
% on just the [x,y] variables, he or she will have to create at least
% one dummy z variable for the interface to provide the user with the
% opportunity to specify the linear cost vector.
%
% Finally, to complete this section we include the structure of
% the Jacobian used internally by MINOS; note that the sparse matrix
% returned by the solvers only includes the rows up to the last of the
% nonlinear constraints (those related to the injection limit on the
% "To" side of the branches).
%
%          nb       nb       ng       ng               ny + nz
%      ----------------------------------------------------------------
%      |   dgP      dgP      dgP            |                         |
%  nb  |   ---      ---      ---       0    |                         |
%      |   dth      dV       dP             |                         |
%      |                                    |                         |
%      |   dgQ      dgQ               dgQ   |                         |
%  nb  |   ---      ---       0       ---   |                         |
%      |   dth      dV                dQ    |                         |
%      |                                    | sparse(2*NB+2*NL,NY+NZ) | M = 2nb
%      |   dSf      dSf                     |                         |    +2nl
%  nl  |   ---      ---       0        0    |                         |    +AM
%      |   dth      dV                      |                         |
%      |                                    |                         |
%      |   dSt      dSt                     |                         |
%  nl  |   ---      ---       0        0    |                         |
%      |   dth      dV                      |                         |
%      ----------------------------------------------------------------
%      |                                                              |
%  AM  |                                A                             |
%      |                                                              |
%      ----------------------------------------------------------------
%

%   MATPOWER
%   $Id: genform.m,v 1.4 2004/09/15 16:23:02 ray Exp $
%   by Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales
%   Copyright (c) 2004 by Power System Engineering Research Center (PSERC)
%   See http://www.pserc.cornell.edu/matpower/ for more info.