On Electricity Market Equilibria with Storages: Modeling, Uniqueness, and a Distributed ADMM

Other publication type


Publication Details

Author(s): Grübel J, Kleinert T, Krebs V, Orlinskaya G, Schewe L, Schmidt M, Thürauf J
Publication year: 2019
Language: English


Abstract

We consider spot-market trading of electricity including storage operators as additional agents besides producers and consumers. Storages allow for shifting produced electricity from one time period to a later one. Due to this, multiple market equilibria may occur even if classical uniqueness assumptions for the case without storages are satisfied. For models containing storage operators, we derive sufficient conditions that ensure uniqueness of generation and demand. We also prove uniqueness of the market equilibrium for the special case of a single storage operator. Nevertheless, in case of multiple storage operators, uniqueness fails to hold in general, which we show by illustrative examples. We conclude the theoretical discussion with a general ex-post condition for proving the uniqueness of a given solution. In contrast to classical settings without storages, the computation of market equilibria is much more challenging since storage operations couple all trading events over time. For this reason, we propose a tailored parallel and distributed alternating direction method of multipliers (ADMM) for efficiently computing spot-market equilibria over long time horizons. We first analyze the parallel performance of the method itself. Finally, we show that the parallel ADMM clearly outperforms solving the respective problems directly and that it is capable of solving instances with more than 42 million variables in less than 13 minutes.


FAU Authors / FAU Editors

Grübel, Julia
Lehrstuhl für Volkswirtschaftslehre, insbesondere Wirtschaftstheorie
Kleinert, Thomas
Juniorprofessur für Optimierung von Energiesystemen
Krebs, Vanessa
Economics - Discrete Optimization - Mathematics (EDOM)
Orlinskaya, Galina
Juniorprofessur für Optimierung von Energiesystemen
Schewe, Lars PD Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen
Thürauf, Johannes
Economics - Discrete Optimization - Mathematics (EDOM)


How to cite

APA:
Grübel, J., Kleinert, T., Krebs, V., Orlinskaya, G., Schewe, L., Schmidt, M., & Thürauf, J. (2019). On Electricity Market Equilibria with Storages: Modeling, Uniqueness, and a Distributed ADMM.

MLA:
Grübel, Julia, et al. On Electricity Market Equilibria with Storages: Modeling, Uniqueness, and a Distributed ADMM. 2019.

BibTeX: 

Last updated on 2019-23-04 at 15:17