  Considering increasing distributed energy resources and responsive loads in
smart grid, this paper proposes a stochastic simulation approach for stability
analysis of a power system having stochastic loads. The proposed approach
solves a stochastic, nonlinear differential equation model of the system in an
analytical way by the Adomian decomposition method and generates
semi-analytical solutions that express both deterministic and stochastic state
variables explicitly as symbolic variables so as to embed stochastic processes
directly into the solutions for efficient stability analysis with
uncertainties. The proposed approach is tested on the New England 10-machine
39-bus system with different penetration levels of stochastic loads. The
approach is also benchmarked with a traditional stochastic simulation approach
based on the Euler-Maruyama method. The results show that the new approach has
better time performance and a comparable accuracy.
