The utility industry is predicting an increase of renewable electrical energy resources into the existing power grid. Understanding the impacts associated with renewable energy penetration are vital for future network planning and operation. Using probabilistic uncertainty models for power injections of these resources, this paper uses their statistical distribution to determine corresponding distributions for network state variables. The Jacobian linearization matrix is determined using the Newton-Raphson power flow method, and the statistical distributions of state variables at all buses in a network are obtained from a linear transformation of the injection distribution function. With these distributions, first and second moments of state variables in a given network can be approximated.
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