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.

Due to various controls in voltage-source converters, their impacts and mutual influences on transient stability of new-generation power systems are still obscure. Different from the mature different-order transient equations for synchronous generator (SG), fully accepted transient equations of converters still lack. In this article, a novel methodology is proposed to uniformly evaluate the controller effects on the transient stability and then establish the hierarchical transient equations of converters based on the properties of controlling-unstable-equilibrium point (CUEP). The participation factors on unstable eigenvalue of CUEP are applied to measure the contribution of state variables in transient dynamics, and dominant variables and key loops of grid-following and grid-forming converters are determined and compared. It is found that the synchronous loop, e.g., phase-locked loop in grid-following converters and virtual-synchronous loop in grid-forming converters, plays a primary role, and the power balance loop on the DC capacitor, including DC-voltage control and DC capacitor dynamics, plays a secondary role. Additionally, the impacts of synchronization and power balance are compared with the rotor swing of the SG. Analytical results are demonstrated by time-domain simulations and transient stability assessments. The dominant transient models and the CUEP-based participation factor analysis provide an improved physical insight on our understanding of transient dynamics in the new-generation power systems dominated by not only grid-following but also grid-forming converters.

Recently large‐scale integration of power‐electronic‐based devices has made system‐level oscillations occur frequently, which posed a big challenge for modern power grids. Previous studies mainly treated sustained oscillations under the framework of (linear) small‐signal stability and/or by incorporating the impact of current saturation, but seldom considered system non‐linearity like phase‐locked‐loop. In this study, the authors established a sixth‐order non‐linear model for a three‐phase voltage‐source converter tied to AC grid, and studied its dynamics completely from non‐linear system theory and signal analysis technique, with all parameters including current controllers, phase‐locked‐loop, line inductance, and grid voltage. They found that the operation point usually becomes unstable by Hopf bifurcation, and the sustained oscillations are possible only for super‐critical Hopf bifurcation. Based on these observations, sustained periodic oscillation should be treated as a limit cycle even without saturation. With saturation, some other phenomena have also been found, such as saturation‐induced instability and saturation‐restricted oscillation. In addition, they discovered that for sustained oscillations, the usual purely sinusoidal three‐phase currents exhibit the form of or , where () denotes basic (modal oscillation) frequency with c a constant. This work could provide an improved understanding of sustained oscillations and associated system dynamics in an overall perspective manner.

Synchronization is one of the key issues in three-phase AC power systems. Its characteristics have been dramatically changed with the large-scale integration of power-electronic-based renewable energy, mainly including a permanent magnetic synchronous generator (PMSG) and a double-fed induction generator (DFIG) for wind energy and a photovoltaic (PV) generator for solar energy. In this paper, we review recent progresses on the synchronization stability and multi-timescale properties of the renewable-dominated power system (RDPS), from nodes and network perspectives. All PMSG, DFIG, and PV are studied. In the traditional synchronous generator (SG) dominated power system, its dynamics can be described by the differential–algebraic equations (DAEs), where the dynamic apparatuses are modeled by differential equations and the stationary networks are described by algebraic equations. Unlike the single electromechanical timescale and DAE description for the SG-dominated power system, the RDPS dynamics should be described by the multiscale dynamics of both nodes and networks. For three different timescales, including the AC current control, DC voltage control, and rotor electromechanical timescales, their corresponding models are well established. In addition, for the multiscale network dynamics, the dynamical network within the AC current control timescale, which should be described by differential equations, can also be simplified as algebraic equations. Thus, the RDPS dynamics can be put into a similar DAE diagram for each timescale to the traditional power system dynamics, with which most of power electrical engineers are familiar. It is also found that the phase-locked loop for synchronization plays a crucial role in the whole system dynamics. The differences in the synchronization and multiscale characteristics between the traditional power system and the RDPS are well uncovered and summarized. Therefore, the merit of this paper is to establish a basic physical picture for the stability mechanism in the RDPS, which still lacks systematic studies and is controversial in the field of electrical power engineering.

Synchronization stability is one of central problems in power systems, and it is becoming much more complicated with the high penetration of renewable energy and power electronics devices. In this paper, we review recent work by several nonlinear models for renewable-dominated power systems in terms of multiple timescales, in particular, grid-tied converters within the DC voltage timescale. For the simplest model, a second-order differential equations called the generalized swing equation by considering only the phase-locked loop (PLL) is obtained, which shows a similar form with the well-known swing equation for a synchronous generator in the traditional power systems. With more outer controllers included, fourth-order and fifth-order models can be obtained. The fourth-order model is called the extended generalized swing equation, exhibiting the combined function of grid synchronization and active power balance on the DC capacitor. In addition, a nonlinear model for a two coupled converter system is given. Based on these studies, we find that the PLL plays a key role in synchronization stability. In summary, the value of this paper is to clarify the key concept of the synchronization stability in renewable-dominated power systems based on different nonlinear models, which still lacks systematic studies and is controversial in the field of electrical power engineering. Meanwhile, it clearly uncovers that the synchronization stability of converters has its root in the phase synchronization concept in nonlinear sciences.

With continuous increase of penetration of renewable energies and power electronic equipment, power grid stability incidents are emerging frequently worldwide. In this paper, the transient stability assessment of renewable dominated power systems with multiple PLL-based voltage source converters (VSCs) is studied by calculating critical clearing time (CCT). A tangent hyperplane method is developed, which approximates the boundary of basin of attraction near unstable equilibrium point by linear system theory. The detailed algorithm is presented, accompanying with four typical case studies, including a single machine infinite system, two parallel VSCs, modified IEEE 9- bus, and modified 39- bus systems. Broad EMT simulations are performed to verify the accuracy and computational effectiveness of the algorithm. In all these tests, we find that the hyperplane method can give accurate estimations of CCTs. Hence it is expected to be an efficient method. In addition, we find that generally the CCT in renewable dominated power systems is around tens of milliseconds, which is much shorter than that in traditional power systems around hundreds of milliseconds. Therefore, it might be imperative to adopt faster controls and protections for renewable dominated power systems.