Representing the production cost curve of a power system using the method of moments

An analytic formula, based upon the equivalent load method, for computing the production cost of a power system is presented. This formula can serve as a complement to larger, more complex production cost models since it requires significantly less data and computational effort when running many variants of a basic system configuration. The formula consists of several terms of a Gram-Charlier series using moments which are computed in one iteration of the usual probabilistic production cost algorithm. This formula is particularly suitable for use in iterative optimization models for generation planning, since its parameters can be recomputed easily to account for changes due to construction of new plants. It also permits simple calculation of the gradient of production cost with respect to the capacities of the candidate units. The formula also is useful in calculating the changes in production cost due to load shape changes associated with demand-side management