## Abstract

This paper presents a solution method for a day-ahead stochastic reserve scheduling (RS) problem using an AC optimal power flow (OPF) formulation. Such a problem is known to be non-convex and in general hard to solve. Existing approaches follow either linearized (DC) power flow or iterative approximation of nonlinearities, which may lead to either infeasibility or computational intractability. In this paper we present two new ideas to address this problem. We first develop an algorithm to determine the level of reserve requirements using vertex enumeration (VE) on the deviation of wind power scenarios from its forecasted value. We provide a theoretical result on the level of reliability of a solution obtained using VE. Such a solution is then incorporated in RS-OPF problem to determine up-and down-spinning reserves by distributing among generators, and relying on the structure of constraint functions with respect to the uncertain parameters. As a second contribution, we use the sparsity pattern of the power system to reduce computational time complexity. We then provide a novel recovery algorithm to find a feasible solution for the RS-OPF problem from the partial solution which is guaranteed to be rank-one. The IEEE 30 bus system is used to verify theoretical developments together with a comparison with DC counterpart using Monte Carlo simulations.

Original language | English |
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Title of host publication | Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC) |

Editors | A Astolfi et al |

Place of Publication | Piscataway, NJ, USA |

Publisher | IEEE |

Pages | 2647-2654 |

ISBN (Electronic) | 978-150902873-3 |

DOIs | |

Publication status | Published - 2017 |

Event | CDC 2017: 56th IEEE Annual Conference on Decision and Control - Melbourne, Australia Duration: 12 Dec 2017 → 15 Dec 2017 http://cdc2017.ieeecss.org/ |

### Conference

Conference | CDC 2017: 56th IEEE Annual Conference on Decision and Control |
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Country | Australia |

City | Melbourne |

Period | 12/12/17 → 15/12/17 |

Other | The CDC is recognized as the premier scientific and engineering conference dedicated to the advancement of the theory and practice of systems and control. The CDC annually brings together an international community of researchers and practitioners in the field of automatic control to discuss new research results, perspectives on future developments, and innovative applications relevant to decision making, systems and control, and related areas. |

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