A description is given of how power system probabilistic production simulations can be performed by using the Legendre series to approximately represent the load and the equivalent load. This implies that knowledge about the minimum and maximum value of the load is used. A new method is used to determine six types of characteristic quantities; the expected value and standard deviation for the ith unit's production, the probabilities of zero and maximum production, loss of load probability, and the expected value of unserved energy. A new concept is introduced to perform convolution/deconvolution by a simple operation on a set of moments representing the equivalent load, in order to commit/remove a generating unit with a forced outage rate and capacity. >