Combined cumulants and Laplace transform method for probabilistic load flow analysis

The simultaneity of power systems development and uncertainty of system elements has promoted the importance of probabilistic load flow (PLF) in the operating and planning studies of the system. This clarifies that the use of the fast and accurate approaches for PLF computation is necessary. To achieve this objective, this study presents an analytical technique, based on the properties of Laplace transform (LT). The suggested methodology is applicable for every continuous probability distribution function as the input random variable. The proposed procedure is applied to the MATPOWER 9- and 118-bus test systems. To validate the combined cumulants and LT (CCLT) technique, the results are compared with the Monte Carlo simulation and the cumulants method combined with the maximum entropy (CCME) principle. The test results show that the proposed approach gives accurate results, with the lower computational burden comparing CCME. Furthermore, the method formulation and case study results demonstrate that the CCLT method is mathematically straightforward and computationally efficient.