Modeling of Electric Power Supply Chain Networks with Fuel Suppliers via Variational Inequalities

The electric power industry in the United States and in other countries is undergoing profound regulatory and operational changes. The underlying rationale behind these transformations is to move once highly monopolized vertically-integrated industry from a centralized operation approach to a competitive one. The emerging competitive markets and an increase in the number of market participants have, in turn, fundamentally changed not only electricity trading patterns but also the structure of the electric power supply chains. This new framework requires new mathematical and engineering models and associated algorithmic tools. Moreover, the availability of fuels for electric power generation is a topic of both economic importance and national security. This paper uses the model developed by Nagurney and Matsypura (2004, 2006) as the foundation for the introduction of explicit fuel suppliers, in the case of nonrenewable and/or renewable fuels, and their optimizing behavior, into a general electric power supply chain network model along with ‘direct-supply’ generation. We derive the optimality conditions for the various decision-makers, including fuel suppliers, power generators, suppliers, as well as the transmission service providers and the consumers at the demand markets. We establish that the governing equilibrium conditions satisfy a finite-dimensional variational inequality problem. We provide qualitative properties of the equilibrium flow pattern; in particular, existence of a solution and uniqueness under suitable assumptions. Finally, we discuss how the equilibrium fuel supply and electric power flow pattern can be computed.