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

TL;DR

This paper introduces a distributionally robust stability-constrained optimization framework for power systems with inverter-based resources, addressing parametric uncertainties in system dynamics through a novel propagation and approximation method.

Contribution

It proposes a new uncertainty propagation mechanism and an approximation approach to incorporate distributionally robust stability constraints in power system optimization.

Findings

Effective uncertainty propagation demonstrated in IEEE 39-bus system

Enhanced stability robustness under parametric uncertainties

Accurate estimation of stability constraint coefficients

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.