Optimal Power Flow is the central decision problem of operating an electric power system: given a network, a set of generators with cost functions, and a forecast demand, what is the cheapest dispatch that respects every physical and operational limit?

Formally it is a constrained optimization problem whose constraints are the nonlinear equations of AC power flow — equations rooted in Maxwell’s laws as they manifest in lumped-element circuit models of transmission networks. Because the AC formulation is non-convex, decades of research have produced a rich landscape of approximations, relaxations, and decompositions, each with its own assumptions, guarantees, and computational profile.

Lirion brings nine of these formulations together under a single API, alongside distributed solution methods (ADMM today, ALADIN soon) — so that researchers and practitioners can compare, combine, and extend them without rewriting infrastructure.