Real Time Pricing and Pivot Mechanism for LQG Power Networks

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 selfish and strategic determinations of private controls by the agents into the optimal public controls that rational agents can accept. The model considered in this paper is the linear models of power networks, which is a special case of the model so-called average system frequency models, but we also include white Gaussian disturbances in each dynamic model of the agents in order to take account into the stochastic nature of renewable resources. Assuming that each private cost functional as well as the public cost functional is quadratic, we derive explicit formulas of the command signalling scheme, i.e., pricing scheme, 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.