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Federated Aggregation of Demand Flexibility

Yifan Dong, Ge Chen, Junjie Qin

TL;DR

Numerical results demonstrate that the proposed framework unlocks substantially more flexibility than the approaches with static base sets, thus providing a promising framework for efficient and privacy-enhanced approaches to coordinate demand flexibility at scale.

Abstract

This paper proposes a federated framework for demand flexibility aggregation to support grid operations. Unlike existing geometric methods that rely on a static, pre-defined base set as the geometric template for aggregation, our framework establishes a true federated process by enabling the collaborative optimization of this base set without requiring the participants sharing sensitive data with the aggregator. Specifically, we first formulate the base set optimization problem as a bilevel program. Using optimal solution functions, we then reformulate the bilevel program into a single-level, unconstrained learning task. By exploiting the decomposable structure of the overall gradient, we further design a decentralized gradient-based algorithm to solve this learning task. The entire framework, encompassing base set optimization, aggregation, and disaggregation, operates by design without exchanging raw user data. Numerical results demonstrate that our proposed framework unlocks substantially more flexibility than the approaches with static base sets, thus providing a promising framework for efficient and privacy-enhanced approaches to coordinate demand flexibility at scale.

Federated Aggregation of Demand Flexibility

TL;DR

Numerical results demonstrate that the proposed framework unlocks substantially more flexibility than the approaches with static base sets, thus providing a promising framework for efficient and privacy-enhanced approaches to coordinate demand flexibility at scale.

Abstract

This paper proposes a federated framework for demand flexibility aggregation to support grid operations. Unlike existing geometric methods that rely on a static, pre-defined base set as the geometric template for aggregation, our framework establishes a true federated process by enabling the collaborative optimization of this base set without requiring the participants sharing sensitive data with the aggregator. Specifically, we first formulate the base set optimization problem as a bilevel program. Using optimal solution functions, we then reformulate the bilevel program into a single-level, unconstrained learning task. By exploiting the decomposable structure of the overall gradient, we further design a decentralized gradient-based algorithm to solve this learning task. The entire framework, encompassing base set optimization, aggregation, and disaggregation, operates by design without exchanging raw user data. Numerical results demonstrate that our proposed framework unlocks substantially more flexibility than the approaches with static base sets, thus providing a promising framework for efficient and privacy-enhanced approaches to coordinate demand flexibility at scale.

Paper Structure

This paper contains 38 sections, 1 theorem, 48 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Boundary aggregation methods
  4. Optimization-based methods
  5. Geometric methods
  6. Federated Framework for Demand Flexibility Aggregation
  7. Overview of the Framework
  8. Preliminaries for Flexibility Aggregation
  9. Individual flexibility set
  10. Aggregate flexibility set
  11. Revisit of Geometric Methods
  12. Base Set Optimization
  13. Federated Base Set Optimization
  14. Unconstrained Reformulation
  15. Federated Gradient-based Algorithm
  16. ...and 23 more sections

Key Result

Lemma 1

Suppose there are two polyhedrons $\mathcal{X} = \{\mathbf x \in \mathbb{R}^{n_x} \mid \mathbf H_x \mathbf x \leq \mathbf h_x\}$ and $\mathcal{Y} = \{\mathbf y \in \mathbb{R}^{n_y} \mid \mathbf H_y \mathbf y \leq \mathbf h_y\}$, where $\mathbf H_x \in \mathbb{R}^{m_x \times n_x}$, $\mathbf H_y \in \

Figures (8)

  • Figure 1: The federated framework for demand flexibility aggregation.
  • Figure 2: The federated gradient-based algorithm for base set optimization.
  • Figure 3: Distributions of normalized volume ratios under different time-horizon lengths. The whiskers delimit the interdecile range, the boxes delimit the interquartile range, and the red lines represent the medians of each distribution.
  • Figure 4: Convergence trajectories of the normalized error $e$ for different numbers of EVs $N=20, 30, 50$.
  • Figure 5: Distributions of the peak power gaps and improvements for the peak power minimization problem \ref{['eq:pp_min']} under different methods.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Remark 1: Generalization to other DSRs
  • Lemma 1
  • Remark 2: Volume and gradient estimation
  • Remark 3: Applicability for non-linear and discrete dynamics