Probabilistic load flow by generalized polynomial chaos method

The probabilistic load flow (PLF) problem is solved by a new approach named generalized polynomial chaos (gPC) method. This method combines the techniques of gPC expansion and Galerkin method and transforms the PLF equations into a set of deterministic equations. After the deterministic equations being solved by conventional methods, the means and variances of PLF random variables can be easily obtained and the probabilistic density functions of relevant variables can be estimated by Monte Carlo simulation. The load flow equations in rectangular form are adopted to avoid high order truncation errors of the expansions of PLF equations. Compared with other analytical PLF methods, this method preserves the nonlinearity of the load flow equations and hence can achieve better accuracy, which are verified by the case studies of a 9 bus system.