State-in-mode analysis of the power flow Jacobian for static voltage stability

In static voltage stability analysis, participation factors have been used as an index that measures the contribution of the critical mode of power flow Jacobian in the system states. However, this index as usually defined is in a mode-in-state manner that cannot adequately reflect the impact of system states on voltage collapse. In this paper we take a new state-in-mode viewpoint to study the power flow Jacobian. We express the critical mode into a weighted sum of system states, which gives rise to the definitions of state-in-mode participation factor (SIMPF) and state-in-mode sensitivity (SIMS). The SIMPF measures the contribution of a system state to the critical mode, and the SIMS measures the control sensitivity of the system state to the critical mode. The proposed SIMPF and SIMS apply to both node states and network states including active/reactive power injections and active power flows across lines. They provide new insights into the mechanism of saddle-node bifurcation and limit-induced bifurcation, two most common types of voltage instability, by revealing the role of system states. The SIMPF and SIMS can also guide the system dispatch for voltage stability enhancement. The obtained results are validated by the simulations on IEEE 118-bus system and Polish 3120-bus system.