### Abstract

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

Original language | English (US) |
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Title of host publication | 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 248-255 |

Number of pages | 8 |

ISBN (Electronic) | 9781509045495 |

DOIs | |

State | Published - Feb 10 2017 |

Event | 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States Duration: Sep 27 2016 → Sep 30 2016 |

### Publication series

Name | 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 |
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### Other

Other | 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 |
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Country | United States |

City | Monticello |

Period | 9/27/16 → 9/30/16 |

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Computational Theory and Mathematics
- Computer Networks and Communications
- Hardware and Architecture
- Control and Optimization

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## Cite this

*54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016*(pp. 248-255). [7852237] (54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2016.7852237