Thomas Kleinert

The Impact of Neighboring Markets on Renewable Locations, Transmission Expansion, and Generation Investment

  • Jonas Egerer
  • Veronika Grimm
  • Thomas Kleinert
  • Martin Schmidt
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    Many long-term investment planning models for liberalized electricity markets either optimize for the entire electricity system or focus on confined jurisdictions, abstracting from adjacent markets. In this paper, we provide models for analyzing the impact of the interdependencies between a core electricity market and its neighboring markets on key long-run decisions. This we do both … Read more

    There’s No Free Lunch: On the Hardness of Choosing a Correct Big-M in Bilevel Optimization

  • Thomas Kleinert
  • Martine Labbé
  • Martin Schmidt
  • Fränk Plein
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities Tags , , , ,

    One of the most frequently used approaches to solve linear bilevel optimization problems consists in replacing the lower-level problem with its Karush-Kuhn-Tucker (KKT) conditions and by reformulating the KKT complementarity conditions using techniques from mixed-integer linear optimization. The latter step requires to determine some big-M constant in order to bound the lower level’s dual feasible … Read more

    Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method

  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , ,

    Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, etc. Often, these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization one develops primal heuristics in order to obtain … Read more

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

  • Julia Grübel
  • Thomas Kleinert
  • Vanessa Krebs
  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
  • Galina Orlinskaya
    • Categories Convex Optimization, Parallel Algorithms, Quadratic Programming Tags , , , , , ,

    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, … Read more

    Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization with Graph Partitioning

  • Mirjam Ambrosius
  • Veronika Grimm
  • Thomas Kleinert
  • Frauke Liers
  • Martin Schmidt
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the … Read more

    Global Optimization of Multilevel Electricity Market Models Including Network Design and Graph Partitioning

  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal network expansion and the optimal zonal configuration of zonal pricing electricity markets, which is an extension of the model discussed in [25] that does not include a network design problem. The two classical discrete optimization … Read more

    Optimal Price Zones of Electricity Markets: A Mixed-Integer Multilevel Model and Global Solution Approaches

  • Veronika Grimm
  • Frauke Liers
  • Martin Schmidt
  • Thomas Kleinert
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design … Read more