Probabilistic load flow using improved three point estimate method

An improved three point-estimate method (I3PEM) scheme is proposed to estimate the probability moments of probabilistic power flow (PLF) in this paper. I3PEM is obtained by the existing three point-estimate method (3PEM), two point-estimate method (2PEM) and Chebyshev inequality. With only first three order moments (mean, standard deviation and skewness) of input random variables, the additional calculations in I3PEM are performed by a newly added pair of estimate points to improve the accuracy of estimated moments for output random variables. It is avoided the calculation of higher order center moments and the non-real number solutions that may occur with normalized center distances. The case studies of IEEE 14-bus and 118-bus system are employed to verify the performance of I3PEM in the presence of Normal distribution inputs, correlated inputs and non-normal inputs. Under the different coefficient of variation (CV) conditions, the results of MCS are used as benchmark. The accuracy of results obtained by I3PEM have been validated by comparing with those obtained from the basic 3PEM and 2PEM. Further, the advantages and applicability of I3PEM are compared.