Probabilistic load flow calculation with quasi-Monte Carlo and multiple linear regression

In this paper, quasi-Monte Carlo combined with multiple linear regression (QMC-MLR) is proposed to solve probabilistic load flow (PLF) calculation. A distinguishing feature of the paper is that PLF is approached by a low-dimensional problem with the concept of the effective dimension, and thus QMC based on low-discrepancy sequences is used to improve the sampling efficiency of the Monte Carlo simulation (MCS). Moreover, according to the relationship between linear correlation and linear regression, the MLR-based correlation control technique is developed to arrange the orders of samples in order to introduce prescribed dependences between variables. The proposed method is tested with the IEEE 118-bus system. Simulation results indicate that the MLR-based technique is robust and efficient in handling correlated non-normal variables and the proposed method shows better performances in PLF calculation compared with other MCS techniques, including simple random sampling (SRS), Latin hypercube sampling (LHS) and Latin supercube sampling (LSS).