Federated Aggregation of Demand Flexibility

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.

💡 Research Summary

The paper addresses the pressing need for scalable, privacy‑preserving aggregation of demand‑side flexibility (DSF) in modern power grids, where high penetration of renewable generation and new loads such as electric vehicles (EVs) and thermostatically controlled loads (TCLs) demand coordinated control. Existing approaches fall into three categories: (i) boundary aggregation, which simply sums upper and lower bounds of each resource and is overly conservative; (ii) optimization‑based methods, which solve a two‑stage robust problem to find a maximal‑volume geometric shape but require repeated mixed‑integer programming and full knowledge of individual resources, raising privacy concerns; and (iii) geometric methods, which share a pre‑defined “base set” (a convex polytope) among all resources, allowing each participant to compute an affine transformation that fits within its own feasible set. While geometric methods are decentralized and privacy‑friendly, their performance heavily depends on the choice of the static base set, often leading to sub‑optimal flexibility.

The authors propose a truly federated framework that treats the base set itself as an optimizable decision variable. They formulate the base‑set optimization as a bilevel program: the upper level maximizes the volume of the aggregated feasible set (approximated by the determinant of the product of all affine transformation matrices), while the lower level consists of each participant’s local linear program that finds the best affine transformation of the current base set within its own polyhedral flexibility set. By introducing optimal solution functions for the lower‑level problems, the bilevel problem is reformulated into a single‑level, unconstrained learning task. The objective is linearized via a first‑order Taylor expansion, turning the determinant into a sum of traces, which makes the overall gradient decomposable across participants.

Exploiting this decomposability, the authors design a decentralized gradient‑based algorithm. In each communication round, every participant locally solves its lower‑level LP, obtains the affine parameters (γ_i, Γ_i) and the associated dual matrix Λ_i, and sends only these low‑dimensional quantities to the aggregator. The aggregator aggregates the local gradients to update the base‑set parameter vector h₀ using a step‑size η. Because only model updates (not raw data) are exchanged, the method preserves user privacy while still achieving the same optimality as a centralized solution. The algorithm converges within a modest number of rounds (≈50‑100) and scales to tens of thousands of resources.

After the base set is learned, the framework seamlessly integrates existing geometric aggregation and disaggregation protocols. In the aggregation phase, each resource computes its affine transformation of the learned base set and returns the parameters; the aggregator then constructs the aggregate set as the Minkowski sum of these transformed base sets, which reduces to a simple linear combination due to the shared template. In the disaggregation phase, a system operator selects a feasible aggregate power trajectory; the aggregator broadcasts a signal that each participant can locally map back to an individual dispatch profile using its stored affine parameters.

Numerical experiments focus on EV charging flexibility modeled as polyhedral sets defined by power limits, energy limits, and plug‑in schedules. Simulations with up to 10,000 EVs demonstrate that the federated, optimizable base set yields a 30 %+ increase in the volume of the approximated aggregate flexibility compared with a static hyper‑cube base set. Communication overhead is dramatically reduced because each participant only transmits the affine parameters (on the order of 2 × T scalars) rather than full constraint data, achieving a >70 % reduction relative to centralized or heuristic methods. The approach also generalizes to other DSFs such as TCLs and stationary storage, provided their feasible sets admit an H‑polytope representation.

In summary, the paper makes three key contributions: (1) it introduces the first federated framework that jointly optimizes the shared geometric template, aggregation, and disaggregation while keeping all raw user data local; (2) it provides a tractable reformulation of a non‑convex bilevel problem into a decomposable learning task and a corresponding decentralized gradient algorithm with provable optimality equivalence to centralized solutions; and (3) it demonstrates that existing geometric aggregation/disaggregation protocols can be directly incorporated, delivering a ready‑to‑deploy solution for large‑scale demand‑flexibility coordination. This work paves the way for privacy‑enhanced, high‑performance demand response programs in future smart grids.