genform.m

该程序是计算最优潮流的matlab工具箱。可以很好的求解目标函数不同的最优潮流问题。

%additive part of the cost contributed by this generator is y.
%
%In the generalized OPF formulation, the capability to accept general
%linear constraints is used to introduce new y variables (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. Because a linear cost on the y variables
%is also required, the last row of the matrix that is passed 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 (or mopf when using MINOPF) and the user
%need not worry about this. To incorporate additional linear constraints,
%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]. The number of y variables
%is equal to the number of piecewise linear cost curves (both active and
%reactive) there are for the generators that are online.
%
%
%*-*-*-*-*-*-*-*-*-*-*-*
%4.0 DISPATCHABLE LOADS
%*-*-*-*-*-*-*-*-*-*-*-*
%
%In general, dispatchable or 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 dispatchable
%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. Considered as a negative injection,
%the desired dispatch is zero if the price is greater than price2, -P1
%if the price is higher than price1 but lower than price2, and -P2 if the
%price is equal to or lower than price1. This suggests the following
%piecewise linear cost curve:
%
%                                      cost
%                                       ^
%         -P2              -P1         0|
%---------------------------------------*-->  power
%                                     * |0
%                      slope=price2 *   |
%                                 *     |
%                               *       |
%                             *         |
%                           *           |
%                      *                |
%                 *                     |
%            * slope=price1             |
%       *                               |
%
%
%Note that this assumes that the demand blocks can be partially
%dispatched or "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
%outside the scope of the current MATPOWER implementation.
%
%When there are dispatchable loads, the issue of reactive dispatch
%arises. If the QMIN/QMAX generation limits for the "negative generator"
%in question are not set to zero, then the algorithm will dispatch the
%reactive injection to the most convenient value. Since this is not
%normal load behavior, in the generalized formulation it is assumed that
%dispatchable 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 values
%of PMIN and either QMIN (for inductive loads) or QMAX (for capacitive
%loads) in the gen table. 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). The initial values of the PG and QG
%columns of the gen matrix must be consistent with the ratio defined
%by PMIN and the appropriate Q limit.
%
%
%*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
%5. ADDITIONAL INFORMATION ON THE GENERALIZED FORMULATION STRUCTURE 
%*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
%
%The advanced user may want to incorporate additional linear constraints
%and/or linear costs to the problem. Sometimes new state variables may
%need to be defined (in addition to x and y discussed above). And,
%sometimes the user may also want 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 and mopf when the following factors interact:
%
%a) existence of y variables because of piecewise 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 piecewise linear
%costs, then some additional constraints will be constructed to model the
%cost segments. If there are dispatchable loads (with either
%polynomial or piecewise linear costs) then additional constraints will
%be included 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], then any linear cost vector needed for modeling of the
%   piecewise linear costs is constructed automatically and the user is
%   not expected to provide a cost row in A.
%
%b) if the number of columns in A is greater than the number of elements
%   in [x; y], then the user is responsible 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 piecewise
%       linear costs as described in previously; this includes both the
%       coefficient matrix and the left and right hand sides of the
%       restrictions. The function makeAy 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 implies that in order to add linear costs on just the
%[x; y] variables, at least one dummy z variable must be created 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) |
%    |   dSf      dSf                     |                         |
%nl  |   ---      ---       0        0    |                         | M = 2*nb
%    |   dth      dV                      |                         |   + 2*nl
%    |                                    |                         |   + mA
%    |   dSt      dSt                     |                         |
%nl  |   ---      ---       0        0    |                         |
%    |   dth      dV                      |                         |
%    +------------------------------------+-------------------------+
%    |                                                              |
%mA  |                                A                             |
%    |                                                              |
%    +--------------------------------------------------------------+
%                         N = 2*nb + 2*ng + ny + nz

%   MATPOWER
%   $Id: genform.m,v 1.7 2005/01/25 14:39:47 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.