Flexibility Characterization of Sustainable Power Systems in Demand Space: A Data-Driven Inverse Optimization Approach

TL;DR

This paper tackles the challenge of high renewable penetration by proposing a data-driven inverse optimization framework to characterize power system flexibility in the demand space. It introduces a data-driven polyhedral uncertainty set (PUS) built from PCA-based analysis of spatially correlated residual demand and projects this uncertainty onto loadability sets ${\Xi}_d(\zeta)$ via umbrella constraint discovery and Fourier–Motzkin elimination. The core contribution is the data-driven inverse optimization (DDIO) approach, which quantifies how far a forecasted residual demand $d^0$ is from the feasibility boundary of ${\mathcal{D}}(\zeta)$ using distance-based metrics $\rho_r$ and RDC, enabling explicit, geometry-based flexibility assessment in operational and planning contexts. Case studies on a Three-Bus system and the IEEE RTS demonstrate that PUS-based uncertainty provides less conservative yet accurate representations of spatial correlations, and DDIO yields practical, interpretable indicators of flexibility adequacy that can support storage, demand response, and resilience planning in low-carbon power systems.

Abstract

The deepening of the penetration of renewable energy is challenging how power system operators cope with their associated variability and uncertainty. The inherent flexibility of dispathchable assets present in power systems, which is often ill-characterized, is essential in addressing this challenge. Several proposals for explicit flexibility characterization focus on defining a feasible region that secures operations either in generation or uncertainty spaces. The main drawback of these approaches is the difficulty in visualizing this feasibility region when there are multiple uncertain parameters. Moreover, these approaches focus on system operational constraints and often neglect the impact of inherent couplings (e.g., spatial correlation) of renewable generation and demand variability. To address these challenges, we propose a novel data-driven inverse optimization framework for flexibility characterization of power systems in the demand space along with its geometric intuition. The approach captures the spatial correlation of multi-site renewable generation and load using polyhedral uncertainty sets. Moreover, the framework projects the uncertainty on the feasibility region of power systems in the demand space, which are also called loadability sets. The proposed inverse optimization scheme, recast as a linear optimization problem, is used to infer system flexibility adequacy from loadability sets.

Figures (6)

• Figure 1: Overview of the method proposed in this paper
• Figure 2: Two-dimensional polyhedral uncertainty set.
• Figure 3: Geometrical interpretation of inverse optimization solution methodology.
• Figure 4: (a) Scatter plot of residual demands for Scenario 1; (b) Uncertainty sets for Scenario 1.
• Figure 5: Flexibility metric ${\rho}_{\infty}$ distribution across the intact loadability sets.