With widespread application of voltage source converter (VSC) as a key energy-conversion power electronic device by using the phase-locked loop (PLL) technique for synchronization, the system dynamics has become much complicated. In this paper, the nonlinear dynamics and transient stability of the PLL-based VSC system are investigated, within a unified framework of the (normalized) generalized swing equation. It is found that there are three different types of bifurcation, including the generalized saddle-node, Hopf, and homoclinic bifurcations. Within the coexistence parameter region, the basin boundary of the stable equilibrium point shows either a closed-loop or a fish-like pattern. With the help of the equal area criterion (EAC), the transient stabilities under different transient disturbances including short circuit, voltage dip, and power rise are analyzed. Because the equivalent damping of the VSC is state-dependent, the theoretical results based on the EAC are examined. Furthermore, based on the analytical results from the generalized swing equation, the principle for all major transient stability enhancement methods is uncovered. All these findings are well verified by extensive electromagnetic transient simulations. Therefore, the generalized swing equation provides a deeper physical insight and plays a crucial role in transient stability problems in power-electronic-dominated power systems, similar to the swing equation in traditional power systems.

The complete synchronization and generalized synchronization (GS) of one-way coupled time-delay systems are studied. We find that GS can be achieved by a single scalar signal, and its synchronization threshold for different delay times shows the parameter resonance effect, i.e., we can obtain stable synchronization at a smaller coupling if the delay time of the driven system is chosen such that it is in resonance with the driving system. Near chaos synchronization, the desynchronization dynamics displays periodic bursts with the period equal to the delay time of the driven system. These features can be easily applied to the recovery of time-delay systems.

Pattern formation of spiral waves in an inhomogeneous excitable medium with small-world connections is investigated. In both cases, with completely local regular connections and with completely random connections, spiral waves cannot survive in the given inhomogeneous medium. It is found that with small-world connections (basically local connections plus a small number of random connections) a well behaved spiral wave can be formed against the destructive role of the inhomogeneous medium. There also exists an optimal fraction of random connections which can greatly enhance the probability of spiral wave formation; this resembles the behavior of stochastic resonance.

Low-frequency signal transmission in one-way coupled bistable systems subject to a high-frequency force is studied. Two cases including the high-frequency force on all sites (case 1) and only on the first site (case 2) are considered. In these two cases, vibrational resonance induced by the high-frequency force can play an active role to effectively improve the signal transmission, and undamped signal transmission can be found in a broad parameter region. The combinative action of injected low-frequency signal, high-frequency driving, and coupling is of importance. Our findings suggest that high-frequency signal could be properly used in low-frequency signal transmission, and especially the implementation of high-frequency force simply on the first site for case 2 is meaningful for its simplicity and high efficiency.

In power systems, voltage source converters (VSCs) are gradually replacing traditional devices and dramatically changing power system dynamic behavior, as the VSC’s intrinsic high-order nonlinearity and multiple time-scale characteristics. As a simple case of transient stability for power-electronic-based power systems, in this work we study a VSC system with a fifth-order nonlinear model, with the aid of nonlinear dynamics analysis. For the transient behavior, we find that both the amplitude and phase of the terminal voltage of VSC show discontinuity when the fault occurs or is cleared. The behavior of time-scale separation is also generally observable, namely, the fast time-scale dynamics damps and disappears quickly, and the system bulk behavior is dominated by the slow time-scale dynamics. In addition, we find that the system transient stability is uniquely determined by whether the fault-clearing state is within or out of the basin of attraction of the post-fault equilibrium point. Finally, simulations and hardware-in-the-loop experiments verify the analytical results. We expect all these interesting findings could provide an improved physical insight on our understanding of transient stability of power-electronic-based power systems.

The dynamical and statistical behavior of lag synchronization in two coupled self-sustained chaotic Rössler oscillators is reexamined. The lack of uniqueness in the conventional characterization of lag synchronization based on the similarity function has caused much skepticism about the existence of lag synchronization. We provide an evidence that the emergence of lag synchronization is associated with the transition from on-off intermittency to a periodic structure in the laminar phase distribution.