Optimization Online


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

Julia Grübel (julia.gruebel***at***fau.de)
Thomas Kleinert(thomas.kleinert***at***fau.de)
Vanessa Krebs(vanessa.krebs***at***fau.de)
Galina Orlinskaya(galina.orlinskaya***at***fau.de)
Lars Schewe(lars.schewe***at***fau.de)
Martin Schmidt(martin.schmidt***at***uni-trier.de)
Johannes Thürauf(johannes.thuerauf***at***fau.de)

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.

Keywords: Electricity markets, Storage, Market equilibria, Uniqueness, ADMM, Parallel computing, Large-scale optimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Optimization Software and Modeling Systems (Parallel Algorithms )


Download: [PDF]

Entry Submitted: 03/11/2019
Entry Accepted: 03/11/2019
Entry Last Modified: 03/11/2019

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society