Equilibrium-Independent Stability Analysis for Distribution Systems with Lossy Transmission Lines

Abstract

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.

Structured Neural-PI Control for Networked Systems: Stability and Steady-State Optimality Guarantees

“…The EIP property has been found in a large class of physical systems, including transportation [4], power systems [17,27], robotics [18], communication [3] and others. Since our goal is to study the stability of the networked system, we make the assumption that each of the subsystems is strictly EIP.…”

“…Passivity is a classical notion in control theory to characterize the inherent property of dynamical systems by how their inputs and outputs correlate [1]. Many systems have been shown to be equilibrium-independent passive (EIP) [4,17,18], which characterize passivity referenced to an arbitrary equilibrium input/output pair. This abstraction allows us to design generalized controllers for networked systems without considering their detailed dynamics.…”