Phase Measurement Accuracy Research Articles

Scalable Synchrophasors Communication Network Design and Implementation for Real-Time Distributed Generation Grid

There has been a growing interest in the deployment of phasor measurement units (PMUs) not only in high-voltage transmission, but in lower-voltage distribution systems. For a distributed generation (DG) grid, this would require deployment of PMUs at critical locations, which implies accurate phase measurement with the support of a low delay, highly reliable network infrastructure. In the absence of such a network, the most cost-effective solution would be to consider a wireless network to support centralized control for situational awareness in the transmission, as well as the DG grid environment. Therefore, the main objective in this paper is to design and implement a scalable synchrophasor network using wireless LAN technology to assess network performance and requirements under real-world conditions. To achieve this, we have designed an emulation platform that can support physical and medium access control layers. The data communication at the application is based on the IEEE C37.118-2011-2 Standard. By considering a hierarchical network architecture for our testbed implementation, we propose an efficient method to reduce bandwidth, as well as provide capabilities for control and management at each hierarchical level. In addition, an efficient tree-based multihop routing protocol has been designed to match a specific distribution feeder structure. The testbed is then used to access different network configurations under various test conditions.

Adaptive Correlation Space Adjusted Open-Loop Tracking Approach for Vehicle Positioning with Global Navigation Satellite System in Urban Areas.

For vehicle positioning with Global Navigation Satellite System (GNSS) in urban areas, open-loop tracking shows better performance because of its high sensitivity and superior robustness against multipath. However, no previous study has focused on the effects of the code search grid size on the code phase measurement accuracy of open-loop tracking. Traditional open-loop tracking methods are performed by the batch correlators with fixed correlation space. The code search grid size, which is the correlation space, is a constant empirical value and the code phase measuring accuracy will be largely degraded due to the improper grid size, especially when the signal carrier-to-noise density ratio () varies. In this study, the Adaptive Correlation Space Adjusted Open-Loop Tracking Approach (ACSA-OLTA) is proposed to improve the code phase measurement dependent pseudo range accuracy. In ACSA-OLTA, the correlation space is adjusted according to the signal . The novel Equivalent Weighted Pseudo Range Error (EWPRE) is raised to obtain the optimal code search grid sizes for different . The code phase measuring errors of different measurement calculation methods are analyzed for the first time. The measurement calculation strategy of ACSA-OLTA is derived from the analysis to further improve the accuracy but reduce the correlator consumption. Performance simulation and real tests confirm that the pseudo range and positioning accuracy of ASCA-OLTA are better than the traditional open-loop tracking methods in the usual scenarios of urban area.

A phasemeter concept for space applications that integrates an autonomous signal acquisition stage based on the discrete wavelet transform

We describe a phasemeter designed to autonomously acquire and track a heterodyne signal with low signal-to-noise ratio in a frequency band that spans from 1 MHz to 25 MHz. The background driving some of the design criterions of the phasemeter comes from studies on future space mission concepts such as orbiting gravitational wave observatories and next generation geodesy missions which all rely on tracking phasemeters in order to meet their mission goal. The phasemeter has been implemented within a field programmable gate array trying to minimize the requirement of computational resources and its performance has been tested using signal generators. Laboratory test has shown that the phasemeter is capable of locking to an input signal in less than half a millisecond, while its phase measurement accuracy is in the micro-radian range for measurement frequencies that span from mHz to Hz.

Note: An improved calibration system with phase correction for electronic transformers with digital output.

The existing electronic transformer calibration systems employing data acquisition cards cannot satisfy some practical applications, because the calibration systems have phase measurement errors when they work in the mode of receiving external synchronization signals. This paper proposes an improved calibration system scheme with phase correction to improve the phase measurement accuracy. We employ NI PCI-4474 to design a calibration system, and the system has the potential to receive external synchronization signals and reach extremely high accuracy classes. Accuracy verification has been carried out in the China Electric Power Research Institute, and results demonstrate that the system surpasses the accuracy class 0.05. Furthermore, this system has been used to test the harmonics measurement accuracy of all-fiber optical current transformers. In the same process, we have used an existing calibration system, and a comparison of the test results is presented. The system after improvement is suitable for the intended applications.

Physical compensation of phase curvature in digital holographic microscopy by use of programmable liquid lens.

Quantitative phase measurements obtained with digital holographic microscopes are strongly dependent on the optical arrangement of the imaging system. The nontelecentric operation provides phase measurements affected by a parabolic phase factor and requires numerical postprocessing, which does not always remove all the perturbation. Accurate phase measurements are achieved by using the imaging system in telecentric mode. Unfortunately, this condition is not accomplished when a commercial microscope is used as the imaging system. In this paper, we present an approach for obtaining accurate phase measurements in nontelecentric imaging systems without the need for numerical postprocessing. The method uses an electrically tunable liquid lens to illuminate the sample so that the perturbing parabolic wavefront is cancelled out. Experimental holograms of a Fresnel lens and a section of the thorax of a Drosophila melanogaster fly are captured to verify the proposed method.

Noise distribution and denoising of current density images.

Current density imaging (CDI) is a magnetic resonance (MR) imaging technique that could be used to study current pathways inside the tissue. The current distribution is measured indirectly as phase changes. The inherent noise in the MR imaging technique degrades the accuracy of phase measurements leading to imprecise current variations. The outcome can be affected significantly, especially at a low signal-to-noise ratio (SNR). We have shown the residual noise distribution of the phase to be Gaussian-like and the noise in CDI images approximated as a Gaussian. This finding matches experimental results. We further investigated this finding by performing comparative analysis with denoising techniques, using two CDI datasets with two different currents (20 and 45mA). We found that the block-matching and three-dimensional (BM3D) technique outperforms other techniques when applied on current density ([Formula: see text]). The minimum gain in noise power by BM3D applied to [Formula: see text] compared with the next best technique in the analysis was found to be around 2dB per pixel. We characterize the noise profile in CDI images and provide insights on the performance of different denoising techniques when applied at two different stages of current density reconstruction.

On the Accuracy of Phasor Angle Measurements in Power Networks

As known, phasor measurement units (PMUs) greatly enhance smart grid monitoring capabilities with advantageous impacts on power network management. Generally, PMUs accuracy is expressed in terms of total vector error, which comprises the joint effect of both angle and magnitude errors, thus possibly concealing the algorithm ability to measure phase. Some recent research works emphasize the importance of measuring current or voltage phasor angle with high accuracy (in the order of a few milliradians) at the distribution level. Because this issue is seldom considered in the literature, in this paper the phase measurement accuracy of three algorithms, namely the basic DFT, the windowed Taylor-Fourier filter, and the interpolated dynamic DFT (IpD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> FT) estimator, is extensively analyzed by means of simulations performed in various conditions described in the Standards IEEE C37.118.1:2011 and EN 50160:2010. In addition, some meaningful considerations about the uncertainty contributions due to imperfect synchronization are reported.

Accurate multipixel phase measurement with classical-light interferometry

We demonstrate accurate phase measurement from low photon level interference data using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have significant noise advantage over traditional methods such as balanced homodyning or phase shifting that treat individual pixels in the interference data as independent of each other. Our interference experiments comparing the optimization method with the traditional phase shifting method show that when the same photon resources are used, the optimization method provides phase recoveries with tighter error bars. In particular, RMS phase error performance of the optimization method for low photon number data (10 photons per pixel) shows $>$ 5X noise gain over the phase shifting method. In our experiments where a laser light source is used for illumination, the results imply phase measurement with accuracy better than the conventional single pixel based shot noise limit (SNL) that assumes independent phases at individual pixels. The constrained optimization approach presented here is independent of the nature of light source and may further enhance the accuracy of phase detection when a nonclassical light source is used.

Phase and pattern calibration of the Jicamarca Radio Observatory radar using satellites

The Jicamarca Radio Observatory (JRO) main 50-MHz array antenna radar system with multiple receivers is being used to study meteors via two interferometric receiving modes. One of the major challenges in these studies is the phase calibration of the various receiver (interferometric) channels (legs). While investigating some ambiguous features in meteor head-echo results, we developed a ‘new’ calibration technique that employs satellite observations to produce more accurate phase and pattern measurements than were previously available. This calibration technique, which resolves head-echo ambiguities, uses the fact that Earth-orbiting satellites are in gravitationally well-defined orbits and thus the pulse-to-pulse radar returns must be consistent (coherent) for an entire satellite pass through the radar beam. In particular, the satellite yields a reliable point source for phase and thus interferometry-derived range, Doppler and trajectory calibration. Using several satellites observed during standard meteor observations, we derive satellite orbital parameters by matching the observed and modelled three-dimensional trajectory and Doppler results. This approach uncovered subtle phase distortions that led to interferometry-derived trajectory distortions that are important only to point targets such as meteor head-echoes. We present the array calibration and radar imaging of satellite passes from our meteor observations of 2010 April 15/16. Future observations of a priori known satellites would likely yield significantly more accurate calibrations, especially of distant side lobes.

Influence of changes in humidity on dry temperature in GPS RO climatologies

Abstract. Radio occultation (RO) data are increasingly used in climate research. Accurate phase (change) measurements of Global Positioning System (GPS) signals are the basis for the retrieval of near-vertical profiles of bending angle, microwave refractivity, density, pressure, and temperature. If temperature is calculated from observed refractivity with the assumption that water vapor is zero, the product is called "dry temperature", which is commonly used to study earth's atmosphere, e.g., when analyzing temperature trends due to global warming. Dry temperature is a useful quantity, since it does not need additional background information in its retrieval. However, it can only be safely used as proxy for physical temperature, where moisture is negligible. The altitude region above which water vapor does not play a dominant role anymore, depends primarily on latitude and season. In this study we first investigated the influence of water vapor on dry temperature RO profiles. Hence, we analyzed the maximum altitude down to which monthly mean dry temperature profiles can be regarded as being equivalent to physical temperature. This was done by examining dry temperature to physical temperature differences of monthly mean analysis fields from the European Centre for Medium-Range Weather Forecasts (ECMWF), studied from 2006 until 2010. We introduced cutoff criteria, where maximum temperature differences of −0.1, −0.05, and −0.02 K were allowed (dry temperature is always lower than physical temperature), and computed the corresponding altitudes. As an example, a temperature difference of −0.05 K in the tropics was found at an altitude of about 14 km, while at higher northern latitudes in winter it was found at an altitude of about 9–10 km, in summer at about 11 km. Furthermore, regarding climate change, we expect an increase of absolute humidity in the atmosphere. This possible trend in water vapor could yield a wrongly interpreted dry temperature trend. As a consequence, we performed a model study, investigating the increase in height of the transition region between moist and dry air. We used data from the fifth phase of the Coupled Model Intercomparison Project (CMIP5), analyzing again monthly mean dry temperature to physical temperature differences, now from the years 2006 to 2050. We used the highest emission scenario RCP8.5 (representative concentration pathway), studying all available models of the CMIP5 project, analyzing one internal run per model, with the goal to identify the altitude region where trends in dry temperature can be safely regarded as reflecting trends in physical temperature. From all models we therefore choose a selection of models ("max 8" CMIP5 models), which showed the largest trend differences. As a result, our trend study suggests that the lower boundary of the region where dry temperature is essentially equal to physical temperature rises about 150 m decade−1.

Full-field reconstruction of ultrashort waveforms by time to space conversion interferogram analysis.

Accurate amplitude and phase measurements of ultrashort optical waveforms are essential for their use in a wide range of scientific disciplines. Here we report the first demonstration of full-field optical reconstruction of ultrashort waveforms using a time-to-space converter, followed by a spatial recording of an interferogram. The algorithm-free technique is demonstrated by measuring ultrashort pulses that are widely frequency chirped from negative to positive, as well as phase modulated pulse packets. Amplitude and phase measurements were recorded for pulses ranging from 0.5 ps to 10 ps duration, with measured dimensionless chirp parameter values from -30 to 30. The inherently single-shot nature of time-to-space conversion enables full-field measurement of complex and non-repetitive waveforms.

Sampling strategies for subsampled segmented EPI PRF thermometry in MR guided high intensity focused ultrasound.

To investigate k-space subsampling strategies to achieve fast, large field-of-view (FOV) temperature monitoring using segmented echo planar imaging (EPI) proton resonance frequency shift thermometry for MR guided high intensity focused ultrasound (MRgHIFU) applications. Five different k-space sampling approaches were investigated, varying sample spacing (equally vs nonequally spaced within the echo train), sampling density (variable sampling density in zero, one, and two dimensions), and utilizing sequential or centric sampling. Three of the schemes utilized sequential sampling with the sampling density varied in zero, one, and two dimensions, to investigate sampling the k-space center more frequently. Two of the schemes utilized centric sampling to acquire the k-space center with a longer echo time for improved phase measurements, and vary the sampling density in zero and two dimensions, respectively. Phantom experiments and a theoretical point spread function analysis were performed to investigate their performance. Variable density sampling in zero and two dimensions was also implemented in a non-EPI GRE pulse sequence for comparison. All subsampled data were reconstructed with a previously described temporally constrained reconstruction (TCR) algorithm. The accuracy of each sampling strategy in measuring the temperature rise in the HIFU focal spot was measured in terms of the root-mean-square-error (RMSE) compared to fully sampled "truth." For the schemes utilizing sequential sampling, the accuracy was found to improve with the dimensionality of the variable density sampling, giving values of 0.65 °C, 0.49 °C, and 0.35 °C for density variation in zero, one, and two dimensions, respectively. The schemes utilizing centric sampling were found to underestimate the temperature rise, with RMSE values of 1.05 °C and 1.31 °C, for variable density sampling in zero and two dimensions, respectively. Similar subsampling schemes with variable density sampling implemented in zero and two dimensions in a non-EPI GRE pulse sequence both resulted in accurate temperature measurements (RMSE of 0.70 °C and 0.63 °C, respectively). With sequential sampling in the described EPI implementation, temperature monitoring over a 192×144×135 mm3 FOV with a temporal resolution of 3.6 s was achieved, while keeping the RMSE compared to fully sampled "truth" below 0.35 °C. When segmented EPI readouts are used in conjunction with k-space subsampling for MR thermometry applications, sampling schemes with sequential sampling, with or without variable density sampling, obtain accurate phase and temperature measurements when using a TCR reconstruction algorithm. Improved temperature measurement accuracy can be achieved with variable density sampling. Centric sampling leads to phase bias, resulting in temperature underestimations.

Measurement of natural convective heat transfer coefficient along the surface of a heated wire using digital holographic interferometry.

In this paper, the local convective heat transfer coefficient (h) is measured along the surface of an electrically heated vertical wire using digital holographic interferometry (DHI). Experiments are conducted on wires of different diameters. The experimentally measured values are within the range as given in the literature. DHI is expected to provide a more accurate local convective heat transfer coefficient (h) as the value of the temperature gradient required for the calculation of "h" can be obtained more accurately than by other existing optical interferometric techniques without the use of a phase shifting technique. This is because in digital holography phase measurement accuracy is expected to be higher.

Thermal imaging of plasma with a phased array antenna in QUEST.

A thermal imaging system to measure plasma Electron Bernstein Emission (EBE) emanating from the mode conversion region in overdense plasma is discussed. Unlike conventional ECE/EBE imaging, this diagnostics does not employ any active mechanical scanning mirrors or focusing optics to scan for the emission cones in plasma. Instead, a standard 3 × 3 waveguide array antenna is used as a passive receiver to collect emission from plasma and imaging reconstruction is done by accurate measurements of phase and intensity of these signals by heterodyne detection technique. A broadband noise source simulating the EBE, is installed near the expected mode conversion region and its position is successfully reconstructed using phase array technique which is done in post processing.

Detection limits of confocal surface plasmon microscopy.

This paper applies rigorous diffraction theory to evaluate the minimum mass sensitivity of a confocal optical microscope designed to excite and detect surface plasmons operating on a planar metallic substrate. The diffraction model is compared with an intuitive ray picture which gives remarkably similar predictions. The combination of focusing the surface plasmons and accurate phase measurement mean that under favorable but achievable conditions detection of small numbers of molecules is possible, however, we argue that reliable detection of single molecules will benefit from the use of structured surfaces. System configurations needed to optimize performance are discussed.

Variable frequency range finding technology based on double polarization modulation method and system implementation

Traditional laser range technology has a poor phase measurement accuracy and an additional phase of the system, which restricts the improvement of its accuracy. In this article, by using the technology of variable frequency measurement based on double polarization modulation the phase shift range-finding technology is improved. With the method of double polarization modulation, the demodulation of the phase information is directly implemented on the phase modulator, which can make the system simpler. The variable frequency technology is used to replace the traditional phase discrimination technology; therefore the measurement accuracy of the system will not be persecuted with the phase crimination any more. The theoretical curve of sine (cosine) relation between modulation frequency and output light intensity is proved experimentally. Owing to the fact that the stability of frequency can be better than 10-6, the measurement accuracy can reach ±10.6 u m@4.5 m. By using this system to measuring a 200 m-long fiber, the clear curve of modulation frequency versus output of system is obtained.

Plasmonic petal-shaped beam for microscopic phase-sensitive SPR biosensor with ultrahigh sensitivity

Differential phase measurement between radially polarized (RP) and azimuthally polarized (AP) beams is an important technique in microscopic surface plasmon resonance (SPR) biosensors as reported in our earlier works [Opt. Lett.37, 2091 (2012); Appl. Phys. Lett.102, 011114 (2013)]. However, such a technique suffers complex beam splitting, detection, and data processing procedures for RP and AP beams which may lower the accuracy of phase measurement. In this Letter, a novel plasmonic petal-shaped vector beam is proposed instead of RP and AP beams, greatly simplifying the sensor system and enabling single measurement in differential interferometry. Moreover, an improved ultrahigh sensitivity on the order of 10(-7) refractive index units (RIUs) is experimentally verified in the proposed system.

Accurate Phase Calibration for Digital Beam-Forming in Multi-Transceiver HF Radar System

Abstract The TIGER-3 radar is being developed as an “all digital” radar with 20 integrated digital transceivers, each connected to a separate antenna. Using phased array antenna techniques, radiated power is steered towards a desired direction based on the relative phases within the array elements. This paper proposes an accurate phase measurement method to calibrate the phases of the radio output signals using Field Programmable Gate Array (FPGA) technology. The method sequentially measures the phase offset between the RF signal generated by each transceiver and a reference signal operated at the same frequency. Accordingly, the transceiver adjusts its phase in order to align to the reference phase. This results in accurately aligned phases of the RF output signals and with the further addition of appropriate phase offsets, digital beamforming (DBF) can be performed steering the beam in a desired direction. The proposed method is implemented on a Virtex-5 VFX70T device. Experimental results show that the calibration accuracy is of 0.153 degrees with 14 MHz operating frequency.

Off-axis setup taking full advantage of incoherent illumination in coherence-controlled holographic microscope

Coherence-controlled holographic microscope (CCHM) combines off-axis holography and an achromatic grating interferometer allowing for the use of light sources of arbitrary degree of temporal and spatial coherence. This results in coherence gating and strong suppression of coherent noise and parasitic interferences enabling CCHM to reach high phase measurement accuracy and imaging quality. The achievable lateral resolution reaches performance of conventional widefield microscopes, which allows resolving up to twice smaller details when compared to typical off-axis setups. Imaging characteristics can be controlled arbitrarily by coherence between two extremes: fully coherent holography and confocal-like incoherent holography. The basic setup parameters are derived and described in detail and experimental validations of imaging characteristics are demonstrated.

A High-Resolution PXI Digitizer for a Low-Value-Resistor Calibration System

This paper characterizes the metrological properties of a dual-channel high-resolution digitizer designed for use in a system to calibrate standard resistors with values between 1 $\hbox{m} \Omega$ and 10 $\Omega$ at frequencies from 40 Hz to 10 kHz. The possibility of using a digitizer to measure the complex voltage ratio is analyzed for both digitizer operating modes: the dual-channel mode with a simultaneous sampling and the single-channel mode with a sequential sampling in which an additional external multiplexer is used. The method of acquiring samples presented in this paper was used to investigate and compare the short-time stability and temperature influences on the metrological properties of the digitizer. This makes it possible to reduce the influence of the instability of the generator, being the signal source for the tested digitizer, on the research results. Moreover, presented in this paper are the frequency characteristics of the magnitude and phase of the complex voltage ratio, as well as the research results of the digitizer linearity and the phase measurement accuracy. All measurements discussed here were performed for both digitizer operating modes.