6 Optimal Power Flow

Matpower includes code to solve both AC and DC versions of the optimal power flow problem. The standard version of each takes the following form:

min f(x)

subject to

   g (x ) = 0                                (6.2)

   h (x ) ≤ 0                                (6.3)
x   ≤  x ≤ x     .                          (6.4)
 min        max
In both cases, the objective function f(x)  consists of the polynomial cost of generator injections, the equality constraints g(x)  are the power balance equations, the inequality constraints h(x )  are the branch flow limits, and the xmin   and xmax   bounds include reference bus angles, voltage magnitudes (for AC) and generator injections.

 6.1 Standard AC OPF
  6.1.1 Cartesian vs. Polar Coordinates for Voltage
  6.1.2 Current vs. Power for Nodal Balance Constraints
 6.2 Standard DC OPF
 6.3 Extended OPF Formulation
  6.3.1 User-defined Variables
  6.3.2 User-defined Constraints
  6.3.3 User-defined Costs
 6.4 Standard Extensions
  6.4.1 Piecewise Linear Costs
  6.4.2 Dispatchable Loads
  6.4.3 Generator Capability Curves
  6.4.4 Branch Angle Difference Limits
 6.5 Solvers
 6.6 runopf