Module opf

Solves an optimal power flow.

Returns a results dict.

The data for the problem can be specified in one of three ways:

1. a string (ppc) containing the file name of a PYPOWER case which defines the data matrices baseMVA, bus, gen, branch, and gencost (areas is not used at all, it is only included for backward compatibility of the API).
2. a dict (ppc) containing the data matrices as fields.
3. the individual data matrices themselves.

The optional user parameters for user constraints (A, l, u), user costs (N, fparm, H, Cw), user variable initializer (z0), and user variable limits (zl, zu) can also be specified as fields in a case dict, either passed in directly or defined in a case file referenced by name.

When specified, A, l, u represent additional linear constraints on the optimization variables, l <= A*[x z] <= u. If the user specifies an A matrix that has more columns than the number of "x" (OPF) variables, then there are extra linearly constrained "z" variables. For an explanation of the formulation used and instructions for forming the A matrix, see the MATPOWER manual.

A generalized cost on all variables can be applied if input arguments N, fparm, H and Cw are specified. First, a linear transformation of the optimization variables is defined by means of r = N * [x z]. Then, to each element of r a function is applied as encoded in the fparm matrix (see MATPOWER manual). If the resulting vector is named w, then H and Cw define a quadratic cost on w: (1/2)*w'*H*w + Cw * w. H and N should be sparse matrices and H should also be symmetric.

The optional ppopt vector specifies PYPOWER options. If the OPF algorithm is not explicitly set in the options PYPOWER will use the default solver, based on a primal-dual interior point method. For the AC OPF this is OPF_ALG = 560. For the DC OPF, the default is OPF_ALG_DC = 200. See ppoption for more details on the available OPF solvers and other OPF options and their default values.

The solved case is returned in a single results dict (described below). Also returned are the final objective function value (f) and a flag which is True if the algorithm was successful in finding a solution (success). Additional optional return values are an algorithm specific return status (info), elapsed time in seconds (et), the constraint vector (g), the Jacobian matrix (jac), and the vector of variables (xr) as well as the constraint multipliers (pimul).

The single results dict is a PYPOWER case struct (ppc) with the usual baseMVA, bus, branch, gen, gencost fields, along with the following additional fields:

• order see 'help ext2int' for details of this field
• et elapsed time in seconds for solving OPF
• success 1 if solver converged successfully, 0 otherwise
• om OPF model object, see 'help opf_model'
• x final value of optimization variables (internal order)
• f final objective function value
• mu shadow prices on ...
  • var
    • l lower bounds on variables
    • u upper bounds on variables
  • nln
    • l lower bounds on nonlinear constraints
    • u upper bounds on nonlinear constraints
  • lin
    • l lower bounds on linear constraints
    • u upper bounds on linear constraints
• g (optional) constraint values
• dg (optional) constraint 1st derivatives
• df (optional) obj fun 1st derivatives (not yet implemented)
• d2f (optional) obj fun 2nd derivatives (not yet implemented)
• raw raw solver output in form returned by MINOS, and more
  • xr final value of optimization variables
  • pimul constraint multipliers
  • info solver specific termination code
  • output solver specific output information
    • alg algorithm code of solver used
• var
  • val optimization variable values, by named block
    • Va voltage angles
    • Vm voltage magnitudes (AC only)
    • Pg real power injections
    • Qg reactive power injections (AC only)
    • y constrained cost variable (only if have pwl costs)
    • (other) any user defined variable blocks
  • mu variable bound shadow prices, by named block
    • l lower bound shadow prices
      • Va, Vm, Pg, Qg, y, (other)
    • u upper bound shadow prices
      • Va, Vm, Pg, Qg, y, (other)
• nln (AC only)
  • mu shadow prices on nonlinear constraints, by named block
    • l lower bounds
      • Pmis real power mismatch equations
      • Qmis reactive power mismatch equations
      • Sf flow limits at "from" end of branches
      • St flow limits at "to" end of branches
    • u upper bounds
      • Pmis, Qmis, Sf, St
• lin
  • mu shadow prices on linear constraints, by named block
    • l lower bounds
      • Pmis real power mistmatch equations (DC only)
      • Pf flow limits at "from" end of branches (DC only)
      • Pt flow limits at "to" end of branches (DC only)
      • PQh upper portion of gen PQ-capability curve(AC only)
      • PQl lower portion of gen PQ-capability curve(AC only)
      • vl constant power factor constraint for loads
      • ycon basin constraints for CCV for pwl costs
      • (other) any user defined constraint blocks
    • u upper bounds
      • Pmis, Pf, Pf, PQh, PQl, vl, ycon,
      • (other)
• cost user defined cost values, by named block