Towards grid-aware multi-period flexibility aggregation - A constrained zonotope approach

TL;DR

The paper tackles the computational bottleneck of time-coupled feasibility set projection in multi-period OPF for TSO-DSO coordination with privacy constraints. It introduces constrained zonotopes ($\mathcal{CZ}$) as a representation that enables fast projection of the feasible operating region (FOR) while accommodating time-coupled dynamics and storage; the FOR is constructed via a three-stage offline process and projected online with a sparse linear map. The key contributions are (i) a practical three-step CZ conversion to encode polyhedral feasibilities, (ii) demonstration of offline/online separation and parallelizable computation, and (iii) numerical evidence showing substantial speedups on a 4-bus test and scalable performance on a 15-bus grid with up to 96 timesteps. The approach facilitates scalable, grid-aware flexibility aggregation and enables dynamic constraint integration, supporting more efficient ADP-based hierarchical optimization in distribution networks.

Abstract

Aggregation schemes provide a means to reduce the computational complexity of power system operation by reducing the number of devices that are considered individually. This can be achieved with tools of computational geometry, where the feasible set is projected onto the decision variables of the point of interconnection. Set projection is computationally expensive, especially in the context of multi-period power system operation. Hence this calls for efficiency improvements via structure exploitation of certain set representations, such as constrained zonotopes. This paper proposes these benefits for efficient flexibility aggregation. We evaluate the performance of the proposed method on a 15-bus distribution grid with time-dependent elements for up to 96 timesteps. The results suggest that the presented method significantly improves computation times.

Figures (5)

• Figure 1: Tree-structured optimization of power system operation adapted from ADP.
• Figure 2: Example of the projection $\operatorname{proj}(\mathcal{X})$ of a three dimensional polytope $\mathcal{X}$ on the $xy$-plane.
• Figure 3: Topology of the 15-bus radial distribution grid with battery highlighted in green.
• Figure 4: FOR at the slack bus modeled as polytope and as $\mathcal{CZ}$ using sufficiently large variable bounds.
• Figure 5: Dependency of $p_{1,2}(1)$ FOR of active and reactive power at the following timestep.