This paper presents an estimation of transient stability regions for large-scale power systems. In Part Ⅰ, a Koopman operator based model reduction (KOMR) method is proposed to derive a low-order dynamical model with reasonable accuracy for transient stability analysis of large-scale power systems. Unlike traditional reduction methods based on linearized models, the proposed method does not require linearization, but captures dominant modes of the original nonlinear dynamics by employing a Koopman operator defined in an infinite-dimensional observable space. Combined with the Galerkin projection, the obtained dominant Koopman eigenvalues and modes produce a reduced-order nonlinear model. To approximate the Koopman operator with sufficient accuracy, we introduce a Polynomial-based Multi-trajectory Kernel Dynamic Mode Decomposition (PMK-DMD) algorithm, which outperforms traditional DMD in various scenarios. In the end, the proposed method is applied to the IEEE 10-machine-39-bus power system and IEEE 16-machine-68-bus power system, which demonstrates that our method is significantly superior to the modal analysis method in both qualitative and quantitative aspects.

This paper proposes an implicit function based open-loop analysis method to detect the subsynchronous resonance(SSR), including asymmetric subsynchronous modal attraction(ASSMA) and asymmetric subsynchronous modal repulsion(ASSMR), of doubly-fed induction generator based wind farms(DFIG-WFs) penetrated power systems. As some important parameters of DFIG-WF are difficult to obtain, reinforcement learning and least squares method are applied to identify those important parameters. By predicting the location of closed-loop subsynchronous oscillation(SSO) modes based on the calculation of partial differentials of characteristic equation, both ASSMA and ASSMR can be found. The proposed method in this paper can select SSO modes which move to the right half complex planes as control parameters change. Besides, the proposed open-loop analysis method is adaptive to parameter uncertainty. Simulation studies are carried out on the 4-machine 11-bus power system to verify properties of the proposed method.

This paper proposes a residue based open-loop modal analysis method to detect low frequency modal resonance(LFMR), including asymmetric low frequency modal attraction(ALFMA) and asymmetric low frequency modal repulsion(ALFMR), of permanent magnetic synchronous generator based wind farms(PMSG-WFs) penetrated power systems. The formation of ALFMA and ALFMR caused by two open-loop low frequency oscillation(LFO) modes moving close and apart is analyzed in detail. Via predicting the trajectories of closed-loop LFO modes based on calculation of residue of open-loop LFO modes, both ALFMA and ALFMR can be detected. The proposed method can select LFO modes which move to the right half complex plane as control parameters vary. Simulation studies are carried out on a three-machine power system and a four-machine 11-bus power system to verify the properties of the proposed method.