Interdependence Among Voltage-Unstable Buses During Cascading Failure in Power Systems

In this paper, we demonstrate the interdependence among buses in power systems that experience voltage instability events by deriving interaction graphs through successive transition probability matrices and the Markov transition matrix. A quasi-stationary convergence has been observed in the probability transition matrices, suggesting a pattern in voltage instability failure. We propose algorithms to identify the pattern, referred to as fault chains, by tracing the interaction graphs. The interaction graphs and fault chains can be used to formulate strategies for enhancing network robustness, including the assignment of new photovoltaic buses, load rescheduling, and equipping droop controllers. Numerical experiments performed on the IEEE 118- and 300-bus systems demonstrate that equipping droop controllers at selected buses is an effective approach for improving network robustness.