//IDX_BRCH   Defines constants for named column indices to branch matrix.
//   Example:
//
//   [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
//   TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
//   ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
//
//   Some examples of usage, after defining the constants using the line above,
//   are:
//
//    branch(4, BR_STATUS) = 0;              % take branch 4 out of service
//    Ploss = branch(:, PF) + branch(:, PT); % compute real power loss vector
// 
//   The index, name and meaning of each column of the branch matrix is given
//   below:
//
//   columns 1-11 must be included in input matrix (in case file)
//    1  F_BUS       f, from bus number
//    2  T_BUS       t, to bus number
//    3  BR_R        r, resistance (p.u.)
//    4  BR_X        x, reactance (p.u.)
//    5  BR_B        b, total line charging susceptance (p.u.)
//    6  RATE_A      rateA, MVA rating A (long term rating)
//    7  RATE_B      rateB, MVA rating B (short term rating)
//    8  RATE_C      rateC, MVA rating C (emergency rating)
//    9  TAP         ratio, transformer off nominal turns ratio
//    10 SHIFT       angle, transformer phase shift angle (degrees)
//    11 BR_STATUS   initial branch status, 1 - in service, 0 - out of service
//    12 ANGMIN      minimum angle difference, angle(Vf) - angle(Vt) (degrees)
//    13 ANGMAX      maximum angle difference, angle(Vf) - angle(Vt) (degrees)
//                   (The voltage angle difference is taken to be unbounded below
//                    if ANGMIN < -360 and unbounded above if ANGMAX > 360.
//                    If both parameters are zero, it is unconstrained.)
//
//   columns 14-17 are added to matrix after power flow or OPF solution
//   they are typically not present in the input matrix
//    14 PF          real power injected into "from" end of branch (MW)
//    15 QF          reactive power injected into "from" end of branch (MVAr)
//    16 PT          real power injected into "to" end of branch (MW)
//    17 QT          reactive power injected into "to" end of branch (MVAr)
//
//   columns 18-21 are added to matrix after OPF solution
//   they are typically not present in the input matrix
//                   (assume OPF objective function has units, u)
//    18 MU_SF       Kuhn-Tucker multiplier on MVA limit at "from" bus (u/MVA)
//    19 MU_ST       Kuhn-Tucker multiplier on MVA limit at "to" bus (u/MVA)
//    20 MU_ANGMIN   Kuhn-Tucker multiplier lower angle difference limit (u/degree)
//    21 MU_ANGMAX   Kuhn-Tucker multiplier upper angle difference limit (u/degree)
//
//   See also DEFINE_CONSTANTS.

//   MATPOWER
//   Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC)
//   by Ray Zimmerman, PSERC Cornell
//
//   This file is part of MATPOWER.
//   Covered by the 3-clause BSD License (see LICENSE file for details).
//   See https://matpower.org for more info.

// define the indices
F_BUS       = 1;    // f, from bus number
T_BUS       = 2;    // t, to bus number
BR_R        = 3;    // r, resistance (p.u.)
BR_X        = 4;    // x, reactance (p.u.)
BR_B        = 5;    // b, total line charging susceptance (p.u.)
RATE_A      = 6;    // rateA, MVA rating A (long term rating)
RATE_B      = 7;    // rateB, MVA rating B (short term rating)
RATE_C      = 8;    // rateC, MVA rating C (emergency rating)
TAP         = 9;    // ratio, transformer off nominal turns ratio
SHIFT       = 10;   // angle, transformer phase shift angle (degrees)
BR_STATUS   = 11;   // initial branch status, 1 - in service, 0 - out of service
ANGMIN      = 12;   // minimum angle difference, angle(Vf) - angle(Vt) (degrees)
ANGMAX      = 13;   // maximum angle difference, angle(Vf) - angle(Vt) (degrees)

// included in power flow solution, not necessarily in input
PF          = 14;   // real power injected at "from" bus end (MW)       (not in PTI format)
QF          = 15;   // reactive power injected at "from" bus end (MVAr) (not in PTI format)
PT          = 16;   // real power injected at "to" bus end (MW)         (not in PTI format)
QT          = 17;   // reactive power injected at "to" bus end (MVAr)   (not in PTI format)

// included in opf solution, not necessarily in input
// assume objective function has units, u
MU_SF       = 18;   // Kuhn-Tucker multiplier on MVA limit at "from" bus (u/MVA)
MU_ST       = 19;   // Kuhn-Tucker multiplier on MVA limit at "to" bus (u/MVA)
MU_ANGMIN   = 20;   // Kuhn-Tucker multiplier lower angle difference limit (u/degree)
MU_ANGMAX   = 21;   // Kuhn-Tucker multiplier upper angle difference limit (u/degree)
