Analyzing dynamic performance of power systems over parameter space using the method of normal forms of vector fields

Today\u27s power systems have become more and more stressed due to the high utilization of available facilities. The complex dynamic behavior of large stressed power systems following disturbances can not be fully explained with present tools, such as linear eigen-analysis tools and nonlinear time-domain simulation methods. This research work applies a nonlinear analytical tool, the method of normal forms of vector fields, to help understand the complex transient oscillations in stressed power systems;The method of normal forms is a well-known mathematical tool to study systems of differential equations. The basic idea is to simplify the dynamical system by a sequence of nonlinear coordinate transformations. If there is no resonance in the system, then the nonlinear vector field can be turned into a linear one by the transformations. Previous work applied the second-order normal form transformation under non-resonance condition to power system dynamical equations. The nonlinear interaction among the fundamental modes was investigated. Based on these efforts, this work extends the application of normal forms to evaluate the dynamic performance of power systems taking into account changing operation conditions;As the resonance and near-resonance could occur in parameter space, a new normal form transformation under second order resonance condition is derived. The analysis shows that the high nonlinearity resulting from the resonance and near-resonance among poorly damped oscillatory modes and control modes is detrimental to the system performance. An approach to determine the resonance and near-resonance regions in parameter space is developed. The modes contributing to the detrimental behavior associated with the near-resonance region are identified by a procedure based on certain modal interaction indices. The state variables showing detrimental behavior are then determined using nonlinear participation factors. The accuracy of the prediction is verified by conducting nonlinear time-domain simulation. In order to compare the effect of nonlinear modal interaction quantitatively under different operating conditions, a new index in the state space of machine variables is developed. The nonlinear modal interaction together with the linear modal characteristics accounts for the dynamic performance of the system over a range of operating conditions. The method and procedures are tested and validated on a sample test system

An immersogeometric formulation for free-surface flows with application to marine engineering problems

An immersogeometric formulation is proposed to simulate free-surface flows around structures with complex geometry. The fluid–fluid interface (air–water interface) is handled by the level set method, while the fluid–structure interface is handled through an immersogeometric approach by immersing structures into non-boundary-fitted meshes and enforcing Dirichlet boundary conditions weakly. Residual-based variational multiscale method (RBVMS) is employed to stabilize the coupled Navier–Stokes equations of incompressible flows and level set convection equation. Other level set techniques, including re-distancing and mass balancing, are also incorporated into the immersed formulation. Adaptive quadrature rule is used to better capture the geometry of the immersed structure boundary by accurately integrating the intersected background elements. Generalized-α role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative; \u3eα method is adopted for time integration, which results in a two-stage predictor multi-corrector algorithm. GMRES solver preconditioned with block Jacobian matrices of individual fluid and level set subproblems is used for solving the coupled linear systems arising from the multi-corrector stage. The capability and accuracy of the proposed method are assessed by simulating three challenging marine engineering problems, which are a solitary wave impacting a stationary platform, dam break with an obstacle, and planing of a DTMB 5415 ship model. A refinement study is performed. The predictions of key quantities of interest by the proposed formulation are in good agreement with experimental results and boundary-fitted simulation results from others. The proposed formulation has great potential for wide applications in marine engineering problems

Machine Learning-based Brokers for Real-time Classification of the LSST Alert Stream

The unprecedented volume and rate of transient events that will be discovered by the Large Synoptic Survey Telescope (LSST) demands that the astronomical community update its followup paradigm. Alert-brokers -- automated software system to sift through, characterize, annotate and prioritize events for followup -- will be critical tools for managing alert streams in the LSST era. The Arizona-NOAO Temporal Analysis and Response to Events System (ANTARES) is one such broker. In this work, we develop a machine learning pipeline to characterize and classify variable and transient sources only using the available multiband optical photometry. We describe three illustrative stages of the pipeline, serving the three goals of early, intermediate and retrospective classification of alerts. The first takes the form of variable vs transient categorization, the second, a multi-class typing of the combined variable and transient dataset, and the third, a purity-driven subtyping of a transient class. While several similar algorithms have proven themselves in simulations, we validate their performance on real observations for the first time. We quantitatively evaluate our pipeline on sparse, unevenly sampled, heteroskedastic data from various existing observational campaigns, and demonstrate very competitive classification performance. We describe our progress towards adapting the pipeline developed in this work into a real-time broker working on live alert streams from time-domain surveys.Comment: 33 pages, 14 figures, submitted to ApJ

Analyzing dynamic performance of power systems over parameter space using the method of normal forms of vector fields

Today's power systems have become more and more stressed due to the high utilization of available facilities. The complex dynamic behavior of large stressed power systems following disturbances can not be fully explained with present tools, such as linear eigen-analysis tools and nonlinear time-domain simulation methods. This research work applies a nonlinear analytical tool, the method of normal forms of vector fields, to help understand the complex transient oscillations in stressed power systems;The method of normal forms is a well-known mathematical tool to study systems of differential equations. The basic idea is to simplify the dynamical system by a sequence of nonlinear coordinate transformations. If there is no resonance in the system, then the nonlinear vector field can be turned into a linear one by the transformations. Previous work applied the second-order normal form transformation under non-resonance condition to power system dynamical equations. The nonlinear interaction among the fundamental modes was investigated. Based on these efforts, this work extends the application of normal forms to evaluate the dynamic performance of power systems taking into account changing operation conditions;As the resonance and near-resonance could occur in parameter space, a new normal form transformation under second order resonance condition is derived. The analysis shows that the high nonlinearity resulting from the resonance and near-resonance among poorly damped oscillatory modes and control modes is detrimental to the system performance. An approach to determine the resonance and near-resonance regions in parameter space is developed. The modes contributing to the detrimental behavior associated with the near-resonance region are identified by a procedure based on certain modal interaction indices. The state variables showing detrimental behavior are then determined using nonlinear participation factors. The accuracy of the prediction is verified by conducting nonlinear time-domain simulation. In order to compare the effect of nonlinear modal interaction quantitatively under different operating conditions, a new index in the state space of machine variables is developed. The nonlinear modal interaction together with the linear modal characteristics accounts for the dynamic performance of the system over a range of operating conditions. The method and procedures are tested and validated on a sample test system.</p

An immersogeometric formulation for free-surface flows with application to marine engineering problems

An immersogeometric formulation is proposed to simulate free-surface flows around structures with complex geometry. The fluid–fluid interface (air–water interface) is handled by the level set method, while the fluid–structure interface is handled through an immersogeometric approach by immersing structures into non-boundary-fitted meshes and enforcing Dirichlet boundary conditions weakly. Residual-based variational multiscale method (RBVMS) is employed to stabilize the coupled Navier–Stokes equations of incompressible flows and level set convection equation. Other level set techniques, including re-distancing and mass balancing, are also incorporated into the immersed formulation. Adaptive quadrature rule is used to better capture the geometry of the immersed structure boundary by accurately integrating the intersected background elements. Generalized-α" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">α method is adopted for time integration, which results in a two-stage predictor multi-corrector algorithm. GMRES solver preconditioned with block Jacobian matrices of individual fluid and level set subproblems is used for solving the coupled linear systems arising from the multi-corrector stage. The capability and accuracy of the proposed method are assessed by simulating three challenging marine engineering problems, which are a solitary wave impacting a stationary platform, dam break with an obstacle, and planing of a DTMB 5415 ship model. A refinement study is performed. The predictions of key quantities of interest by the proposed formulation are in good agreement with experimental results and boundary-fitted simulation results from others. The proposed formulation has great potential for wide applications in marine engineering problems.This is a manuscript of an article published as Zhu, Qiming, Fei Xu, Songzhe Xu, Ming-Chen Hsu, and Jinhui Yan. "An immersogeometric formulation for free-surface flows with application to marine engineering problems." Computer Methods in Applied Mechanics and Engineering (2019): 112748. DOI: 10.1016/j.cma.2019.112748. Posted with permission.</p

Effects of Static Magnetic Field on the Microstructure of Selective Laser Melted Inconel 625 Superalloy: Numerical and Experiment Investigations

A number of researchers have reported that a static magnetic field (SMF) will affect the process of selective laser melting (SLM), which is achieved mainly through affecting molten pool evolution and microstructure growth. However, its underlying mechanism has not been fully understood. In this work, we conducted a comprehensive investigation of the influence of SMF on the SLM Inconel 625 superalloy through experiments and multi-scale numerical simulation. The multi-scale numerical models of the SLM process include the molten pool and the dendrite in the mushy zone. For the molten pool simulation, the simulation results are in good agreement with the experimental results regarding the pool size. Under the influence of the Lorentz force, the dimension of the molten pool, the flow field, and the temperature field do not have an obvious change. For the dendrite simulation, the dendrite size obtained in the experiment is employed for setting up the dendrite geometry in the dendrite numerical simulation, and our findings show that the applied magnetic field mainly influences the dendrite growth owing to thermoelectric magnetic force (TEMF) on the solid–liquid interface rather than the Lorentz force inside the molten pool. Since the TEMF on the solid–liquid interface is affected by the interaction between the SMF and thermal gradient at different locations, we changed the SLM parameters and SMF to investigate the effect on the TEMF. The simulation shows that the thermoelectric current is highest at the solid–liquid interface, resulting in a maximum TEMF at the solid–liquid interface and, as a result, affecting the dendrite morphology and promoting the columnar to equiaxed transition (CET), which is also shown in the experiment results under 0.1 T. Furthermore, it is known that the thermoelectric magnetic convection (TEMC) around the dendrite can homogenize the laves phase distribution. This agrees well with the experimental results, which show reduced Nb precipitation from 8.65% to 4.34% under the SMF of 0.1 T. The present work can provide potential guidance for microstructure control in the SLM process using an external SMF

Effects of Static Magnetic Field on the Microstructure of Selective Laser Melted Inconel 625 Superalloy: Numerical and Experiment Investigations

A number of researchers have reported that a static magnetic field (SMF) will affect the process of selective laser melting (SLM), which is achieved mainly through affecting molten pool evolution and microstructure growth. However, its underlying mechanism has not been fully understood. In this work, we conducted a comprehensive investigation of the influence of SMF on the SLM Inconel 625 superalloy through experiments and multi-scale numerical simulation. The multi-scale numerical models of the SLM process include the molten pool and the dendrite in the mushy zone. For the molten pool simulation, the simulation results are in good agreement with the experimental results regarding the pool size. Under the influence of the Lorentz force, the dimension of the molten pool, the flow field, and the temperature field do not have an obvious change. For the dendrite simulation, the dendrite size obtained in the experiment is employed for setting up the dendrite geometry in the dendrite numerical simulation, and our findings show that the applied magnetic field mainly influences the dendrite growth owing to thermoelectric magnetic force (TEMF) on the solid–liquid interface rather than the Lorentz force inside the molten pool. Since the TEMF on the solid–liquid interface is affected by the interaction between the SMF and thermal gradient at different locations, we changed the SLM parameters and SMF to investigate the effect on the TEMF. The simulation shows that the thermoelectric current is highest at the solid–liquid interface, resulting in a maximum TEMF at the solid–liquid interface and, as a result, affecting the dendrite morphology and promoting the columnar to equiaxed transition (CET), which is also shown in the experiment results under 0.1 T. Furthermore, it is known that the thermoelectric magnetic convection (TEMC) around the dendrite can homogenize the laves phase distribution. This agrees well with the experimental results, which show reduced Nb precipitation from 8.65% to 4.34% under the SMF of 0.1 T. The present work can provide potential guidance for microstructure control in the SLM process using an external SMF