Stochastic power flow of distribution networks including dispersed generation system

The insertion of stochastic renewable energies in distribution grids generates important voltage fluctuations. However, the influence of the On Load Tap Changer and Distributed Generators (DGs) controllers, and specifically the existence of dead-bands in the control laws, has been seldom evaluated. Under the assumptions of Gaussian inputs and a linear model of the grid, it is shown that node voltages can be approximated either by Gaussian variables or sums of truncated Gaussian variables. A procedure is necessary to select the Probability Density Function (PDF) which fits best each node voltage. A signal based method and another algorithm relying on the grid topology are presented and compared when the modeling is applied to a real distribution grid. The model is accurate and can be used for confidence level or chance-constrained optimization of control parameters.