An Insightful Marginal Cost Analysis for an Electric Utility Capacity Planning Problem

Abstract

Abstract Given a situation in which a finite number of load curves occur with either known probabilities or over nonoverlapping fractions of time, the problem addressed herein is to conduct a marginal cost analysis for allocating to the various load curves, the capital costs of equipments used in an optimal capacity expansion plan. Such an allocation may be used, for example, in determining a marginal cost time-of-day pricing scheme. A recent paper solves this problem through a formal mathematical programming duality approach. The purpose of the present paper is to first demonstrate that closed form expressions for such marginal cost capital allocations can be readily obtained through an intuitive and insightful perturbation analysis, without any recourse to mathematical programming techniques. Hence, a practitioner can therefore more easily understand and interpret the available duality results. Furthermore, the analysis contained in this paper helps to unify and generalize some existing contributions in the literature, and sheds light on the extent of information contained in the so-called equivalent load duration curve. By way of this analysis, a new set of easier to use and more general capital cost allocation formulae are also obtained.