A method for the forecasting of the probability density function of power system loads

Conventional load forecasting involves the prediction of the mean value of the demand of an electric power system. The mean value of a quantity which is subject to uncertainty does not fully characterize that quantity. In this paper, two well known load forecasting methods are generalized to predict the entire probability density function of the load. Note that the proposed technique is not to calculate the probability density of the forecasted load, but, rather, the probability density function of the load itself. From this density function, a wide variety of quantities may be calculated: the mean value; the probability that the load will exceed some threshold; a figure of confidence of the forecast mean; conditional probabilities (under special conditions such as negative generation margin), and conditional expectations. Both methods presented rely on the forecasting of the statistical moments of the demand, and using those moments to calculate the probability density function using the Gram-Charlier series type A. An example using typical data is given.