A Distributionally Robust Optimization Framework for Stochastic Assessment of Power System Flexibility in Economic Dispatch

TL;DR

This work addresses the challenge of evaluating power-system flexibility under high net-load variability by introducing a distributionally robust optimization framework that extends deterministic assessments to a stochastic setting with a hyperbox uncertainty set $U(\\lambda)$ and an ambiguity set $\\mathcal{D}(\\lambda)$. The approach solves sequential real-time economic dispatch (RTED) problems, optimizing a flexibility parameter $\\lambda_t$ at each interval while bounding expected constraint violations with a threshold $\\beta$, via a MILP formulation built on duality and McCormick envelopes. Key findings show that the stochastic (DRO) assessment yields less conservative flexibility than a deterministic approach, maintains nonzero flexibility under extreme scenarios, and reveals how energy storage systems interact with large-scale generation in affecting flexibility. The results demonstrate computational efficiency and scalability on larger networks, making the method practical for real-time operation and risk-managed planning.

Abstract

Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the real-time economic dispatch problem on four IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.

Figures (3)

• Figure 1: Illustration of the flexibility assessment process for the RTED model.
• Figure 2: Comparative flexibility outcomes: deterministic vs. stochastic assessments across single and multi net-load scenarios.
• Figure 3: ESS impact on system flexibility metric under stochastic assessment.