Static Coordinates Research Articles

One loop field strengths of charges and dipoles on a locally de Sitter background

We use the one loop vacuum polarization induced by scalar quantum electrodynamics to compute the electric and magnetic fields of point charges and magnetic dipoles on a locally de Sitter background. Our results are consistent with the physical picture of an inflating universe filling with a vast sea of charged particles as more and more virtual infrared scalar are ripped out of the vacuum. One consequence is that vacuum polarization quickly becomes nonperturbatively strong. Our computation employs the Schwinger–Keldysh effective field equations and is done in flat, conformal coordinates. Results are also obtained for static coordinates.

Quantum field theory in de Sitter and quasi–de Sitter spacetimes revisited

It is possible to associate temperatures with the nonextremal horizons of a large class of spherically symmetric spacetimes using periodicity in the Euclidean sector, and this procedure works for the de Sitter spacetime as well. But unlike, e.g., the black hole spacetimes, the de Sitter spacetime also allows a description in Friedmann coordinates. This raises the question of whether the thermality of the de Sitter horizon can be obtained working entirely in the Friedmann coordinates, without reference to the static coordinates or using the symmetries of de Sitter spacetime. We discuss several aspects of this issue for de Sitter and approximately de Sitter spacetimes in the Friedmann coordinates (with a time-dependent background and the associated ambiguities in defining the vacuum states). The different choices for the vacuum states, the behavior of the mode functions and the detector response are studied in both ($1+1$) and ($1+3$) dimensions. We compare and contrast the differences brought about by the different choices. In the last part of the paper, we also describe a general procedure for studying quantum field theory in spacetimes which are approximately de Sitter and, as an example, derive the corrections to the thermal spectrum due to the presence of pressure-free matter.

Proportional resonant individual pitch control for mitigation of wind turbines loads

This study addresses the mitigation of wind turbine loads and fatigue such as blade bending moments, tilt and yaw moments etc. Currently, the wind turbine blades are normally controlled to turn collectively to limit the excess of wind power above rated wind speed conditions without any load attenuation. The individual pitch control (IPC) is a promising way to reduce the wind turbine loads. This study presents a proportional resonant (PR) IPC, which does not need the measurement of blade azimuth angle and multiple complex Coleman transformations between rotational coordinate frame and stationary coordinate frame. The new strategy can attenuate the 1p and higher harmonics on the wind turbine blades as well as 3p on the hub without any filters. The wind turbine code fatigue, aerodynamics, structures and turbulence is applied to a doubly fed induction generator-based wind power generation system. The simulations are performed on the National Renewable Energy Laboratory 1.5 MW upwind reference wind turbine model. The simulation results are presented and discussed to demonstrate the capability and effectiveness of the proposed PR IPC method.

AC-DC Converter with Asymmetrical Higher Harmonics Compensation Function in Sustainable AC Grid

AbstractIn this paper the grid current higher harmonic compensation method for two level AC-DC converters in sustainable AC grid is described. The algorithm is based on Direct Power Control with Space Vector Modulator (DPC-SVM), which was extended by additional Higher Harmonics Compensation (HHC) module. The HHC block is composed of several resonant filters tuned to appropriate frequencies. Both, symmetrical and asymmetrical types of grid currents distortions are analyzed. Operation of the HHC module in stationary αβ coordinates and rotating dq coordinates is discussed. Selected waveforms illustrating operation of the developed algorithm are presented. It is shown that in dq coordinates asymmetrical voltage distortions needs additional effort for its compensation in comparison to symmetrical higher harmonics. The subject is important because in practice asymmetrical higher harmonics usually can appear when one phase nonlinear load is connected to the grid. Even within such conditions the grid connected ACDC converter (GCC) should provide sinusoidal-like current. This assumption provides the reduction of negative impact of the GCC in power quality in Point of Common Coupling (PCC) in sustainable AC grid

Studying the cosmological apparent horizon with quasistatic coordinates

This article aims at a natural generalization of the static coordinates to the (n + 1)-dimensional Friedmann–Lemaitre–Robertson–Walker (FLRW) Universe. After demonstrating a no-go theorem, we put forward the quasistatic coordinates for the FLRW Universe. Then, the quasistatic coordinates are utilized to study the unified first law and the scalar-type perturbations on the cosmological apparent horizon.

Three-Phase Induction Motor Modeling and Control Based on the EL Equation

The Euler-Lagrange (EL) model of the three-phase induction motor is set up based on the mathematical model of the three-phase induction motor in the two-phase static coordinate. The passivity and dissipativity of the three-phase induction motor are studied by EL model. Based on the passivity of induction motor, the passivity-based controller of system is designed with the method of damping injection under the conditions of the stator flux oriented.The system simulation model of the three-phase induction motor is established under MATLAB/Simulink environment. The Simulation results show that the passivity-based controller designed with the method of damping injection under the conditions of the stator flux orientedis feasible.

A Low-Cost Hybrid Active Power Filter for High Voltage System

A novel low-cost shunt hybrid active power filter for power quality in high voltage system is proposed in the paper. The active power filter is based on three-phase four-switch structure. An inductor is parallel in the second-side of the transform, instead of connected in the first-side of transform. An improved SVPWM is proposed according to the APF structure. A novel coordinate matrix is proposed to transform three-phase circumrotating coordinate into two-phase static coordinate. The zero vector is composed of two space voltage vectors with same breadth and contrary direction at same working time in a switch period. Simulation results confirm the validity of the proposed structure and the improved SVPWM.

A New Phase-Angle Measurement Algorithm Based on Virtual $\alpha \beta$ Stationary Coordinate

This letter proposes a novel phase-angle measurement algorithm through establishing a mathematical model of virtual αβ stationary coordinate that utilizes two expression forms of a positive-sequence component in two axes stationary reference frame. This method could greatly eliminate the sinusoidal error of the conventional discrete Fourier transform (DFT) algorithm. The accuracy and performance of the proposed algorithm are proved by relevant simulation results.

Investigation of unsteady flow-induced impeller oscillations of a single-blade pump under off-design conditions

The periodically unsteady flow-induced impeller oscillations for a single-blade pump are investigated both numerically and experimentally under off-design conditions. A partitioned strategy with load transfer method is selected for achieving successful fluid–structure interaction (FSI) simulations with strong two-way coupling. Three-dimensional, unsteady Reynolds-averaged Navier–Stokes equations are solved with a shear stress transport turbulence model for the fluid side, while a transient structure dynamic analysis with the finite element method is employed for the structure side. Radial deflections of the pump impeller are successfully measured using proximity sensors to validate the FSI results. The comparison of the deflection results focuses on both phase and amplitude aspects under different operational conditions. The FSI calculation results are confirmed by the experiment, but deviations are still observed for about half of an impeller rotation. Therefore, a rigorous analysis of the comparison between the angles of the obtained x and y components is carried out to understand the cause of the deviation. Meanwhile, the transient pressure measured at the casing by both computational fluid dynamics and experimental methods is qualitatively analyzed. Furthermore, hydrodynamic forces are also analyzed considering a strong FSI effect in both the rotating and stationary coordinate frame under off-design conditions to understand the behavior of the transient excitation forces, which directly lead to the rotor deflection.

Control of grid inverter based on opposite vectors hodographs

Purpose – This paper presents control strategy of VSC connected to the unbalanced grid in stationary coordinates system. The algorithm shown in the paper can be applied to typical inverter to reduce or even eliminate oscillation of DC‐link voltage under unbalanced operation. That has a direct influence on constant flow of p component of power which is essential for drives system for reducing torque ripples.Design/methodology/approach – The presented strategy of control assumes that orientation of grid voltage and line current vectors hodographs have to be opposite. Mathematical analysis and simulation has been done. Laboratory tests on low power has also been carried out.Findings – This method leads to fixed p component of power flow and fixed DC bus voltage. The presented idea of control may cause reduction of voltages asymmetry in three‐phase network with significant impedance (local grid, microgrid, isolated grid).Research limitations/implications – For 50 Hz power system, the presented control strateg...

Grid synchronization and symmetrical components extraction with PLL algorithm for grid connected power electronic converters - a review

Grid synchronization and symmetrical components extraction with PLL algorithm for grid connected power electronic converters - a reviewIn this paper, a review of Phase Locked Loop (PLL) algorithms and symmetrical component extraction methods intended for grid-connected power electronic converters are presented. Proposed classification is based on voltage representation in three coordinates: natural (abc), stationary (αβ) and rotating coordinates (dq). The three selected algorithms are described in details: Dual Second Order Generalized Integrator (DSOGI-PLL), Dual Virtual Flux - both in stationary coordinates. The third one, in rotating dq coordinates, is Dual Synchronous Reference Frame PLL (DSRF-PLL). A comparison of PLL algorithms is presented. Also, selected experimental results are given to verify practical application of discussed algorithms.

Hawking temperature of constant curvature black holes

The constant curvature (CC) black holes are higher dimensional generalizations of Banados-Teitelboim-Zanelli black holes. It is known that these black holes have the unusual topology of ${\mathcal{M}}_{D\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}{S}^{1}$, where $D$ is the spacetime dimension and ${\mathcal{M}}_{D\ensuremath{-}1}$ stands for a conformal Minkowski spacetime in $D\ensuremath{-}1$ dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using a globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperature takes the same form when using both the static and global coordinates. Also, it is identical to the Gibbons-Hawking temperature of the boundary de Sitter spaces of these CC black holes.

Fixed-Reference-Frame Phase-Locked Loop for Grid Synchronization Under Unbalanced Operation

This paper presents a grid synchronization scheme aimed to provide an estimation of the angular frequency and both the positive and negative sequences of the fundamental component of an unbalanced three-phase signal. These sequences are provided in fixed-reference-frame coordinates, and thus, the proposed algorithm is referred to as fixed-reference-frame phase-locked loop (PLL) (FRF-PLL). In fact, the FRF-PLL does not require transformation of variables into the synchronous frame coordinates as in most PLL schemes. Therefore, the proposed scheme is not based on the phase angle detection. Instead, the angular frequency is detected and used for synchronization purposes. The design of the FRF-PLL is based on a complete description of the source voltage involving both positive and negative sequences in stationary coordinates and considering the angular frequency as an uncertain parameter. Therefore, the FRF-PLL is intended to perform properly under severe unbalanced conditions and to be robust against angular frequency variations, sags, and swells in the three-phase utility voltage signal. Due to the selective nature of the scheme, it shows certain capability to alleviate the effect of harmonic distortion that is present in the utility voltage signal.

Hybrid mixture theory based moisture transport and stress development in corn kernels during drying: Coupled fluid transport and stress equations

In first part, a solution scheme for the multiscale fluid transport equation of Singh et al. (2003a) was developed, which could be easily implemented in a commercial finite elements package for solving swelling/shrinking problems. The solution scheme was applied to drying of corn kernels. Laplace transformation was used to convert the integral part of the fluid transport equation to a set of differential equations. In materials undergoing volume change during drying, a moving mesh is needed in Eulerian coordinates, which is tedious to implement. An alternate method was used that involved transforming the equation to stationary Lagrangian coordinates. Once the equations were solved, the data was transformed back to the moving Eulerian coordinates during post-processing. Corn heterogeneity was taken into account by using different coefficient of diffusivity values for various corn components. To predict stresses, it was assumed that the shape of a kernel remains geometrically similar to its initial shape during drying. Using this assumption a relation between the strain tensor and volume fraction of water was developed. The viscoelastic stress–strain constitutive equation was used to calculate the magnitude of stresses at different spatial locations inside a corn kernel. In the companion paper (part 2), the experimental validation of the solution, simulation results for various drying conditions and the practical implications are discussed.

Trumpet solution from spherical gravitational collapse with puncture gauges

We investigate the stationary end-state obtained by evolving a collapsing spherical star with the gauges routinely adopted to study puncture black holes. We compare the end-state of the collapse with the trumpet solution found in the evolution of a single wormhole slice and show that the two solutions closely agree. We demonstrate that the agreement is caused by the use of the Gamma-driver shift condition, which allows the matter to fall inwards into a region of spacetime that is not resolved by the numerical grid, and which simultaneously finds the stationary coordinates of the trumpet outside the matter.

A Study on Measuring Method for 3D Motion of Balls in High-Speed Ball Bearings

In order to simply and accurately measure the realistic motion of balls in a ball bearing, a method called the static oblique coordinates is proposed to measure the 3D motion of balls in an angular contact ball bearing. This measuring method utilizes Hall elements as the sensors which are assembled on the side of outer race and cage of the ball bearing with magnetized balls. The voltage signals of the Hall sensors are collected online and applied to calculate and analyze the variation of magnetic axis of the magnetized ball, from which the 3D motion of the balls can be calculated. The basic principles and experiment method of the measuring method are illustrated. This method has simple structure without damaging the bearing, by which the bearing’s real motion can be studied consequently with a high precision. The magnetization and magnetic pole detection methods in this study effectively solved the problem of magnetized balls’ magnetism un-uniformity which causes the measure signal chaos.

Improved control strategy for stand-alone distributed generation system under unbalanced and non-linear loads

This study presents an improved control strategy for a distributed generation system under stand-alone mode. Since there is no grid supply in a stand-alone system, the output voltage has to be controlled in the constant amplitude and frequency by the load-side inverter under the unbalanced and non-linear loads. The mathematic model of the load-side inverter is described. The dual-loop control method based on the stationary αβ reference coordinate is used for the load-side inverter so that the coordinate transformation is not needed. The outer-loop voltage controller consists of a proportional controller and a resonant regulator tuned at low-order harmonic frequency to compensate for the low-order harmonic components of the output voltage. A predictive current control scheme based on space vector modulation is adopted in the inner-loop current controller to improve the transient performance under the sudden load disturbances. Finally, experiment studies are carried out on a 5 kW stand-alone generation system. The experiment results show the excellent output voltage performance under both the steady-state and dynamic process with the load-adaptive ability.

On exact solutions for quantum particles with spin S = 0, 1/2, 1 and de Sitter event horizon

Exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space-time model are examined in detail. Firstly, for a scalar particle, two pairs of linearly independent solutions are specified explicitly: running and standing waves. A known algorithm for calculation of the reflection coefficient $R_{\epsilon j}$ on the background of the de Sitter space-time model is analyzed. It is shown that the determination of R_{\epsilon j} requires an additional constrain on quantum numbers \epsilon \rho / \hbar c >> j, where \rho is a curvature radius. When taken into account of this condition, the R_{\epsilon j} vanishes identically. It is claimed that the calculation of the reflection coefficient R_{\epsilon j} is not required at all because there is no barrier in an effective potential curve on the background of the de Sitter space-time. The same conclusion holds for arbitrary particles with higher spins, it is demonstrated explicitly with the help of exact solutions for electromagnetic and Dirac fields.

Research on Spindle Induction Motor Stator Flux Observer Algorithm

In order to enhance observation accuracy of the spindle induction stator flux and decrease observation error which is influenced by temperature, frequency and magnetic path in operation process, a full order observer was used to observe stator flux. The change of stator flux observer which adopted u-i model and low pass filter estimation model observation error was analyzed when the parameters of motor changed through the mathematical model in the stationary coordinates. A method to determine the gain matrix of full order observer was presented. The results showed that the error changed with the changes of motor speed and torque. On the premise of assuring stability of the observer, according to different speed ranges, choosing the proper observer pole assignment, the method can be used to enhance the observation accuracy of stator flux at high speed, and it is also validated in the Matlab/Simulink condition. It is shown that it can improve observer accuracy of the induction motor stator flux effectively.

Toward a dynamical shift condition for unequal mass black hole binary simulations

Moving puncture simulations of black hole binaries rely on a specific gauge choice that leads to approximately stationary coordinates near each black hole. Part of the shift condition is a damping parameter, which has to be properly chosen for stable evolutions. However, a constant damping parameter does not account for the difference in mass in unequal mass binaries. We introduce a position-dependent shift damping that addresses this problem. Although the coordinates change, the changes in the extracted gravitational waves are small.