Orthogonal arrays-based method for the probabilistic voltage stability analysis of unbalanced power systems

• A probabilistic voltage stability analysis for unbalanced power systems is addressed. • Unbalanced transmission systems in the presence of wind farms are considered. • A non-linear, constrained optimization problem is solved to determine the maximum load margin. • The Orthogonal Arrays-Based Method is applied. • Numerical applications for an unbalanced test system and comparisons with other probabilistic techniques are presented. In the newly liberalized market, transmission and distribution systems are widely recognized as large-scale uncertain systems due to the stochastic nature of renewable generation and load demands. In this context, probabilistic voltage stability analysis is crucial for ensuring secure system operation. This paper proposes a novel probabilistic approach, the Orthogonal Arrays-Based Method (OABM), to address uncertainties in probabilistic voltage stability analysis for unbalanced power systems. OABM is a computationally efficient probabilistic approximation method that preserves the essential statistical properties of input random variables. The maximum load margin is used as the voltage stability index, and a nonlinear, constrained optimization model, employing complementarity constraints (CCs), is utilized to identify critical voltage stability conditions. CCs accurately model synchronous machines, enabling a seamless transition between PV and PQ bus operation. Numerical applications on a test system, compared with more traditional probabilistic techniques such as Monte Carlo and Point Estimate methods, demonstrate the high accuracy and low computational cost of the proposed OABM approach.