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With increasing the presence of co- and tri-generating units, energy hub operators are encouraged to optimally schedule the available energy resources in an economic way. This scheduling needs to be run in an online manner due to the uncertainties in energy prices and demands. In this paper, the real-time scheduling problem of energy hubs is formulated in a dynamic pricing market. The energy hubs interaction is modeled as an exact potential game to optimize each energy hub's payments to the electricity and gas utilities, as well as the customers' satisfaction from energy consumption. The potential game approach enables us to study the existence and uniqueness of the Nash equilibrium and to design an online distributed algorithm to achieve that equilibrium. Simulations results show that the proposed algorithm can increase the energy hubs' average payoff by 18.8%. Furthermore, energy service companies can improve the technical performance of energy networks by reducing the peak-to-average ratio in the electricity and natural gas by 27% and 7%, respectively. When compared with a centralized approach with the objective of social welfare, the proposed algorithm has a significantly lower running time at the cost of lower social welfare.
Bahrami et al. (Tue,) studied this question.