Unstable Limit Cycle and Transient Stability Assessment of VSC Grid-Tied Systems by Center Manifold

With rapid development of renewable energy, voltage source converter (VSC) has been widely used in modern power grid for energy conversion. Compared to synchronous generator, the transient stability analysis of VSC grid-tied systems becomes more difficult. It has been found that unstable limit cycle (ULC) is very common, while most existing transient stability assessment methods for the VSC grid-tied systems are based on unstable equilibrium point. For high-dimensional VSC systems, the basin boundary of a stable equilibrium point surrounded by the ULC should be the whole stable manifold of the ULC, which is still high-dimensional and usually hard to obtain. In this article, by using the center manifold method, a transient stability assessment method for the ULC-dominated stability region boundary of high-dimensional VSC systems is proposed, by mapping the high-dimensional stability boundary determined by the ULC into an ULC on the reduced-order center-manifold plane. The detailed algorithm is presented and error analyses for different parameters and different faults are carried out. In addition, the validity is supplemented by a modified 3-generator-9-bus system. Therefore, the center manifold method is efficient and able to solve the transient stability assessment for ULC-dominated stability boundary in VSC systems.