With the development of the concept of the smart grid, the Autonomous Demand Side Management (ADSM) has been extensively considered by researchers. In autonomous management, each consumer automatically plans his load pattern by using communication network and receiving energy cost information. As a result, consumers’ pay off will be affected by the others’ behavior, and an interaction occurs in consumption scheduling on demand side. Thus, the behavior of an ADSM system can be investigated in a game theory framework. In general, it is difficult to ensure the existence of an equilibrium state in the ADSM system, and the convergence to it. In a special case, the problem can be easily solved if the interaction of the consumers in the ADSM system is characterized by a potential game. For consumers, we proposed a billing function which includes a part of production costs with a set of bilateral symmetry function among consumers. The bilateral symmetry function has special features as if two consumers have same load, they should pay more, and otherwise they should pay less. We proved that the ADSM system with such billing mechanism yields a potential game. Based on the properties of potential game, the existence of Nash equilibrium is guaranteed; moreover, using a round-Robin algorithm, the consumers converges to the equilibrium. Simulation results show that the proposed billing function leads to reducing cost, peak load and bill of consumers while fairness is acceptable. key word: Smart Grid , Autonomous Demand Side Management , Game Theory , Potential Game .
