## Abstract

The paper proposes a formulation for a generalized Nash equilibrium model which incorporates the strategic biddings of some consumers capable of providing reserve and balancing services in the day-ahead and balancing markets, respectively. The strategic bidding in the electricity market is modelled using a bilevel optimization programming, where the electricity cost

of consumers is minimized at the upper level (UL), and the energy and reserve costs in the market clearing process are co-optimized at the lower level (LL). By means of the strong duality theorem, the original bilevel model is transformed into an equivalent single-level mathematical problem with equilibrium constraints (MPEC). The joint problem of all MPECs, one per consumer, constitutes an equilibrium problem with equilibrium constraints (EPEC). The resulting EPEC is finally formulated as an auxiliary mixed-integer linear programming (MILP) problem. To this end, an exact linearization technique and Fortuny-Amat transformation are adopted to substitute the nonlinear terms and the complementarity conditions. In addition, a parametrization technique is used to replace the dual variable associated with the strong duality equation which appears in the EPEC problem. The diagonalization method is also adopted in this part as an ex-post analysis to verify the obtained solutions of the resulted MILP. Finally, a 3-bus illustrative example and the IEEE RTS 24-Bus System and 118-Bus System are considered to investigate the performance of the proposed approach.

of consumers is minimized at the upper level (UL), and the energy and reserve costs in the market clearing process are co-optimized at the lower level (LL). By means of the strong duality theorem, the original bilevel model is transformed into an equivalent single-level mathematical problem with equilibrium constraints (MPEC). The joint problem of all MPECs, one per consumer, constitutes an equilibrium problem with equilibrium constraints (EPEC). The resulting EPEC is finally formulated as an auxiliary mixed-integer linear programming (MILP) problem. To this end, an exact linearization technique and Fortuny-Amat transformation are adopted to substitute the nonlinear terms and the complementarity conditions. In addition, a parametrization technique is used to replace the dual variable associated with the strong duality equation which appears in the EPEC problem. The diagonalization method is also adopted in this part as an ex-post analysis to verify the obtained solutions of the resulted MILP. Finally, a 3-bus illustrative example and the IEEE RTS 24-Bus System and 118-Bus System are considered to investigate the performance of the proposed approach.

Original language | English |
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Pages (from-to) | 225-247 |

Number of pages | 23 |

Journal | International Review of Electrical Engineering: IREE |

Volume | 17 |

Issue number | 3 |

Early online date | 18 Aug 2022 |

DOIs | |

Publication status | Published - 2022 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- bilevel programming
- electricity market
- mathematical program with equilibrium constraints (MPEC)
- renewable energy generation
- strategic bidding