Collection of Power Flow models: Mathematical formulations

In its most general form, the optimal power flow (OPF) problem is a cost minimization problem with equality constraints enforcing Kirchhoff’s current law, i.e. power balance at each bus in the network, and inequality constraints enforcing physical and stability limits on power generation and flow. Several different formulations exist for the the power flow equations, the most popular of which are the polar power-voltage formulation (P), the rectangular power-voltage forumulation (R), the rectangular current-voltage (IV), and the DC approximation (DC) which is a linearization of the problem. Cost functions (1) can be given as quadratic coefficients or as a list of points specifying a piecewise linear function. Piecewise linear functions must be convex at this time.