Complexity Reduction for TSO-DSO Coordination: Flexibility Aggregation vs. Distributed Optimization

TL;DR

The paper addresses TSO-DSO coordination under rising distributed energy resources by comparing two complexity-reduction strategies: flexibility aggregation via FP-ADP and distributed optimization via ADMM. FP-ADP replaces DSOs with value functions $V_i(z_i)$, reducing the problem to a low-dimensional TSO optimization that relies on projections of DSO constraints onto the coupling space, with feasibility guaranteed under exact projections and exact $V_i$; ADMM, in contrast, solves a consensus-form AC-OPF through iterative local solves and multiplier updates, without relying on such approximations. Numerical results on a tree-structured network show that FP-ADP with a cost-approximation for $V_i$ can deliver near-central performance with far fewer communication rounds, while ADMM achieves closer-to-central optimality at the expense of many iterations and higher communication overhead; the quality of FP-ADP is highly sensitive to the accuracy of the FOR projection and the $V_i$ approximation. The findings provide practical guidance on choosing complexity-reduction strategies based on communication budgets and the trustworthiness of FOR approximations, and suggest directions for improving feasibility guarantees and reducing ADMM communication in real-world TSO-DSO coordination.

Abstract

The increasing number of flexible devices and distributed energy resources in power grids renders the coordination of transmission and distribution systems increasingly complex. In this paper, we discuss and compare two different approaches to optimization-based complexity reduction: Flexibility aggregation via Approximate Dynamic Programming (ADP) and distributed optimization via the Alternating Direction Method of Multipliers (ADMM). Flexibility aggregation achieves near-optimal solutions with minimal communication. However, its performance depends on the quality of the approximation used. In contrast, ADMM attains results closer to the centralized solution but requires significantly more communication steps. We draw upon a case study combining different matpower benchmarks to compare both methods.

Figures (3)

• Figure 1: $\mathcal{P}_i$ for DSO's 1 and 2.
• Figure 2: Value of $z_i$ at the interconnection using Loss Linearization formulation for aggregation
• Figure 3: Value of $z_i$ at the interconnection using LinDistFlow formulation for aggregation