Voltage Stability Assessment Through Modal Analysis Using a Smooth Formulation of the Power Flow Problem Based on Sigmoid Functions

This paper introduces a voltage stability analysis based on an innovative formulation of the power flow problem designed to address and eliminate discontinuities associated with reactive power limits from synchronous generators, synchronous compensators, and static VAr compensators. By replacing these discontinuities with appropriately tuned sigmoid functions, we achieve smooth behavior without compromising accuracy. A key advantage of this formulation is its ability to convert limit-induced bifurcations into saddle-node bifurcations. This conversion allows the voltage security studies to focus solely on identifying saddle-node bifurcations, leading to significant computational efficiency. In the present context of modern power systems, characterized by growing demand and uncertainties in generation capacity, this new approach is relevant for ensuring the computational feasibility of highly uncertain scenarios. The effectiveness of the proposed formulation is validated using a modal analysis of the reduced Jacobian matrix, which focuses mainly on the smooth control equations incorporated into the solution of the problem using Newton’s method. Our findings are substantiated by simulations on four test systems, including the IEEE 118-Bus system, which shows the conversion process of bifurcations as described. The results presented validate and indicate the effectiveness of the proposed technique.