Managing the Uncertainty in System Dynamics Through Distributionally Robust Stability-Constrained Optimization

TL;DR

The paper tackles stability guarantees in power systems with high inverter-based resources under uncertainty in dynamic parameters. It develops a distributionally robust stability-constrained optimization framework that propagates parametric uncertainty to stability-constraint coefficients using Taylor expansion and the Delta method, yielding a moment-based ambiguity set for an SOC constraint. The method is validated on a modified IEEE-39-bus system, showing improved robustness with manageable conservatism and demonstrating scalability to larger networks. The results reveal trade-offs between wind curtailment, operating costs, and stability margins under uncertainty, highlighting practical applicability for system operators.

Abstract

With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to manage the parametric uncertainty due to inaccurate modeling that influences the system dynamics, this work proposes a distributionally robust stability constraint formulation. However, the uncertainty of system dynamic parameters influences the stability constraints indirectly through a nonlinear and implicit relationship. To address this issue, a propagation mechanism from the uncertainty of the system dynamic parameters to the stability constraint coefficients is established. Since these coefficients are connected to the uncertain parameters through highly nonlinear and implicit functions, an approximation approach utilizing Taylor expansion and the Delta method is developed to estimate the statistical moments of the stability constraint coefficients based on the first and second-order derivatives, with which an ambiguity set for the distributionally robust optimization can be formulated. The accuracy of the uncertainty propagation as well as the effectiveness of the distributionally robust stability constraints are demonstrated through detailed case studies in the modified IEEE 39-bus system.

Figures (9)

• Figure 1: Modified IEEE-39 bus system.
• Figure 2: Relationship between stability constraint coefficients and uncertain parameters.
• Figure 3: Sample averages at different sample sizes.
• Figure 4: System operation costs with varying wind capacity.
• Figure 5: Stability constraint violation rates in different cases with varying wind capacity.