Harmonic Measurements Research Articles

The two-phase problem for harmonic measure in VMO and the chord-arc condition

Let Ω + ⊂ R n + 1 \Omega ^+\subset \mathbb {R}^{n+1} be a bounded δ \delta -Reifenberg flat domain, with δ > 0 \delta >0 small enough, possibly with locally infinite surface measure. Assume also that Ω − = R n + 1 ∖ Ω + ¯ \Omega ^-= \mathbb {R}^{n+1}\setminus \overline {\Omega ^+} is an NTA (non-tangentially accessible) domain as well and denote by ω + \omega ^+ and ω − \omega ^- the respective harmonic measures of Ω + \Omega ^+ and Ω − \Omega ^- with poles p ± ∈ Ω ± p^\pm \in \Omega ^\pm . In this paper we show that the condition that log ⁡ d ω − d ω + ∈ VMO ⁡ ( ω + ) \log \dfrac {d\omega ^-}{d\omega ^+} \in \operatorname {VMO}(\omega ^+) is equivalent to Ω + \Omega ^+ being a chord-arc domain with inner unit normal belonging to VMO ⁡ ( H n | ∂ Ω + ) \operatorname {VMO}(\mathcal {H}^n|_{\partial \Omega ^+}) .

Colossal Strain Tuning of Ferroelectric Transitions in KNbO3 Thin Films.

Strong coupling between polarization (P) and strain (ɛ) in ferroelectric complex oxides offers unique opportunities to dramatically tune their properties. Here colossal strain tuning of ferroelectricity in epitaxial KNbO3 thin films grown by sub-oxide molecular beam epitaxy is demonstrated. While bulk KNbO3 exhibits three ferroelectric transitions and a Curie temperature (Tc) of ≈676K, phase-field modeling predicts that a biaxial strain of as little as -0.6% pushes its Tc >975K, its decomposition temperature in air, and for -1.4% strain, to Tc >1325K, its melting point. Furthermore, a strain of -1.5% can stabilize a single phase throughout the entire temperature range of its stability. A combination of temperature-dependent second harmonic generation measurements, synchrotron-based X-ray reciprocal space mapping, ferroelectric measurements, and transmission electron microscopy reveal a single tetragonal phase from 10 K to 975K, an enhancement of ≈46% in the tetragonal phase remanent polarization (Pr),and a ≈200% enhancementin its optical second harmonic generation coefficients over bulk values. These properties in a lead-free system, but with properties comparable or superior to lead-based systems, make it an attractive candidate for applications ranging from high-temperature ferroelectric memory to cryogenic temperature quantum computing.

Assessment of the spectral energy of zero-sequence currents in protected feeders with the presence of single-phase to ground fault in the isolated network

Subject of research: methods of relative measurement of higher harmonics for detecting a faulty feeder with a single-phase ground fault. Purpose of research: evaluation of sensitivity of the methodology of faulty feeder search using wavelet transform. Object of research: distribution networks of 6(10) kV. Main results of research: the level of higher harmonics does not affect the performance of the technique, regardless of the point of the fault and the harmonic composition of the load, the damaged connection is the highest value of the spectrum energy.

Equilibrium measures on Julia sets of random quadratic polynomials

Abstract We consider sequences of compositions of quadratic polynomials f c n ( z ) = z 2 + c n . For such sequences one can naturally generalise the definitions of the Julia set and basin of infinity from the autonomous case. In this setting the Julia set depends on a sequence ω = ( c 0 , c 1 , … ) . We study the equilibrium (harmonic) measure on such Julia sets. In particular, we calculate the Hausdorff dimension of the equilibrium measure and study its dependence on the ‘scale of randomnes’.

Out-of-plane polarization induces a picosecond photoresponse in rhombohedral stacked bilayer WSe2.

Constructing van der Waals materials with spontaneous out-of-plane polarization through interlayer engineering expands the family of two-dimensional ferroelectrics and provides an excellent platform for enhancing the photoelectric conversion efficiency. Here, we reveal the effect of spontaneous polarization on ultrafast carrier dynamics in rhombohedral stacked bilayer WSe2. Using precise stacking techniques, a 3R WSe2-based vertical heterojunction was successfully constructed and confirmed by polarization-resolved second harmonic generation measurements. Through output characteristics and the scanning photocurrent map under zero bias, we reveal a non-zero short-circuit current in the graphene/3R WSe2/graphene heterojunction region, demonstrating the bulk photovoltaic effect. Furthermore, the out-of-plane polarization enables the 3R WSe2 heterojunction region to achieve an ultrafast intrinsic photoresponse time of approximately 3 ps. The ultrafast response time remains consistent across varying detection powers, demonstrating environmental stability and highlighting the potential in optoelectronic applications. Our study presents an effective strategy for enhancing the response time of photodetectors.

Measurement Technique for the Absolute Acoustic Nonlinearity Parameter Employing Only a Narrowband Pulser

In the nonlinear ultrasonic technique, the measurement of the absolute acoustic nonlinearity parameter is employed to obtain quantitative material nonlinearity. In the piezoelectric method, this measurement involves two processes: calibration and harmonic measurements. In the calibration process, a transfer function is obtained, and distortion of the propagating wave is measured in the harmonic measurement. In the conventional method for this measurement, a narrowband pulser is typically used for the harmonic measurement, while a broadband pulser is used for the calibration measurement. In this study, we propose a technique that utilizes a narrowband pulser for both harmonic and calibration measurements. First, we introduced the proposed method to measure the transfer function in the calibration measurement employing the narrowband pulser. Then, we compared the results of the transfer functions and the absolute acoustic nonlinearity parameters obtained using both a narrowband and broadband pulser in the calibration. Based on the experimental results, we found that the results obtained using both the proposed and conventional methods are highly similar, confirming the validity of the proposed measurement technique. In conclusion, even though we exclusively employ the narrowband pulser, we can accurately measure the absolute nonlinearity parameter, leading to a reduction in the required measurement equipment.

Harmonics Measurement Errors in Grids with High Presence of Power Electronics Converters

The article presents field results and discusses the harmonic measurement errors of power quality analyzers (PQA) due to sampling aliasing of currents and voltages in grids with the presence of power electronics converters (PEC). The PQA may imply non-existing harmonic components incorrectly depending on the sampling rate of the PQA and the switching frequency of the PEC. Such phenomenon is prone to become more common and unpredictable due to the amplification of high-frequency components in voltages and currents due to interactions between PEC, loads, and grid elements. The conclusion is that PQAs, as required by standards in use currently, are not prepared to identify and quantify, when necessary and correctly, the high-frequency components that are present in modern electric networks with multiple PECs.

Harmonic measure in a multidimensional gambler’s problem

Harmonic measure in a multidimensional gambler’s problem

Processing techniques for metrological improvement of low-cost smart meter hardware solution for IEC 61000-4-7 Class I harmonics measurements

The work investigates the feasibility of harmonic analysis implementation on smart meter microcontroller devices, according to IEC 61000-4-30 Class A and IEC 61000-4-7 Class I requirements. The final aim was to evaluate to what extent Class I harmonic analysis can be integrated into existing low-cost hardware platforms for smart metering, which normally have limited hardware features, especially concerning the ADC and the possibility of varying the sampling frequency with high resolution, according to the power system signal frequency. An extended experimental characterization is carried out on a case study device, aimed at analyzing its performances in terms of both measurement accuracy and computational burden. To increase metrological ADC behavior and decrease computational costs, sampling strategies and optimized interpolation algorithm have been implemented and tested verifying the feasibility of harmonic analysis implementation on smart meter microcontroller devices, according to IEC 61000-4-30 Class A and IEC 61000-4-7 Class I requirements.

Experimental study and techno-economic evaluation of an active fault detection kit in the prospect of future zero energy building installations

This article presents an active fault detection kit, applicable to low voltage single-phase electrical installations, in the prospect of the Zero Energy Building concept, integrating on-site renewable energy generation and energy storage. This simple, flexible, self-powered and compact kit is capable of detecting faults, such as power theft (meter tampering), unintentional islanding and neutral conductor loss. Its operation is based on harmonic voltage injection, in series with the electrical installation, through a low-power H-bridge inverter and a current transformer, along with the corresponding harmonic current measurement, to estimate the impedance and effectively detect faulty conditions; the fast and robust Goertzel algorithm is utilized. Moreover, it features IoT communication capabilities, employing the ESP32 microcontroller, to exchange data and information with the installation meters. The functionality and effective fault detection of the proposed device are validated, through experimental tests on a custom-developed hardware prototype; IoT connectivity and data uploading are experimentally tested and verified, too. Finally, a sustainability assessment study is performed, using the Life Cycle Cost Analysis tool.

Synthesis and crystal structure of acentric anhydrous beryllium carbonate Be(CO3).

The anhydrous alkaline earth metal carbonate Be(CO3) was synthesized in a laser-heated diamond anvil cell at moderate pressures and temperatures (20(2) GPa and 1500(200) K) by a reaction of BeO with CO2. It crystallizes in the acentric, trigonal space group P3121 with Z = 3. The crystal structure was obtained from synchrotron single crystal X-ray diffraction data and confirmed by density functional theory-based calculations in combination with Raman spectroscopy. Second harmonic generation measurements were employed to verify the acentric space group symmetry. The crystal structure of Be(CO3) is characterized by the presence of isolated [CO3]2--groups and BeO4-tetrahedra. This is a new structure type and such a topology has not been observed in carbonates before. Be(CO3) can be recovered to ambient conditions and is not undergoing a phase transition during decompression.

Harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a capacitive voltage transformer

AbstractHarmonic state estimation, which highly depends on accurate synchronised phasors, is a crucial basis for the location, traceability, and governance of harmonics in power systems. However, most existing synchronous phasor measurement units (PMUs) provide power frequency phasors rather than harmonic phasors. In addition, as the dominant voltage signal provider for PMUs in power systems, capacitive voltage transformers (CVTs) have complex frequency responses and cannot be directly used for harmonic measurement. Therefore, accurate harmonic state estimation is difficult to achieve in applications. A method for harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a CVT is proposed. First, the reasons for harmonic voltage measurement errors were analysed. Second, the scattering parameter method was used to measure the wideband voltage transfer characteristics of CVT. Third, a voltage reconstruction method was proposed to improve the measurement accuracy and expand the frequency range of synchronous phasor measurement. Fourth, this method was applied to harmonic state estimation, and the performance of harmonic state estimation before and after voltage reconstruction was quantitatively compared. Results showed that the proposed method can remarkably improve the accuracy of harmonic state estimation. Finally, some factors, such as state observability, complex error disturbances, CVT structure, and harmonic order, influencing the performance of the proposed method were investigated. Results further demonstrated that the method has high accuracy, strong anti‐interference, and adaptability, and can provide basic information for harmonic localisation and traceability.

A reconstruction method for harmonic measurement in distribution networks based on equivalent harmonic source approach

Abstract In recent years, with a large number of nonlinear devices connected to the distribution network, harmonic problems have been inevitably generated during operation, which makes harmonic problems more complex in the distribution network. However, it is important to master the real-time harmonic level of the distribution network for the analysis and management of the harmonic problems in the grid. However, because of economic reasons and decentralized nodes, it is impractical to install a harmonic measurement device at each node in engineering. Moreover, it is important to know how to measure harmonics at important nodes in a distribution network using a limited number of measurement devices. Therefore, a harmonic measurement reconstruction method for distribution networks is proposed based on the equivalent harmonic source method. This method aims to obtain more harmonic source state information with a minimum economic cost. First, a mathematical model of the harmonic currents is established. Subsequently, an equivalent harmonic source method is proposed, and a harmonic reconstruction model based on the equivalent harmonic source method is presented. Finally, an example of an IEEE 14-node distribution network is used to verify the effectiveness of the equivalent harmonic source method.

High harmonic Mach–Zehnder interferometer for probing sub-laser-cycle electron dynamics in solids

High harmonic emissions from crystalline solids contain rich information on the dynamics of electrons driven by intense infrared laser fields and have been intensively studied owing to their potential use as a probe of microscopic electronic structures. In particular, the ability to measure the temporal response of high harmonics may allow us to investigate electron dynamics directly. Here, we demonstrate a Mach–Zehnder high harmonic interferometer, where high harmonics are generated in each path of a Mach–Zehnder interferometer and an interferogram of them is captured. The high harmonic interferometer allows us to detect high harmonic signals with higher sensitivity than conventional high harmonic intensity measurements, and achieve a relative time resolution between the target and reference high harmonics of less than 150 attoseconds, which is sufficient to track sub-cycle dynamics of electrons in solids. Using high harmonic interferometry, we succeeded in capturing the real time dynamics of Floquet states in WSe2, whose indirect signature has so far been caught only by time-averaged measurements. Our simple technique could enable to access attosecond electron dynamics in solids.

Field Harmonic Measurement of High-Gradient Permanent Magnet Quadrupoles for NSLS- II Upgrade

Field Harmonic Measurement of High-Gradient Permanent Magnet Quadrupoles for NSLS- II Upgrade

Harmonic voltage measurement based on capacitive equipment dielectric equivalent model and responding current

Abstract With the increasing proportion of new energy and the power electronic equipment in the power grid, accurate measurement of harmonic voltage has become increasingly important for power quality monitoring. In order to solve the problem of high-precision measurement of harmonic voltage in the power grid, this manuscript proposes a high-precision harmonic voltage measurement method based on the dielectric equivalent model (DEM) of capacitive equipment and its responding current. Based on DEM, a voltage-current transfer function of the capacitive device is established, and harmonic voltage is reconstructed with the responding current. Considering the dielectric relaxation characteristics of capacitive device other than a pure capacitor model, this manuscript analyzes the fitting performance of different equivalent capacitance models and improves the traditional pure capacitance model to a more suitable DEM for harmonic voltage reconstruction. The DEM parameters of capacitive devices are obtained through the frequency domain spectroscopy (FDS) and intelligent parameter identification algorithms, which improved the measurement accuracy of harmonic voltage and reduced computational complexity. The harmonic voltage testing platform is established to test the simulated high-voltage harmonics and the harmonic voltage of the actual grid voltage. The results show that the proposed harmonic voltage measurement method can meet the high-precision reconstruction of harmonic voltage in the frequency range of 50~2500Hz, and the system testing error with sensors is less than 2%. The testing accuracy is higher than traditional voltage transformers and testing systems based on pure capacitance models.

The High-Order Corrections of Discrete Harmonic Measures and Their Correction Constants

The High-Order Corrections of Discrete Harmonic Measures and Their Correction Constants

Geometric Description of Some Loewner Chains with Infinitely Many Slits

We study the chordal Loewner equation associated with certain driving functions that produce infinitely many slits. Specifically, for a choice of a sequence of positive numbers (bn)n≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(b_n)_{n\\ge 1}$$\\end{document} and points of the real line (kn)n≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(k_n)_{n\\ge 1}$$\\end{document}, we explicitily solve the Loewner PDE ∂f∂t(z,t)=-f′(z,t)∑n=1+∞2bnz-kn1-t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\dfrac{\\partial f}{\\partial t}(z,t)=-f'(z,t)\\sum _{n=1}^{+\\infty }\\dfrac{2b_n}{z-k_n\\sqrt{1-t}} \\end{aligned}$$\\end{document}in H×[0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {H}\ imes [0,1)$$\\end{document}. Using techniques involving the harmonic measure, we analyze the geometric behaviour of its solutions, as t→1-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\rightarrow 1^-$$\\end{document}.

Electric field induced second harmonic generation in arsenic sulfide deposited by thermal evaporation.

Electric field induced second harmonic (EFISH) measurements are performed on thin films of arsenic sulfide deposited on chromium coated fused silica substrates by thermal evaporation of amorphous As2S3 bulk material. EFISH allows to widely tune the second-order optical susceptibility (χ(2)). An observed shift of the minimum of the second harmonic generation (SHG) intensity away from 0 V reveals a non-EFISH bulk χ(2), which is unexpected for amorphous materials. Additional SHG measurements on as-deposited films for investigation of the non-EFISH bulk χ(2) show Maker fringe patterns. Analyzing them and calibrating the SHG response against beta barium borate (BBO) crystal allows us to extract the components of the χ(2) tensor. The main component of this non-EFISH bulk χ(2) has a value of ∼0.22 pm/V. By increasing the χ(2) by applying the dc electric field a maximum value of 3.8 pm/V was achieved in EFISH measurements. This value is comparable to the χ(2) of traditional nonlinear crystals, e.g., BBO, which makes arsenic sulfide an interesting candidate for nonlinear hybrid structures.

To Evaluate the Degradation of Heat Damaged Concrete Specimens after Curing Using Non-Linear Ultrasound Technique

In this research, Non-linear Ultrasound (NLU) technique was used to evaluate the degradation on heat damaged cement mortar specimen behaving explicit nonlinear. Mortars of Portland cement type I (or normal cement, NC) were chosen to mold the specimens with water cement ratios of 0.4, 0.5 and 0.6, and size of 5x5x5cm-cube and 5x5x2cm-brick. The specimens were grouped for heating at different temperatures (30, 200, 300, 400, 600, 800℃ for 24 hours) to create degradations of different levels. After curing process in water for 28 days, mechanical property tests were carried out on each cube to get its stress-strain relation and strength. NLU tests were conducted on the brick specimens. The RITEC SNAP System with 250kHz/transmit and 500kHz/receive transducers was used to conduct the measurement of harmonics. The obtained amplitudes in spectrum of fundamental, 2nd and 3rd harmonics (A1, A2 and A3) and the amplitudes due to the background nonlinearity by facility (A01, A02 and A03) were analyzed to approach the nonlinear parameters for each specimen, such as the β and γ. The [(A01- A1),(A03/A 3 2 01 -A3/A13)] and[(A01-A1), |A02/A01 -A2/A12|] were applied as a nonlinear characteristic index to mark the quality of the microstructure of material, which could be related to the durability and workability of the material. The results showed a promised quantification method using NLU. Extended application can be expected.