Reachable Power Flow: Theory to Practice

Reachable power flow (ReachFlow) is a newly developed formal method for enclosing the complete set of uncertain power flow states. To enable ReachFlow's transition from theory to practice, the paper makes three major contributions: (1) both small- and large- signal stability proofs for the ordinary differential equation (ODE)-based power flow are devised to theoretically ensure the robustness of ReachFlow; (2) a model-order-reduction-empowered ReachFlow(${ReachFlow}^R$) algorithm is created for analyzing interested regions in large power systems; and (3) a parallel ReachFlow(${ReachFlow}^P$) algorithm is established to scale up ReachFlow for the accurate analysis of very large power systems. Extensive case studies are performed on a series of test systems, ranging from a 33-bus microgrid to a 2,000-bus power system, to thoroughly verify the correctness, efficacy and practicality of ReachFlow in formally verifying microgrid and macrogrid power flows as well as power flow control strategies.