Quadratic probabilistic load flow with linearly modelled dispatch

A second-order probabilistic load flow technique is presented, which takes into account the effects of nonlinearities in the system equations and of different dispatching strategies. This approach uses as input a normal probability distribution for the loads. The probability distribution for the generated powers is computed by linearly modelling the dispatching activity. The technique of moments is then applied to second-order approximations for the load flow and current equations, allowing the noniterative computation of the means and standard deviations for the various output quantities. Generation outages are separately treated, with the possibility of embedding different postoutage dispatching strategies. The cumulative results are finally obtained by combining the pertinent probabilistic load flows with the occurrence probabilities of the various conditions. Results on two sample systems are given.