A Convexified Eulerian Framework for Scalable Coordination of Massive DER Populations

TL;DR

This paper introduces a scalable, privacy-preserving coordination framework for large populations of distributed energy resources using a PDE-based Eulerian model, convexification, and a two-layer control architecture.

Contribution

It develops a convexification approach for PDE-constrained optimization and a two-layer architecture that ensures scalability and privacy in DER coordination.

Findings

Framework is scalable and computationally independent of population size.

Convexification reformulates the problem into a sparse linear program.

Numerical results demonstrate improved economic performance and feasibility.

Abstract

This paper proposes a scalable coordination framework with aggregator-side privacy protection for storage-like distributed energy resources (DERs). The framework adopts a two-layer architecture. At the macroscopic layer, building upon an \emph{Eulerian} modeling perspective, the DER population is represented as a continuum whose density evolution is governed by a partial differential equation (PDE), such that the computational complexity is independent of the population size. To address the bilinear non-convexity in this PDE-constrained optimization problem, we develop a convexification method that combines finite-volume discretization with a flux-lifting technique, reformulating the macroscopic problem into a sparse linear program (LP). The LP solution yields a unified, state-dependent broadcast signal for population coordination. Furthermore, a Wasserstein-based relaxation is introduced to replace rigid cyclic constraints and provide additional operational flexibility for improved economic performance. At the microscopic layer, individual resources autonomously recover local setpoints from the broadcast signal and their local states, while an upstream data-mixing protocol aggregates individual states into a macroscopic density histogram without exposing raw individual states to the aggregator. Numerical studies validate the scalability, feasibility, and economic effectiveness of the proposed framework.