## Abstract

This paper considers imbalance problems arising in Energy Management in Smart Grids (SG) as discrete-time stochastic linear systems subject to chance constraints, and proposes a Model Predictive Control (MPC) approach to solve them. It is well-known that handling the closed-loop constraint feasibility of such systems is in general difficult due to the presence of a potentially unbounded uncertainty source. To overcome such a difficulty, we propose two new ideas. We first reformulate the chance constraint using the so-called Conditional Value at Risk (CVaR), which is known to be the tightest convex approximation for chance constraints. We then relax the CVaR constraint using a penalty function depending on a coefficient parameter. An optimal solution is therefore obtained by solving a single unconstrained problem which, intuitively, takes into consideration a risk of the system trajectories in an undesirable state. A case study using an academic example is presented to estimate the a-posteriori probability of the coefficient parameter in order to show when such a penalty function is exact by means of probabilistic constraint fulfillment.

Original language | English |
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Title of host publication | Proceedings of the 2020 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe) |

Place of Publication | Piscataway, NJ, USA |

Publisher | IEEE |

Pages | 309-313 |

ISBN (Electronic) | 978-1-7281-7100-5 |

ISBN (Print) | 978-1-7281-7101-2 |

DOIs | |

Publication status | Published - 2020 |

Event | 10th IEEE PES Innovative Smart Grid Technologies Europe, ISGT-Europe 2020 - Virtual/online event due to COVID-19, Delft, Netherlands Duration: 26 Oct 2020 → 28 Oct 2020 Conference number: 10 https://ieee-isgt-europe.org/ |

### Conference

Conference | 10th IEEE PES Innovative Smart Grid Technologies Europe, ISGT-Europe 2020 |
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Abbreviated title | ISGT-Europe 2020 |

Country/Territory | Netherlands |

City | Delft |

Period | 26/10/20 → 28/10/20 |

Other | Virtual/online event due to COVID-19 |

Internet address |