Hsiao-Dong Chiang

Xiaozhe Wang, Tao Wang, Hsiao-Dong Chiang et al.

We propose a framework employing stochastic differential equations to facilitate the long-term stability analysis of power grids with intermittent wind power generations. This framework takes into account the discrete dynamics which play a critical role in the long-term stability analysis, incorporates the model of wind speed with different probability distributions, and also develops an approximation methodology (by a deterministic hybrid model) for the stochastic hybrid model to reduce the computational burden brought about by the uncertainty of wind power. The theoretical and numerical studies show that a deterministic hybrid model can provide an accurate trajectory approximation and stability assessments for the stochastic hybrid model under mild conditions. In addition, we discuss the critical cases that the deterministic hybrid model fails and discover that these cases are caused by a violation of the proposed sufficient conditions. Such discussion complements the proposed framework and methodology and also reaffirms the importance of the stochastic hybrid model when the system operates close to its stability limit.

Yifan Zhang, Yunjie Gu, Yue Zhu et al.

Grid-following inverters have been widely adopted as a grid interface for renewable energy, and ensuring their small-signal and large-signal stability is critical to modern power systems. Their large-signal, or transient, stability is a significant challenge to analyze because of the interaction of the phase-locked loop (PLL), which must maintain synchronism with various outer-loop controllers. Simple analysis in which outer-loop controllers are idealized is insufficient, and the interactions between the nonlinear dynamics of the PLL and the dynamics of the DC-link voltage control (DVC), as well as the AC terminal voltage control (TVC) when present, must be considered. An asymptotic analysis approach, termed the bandwidth separation method, is proposed. This method enables simplification and order reduction of the original differential equations when sufficient bandwidth separation exists. Through this method, the interaction between the DVC and PLL is explicitly characterized, revealing that such interaction degrades system stability and shrinks the stability region. The analysis also indicates that voltage instability, rather than PLL loss of synchronization alone, is often the root cause of transient instability. Optimal bandwidth configurations for the PLL and DVC are identified under various grid fault conditions: a larger PLL bandwidth improves resilience to phase-jump faults, while a larger DVC bandwidth enhances tolerance to power fluctuations. In addition, the influence of the TVC loop is analyzed, showing that a high TVC bandwidth can mitigate the destabilizing effects of PLL-DVC interaction and further improve transient stability. All analytical findings are validated through hardware-in-the-loop (HIL) experiments.

Thanh Long Vu, Spyros Chatzivasileiadis, Hsiao-Dong Chiang et al.

Power grids normally operate at some stable operating condition where power supply and demand are balanced. In response to emergency situations, load shedding is a prevailing approach where local protective devices are activated to cut a suitable amount of load to quickly rebalance the supply demand and hopefully stabilize the system. This traditional emergency control results in interrupted service with severe economic damage to customers. Also, such control is usually less effective due to the lack of coordination among protective devices. In this paper, we propose a novel structural emergency control to render post-fault dynamics from the critical/emergency fault-cleared state to the stable equilibrium point. This is a new control paradigm that does not rely on any continuous measurement or load shedding, as in the classical setup. Instead, the grid is made stable by discretely relocating the equilibrium point and its stability region such that the system is consecutively attracted from the fault-cleared state back to the original equilibrium point. The proposed control is designed by solving linear and convex optimization problems, making it possibly scalable to large-scale power grids. Finally, this emergency control scheme can be implemented by exploiting transmission facilities available on the existing grids.

Thanh Long Vu, Hsiao-Dong Chiang, Konstantin Turitsyn

Power systems normally operate at their stable operating conditions where the power supply and demand are balanced. In emergency situations, the operators proceed to cut a suitable amount of loads to rebalance the supply-demand and hopefully stabilize the system. This traditional emergency control scheme results in interrupted service with severely economic damages to customers. In order to provide seamless electricity service to customers, this paper proposes a viable alternative for traditional remedial controls of power grids by exploiting the plentiful transmission facilities. In particular, we consider two emergency control schemes involving adjustment of the susceptance of a number of selected transmission lines to drive either fault-on dynamics or post-fault dynamics, and thereby stabilize the system under emergency situations. The corresponding emergency control problems will be formulated and partly solved in some specific cases. Simple numerical simulation will be used to illustrate the concept of this paper.

Yifan Zhang, Yaoxin Wang, Yunjie Gu et al.

Grid-following (GFL) inverters have very different large-signal stability characteristics to synchronous generators, and convenient concepts such as the equal-area criterion and global energy function do not apply in the same way. Existing studies mainly focus on the synchronization stability of an individual GFL inverter, while interactions between multiple inverters are less often addressed. This paper elucidates the interaction mechanisms between heterogeneous inverters, covering GFL, grid-forming (GFM), and grid-supporting (GSP) types, to determine the stability boundaries of systems with mixed inverter compositions. The generalized large-signal model for two-inverter systems is derived for various inverter combinations. This paper establishes that systems containing GFL inverters do not admit a global energy function, fundamentally limiting the applicability of traditional direct methods. To overcome this barrier, a manifold method is employed to accurately determine the region of attraction (ROA). To address the computational complexity of the manifold method, reduced-order models of inverter are used based on multiscale analysis. The large-signal stability margin is assessed by the shortest distance from a stable equilibrium point (SEP) to the boundary of the ROA, which is called the stability radius (SR). Using the proposed framework, the analysis reults of two-inverter system show that both GFM and GSP inverters significantly enhance the large-signal stability of a two-inverter system where the other inverter is GFL, with GFM providing slightly superior performance. This improvement is attributed to the voltage support effects and is maximized when the GFM or GSP inverter is located at the midpoint of the transmission line, where the voltage is lowest. All findings in this paper are validated through both EMT simulations and power hardware-in-the-loop (PHIL) experiments.

Yifan Zhang, Hsiao-Dong Chiang, Yitong Li et al.

The increasing penetration of inverter-based resources (IBRs) has fundamentally altered the transient stability characteristics of modern power systems. IBRs typically rely on proportional--integral (PI) controllers for synchronization and regulation, resulting in nonlinear swing equations that differ significantly from those of synchronous generators (SGs) and exhibit state-dependent damping. Consequently, although the classical energy function is often adopted in IBR analysis by analogy with SGs, it cannot be directly applied to IBRs with PI controller. A new energy function explicitly tailored to PI controller is proposed in this letter. It admits a unified form and can be applied to a class of nonlinear systems with PI controllers. Two representative cases are considered, including a grid-following (GFL) inverter and a DC-voltage-controlled grid-forming (GFM) inverter, demonstrating less conservative and more effective estimation of the region of attraction (ROA). All findings are verified through hardware-in-the-loop (HIL) experiments.

Zhiyong Hao, Yixuan Jiang, Huihua Yu et al.

Recent progress on deep learning relies heavily on the quality and efficiency of training algorithms. In this paper, we develop a fast training method motivated by the nonlinear Conjugate Gradient (CG) framework. We propose the Conjugate Gradient with Quadratic line-search (CGQ) method. On the one hand, a quadratic line-search determines the step size according to current loss landscape. On the other hand, the momentum factor is dynamically updated in computing the conjugate gradient parameter (like Polak-Ribiere). Theoretical results to ensure the convergence of our method in strong convex settings is developed. And experiments in image classification datasets show that our method yields faster convergence than other local solvers and has better generalization capability (test set accuracy). One major advantage of the paper method is that tedious hand tuning of hyperparameters like the learning rate and momentum is avoided.

Xiaozhe Wang, Hsiao-Dong Chiang, Jianhui Wang et al.

In this paper, the variable wind power is incorporated into the dynamic model for long-term stability analysis. A theory-based method is proposed for power systems with wind power to conduct long-term stability analysis, which is able to provide accurate stability assessments with fast simulation speed. Particularly, the theoretical foundation for the proposed approximation approach is presented. The accuracy and efficiency of the method are illustrated by several numerical examples.