Prospect Theory for Enhanced Smart Grid Resilience Using Distributed\n Energy Storage

The proliferation of distributed generation and storage units is leading to\nthe development of local, small-scale distribution grids, known as microgrids\n(MGs). In this paper, the problem of optimizing the energy trading decisions of\nMG operators (MGOs) is studied using game theory. In the formulated game, each\nMGO chooses the amount of energy that must be sold immediately or stored for\nfuture emergencies, given the prospective market prices which are influenced by\nother MGOs' decisions. The problem is modeled using a Bayesian game to account\nfor the incomplete information that MGOs have about each others' levels of\nsurplus. The proposed game explicitly accounts for each MGO's subjective\ndecision when faced with the uncertainty of its opponents' energy surplus. In\nparticular, the so-called framing effect, from the framework of prospect theory\n(PT), is used to account for each MGO's valuation of its gains and losses with\nrespect to an individual utility reference point. The reference point is\ntypically different for each individual and originates from its past\nexperiences and future aspirations. A closed-form expression for the Bayesian\nNash equilibrium is derived for the standard game formulation. Under PT, a best\nresponse algorithm is proposed to find the equilibrium. Simulation results show\nthat, depending on their individual reference points, MGOs can tend to store\nmore or less energy under PT compared to classical game theory. In addition,\nthe impact of the reference point is found to be more prominent as the\nemergency price set by the power company increases.\n