Constrained stochastic power flow analysis

Analytic stochastic power flow methods normally employ linear load flow transformations. This is necessary since the statistics of voltages and line power flows cannot be determined through the nonlinear power flow equations. Linear load flow methods do not reflect the full finite ranges of voltage control mechanisms such as generator excitation systems and tap changing under load transformers, and thus traditionally give unsatisfactory results for systems which are sensitive to voltage control. In this work, the statistical mean and variance of load flow output quantities in response to random loading are computed with the consideration of var and tap limits. Multiple linear transformations are employed, with var or tap limits providing the discrete points at which each transformation is utilized.