Demand dispatch is the science of extracting virtual energy storage through the automatic control of deferrable loads to provide balancing or regulation services to the grid, while maintaining consumerend quality of service. The control of a large collection of heterogeneous loads is in part a resource allocation problem, since different classes of loads are more valuable for different services. The goal of this paper is to unveil the structure of the optimal solution to the resource allocation problem, and investigate short-term market implications. It is found that the marginal cost for each load class evolves in a two-dimensional subspace: spanned by a co-state process and its derivative. The resource allocation problem is recast to construct a dynamic competitive equilibrium model, in which the consumer utility is the negative of the cost of deviation from ideal QoS. It is found that a competitive equilibrium exists with the equilibrium price equal to the negative of an optimal costate process. Moreover, the equilibrium price is different than what would be obtained based on the standard assumption that the consumer's utility is a function of power consumption.
This paper surveys the development of marginal cost theories used in the optimal allocation of scarce resources, and examines the application of these theories to current-day electricity capacity markets. The different approaches in use today to ensure grid reliability and incentivize new resources are examined. Market challenges are surveyed, as well as empirical findings that suggest that current market approaches do not provide proper incentives. We conclude that the so-called "missing money" is not missing because of defects in market designs, or socalled administrative actions-money to incentivize investments is missing due to a misapplication of marginal cost theory.Acknowledgements Research supported by the National Science Foundation under grants CPS-0931416 and EPCN-1609131. We thank Professors David Spence, Amy Stein, and Seth Blumsack for their insightful comments and encouragement. Their input as well as suggestions from the reviewers were carefully considered in the revised manuscript.
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