A Stackelberg game approach for price response coordination of thermostatically controlled loads

In this paper, we study the demand response of the thermostatically controlled loads (TCLs) to control their set-point temperatures by considering the tradeoff between the electricity payment and TCL user's comfort preference. Based upon the dynamics of the TCLs, we set up the relationship between the set-point temperature and the energy demand. Then, we define a discomfort function with respect to the associated energy demand which represents the discomfort level of the set-point temperature. More specifically, the system is equipped with a coordinator named electric energy control center (EECC) which can buy energy resources from the electricity market and sell them to TCL users. Due to the interaction between EECC and TCL users, we formulate the specific energy trading process as a one-leader multiple-follower Stackelberg game. As the main contributions of this work, we show the existence and uniqueness of the equilibrium for the underlying Stackelberg games, and develop a DR algorithm based on the so-called Backward Induction to achieve the equilibrium. Several numerical simulations are presented to verify the developed results in this work.