An approximate dynamic integration mechanism for LQ power networks with multi-time scale structures

This paper investigates a dynamic integration mechanism with a multi-time scale structure via economic theory for a power network system. The participant in the power network is divided into two kind of players, that are generators and/or consumers, called agents, and one public commission, called utility. In the power network, the dynamics of agents converges much faster than that of the utility. In this setting, based on singularly perturbation theory, we discuss the public control law that can maximize social welfare for the whole power network. Inspired by the transfer function in mechanism design theory, we design an approximate dynamic mechanism that integrates strategic determinations of private controls by the rational agents into the optimal public controls with real time pricings imposing monetary transfer costs. The proposed dynamic integration mechanism with a multi-time scale structure aims for both social welfare maximization and incentive compatibility.