Probabilistic power flow calculation using the Johnson system and Sobol's quasi-random numbers

This study puts forward a probabilistic power flow calculation method based on the Johnson system and Sobol's quasi-random numbers. The Johnson system is utilised to simulate the distribution function of one dimensional variable and model the correlation of multiple uncertainties with historical data of the uncertainties. The improved Sobol's quasi-random number generator is adopted to produce the low-discrepancy samples in Monte Carlo simulation. The accuracy of the Johnson system is compared with other modelling methods of uncertainties and the comparison of Sobol's quasi-random numbers and other techniques, such as Latin hypercube sampling and simple random sampling are presented for the cases of IEEE 30-bus system and IEEE 118-bus system.