arXiv subjects
Publications and source records attributed to Tuyen Vu.
We consider the magnetic Neumann Laplacian on rectangles, subject to non-homogeneous fields. We prove that the square is a local minimiser of the lowest eigenvalue among all rectangles of a fixed area for weak magnetic fields . We conjecture that it is a global minimiser both under the area or perimeter constraints and partially prove the conjecture by establishing lower and upper bounds to the principal eigenvalue.
Novel findings on nanostructures in semi-metal and semi-graphene materials are discussed regarding rectangular quantum dots with zigzag edges, MIT bag models, and Dirichlet boundary conditions. The article theoretically investigates some models of quantum dots for these hybrid materials and the point spectra of the semi-Dirac semi-Laplacians via one-dimensional Laplace and Dirac operators. We also prove the self-adjointness of the semi-Laplacian defined on a rectangle, subject to zigzag and hard-wall boundary conditions, and study its spectral properties.
The rapid rise in inverter-based renewable resources has heightened concerns over subsynchronous resonance and oscillations, thereby challenging grid stability. This paper reviews approaches to identify and mitigate these issues, focusing on frequency scanning methods for stability assessment. It categorizes white-, black-, and gray-box modeling techniques, compares positive-sequence, dq-frame, and alpha-beta domain scanning, and examines perturbation shapes like step, ramp, and chirp. A comparative study highlights their strengths, limitations, and suitability for specific scenarios. By summarizing past events and surveying available tools, this work guides operators and researchers toward more effective, reliable stability analysis methods in grids with high renewable penetration.
As power systems become more complex with the continuous integration of intelligent distributed energy resources (DERs), new risks and uncertainties arise. Consequently, to enhance system resiliency, it is essential to account for various uncertain events when implementing the optimization problem for the energy management system (EMS). This paper presents a preventive EMS considering the probability of failure (PoF) of each system component across different scenarios. A conditional-value-at-risk (CVaR)-based framework is proposed to integrate the uncertainties of the distribution network. Loads are classified into critical, semi-critical, and non-critical categories to prioritize essential loads during generation resource shortages. A proximal policy optimization (PPO)-based reinforcement learning (RL) agent is used to solve the formulated problem and generate the control decisions. The proposed framework is evaluated on a notional MVDC ship system and a modified IEEE 30-bus system, where the results demonstrate that the PPO agent can successfully optimize the objective function while maintaining the network and operational constraints. For validation, the RL-based method is benchmarked against a traditional optimization approach, further highlighting its effectiveness and robustness. This comparison shows that RL agents can offer more resiliency against future uncertain events compared to the traditional solution methods due to their adaptability and learning capacity.
This paper presents novel methods for tuning inverter controller gains using deep reinforcement learning (DRL). A Simulink-developed inverter model is converted into a dynamic link library (DLL) and integrated with a Python-based RL environment, leveraging the multi-core deployment and accelerated computing to significantly reduce RL training time. A neural network-based mechanism is developed to transform the cascaded PI controller into an actor network, allowing optimized gain tuning by an RL agent to mitigate scenarios such as subsynchronous oscillations (SSO) and initial transients. Two distinct tuning approaches are demonstrated: a fixed gain strategy, where controller gains are represented as RL policy (actor network) weights, and an adaptive gain strategy, where gains are dynamically generated as RL policy (actor network) outputs. A comparative analysis of these methods is provided, showcasing their effectiveness in stabilizing the transient performance of grid-forming and grid-following converters and deployment challenges in hardware. Experimental results are presented, demonstrating the enhanced robustness and practical applicability of the RL-tuned controller gains in real-world systems.
The integration of power electronics building blocks in modern MVDC 12kV Naval ship systems enhances energy management and functionality but also introduces complex fault detection and control challenges. These challenges strain traditional fault diagnostic methods, making it difficult to detect and manage faults across multiple locations while maintaining system stability and performance. This paper proposes a temporal recurrent graph transformer network for fault diagnosis in naval MVDC 12kV shipboard systems. The deep graph neural network uses gated recurrent units to capture temporal features and a multi-head attention mechanism to extract spatial features, enhancing diagnostic accuracy. The approach effectively identifies and evaluates successive multiple faults with high precision. The method is implemented and validated on the MVDC 12kV shipboard system designed by the ESDRC team, incorporating all key components. Results show significant improvements in fault localization accuracy, with a 1-4% increase in performance metrics compared to other machine learning methods.
The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes the square and the spectrum of the operator. We also set up sufficient conditions for the existence of the point and discrete spectrum by including some appropriate potentials in the problem and study the spectral stability properties for perturbed operators.
The article provides proofs for the regularity of Dirac eigenfunctions, subject to MIT boundary conditions employed on various types of open sets ranging from smooth ones to convex polygons in two dimensions, as well as on half-space and smooth bounded domains in three-dimensional space.
This paper presents an original energy management methodology to enhance the resilience of ship power systems. The integration of various energy storage systems (ESS), including battery energy storage systems (BESS) and super-capacitor energy storage systems (SCESS), in modern ship power systems poses challenges in designing an efficient energy management system (EMS). The EMS proposed in this paper aims to achieve multiple objectives. The primary objective is to minimize shed loads, while the secondary objective is to effectively manage different types of ESS. Considering the diverse ramp-rate characteristics of generators, SCESS, and BESS, the proposed EMS exploits these differences to determine an optimal long-term schedule for minimizing shed loads. Furthermore, the proposed EMS balances the state-of-charge (SoC) of ESS and prioritizes the SCESS's SoC levels to ensure the efficient operation of BESS and SCESS. For better computational efficiency, we introduce the receding horizon optimization method, enabling real-time EMS implementation. A comparison with the fixed horizon optimization (FHO) validates its effectiveness. Simulation studies and results demonstrate that the proposed EMS efficiently manages generators, BESS, and SCESS, ensuring system resilience under generation shortages. Additionally, the proposed methodology significantly reduces the computational burden compared to the FHO technique while maintaining acceptable resilience performance.
Reducing the fuel consumption within a power network is crucial to enhance the overall system efficiency and minimize operating costs. Fuel consumption minimization can be achieved through different optimization techniques where the output power of the generators is regulated based on their individual efficiency characteristics. Existing studies primarily focus either on maximizing the efficiency function or minimizing the operating cost function of the generators to minimize fuel consumption. However, for practical implementation, it becomes imperative to incorporate a function within the optimization framework to represent the fuel consumption rate directly. This study introduces a novel approach by formulating a minimization problem with a sum-of-ratios objective function representing the fuel consumption rate. However, optimization problems with sum-of-ratios objective functions or constraints are extremely challenging to solve because of their strong nonlinearity. To efficiently solve the formulated problem, a fractional programming (FP) approach is adopted in this study. This reformulation technique significantly reduces the solution time of the optimization problem and provides a better solution than nonlinear programming (NLP). In addition, the reformulated problem can also be applied to large-scale systems where the NLP fails to converge. The proposed methodology of this study is tested on the notional MVAC ship system, modified IEEE 30-bus and IEEE 118-bus systems. The results demonstrate that the model successfully minimizes fuel consumption by effectively scheduling the generator and ESS dispatch.
This paper presents a novel Cyber-Hardware-in-the-Loop (Cyber-HIL) platform for assessing control operation in ship cyber-physical systems. The proposed platform employs cutting-edge technologies, including Docker containers, real-time simulator $OPAL-RT$, and network emulator $ns3$, to create a secure and controlled testing and deployment environment for investigating the potential impact of cyber attack threats on ship control systems. Real-time experiments were conducted using an advanced load-shedding controller as a control object in both synchronous and asynchronous manners, showcasing the platform's versatility and effectiveness in identifying vulnerabilities and improving overall Ship Cyber Physical System (SCPS) security. Furthermore, the performance of the load-shedding controller under cyber attacks was evaluated by conducting tests with man-in-the-middle (MITM) and denial-of-service (DoS) attacks. These attacks were implemented on the communication channels between the controller and the simulated ship system, emulating real-world scenarios. The proposed Cyber-HIL platform provides a comprehensive and effective approach to test and validate the security of ship control systems in the face of cyber threats.
This paper addresses the load restoration problem after power outage events. Our primary proposed methodology is using multi-agent deep reinforcement learning to optimize the load restoration process in distribution systems, modeled as networked microgrids, via determining the optimal operational sequence of circuit breakers (switches). An innovative invalid action masking technique is incorporated into the multi-agent method to handle both the physical constraints in the restoration process and the curse of dimensionality as the action space of operational decisions grows exponentially with the number of circuit breakers. The features of our proposed method include centralized training for multi-agents to overcome non-stationary environment problems, decentralized execution to ease the deployment, and zero constraint violations to prevent harmful actions. Our simulations are performed in OpenDSS and Python environments to demonstrate the effectiveness of the proposed approach using the IEEE 13, 123, and 8500-node distribution test feeders. The results show that the proposed algorithm can achieve a significantly better learning curve and stability than the conventional methods.
We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter.
We consider the Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimised by the isosceles right triangle both under the area or perimeter constraints. We prove this conjecture under extra geometric hypotheses relying on a recent approach of Ph. Briet and D. Krej{č}i{ř}{í}k for Dirac rectangles [2].
This paper presents the operation modes and control architecture of the grid-connected hydrogen electrolyzer systems for the provision of frequency and voltage supports. The analysis is focused on the primary and secondary loops in the hierarchical control scheme. At the power converter inner control loop, the voltage- and current-control modes are analyzed. At the primary level, the droop and opposite droop control strategies to provide voltage and frequency support are described. Coordination between primary control and secondary, tertiary reserves is discussed. The case studies and real-time simulation results are provided using Typhoon HIL to back the theoretical investigation.
This paper presents a 1-D convolutional graph neural network for fault detection in microgrids. The combination of 1-D convolutional neural networks (1D-CNN) and graph convolutional networks (GCN) helps extract both spatial-temporal correlations from the voltage measurements in microgrids. The fault detection scheme includes fault event detection, fault type and phase classification, and fault location. There are five neural network model training to handle these tasks. Transfer learning and fine-tuning are applied to reduce training efforts. The combined recurrent graph convolutional neural networks (1D-CGCN) is compared with the traditional ANN structure on the Potsdam 13-bus microgrid dataset. The achievable accuracy of 99.27%, 98.1%, 98.75%, and 95.6% for fault detection, fault type classification, fault phase identification, and fault location respectively.
Fault diagnostics are extremely important to decide proper actions toward fault isolation and system restoration. The growing integration of inverter-based distributed energy resources imposes strong influences on fault detection using traditional overcurrent relays. This paper utilizes emerging graph learning techniques to build a new temporal recurrent graph neural network models for fault diagnostics. The temporal recurrent graph neural network structures can extract the spatial-temporal features from data of voltage measurement units installed at the critical buses. From these features, fault event detection, fault type/phase classification, and fault location are performed. Compared with previous works, the proposed temporal recurrent graph neural networks provide a better generalization for fault diagnostics. Moreover, the proposed scheme retrieves the voltage signals instead of current signals so that there is no need to install relays at all lines of the distribution system. Therefore, the proposed scheme is generalizable and not limited by the number of relays installed. The effectiveness of the proposed method is comprehensively evaluated on the Potsdam microgrid and IEEE 123-node system in comparison with other neural network structures.
This paper proposes a novel integrated multiport bidirectional back-to-back power converter for a type-4 wind turbine that accommodates a battery and supercapacitor for energy storage. The circuit topology reduces 4 switches compared to the traditional configuration. Moreover, owing to the dual-buck structure embedded in the phase leg, the circuitry has no short-circuit path, therefore it withstands short-circuited events for a much longer time than the normal phase-leg and prevents the reverse current in turn-off recovery. The use of a hybrid energy storage system with battery and supercapacitor helps smooth out the power output under wind gusts and stabilizes the DC-link voltage under grid fault conditions. The case studies are carried out with a 1.5 MW wind turbine system. Simulation results are provided for the theoretical validation.