Comparison parametric and non-parametric methods in probabilistic load flow studies for power distribution networks

Uncertainty assessment of distribution systems performance is an obligation because of the intermittent nature of solar and wind distributed energy resources, as well as uncertainties in power demand and charging stations of electric vehicles. Consequently, efficient tools are required for load flow analysis. Many of the existing papers assume a set of given probability density functions (PDFs) to model uncertainties and develop parametric probabilistic load flow tools. However, the uncertainties might not fall in any standard class of PDFs. As a result, non-parametric tools are required. This study compares parametric and non-parametric approaches for determining the PDFs of load flow outputs, as well as Monte Carlo simulation. To compare the methods, the unscented transform and two-point estimation approaches have been considered as parametric methods, while for non-parametric methods, saddle point approximation and kernel density estimation methods have been considered. To examine the performance of the proposed parametric and non-parametric methods, IEEE 28-bus, 33-bus, 37-bus, 69-bus and 210-bus test systems are taken into consideration and results are compared with generalized Polynomial Chaos algorithm, Latin Hypercube Sampling with Cholesky Decomposition, Cornish-Fisher expansion and clustering analysis. In terms of both accuracy and execution time, the results produced by non-parametric approaches are compared to those obtained by parametric methods. They show that the non-parametric estimators produce reliable results in estimating the density function of output random variables, while can reduce the run time for the power-flow problem in an acceptable level.