Ahmed Mesfer Alkhudaydi

Ahmed Mesfer Alkhudaydi, Bai Cui

The progression of modern power systems towards converter-rich operations calls for new models and analytics in steady-state voltage stability assessment. The classic modeling assumption of the generators as stiff voltage sources no longer holds. Instead, the voltage- and current-limited behaviors of converters need to be considered. In this paper, we develop a Wirtinger derivative-based formulation for the power flow Jacobian and derive an explicit sufficient condition for its singularity. Compared to existing works, we extend the explicit sufficient singularity condition to incorporate all bus types instead of only slack and PQ types. We prove that the singularity of the alternative Jacobian coincides with that of the conventional one. A bus-wise voltage stability index, denoted $C_{\mathrm{W}}$, is derived from diagonal dominance conditions. The condition $\min_i C_{W,i}$ being greater than one certifies the nonsingularity of the Jacobian and provides a fast, non-iterative stability margin. Case studies in standard IEEE test systems show that the proposed index yields less conservative and more localized assessments than classical indices such as the L-index, the $K_{\mathrm{R}}$ index, and the SCR index.

Ahmed Mesfer Alkhudaydi, Bai Cui

The rapid growth of large, power-electronics-rich data center (DC) loads is creating new operational challenges for bulk power systems. A key risk arises when a DC uninterruptible power supply (UPS) disconnects the facility during voltage/frequency disturbances and then reconnects it while the bulk grid is still dynamically settling to a new equilibrium point. Poorly timed reconnection can amplify electromechanical oscillations, deepen frequency deviations, and lead to repeated connect-disconnect \emph{flapping}. In this paper, we develop an analytical framework to characterize the \emph{safe reconnection time} for large DC loads after a disturbance-induced disconnection that avoids flapping. Using a model in the spirit of the classical single-machine infinite-bus system, we capture (i) swing dynamics during the disconnection interval and (ii) voltage-angle coupling at the load bus, which determines the electrical power step at reconnection under constant-power load assumptions. Using energy function method, we characterize the critical safe reconnection time such that for any reconnection time after the critical safe reconnection time, the post-reconnection trajectory is guaranteed to remain within operational limits (frequency/angle/voltage) and converge to the post-reconnection equilibrium, thereby preventing flapping. Time-domain simulations validate the effectiveness of the proposed analytical approach. The results provide a simple, physics-informed criterion that can be used to bound reconnection windows for large DC facilities and inform UPS reconnection logic.