arXiv subjects

Yan Jiang

Publications and source records attributed to Yan Jiang.

At least 109 records · Page 6Linked to original sources

arXiv2022

Boundary localization of transmission eigenfunctions in spherically stratified media

Consider the transmission eigenvalue problem for $u \in H^1(Ω)$ and $v\in H^1(Ω)$ associated with $(Ω; σ, \mathbf{n}^2)$, where $Ω$ is a ball in $\mathbb{R}^N$, $N=2,3$. If $σ$ and $\mathbf{n}$ are both radially symmetric, namely they are functions of the radial parameter $r$ only, we show that there exists a sequence of transmission eigenfunctions $\{u_m, v_m\}_{m\in\mathbb{N}}$ associated with $k_m\rightarrow+\infty$ as $m\rightarrow+\infty$ such that the $L^2$-energies of $v_m$'s are concentrated around $\partialΩ$. If $σ$ and $\mathbf{n}$ are both constant, we show the existence of transmission eigenfunctions $\{u_j, v_j\}_{j\in\mathbb{N}}$ such that both $u_j$ and $v_j$ are localized around $\partialΩ$. Our results extend the recent studies in [15,16]. Through numerics, we also discuss the effects of the medium parameters, namely $σ$ and $\mathbf{n}$, on the geometric patterns of the transmission eigenfunctions.

math.AP↗

arXiv2021

Reinforcement Learning for Optimal Primary Frequency Control: A Lyapunov Approach

As more inverter-connected renewable resources are integrated into the grid, frequency stability may degrade because of the reduction in mechanical inertia and damping. A common approach to mitigate this degradation in performance is to use the power electronic interfaces of the renewable resources for primary frequency control. Since inverter-connected resources can realize almost arbitrary responses to frequency changes, they are not limited to reproducing the linear droop behaviors. To fully leverage their capabilities, reinforcement learning (RL) has emerged as a popular method to design nonlinear controllers to optimize a host of objective functions. Because both inverter-connected resources and synchronous generators would be a significant part of the grid in the near and intermediate future, the learned controller of the former should be stabilizing with respect to the nonlinear dynamics of the latter. To overcome this challenge, we explicitly engineer the structure of neural network-based controllers such that they guarantee system stability by construction, through the use of a Lyapunov function. A recurrent neural network architecture is used to efficiently train the controllers. The resulting controllers only use local information and outperform optimal linear droop as well as other state-of-the-art learning approaches.

eess.SY↗

arXiv2021

On the Stability, Economic Efficiency and Incentive Compatibility of Electricity Market Dynamics

This paper focuses on the operation of an electricity market that accounts for participants that bid at a sub-minute timescale. To that end, we model the market-clearing process as a dynamical system, called market dynamics, which is temporally coupled with the grid frequency dynamics and is thus required to guarantee system-wide stability while meeting the system operational constraints. We characterize participants as price-takers who rationally update their bids to maximize their utility in response to real-time schedules of prices and dispatch. For two common bidding mechanisms, based on quantity and price, we identify a notion of alignment between participants' behavior and planners' goals that leads to a saddle-based design of the market that guarantees convergence to a point meeting all operational constraints. We further explore cases where this alignment property does not hold and observe that misaligned participants' bidding can destabilize the closed-loop system. We thus design a regularized version of the market dynamics that recovers all the desirable stability and steady-state performance guarantees. Numerical tests validate our results on the IEEE 39-bus system.

math.OC↗

arXiv2021

An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations

In this paper, we develop an oscillation free local discontinuous Galerkin (OFLDG) method for solving nonlinear degenerate parabolic equations. Following the idea of our recent work [J. Lu, Y. Liu, and C.-W. Shu, SIAM J. Numer. Anal. 59(2021), pp. 1299-1324.], we add the damping terms to the LDG scheme to control the spurious oscillations when solutions have a large gradient. The $L^2$-stability and optimal priori error estimates for the semi-discrete scheme are established. The numerical experiments demonstrate that the proposed method maintains the high-order accuracy and controls the spurious oscillations well.

math.NA↗

arXiv2021

Deep Analysis on Subgraph Isomorphism

Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works have been done since 2012, mainly optimizing pruning rules and matching orders to accelerate enumerating all isomorphic subgraphs. Nevertheless, their correctness and performance are not well studied. First, different languages are used in implementation with different compilation flags. Second, experiments are not done on the same platform and the same datasets. Third, some ideas of different works are even complementary. Last but not least, there exist errors when applying some algorithms. In this paper, we address these problems by re-implementing seven representative subgraph isomorphism algorithms as well as their improved versions, and conducting comprehensive experiments on various graphs. The results show pros and cons of state-of-the-art solutions and explore new approaches to optimization.

cs.DB↗

arXiv2021

On new surface-localized transmission eigenmodes

Consider the transmission eigenvalue problem \[ (Δ+k^2\mathbf{n}^2) w=0,\ \ (Δ+k^2)v=0\ \ \mbox{in}\ \ Ω;\quad w=v,\ \ \partial_νw=\partial_νv=0\ \ \mbox{on} \ \partialΩ. \] It is shown in [12] that there exists a sequence of eigenfunctions $(w_m, v_m)_{m\in\mathbb{N}}$ associated with $k_m\rightarrow \infty$ such that either $\{w_m\}_{m\in\mathbb{N}}$ or $\{v_m\}_{m\in\mathbb{N}}$ are surface-localized, depending on $\mathbf{n}>1$ or $0<\mathbf{n}<1$. In this paper, we discover a new type of surface-localized transmission eigenmodes by constructing a sequence of transmission eigenfunctions $(w_m, v_m)_{m\in\mathbb{N}}$ associated with $k_m\rightarrow \infty$ such that both $\{w_m\}_{m\in\mathbb{N}}$ and $\{v_m\}_{m\in\mathbb{N}}$ are surface-localized, no matter $\mathbf{n}>1$ or $0<\mathbf{n}<1$. Though our study is confined within the radial geometry, the construction is subtle and technical.

math.AP↗

arXiv2020

Modified Gaussian Process Regression Models for Cyclic Capacity Prediction of Lithium-ion Batteries

This paper presents the development of machine learning-enabled data-driven models for effective capacity predictions for lithium-ion batteries under different cyclic conditions. To achieve this, a model structure is first proposed with the considerations of battery ageing tendency and the corresponding operational temperature and depth-of-discharge. Then based on a systematic understanding of covariance functions within the Gaussian process regression, two related data-driven models are developed. Specifically, by modifying the isotropic squared exponential kernel with an automatic relevance determination structure, 'Model A' could extract the highly relevant input features for capacity predictions. Through coupling the Arrhenius law and a polynomial equation into a compositional kernel, 'Model B' is capable of considering the electrochemical and empirical knowledge of battery degradation. The developed models are validated and compared on the Nickel Manganese Cobalt Oxide (NMC) lithium-ion batteries with various cycling patterns. Experimental results demonstrate that the modified Gaussian process regression model considering the battery electrochemical and empirical ageing signature outperforms other counterparts and is able to achieve satisfactory results for both one-step and multi-step predictions. The proposed technique is promising for battery capacity predictions under various cycling cases.

cs.LG↗

arXiv2020

Analyzing Growth Kinematics and Fractal Dimensions of Molybdenum Disulfide Films

Through the positive role of alkali halides in realizing large area growth of transition metal-di-chalcogenide layers has been validated, the film-growth kinematics has not yet been fully established. This work presents a systematic analysis of the MoS$_2$ morphology for films grown under various pre-treatment conditions of the substrate with sodium chloride (NaCl). At an optimum NaCl concentration, the domain size of the monolayer increased by almost two orders of magnitude compared to alkali-free growth of MoS$_2$. The results show an inverse relationship between fractal dimension and areal coverage of the substrate with monolayers and multi-layers, respectively. Using the Fact-Sage software, the role of NaCl in determining the partial pressures of Mo- and S-based compounds in gaseous phase at the growth temperature is elucidated. The presence of alkali salts is shown to affect the domain size and film morphology by affecting the Mo and S partial pressures. Compared to alkali-free synthesis under the same growth conditions, MoS$_2$ film growth assisted by NaCl results in $\approx$ 81$\%$ of the substrate covered by monolayers. Under ideal growth conditions, at an optimum NaCl concentration, nucleation was suppressed, and domains enlarged, resulting in large area growth of MoS$_2$ monolayers. The monolayers were found to be free of unintentional doping with alkali metal and halogen atoms and exhibit high crystallinity and excellent opto-electronic quality.

cond-mat.mtrl-sci↗

arXiv2020

Long-term Stability of Bilayer MoS2 in Ambient Air

We report that chemical vapor deposition (CVD) grown bilayer and thicker-layered MoS2 are structurally and optically stable under ambient conditions, in comparison to CVD-grown monolayer MoS2 and other transition metal dichalcogenides (TMDs) that have been reported to degrade under the same conditions, hindering their many potential applications. We present atomic force microscopy (AFM), and Raman and photoluminescence (PL) spectroscopy measurements of as-grown and preheated multilayer MoS2 after exposure to ambient conditions for periods of up to 2 years. The AFM images show that, under ambient conditions, as-grown and preheated bilayer and thicker-layered MoS2 films do not exhibit the growth of dendrites that is characteristic of monolayer degradation. Dendrites are observed to stop at the monolayer-bilayer boundary. Raman and PL spectra of the aged bilayer and thicker-layered films are comparable to those of as-grown films. The greater stability of bilayers and thicker layers supports a previously reported mechanism for monolayer degradation involving Förster resonance energy transfer. Our results show that bilayer and thicker-layered TMDs are promising materials for applications requiring ambient stability.

cond-mat.mtrl-sci↗

arXiv2020

Grid-forming frequency shaping control

As power systems transit to a state of high renewable penetration, little or no presence of synchronous generators makes the prerequisite of well-regulated frequency for grid-following inverters unrealistic. Thus, there is a trend to resort to grid-forming inverters which set frequency directly. We propose a novel grid-forming frequency shaping control that is able to shape the aggregate system frequency dynamics into a first-order one with the desired steady-state frequency deviation and Rate of Change of Frequency (RoCoF) after a sudden power imbalance. The no overshoot property resulting from the first-order dynamics allows the system frequency to monotonically move towards its new steady-state without experiencing frequency Nadir, which largely improves frequency security. We prove that our grid-forming frequency-shaping control renders the system internally stable under mild assumptions. The performance of the proposed control is verified via numerical simulations on a modified Icelandic Power Network test case.

eess.SY↗

arXiv2020

Storage-Based Frequency Shaping Control

With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage -- frequency shaping control -- that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.

eess.SY↗

arXiv2020

Free-stream preserving finite difference schemes for ideal magnetohydrodynamics on curvilinear meshes

In this paper, a high order free-stream preserving finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the ideal magnetohydrodynamic (MHD) equations on curvilinear meshes. Under the constrained transport framework, magnetic potential evolved by a Hamilton-Jacobi (H-J) equation is introduced to control the divergence error. In this work, we use the alternative formulation of WENO scheme [10] for the nonlinear hyperbolic conservation law, and design a novel method to solve the magnetic potential. Theoretical derivation and numerical results show that the scheme can preserve free-stream solutions of MHD equations, and reduce error more effectively than the standard finite difference WENO schemes for such problems.

math.NA↗

arXiv2020

A Kernel Based Unconditionally Stable Scheme for Nonlinear Parabolic Partial Differential Equations

In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a special kernel-based formulation of the solutions and successive convolution. However, disadvantages appear when we extend the previous method to our equations, such as inefficient choice of parameters and unprovable stability for high-dimensional problems. To overcome these difficulties, a new kernel-based formulation is designed to approach the spatial derivatives. It maintains the good properties of the original one, including the high order accuracy and unconditionally stable for one-dimensional problems, hence allowing much larger time step evolution compared with other explicit schemes. In additional, without extra computational cost, the proposed scheme can enlarge the available interval of the special parameter in the formulation, leading to less errors and higher efficiency. Moreover, theoretical investigations indicate that it is unconditionally stable for multi-dimensional problems as well. We present numerical tests for one- and two-dimensional scalar and system, demonstrating the designed high order accuracy and unconditionally stable property of the scheme.

math.NA↗

arXiv2019

An adaptive high-order piecewise polynomial based sparse grid collocation method with applications

This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well studied in the literature. The contribution of this work is the introduction of a systematic framework for collocation onto high-order piecewise polynomial space that is allowed to be discontinuous. We consider both Lagrange and Hermite interpolation methods on nested collocation points. Our construction includes a wide range of function space, including those used in sparse grid continuous finite element method. Error estimates are provided, and the numerical results in function interpolation, integration and some benchmark problems in uncertainty quantification are used to compare different collocation schemes.

math.NA↗

arXiv2019

Dynamic Droop Approach for Storage-based Frequency Control

Transient frequency dips that follow sudden power imbalances --frequency Nadir-- represent a big challenge for frequency stability of low-inertia power systems. Since low inertia is identified as one of the causes for deep frequency Nadir, virtual inertia, which is provided by energy storage units, is said to be one of the solutions to the problem. In the present paper, we propose a new method for frequency control with energy storage systems (ESS), called dynamic droop control (iDroop), that can completely eliminate frequency Nadir during transients. Nadir elimination allows us to perform frequency stability assessment without the need for direct numerical simulations of system dynamics. We make a direct comparison of our developed strategy with the usual control approaches --virtual inertia (VI) and droop control (DC)-- and show that iDroop is more effective than both in eliminating the Nadir. More precisely, iDroop achieves the Nadir elimination under significantly lower gains than virtual inertia and requires almost $40\%$ less storage power capacity to implement the control. Moreover, we show that rather unrealistic control gains are required for virtual inertia in order to achieve Nadir elimination.

eess.SY↗

arXiv2019

Dynamic Droop Control in Low-inertia Power Systems

A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the grid's stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverter-based frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies --droop control (DC) and virtual inertia (VI)-- on several performance metrics induced by $\mathcal L_2$ and $\mathcal L_\infty$ signal norms. By extending a recently proposed modal decomposition method, we capture the effect of step and stochastic power disturbances, and frequency measurement noise, on the overall transient and steady-state behavior of the system. Our analysis unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without increasing steady-state control effort, or the large frequency variance that VI introduces in the presence of measurement noise. We further propose a novel dynam-i-c Droop controller (iDroop) that overcomes the limitations of DC and VI. More precisely, we show that iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or frequency overshoot (Nadir) elimination without affecting the steady-state control effort share, and propose a tuning recommendation that strikes a balance among these objectives. Extensive numerical experimentation shows that the proposed tuning is effective even when our proportionality assumptions are not valid, and that the particular tuning used for Nadir elimination strikes a good trade-off among various performance metrics.

eess.SY↗

arXiv2019

A Kernel Based High Order "Explicit" Unconditionally Stable Constrained Transport Method for Ideal Magnetohydrodynamics

The ideal Magnetohydrodynamics (MHD) equations are challenging because one needs to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Many numerical methods have been developed to enforce this condition. In this work, we further our work on mesh aligned constrained transport by developing a new kernel based approach for the vector potential in 2D and 3D. The approach for solving the vector potential is based on the method of lines transpose and is A-stable, eliminating the need for diffusion limiters needed in our previous work in 3D. The work presented here is an improvement over the previous method in the context of problems with strong shocks due to the fact that we could eliminate the diffusion limiter that was needed in our previous version of constrained transport. The method is robust and has been tested on the 2D and 3D cloud shock, blast wave and field loop problems.

math.NA↗

arXiv2018

Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs

Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers. In this paper we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.

math.OC↗