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A polynomial-time algorithm for the optimal offer in Single-Area Day-Ahead Electricity Markets

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Abstract

Efficiently devising optimal offers for Generation Companies (GenCos) in Day-Ahead Electricity Markets is a challenging task. Most solution procedures found in technical literature are built upon non-convex optimization structures, known as Mathematical Programming with Equilibrium Constraints (MPECs), that are difficult to scale to realistic-size instances. Therefore, the main objective of this work is to propose an efficient procedure to aid GenCos to devise optimal offering strategies in Day-Ahead Electricity Markets composed of a single bidding area. Supported by a set of technical results and strong duality theory, a tailored procedure that can be executed in polynomial-time in the number of firms is constructed with global-optimality guarantees. Numerical experiments are conducted, benchmarking the proposed approach against the standard MPEC-derived procedure typically found in the technical literature to solve the offering problem. We found that the proposed solution approach grows (roughly) linearly with the instance size and significantly overcomes (in the order of 20–25 times faster) its counterpart in the most demanding instances. Furthermore, the scalability of the MPEC-derived procedure is challenged even for medium-scale instances, whilst the proposed polynomial-time procedure was able to handle all instances in a reasonable computational time.

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Notes

  1. In (13), the positive truncation function has the following definition \(\big [ \lambda - p^{*}_{S,j} \big ]^{+} \triangleq \max \big \{\lambda - p^{*}_{S,j}, 0\big \}, ~ \forall ~ j \in {\mathcal {N}}_{S}\) and \(\big [ \lambda - p_{R,i} \big ]^{+} \triangleq \max \big \{\lambda - p_{R,i}, 0\big \}, ~ \forall ~ i \in {\mathcal {N}}_{R}\). This definition is used in the remainder of this paper.

  2. Following the standard analysis in computational complexity theory the worst-case analysis refers to the performance of a theoretical analysis of the complexity of the algorithmic procedure. Roughly speaking, the worst-case analysis provides upper bounds on the number of steps that a given computational procedure can take on any problem instance. In this analysis, the largest possible number of steps is counted; consequently, it provides a guarantee on the number of steps an algorithm will take to solve any problem instance [37, 38].

  3. \({\mathcal {O}}\big (n^{3.5}L^{2})\) for the algorithm designed in [34] or \({\mathcal {O}}\big (n^{6} L^{2}\big )\) for the ellipsoid algorithm, with n the number of decision variables and L the number of bits in the input instance.

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Acknowledgements

The author would like to express his sincere acknowledgment to the editor and the anonymous referee for their constructive comments that enhanced the quality and presentation of this paper.

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  1. Industrial Engineering Department, PUC-Rio, Rio de Janeiro, RJ, Brazil

    Bruno Fanzeres

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This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. Bruno Fanzeres was partially supported by CNPq, project 309064/2021-0, and FAPERJ, project E-26/202.825/2019.

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Fanzeres, B. A polynomial-time algorithm for the optimal offer in Single-Area Day-Ahead Electricity Markets. Energy Syst (2023). https://doi.org/10.1007/s12667-023-00629-5

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