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

The author presents an analytic formula, based on the equivalent load method, to calculate the production cost curve of a power system. A totally thermal generating system is assumed, although with some exceptions discussed the results extend to systems with limited energy and storage units. Their loading order positions are assumed known and fixed when the curves are calculated, determined beforehand by running a full production cost model. 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. The author demonstrates how to calculate the total production cost from the marginal cost curve, and shows how to decompose the system cost curve to simplify the repeated production cost calculations needed in generation planning models. Computational experience is discussed. Some mathematical details are presented