Probabilistic Evaluation of Line Loading and Line Active Power in an Active Distribution Network Using Numerical and Analytical Approaches

In recent years, active distribution networks have gained in importance due to increased emphasis on renewable energy sources. The integration of these sources into the power system is intrinsically related to various types of uncertainties. In such cases, evaluating line loading and line active power is of immense importance in providing comprehensive details for use in power system planning. This paper presents two key (numerical and analytical) approaches for comparing computational times and accuracy for line loading and active power in an active distribution network. Monte Carlo and quasi-Monte Carlo simulations are categorized as numerical methods and combined cumulants and Gram-Charlier expansion is an analytical approach. The IEEE 13-bus test system was employed to conduct the required analysis. It was determined that the combined cumulants and Gram-Charlier expansion method is quite accurate and computationally efficient when compared to Monte Carlo and quasi-Monte Carlo methods.