Probabilistic load flow with correlated input random variables using uniform design sampling

This paper proposes a probabilistic load flow (PLF) methodology using uniform design sampling (UDS). The correlation between input random variables has been taken into consideration. The random numbers of random variables uniformly distributed in (0, 1) are generated by UDS, and subsequently converted into random numbers of input random variables with desired marginal distributions by marginal transformation. Then these random numbers of input random variables are permutated by a method based on rank correlation to satisfy the desired correlation between input random variables. The statistical properties and probability distributions of node voltage and line flow are calculated by Monte Carlo simulation method and statistical method. Considering the uncertainty of correlated wind power and loads, the performance of the proposed PLF methodology is investigated using modified IEEE 14-bus and IEEE 57-bus test systems.