Economic Management of Electric Power Systems

The theory of dynamic optimization and optimal automatic control is rich and continues its development in different areas including engineering, mathematics, and the focus of this chapter, economics. The objective of this chapter is to introduce these concepts for early graduate students, as a toolset in their graduate studies and beyond. Due to space limitations by the editors, in this synthesis we present introductory theory, and the applications we include are focused on electric power systems. For further and more in depth presentation of the theory, we refer the reader to sources along the text. We start with a review of the Lagrangean Method, the intuition behind the formulation, and a sketch of the economic applications as shadow prices. I then review the basic dynamic optimization problem in Sect. 12.1, starting with Deterministic formulations of the discrete and the continuous problem and present an example applied to the replacement of an energy storage system (ESS). Section 12.2 presents the stochastic formulation based on geometric Brownian motion (GBM), and presents an example of an agent optimizing the use of an ESS. In Sect. 12.3 I introduce the formulation of stochastic programs and decision making under uncertainty. The reader familiar with research in electricity systems with uncertainty can easily recognize the underlying generalization presented. I present an example of a unit commitment problem and potential ways to deal with the curse of dimensionality. The author is particularly indebted to Yihsu Chen, Jon Conrad and Tim Mount for their inputs and feedback.