Dynamics of ancillary service prices in power distribution systems

This paper concerns resource allocation, and performance evaluation in large-scale electric power markets. Our ultimate goal is the integration of new approaches to dynamic control of stochastic networks, with recent results concerning the competitive market equilibrium in network industries, to obtain rigorous, yet comprehensive approaches to model reduction and control for network-level power distribution systems that share these features: (i) information is distributed; (ii) users have distributed, potentially conflicting objectives; (iii) high variability; and (iv) high costs when constraints are violated. Distributed control problems of this form arise in many current application areas, including the power distribution systems considered here. The main result shows how flow models may be constructed in analogy with queuing models for the purposes of design and analysis. Based on this model, we obtain a formula for ancillary service prices in a simple power system model. Generalizations to more complex models are also described.