Distributed coordination of power generators for a linearized optimal power flow problem

This paper considers the problem of optimally dispatching a set of generators in a power system; these generators are interconnected to some loads via a network of buses. We consider scenarios when the power network is operating at a steady state, and a small change in the load occurs at some of the load buses. Upon occurrence of this event, the network seeks to find the change in generator injections and voltage phase angles that makes the new steady state meet the modified load with minimum total generation cost (corresponding to the summation of the individual convex cost functions of the generating units). The resulting optimization problem is nonconvex due to the nonconvex power balance constraints at the buses. We consider a convex approximation of the problem where the power balance constraints are linearized around the initial steady-state operating point. Assuming that each bus can communicate with buses connected to it in the physical power network, we provide two provably correct continuous-time distributed strategies that allow the generators to find the optimal power set points. Both designs build on the saddle-point dynamics of the Lagrangian of the optimization problem. Various simulations illustrate our results.