A dynamic mechanism for LQG power networks with random type parameters and pricing delay

We consider a dynamic game model of power networks with generators and/or consumers, called agents, and one public commission, called utility; a game with a prescribed dynamic mechanism is performed such that each agent decides a private control to minimize its own cost functional, and the utility manages information transmissions between the utility and agents and decides command signals, called prices, to minimize a public cost functional. We discuss designs of the mechanism that integrates strategic determinations of private controls by the agents into the optimal public controls that achieve the optimal social welfare and rational agents can accept. The model of this paper is a generic linear Gaussian model of power networks, which is motivated by so-called average system frequency models; in each model of the agents, we includes the type parameter presenting each agent´s private information; we also consider the time delay in calculation of prices by utility. Assuming that each private cost functional as well as the public cost functional is quadratic, we derive formulas of the pricing schemes, and the incentive cost, inspired by the pivot function in the mechanism design theory literate from economics, that characterize our mechanism design in both formulations of the fixed horizon control and the receding horizon control cases.