Comprehensive uncertainty quantification for renewable penetrated power system dynamics considering different timescale characterizations of uncertainties

Regarding uncertainty quantification (UQ) for renewable penetrated power system (RPPS) dynamics, most studies exclusively focus on the randomness of steady-state operating points (defined as slow timescale characterizations of uncertainties (STCUs)). The rest are only concerned about fast time-varying properties of disturbances (defined as fast timescale characterizations of uncertainties (FTCUs)). However, RPPS dynamics are affected by both of them, only modeling uncertainties with one of them is inaccurate or inefficient, and methods capable of addressing them together are lacking. Thus, this paper proposes an efficient UQ framework to assess RPPS dynamics considering STCUs and FTCUs simultaneously and to provide comprehensive UQ outcomes from different aspects. Firstly, FTCUs are approximated by the superposition of finite STCUs through Karhunen-Loe`ve expansion (KLE) to make them suitable for the proposed uncertainty propagation analysis (UPA) method. Then, UPA is accurately and efficiently conducted based on the proposed statistic-constrained sparse and arbitrary polynomial chaos expansion. Moreover, sensitivity analysis is conducted based on the proposed method to study the impact of STCUs and FTCUs on RPPS stability. Comparisons are performed with Monte Carlo simulation (MCS), Sobol quasi-MCS (SQ), and KLE-sparse polynomial chaos expansion (SPCE) on modified IEEE 39-bus system and 240-bus WECC system with different uncertainty quantities. Results show that the proposed method significantly improves efficiency compared to MCS and possesses higher accuracy compared to SQ and KLE-SPCE. And both STCUs and FTCUs may have relevant high sensitivity results associated with RPPS stability indices, demonstrating the necessity of considering STCUs and FTCUs together in evaluating RPPS dynamics.