Fixed-Point Theorem-Based Voltage Stability Margin Estimation Techniques for Distribution Systems With Renewables

The future distribution systems expose to an unprecedented level of uncertainties due to renewable resources, nontraditional loads, aging infrastructure, etc., posing potential risks to secure operation of the system.This article proposes a new technique to estimate the voltage stability margin of the distribution systems with high penetration of renewables.Its convergence and robustness under complex and stressed working conditions are guaranteed in theory. This technique is handy for the operation as it features self-adaptive step size and is applicable to general system topology. It leverages a newly derived analytical solvability certificate based on the Kantorovich fixed-point theorem. A fast version of the proposed technique is duly proposed to speed up the computation up to 8 times while maintaining high accuracy, which lends itself to online and time-sensitive emergency tasks. Numerical simulations with various IEEE test feeders verify the performance of the techniques.