Polynomial Normal Transformations and Quasi-Monte Carlo Method for Probabilistic Voltage Stability Analysis

The inherent randomness of renewable and demand powers has significantly increased the importance of probabilistic techniques in the operation and planning of power systems. In this context, the paper introduces a novel approach for probabilistic voltage stability analysis in unbalanced power systems. We employ the polynomial normal transformations (PNTs) to accurately model input variable uncertainties. PNT’s versatility allows it to represent a wide range of probability distributions and effectively handle complex correlations among random variables. To enhance computational efficiency without sacrificing essential statistical information, the PNT is integrated with quasi-Monte Carlo simulation, which usually offers a significantly faster convergence rate compared to Monte Carlo methods. To quantify the operational limits of voltage stability, a nonlinear optimization model subject to a set of constraints is utilized. The model (i) employs complementarity constraints to manage the PV-to-PQ transition resulting from generator reactive power saturation and (ii) incorporates the direction of load power increments, thereby capturing the specific pattern of load demand growth across the network. Numerical simulations on a representative system validate the proposed method’s effectiveness. A series of analyses were conducted, varying both the representation of the random input data (using predefined probability distributions like normal and Weibull as well as measured input data) and the PNT order to find the most adequate one. Comparisons against the classical Monte Carlo approach and the point estimate method confirm the robust performance of the adopted methodology.