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.