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Scalable and Efficient Aggregation of Energy-Constrained Flexible Loads

Julie Rousseau, Philipp Heer, Kristina Orehounig, Gabriela Hug

Abstract

Loads represent a promising flexibility source to support the integration of renewable energy sources, as they may shift their energy consumption over time. By computing the aggregated flexibility of power and energy-constrained loads, aggregators can communicate the group's flexibility without sharing individual private information. However, this computation is, in practice, challenging. Some studies suggest different inner approximations of aggregated flexibility polytopes, but all suffer from large computational costs for realistic load numbers and horizon lengths. In this paper, we develop a novel approximation of the aggregated flexibility of loads based on the concept of worst-case energy dispatch, i.e., if aggregated energy consumptions are assumed to be dispatched in the worst manner possible. This leads to conservative piecewise linear bounds that restrict the aggregated energy consumption only based on the previous aggregated energy consumed. A comparative case study reveals that our method can compute an approximation of the aggregation of thousands of loads efficiently, while displaying an accuracy comparable to other approximation techniques.

Scalable and Efficient Aggregation of Energy-Constrained Flexible Loads

Abstract

Loads represent a promising flexibility source to support the integration of renewable energy sources, as they may shift their energy consumption over time. By computing the aggregated flexibility of power and energy-constrained loads, aggregators can communicate the group's flexibility without sharing individual private information. However, this computation is, in practice, challenging. Some studies suggest different inner approximations of aggregated flexibility polytopes, but all suffer from large computational costs for realistic load numbers and horizon lengths. In this paper, we develop a novel approximation of the aggregated flexibility of loads based on the concept of worst-case energy dispatch, i.e., if aggregated energy consumptions are assumed to be dispatched in the worst manner possible. This leads to conservative piecewise linear bounds that restrict the aggregated energy consumption only based on the previous aggregated energy consumed. A comparative case study reveals that our method can compute an approximation of the aggregation of thousands of loads efficiently, while displaying an accuracy comparable to other approximation techniques.

Paper Structure

This paper contains 26 sections, 15 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Energy-Constrained Loads
  3. Individual Loads' Polytope
  4. Power Polytope
  5. Energy Polytope
  6. Assumptions
  7. Properties of the Aggregated Loads' Polytope
  8. Load aggregation over a two-timestep horizon
  9. Time-coupling in the aggregated polytope
  10. Aggregation of Energy-Constrained Loads: A Worst-Case Energy Dispatch Approach
  11. Description of our Approach
  12. Worst-Case Energy Dispatch
  13. Definition
  14. Computation
  15. Worst-Case Energy Bound Computation
  16. ...and 11 more sections

Figures (7)

  • Figure 1: Aggregation of two loads over two timesteps.
  • Figure 2: Example of the aggregation of 7 loads over a 3-hour horizon ($T=12$).
  • Figure 3: Evolution of the total computation time (top) and the total energy cost increase (bottom) for different horizon lengths and aggregated load numbers.
  • Figure 4: Evolution of the total computation time (top) and the aggregated peak increase (bottom) for different horizon lengths and aggregated load numbers.
  • Figure 5: Evolution of the total computation time for different horizon lengths and large aggregated load numbers.
  • ...and 2 more figures