Second order exponential asymptotic expansion for probabilistic load flow analysis

• A novel non-iterative method is developed for probabilistic load flow analysis. • The proposed method is independent of input RVs’ type and sample size. • It estimates PDFs and CDFs accurately without requiring numerical integration. • Results on two test systems confirm its high accuracy and low computational cost. Due to the inherent randomness in certain resources and load demands, load flow analysis must be performed using efficient and robust probabilistic methods to accurately capture power system uncertainties. This paper proposes a novel non-iterative and non-parametric framework, called the second-order exponential asymptotic expansion (SOEAE) method, to solve the probabilistic load flow problem. Unlike classical methods such as first-order second moment, saddlepoint approximation method, or point estimation methods, the proposed technique maintains a consistent computational cost regardless of the number of random variables. Hence, only a single iteration is sufficient to obtain the Taylor series expansion of the output variables as functions of the input random variables. Also, this method can approximate the density functions of unknown variables, regardless of the input variables’ distribution type. In addition to lower computational cost and higher accuracy, the proposed method preserves key advantages of traditional methods and derives cumulative distribution functions without integration. The suggested method is examined on IEEE 14-bus and IEEE 118-bus test systems, and results with reasonable accuracy are achieved. The results are compared with those obtained using Monte Carlo simulation and saddlepoint approximation methods.