The paper considers the coordination of controlled loads in a setting where the loads are
connected to the distribution network through transformers. Our objective is to design a
decentralized control method that can motivate selfish loads to achieve global benefits. This
problem has a hierarchical structure. At the lower level, each transformer broadcasts a price
signal to the loads connect to it, under which loads establish their best usage strategies. At
the upper level, transformers communicate with the distribution network and obtain a price …