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Improving the Optimization in Model Predictive Controllers: Scheduling Large Groups of Electric Vehicles

Leoni Winschermann, Marco E. T. Gerards, Johann Hurink

Abstract

In parking lots with large groups of electric vehicles (EVs), charging has to happen in a coordinated manner, among others, due to the high load per vehicle and the limited capacity of the electricity grid. To achieve such coordination, model predictive control can be applied, thereby repeatedly solving an optimization problem. Due to its repetitive nature and its dependency on the time granularity, optimization has to be (computationally) efficient. The work presented here focuses on that optimization subroutine, its computational efficiency and how to speed up the optimization for large groups of EVs. In particular, we adapt FOCS, an algorithm that can solve the underlying optimization problem, to better suit the repetitive set-up of model predictive control by adding a pre-mature stop feature. Based on real-world data, we empirically show that the added feature speeds up the median computation time for 1-minute granularity by up to 44%. Furthermore, since FOCS is an algorithm that uses maximum flow methods as a subroutine, the impact of choosing various maximum flow methods on the runtime is investigated. Finally, we compare FOCS to a commercially available solver, concluding that FOCS outperforms the state-of-the-art when making a full-day schedule for large groups of EVs.

Improving the Optimization in Model Predictive Controllers: Scheduling Large Groups of Electric Vehicles

Abstract

In parking lots with large groups of electric vehicles (EVs), charging has to happen in a coordinated manner, among others, due to the high load per vehicle and the limited capacity of the electricity grid. To achieve such coordination, model predictive control can be applied, thereby repeatedly solving an optimization problem. Due to its repetitive nature and its dependency on the time granularity, optimization has to be (computationally) efficient. The work presented here focuses on that optimization subroutine, its computational efficiency and how to speed up the optimization for large groups of EVs. In particular, we adapt FOCS, an algorithm that can solve the underlying optimization problem, to better suit the repetitive set-up of model predictive control by adding a pre-mature stop feature. Based on real-world data, we empirically show that the added feature speeds up the median computation time for 1-minute granularity by up to 44%. Furthermore, since FOCS is an algorithm that uses maximum flow methods as a subroutine, the impact of choosing various maximum flow methods on the runtime is investigated. Finally, we compare FOCS to a commercially available solver, concluding that FOCS outperforms the state-of-the-art when making a full-day schedule for large groups of EVs.
Paper Structure (16 sections, 2 theorems, 7 equations, 8 figures, 1 table)

This paper contains 16 sections, 2 theorems, 7 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. EV scheduling problem and algorithms
  3. Problem definition
  4. The general working of Focs
  5. Adapting Focs for model predictive control
  6. Methods
  7. QP implementation
  8. Focs implementation
  9. Dataset
  10. Numerical experiments
  11. Results
  12. Focs-pm
  13. Maximum flow method comparison
  14. Runtime comparison
  15. Discussion
  16. ...and 1 more sections

Key Result

Lemma 1

(Lemma 2 in 2023WinschermannFOCSArxiv) If a critical interval $I_i$ and its aggregated power are found, and if there is at least one interval $I_{i'}$ left that at that point has not yet been scheduled, then no scheduled charging work can feasibly be moved from $I_i$ to $I_{i'}$ for any such $I_{i'}

Figures (8)

  • Figure 1: Schematic of flow network structure of EV charging schedule.
  • Figure 2: Intermediate states of Focs with pre-mature stop for an example instance, tracked over rounds and iterations.
  • Figure 3: Runtimes relative to instance size, for various time granularities, solved for the whole day and using shortest_augmenting_path().
  • Figure 4: Runtimes for instances solved at noon using shortest_augmenting_path().
  • Figure 5: Runtimes for solving only for quarterly granularity, comparing maximum flow algorithms applied in Focs.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2