  Power distribution systems are becoming much more active with increased
penetration of distributed energy resources. Because of the intermittent nature
of these resources, the stability of distribution systems under large
disturbances and time-varying conditions is becoming a key issue in practical
operations. Because the transmission lines in distribution systems are lossy,
standard approaches in power system stability analysis do not readily apply and
the understanding of transient stability remains open even for simplified
models.
  This paper proposes a novel equilibrium-independent transient stability
analysis of distribution systems with lossy lines. We certify network-level
stability by breaking the network into subsystems, and by looking at the
equilibrium-independent passivity of each subsystem, the network stability is
certified through a diagonal stability property of the interconnection matrix.
This allows the analysis scale to large networked systems with time-varying
equilibria. The proposed method gracefully extrapolates between lossless and
lossy systems, and provides a simple yet effective approach to optimize control
efforts with guaranteed stability regions. Case studies verify that the
proposed method is much less conservative than existing approaches and also
scales to large systems.
