Mixed-Integer vs. Real-Valued Formulations of Battery Scheduling Problems

Murray, Alexander; Faulwasser, Timm; Hagenmeyer, Veit

doi:10.1016/j.ifacol.2018.11.727

Cited by 8 publications

(4 citation statements)

References 22 publications

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“…Alternatively, absolute value functions may be used, but this would imply solving a real-valued Nonlinear Program (NLP) instead of a Mixed Integer Linear Program (MILP). As shown in Murray, Faulwasser, and Hagenmeyer (2018), the latter generally gives better results for the BATSS problem (Table 1).…”

Section: Model Of Connection To Main Gridmentioning

confidence: 69%

“…There exist nonlinear approaches to model effects such as preventing a simultaneous charging and discharging of the battery (Appino et al 2018). Alternatively, Murray, Faulwasser, and Hagenmeyer (2018); Sass et al (2020) illustrate how such nonlinear battery models can be reformulated with mixed-integer linear approaches. In Bösenberg et al (2015), it is shown that higher cycling rates can reduce battery lifetime, and thus a controller which avoids this can reduce long term maintenance costs.…”

Section: Energy System Modellingmentioning

confidence: 99%

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On modelling effects in the battery and thermal storage scheduling problem

Murray

Schütz

Pan

et al. 2020

Journal of Building Performance Simulation

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The growing use of intermittent renewable energy sources requires an increased amount of storage capacity to match uncertain generation with uncertain demand. A possible solution is the use of thermal and electrical storages. This paper compares several model formulations: mixed integer linear programs (MILPs), nonlinear programs (NLPs), mixed integer nonlinear programs (MINLPs) for optimizing the operation of a multi-modal home energy system comprising heating and electricity subsystems. The respective optimization problems are then resolved within a model predictive control scheme and the final solutions are compared in terms of runtime and optimality. The results indicate that a thermocline-based thermal storage model leads to the overall lowest costs while not significantly impeding computing times. Additionally, the results show that a continuous heat pump model leads to reduced computing times without affecting the modelling accuracy.

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Section: Model Of Connection To Main Gridmentioning

confidence: 69%

Section: Energy System Modellingmentioning

confidence: 99%

On modelling effects in the battery and thermal storage scheduling problem

Murray

Schütz

Pan

et al. 2020

Journal of Building Performance Simulation

Self Cite

View full text Add to dashboard Cite

show abstract

“…These methods typically require communication of the solutions of the decoupled problems between neighbours or to a central coordinator [10]. Although some researchers, [39,55], have attempted to apply these distributed local optimization methods in a heuristic manner, these methods cannot find global minimizers of non-convex problems reliably. This is due to the fact that ADMM, ALADIN, or similar distributed convex optimization method typically rely on strong duality results for augmented Lagrangians [52,54], which fail to hold in the presence of integrality constraints.…”

Section: Introductionmentioning

confidence: 99%

Partially distributed outer approximation

et al. 2021

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This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

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“…These methods typically require communication of the solutions of the decoupled problems between neighbors or to a central coordinator [9]. Although some researchers, [46,34], have attempted to apply these distributed local optimization methods in a heuristic manner, these methods cannot find global minimizers of non-convex problems reliably. This is due to the fact that ADMM, ALADIN, or similar distributed convex optimization method typically rely on strong duality results for augmented Lagrangians [45,43], which fail to hold in the presence of integrality constraints.…”

Section: Introductionmentioning

confidence: 99%

Partially Distributed Outer Approximation

Murray¹,

Faulwasser²,

Hagenmeyer³

et al. 2019

Preprint

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This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming (MICP) problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads.

show abstract

Mixed-Integer vs. Real-Valued Formulations of Battery Scheduling Problems

Cited by 8 publications

References 22 publications

On modelling effects in the battery and thermal storage scheduling problem

On modelling effects in the battery and thermal storage scheduling problem

Partially distributed outer approximation

Partially Distributed Outer Approximation

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