As correlated uncertainties in power grids become more prevalent, modeling of stochastic dependencies is becoming increasingly necessary. Independent probability distributions disregard these correlated uncertainties, potentially leading to significant errors, underscoring the necessity of dependence structures. This paper presents a probabilistic approach for modeling uncertain system parameters with their inherent correlations. The proposed approach is validated through various aspects of system voltage measures, including voltage profile and static and dynamic voltage stability. In total, nine alternative sampling generation techniques are employed, and their accuracy is measured based on real-world data using root mean square error (RMSE) and coefficient of determination (R2) criteria. The result suggests that multivariate (Gaussian and Student's) copula techniques accurately represent the real system data, consistently achieving high accuracy rates of 98 % for voltage profiles, 97 % for static voltage stability, and 93 % for dynamic voltage stability. In contrast, the independent sampling technique failed to follow the real-world system data for the different aspects of system voltage measures.