David P. Chassin, Sahand Behboodi, and L. Lynne Kiesling

A combination of environmental policy and falling production costs has led to the proliferation of distributed energy resources (DERs) in electric power systems. Transactive energy has emerged as a fundamentally new approach to managing electric energy delivery in systems with very high levels of DERs. In this paper we address the question “Can we prove the optimality and stability of general transactive energy systems?” To better understand, observe and control the behavior of transactive control systems we generalize an existing solution to the optimal dispatch function that minimizes the cost objective function in a system with an energy storage price, a power capability price and a ramping response price. We use this generalization to model the behavior of a transactive system that maximizes economic surplus. The Lagrangian solution allows us to derive a Hamiltonian formulation, which we use to explore the properties of the model transactive system. We use this result to derive a linear relationship between the surplus maximizing power dispatch and ramping price. We also find that transactive systems with convex cost functions are always stable but systems with cost functions that have time dynamics of order two or greater cannot be stable.

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