Probabilistic voltage solution method for distribution systems with wind electric generators

A distribution system planning exercise forecasts both buswise peak load and annual wind generation and typically these forecasts have different probability distributions. A solution method for power balance equations of such a planned system should include probabilistic modeling of bus loads and wind generation. This paper proposes a probabilistic load flow method for a distribution system that takes into account the stochastic nature of wind generation and forecasted buswise peak load. This paper models the annual wind generation forecast using a Weibull distribution function and the annual buswise peak load forecast using a normal distribution function. Assuming the annual load forecasts and wind generation forecasts as independent probabilistic events and using load-duration curves, several sets of data are created with individual probability of occurrence. Each set of generation and load with a probability of occurrence is used to determine a corresponding voltage solution using a Newton-Raphson Method of solution. The probability distribution functions (PDF) for bus voltages are recreated from the resultant data. The resultant PDFs for voltages and other resultant data are analyzed using a curve fitting technique. The method is tested on a modified 70-bus distribution system and the results are reported.