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Practical Implementation and Operational Experience of dynamic mode decomposition in Wide-area Monitoring Systems of Italian Power System

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Journal of modern Power Systems and Clean Energy 2023年第3期11卷 793-802页

作者： Andrea Vicario Alberto Berizzi Giorgio Maria Giannuzzi Cosimo Pisani Department of Energy at Politecnico di Milano MilanItaly Terna S.p.A. RomeItaly

This study presents the assumptions and strategies for the practical implementation of the dynamic mode decomposition approach in the wide-area monitoring system of the Italian transmission system operator,Terna.The procedure setup aims to detect poorly damped interarea oscillations of power systems.dynamic mode decomposition is a data-driven technique that has gained increasing attention in different fields;the proposed implementation can both characterize the oscillatory modes and identify the most influenced areas.This study presents the results of its practical implementation and operational experience in power system monitoring.It focuses on the main characteristics and solutions identified to reliably monitor the interarea electromechanical modes of the interconnected European power system.Moreover,conditions to issue an appropriate alarm in case of critical operating conditions are described.The effectiveness of the proposed approach is validated by its application in three case studies:a critical oscillatory event and a short-circuit event that occurred in the Italian power system in the previous years,and a 15-min time interval of normal grid operation recorded in March 2021.

关键词： Power system control power system dynamics wide-area monitoring system(WAMS) dynamic mode decomposition

Visualization and selection of dynamic mode decomposition components for unsteady flow

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Visual Informatics 2021年第3期5卷 15-27页

作者： T.Krake S.Reinhardt M.Hlawatsch B.Eberhardt D.Weiskopf Visualization Research Center(VISUS) Allmandring 1970569 StuttgartGermany Hochschule der Medien Nobelstraße 1070569 StuttgartGermany

dynamic mode decomposition(DMD)is a data-driven and model-free decomposition technique.It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data.Conceptually,DMD performs a low-dimensional spectral decomposition of the data into the following components:the modes,called DMD modes,encode the spatial contribution of the decomposition,whereas the DMD amplitudes specify their impact.Each associated eigenvalue,referred to as DMD eigenvalue,characterizes the frequency and growth rate of the DMD mode.In this paper,we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields.We begin with the theoretical background of DMD and its application to unsteady flow.Next,we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform.Our analysis shows that the current use of DMD components has several drawbacks.To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition:we show that our improved components capture the spatio-temporal patterns of the flow better.Moreover,we remove redundancies in the decomposition and clarify the interplay between components,allowing users to understand the impact of components.These new representations,which respect the spatio-temporal character of DMD,enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components.With a number of typical examples,we demonstrate that the combination of these techniques allows new insights with DMD for unsteady flow.

关键词： dynamic mode decomposition Spectral decomposition

A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

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Theoretical & Applied Mechanics Letters 2023年第5期13卷 353-356页

作者： Wengang Chen Jiaqing Kou Wenkai Yang Changzhou Institute of Technology Changzhou 213032China Institute of Aerodynamics RWTH Aachen UniversityWüllnerstraße 5a52062 AachenGermany

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(DMD).The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system.Thereafter,DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching.First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step.Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example,the efficiency of solving unsteady adjoint equations is significantly improved.Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics,and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors,which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

关键词： Acceleration method Unsteady adjoint dynamic mode decomposition Optimization efficiency

Stability analysis for flow past a cylinder via lattice Boltzmann method and dynamic mode decomposition

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Chinese Physics B 2015年第6期24卷 378-384页

作者：张伟王勇钱跃竑 Department of Mechanical Enignneering National University of Singapore Department of Mechanical and Aerospace Engineering University of California Shanghai Institute of Applied Math and Mechanics Shanghai University

A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.

关键词： lattice Boltzmann dynamic mode decomposition stability analysis graphical processing unit

Flow field reconstruction and characteristic analysis of dual-throat control vector nozzle based on dynamic mode decomposition

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Hangkong Dongli Xuebao/Journal of Aerospace Power 2024年第6期39卷

作者： Wang, Jianming Liu, Xiaodong Xia, Xuanze Wang, Chengjun Liaoning Key Laboratory of Advanced Test Technology for Aeronautical Propulsion System School of Aero-engine Shenyang Aerospace University Shenyang 110136 China

The three-dimensional flow field of the thrust vectoring nozzle was simulated by detached eddy simulation method, and the pressure coefficient and density gradient distribution of flow field were analyzed. The dynamic modal decomposition (DMD) technology was applied to modal decomposition of the pressure coefficient of the z=0 section, the obtained modal recombination flow field was selected to evolve in time. The results indicated that the first five-order modes obtained by dynamic modal decomposition can be used to reconstruct the pressure coefficient field of the dual-throat control vector nozzle more completely. The first-order mode mainly illustrated the swing phenomenon of the separated shock wave and its influence on the pressure pulsation of the shear layer between the recirculation zone and the main flow; the second-order mode mainly illustrated the separation of the vortex system in the shear layer. The third-order mode mainly illustrated the change in the intensity of the separated shock wave, the fourth and fifth-order modes were mainly manifested as high-order oscillations in the position and intensity of the separated shock wave and the shear layer near the recirculation zone. © 2024 Beijing University of Aeronautics and Astronautics (BUAA). All rights reserved.

关键词： dynamic mode decomposition

Application of Hankel dynamic mode decomposition for Wide Area Monitoring of Subsynchronous Resonance

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Energy Engineering 2023年第4期120卷 851-867页

作者： Lei Wang Tiecheng Li Hui Fan Xuekai Hu Lin Yang Xiaomei Yang State Grid Hebei Electric Power Research Institute Shijiazhuang050021China State Grid Hebei Electric Power Company Shijiazhuang050021China The College of Electrical Engineering Sichuan UniversityChengdu610065China

In recent years,subsynchronous resonance(SSR)has frequently occurred in DFIG-connected series-compensated systems.For the analysis and prevention,it is of great importance to achieve wide area monitoring of the incident.This paper presents a Hankel dynamic mode decomposition(DMD)method to identify SSR parameters using synchrophasor data.The basic idea is to employ the DMD technique to explore the subspace of Hankel matrices constructed by synchrophasors.It is analytically demonstrated that the subspace of these Hankel matrices is a combination of fundamental and SSR modes.Therefore,the SSR parameters can be calculated once the modal parameter is extracted.Compared with the existing method,the presented work has better dynamic performances as it requires much less data.Thus,it is more suitable for practical cases in which the SSR characteristics are timevarying.The effectiveness and superiority of the proposed method have been verified by both simulations and field data.

关键词： Hankel dynamic mode decomposition time-varying sub-synchronous oscillation synchrophasor

Numerical analysis of the correlation between fluid dynamic modes and hydrodynamic noise in flows around a three-dimensional circular cylinder

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Journal of Hydrodynamics 2024年第1期36卷 119-129页

作者： Jia-jia Qin Ming-xin Zou Yuan Zhuang De-cheng Wan Computational Marine Hydrodynamics Lab(CMHL) School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai200240China Wuhan Second Ship Design and Research Institute Wuhan430205China

The flow around a circular cylinder for Re=1000 is characterized by flow separation and Karman vortex street.The typical flow features can be captured to study the correlation between fluid fields and sound fields.In this paper,the three-dimensional circular cylinder is taken as the research object,and the probes of surface fluctuating pressure and far field sound pressure are arranged every 10°.The directional diagram and the coherence of fluctuating pressure and sound pressure are analyzed.The relationship between the flow mode and hydrodynamic noise is studied by using dynamic mode decomposition(DMD).The characteristics of the dipole and quadrupole sound source term of a long span cylinder are studied.The results show that at the angles between 30°–120°and 190°–350°,the fluctuating pressure contributes more to the generation of dipole sounds.The quadrupole sound source shows three-dimensional effects,which is more obvious in a cylinder with large spanwise length.

关键词： Pressure coherence dynamic mode decomposition flow-sound correlation circular cylinder

Modal Analysis of Axial Compressor Tip Rotating Instability under Varying Operating Conditions

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Journal of Thermal Science 2023年第4期32卷 1345-1356页

作者： LI Tao WU Yadong TIAN Jie OUYANG Hua School of Mechanical Engineering Shanghai Jiao Tong UniversityShanghai200240China Engineering Research Centre of Gas Turbine and Civil Aero Engine Ministry of EducationShanghai Jiao Tong UniversityShanghai200240China

The full annulus numerical research was performed on a low-speed compressor rotor to investigate the rotating instability in the tip region.The frequency spectra show the existence of rotating instability at narrow stable operating range.With the decrease of flow rate,31 cells of flow disturbance can be found in the instantaneous flow field.The distribution of vortex suggests that the circumferential propagation of the interaction between tip leakage vortex and adjacent blade brings about these cells.The dynamic mode decomposition(DMD)method and spatial discrete Fourier transform(SDFT)were applied to obtain the circumferential mode features,and the results indicate that the rotating instability is associated with the 31 cells of flow disturbance.Then the DMD method was further applied on the pressure data from a circle and an annulus domain,so as to extract different mode components with the corresponding spatial structures,frequencies and amplitudes.The results suggest that DMD modes can display the flow feature and explore the evolution of each instability source in the tip flow field.

关键词： axial compressor rotating instability flow structure circumferential mode dynamic mode decomposition

Comparative study of reduced-order modeling method for the cavitating flow over a hydrofoil

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Journal of Hydrodynamics 2023年第4期35卷 679-699页

作者： Yan-zhao Wu Ran Tao Di Zhu Ruo-fu Xiao College of Water Resources and Civil Engineering China Agricultural UniversityBeijing100083China Beijing Engineering Research Center of Safety and Energy Saving Technology for Water Supply Network System China Agricultural UniversityBeijing100083China College of Engineering China Agricultural UniversityBeijing100083China

As a high-dimensional complex nonlinear dynamic system,the analysis of the essence of flow has always been a difficult problem,especially in the flow including phase change.In recent years,it has become a feasible method to reduce the dimension of flow structure by reduced-order modeling(ROM)methods.In this paper,through the cavitation numerical simulation of NACA0015 hydrofoil,two ROM methods are used to reduce and restore three different cavitation respectively-proper orthogonal decomposition(POD)and dynamic mode decomposition(DMD).The applicability of two methods in cavitation is discussed and reasons are analyzed.The results show that for stable cavitation,POD,DMD methods can accurately restore the flow field of a few modes with high energy.For unstable cavitation,only POD method can restore real flow field well.This situation is mainly due to the fact that POD,DMD method are applicable to different energy ratios,and different main mode selection criterion of DMD will lead to different main mode.ROM can greatly simplify the complexity of flow.Selecting a reasonable ROM can improve the accuracy of a small amount of database,and provide a basis for intelligent prediction of flow analysis.

关键词： Hydrofoil cavitation reduced-order model proper orthogonal decomposition dynamic mode decomposition