Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse

TLDR

The paper analyzes static stability in electric power systems. The authors model generators with the classical swing equation and loads as constant admittance, PV, or PQ buses, define static stability rigorously, and analyze load‑flow bifurcations via Liapunov‑Schmidt reduction, Taylor expansion, and symbolic computation in MASYMA. They show that load‑flow bifurcations correspond to either divergence‑type instability or loss of causality, and that causality issues are key to voltage collapse and global dynamics when non‑constant‑admittance loads are present.

Abstract

This paper presents an analysis of static stability in electric power systems. The study is based on a model consisting of the classical swing equation characterization for generators and constant admittance, PV bus and/or PQ bus load representations which, in general, leads to a semi-explicit (or constrained) system of differential equations. A precise definition of static stability is given and basic concepts of static bifurcation theory are used to show that this definition does include conventional notions of steady-state stability and voltage collapse, but it provides a basis for rigorous analysis. Static bifurcations of the load flow equations are analyzed using the Liapunov-Schmidt reduction and Taylor series expansion of the resulting reduced bifurcation equation. These procedures have been implemented using symbolic computation (in MASYMA). It is shown that static bifurcations of the load flow equations are associated with either divergence-type instability or loss of causality. Causality issues are found to be an important factor in understanding voltage collapse and play a central role in organizing global power system dynamics when loads other than constant admittance are present.