Harmonic State Research Articles

Power Quality State Estimation for Distribution Grids Based on Physics-Aware Neural Networks—Harmonic State Estimation

In the transition from traditional electrical energy generation with mainly linear sources to increasing inverter-based distributed generation, electrical power systems’ power quality requires new monitoring methods. Integrating a high penetration of distributed generation, which is typically located in medium- or low-voltage grids, shifts the monitoring tasks from the transmission to distribution layers. Compared to high-voltage grids, distribution grids feature a higher level of complexity. Monitoring all relevant nodes is operationally infeasible and costly. State estimation methods provide knowledge about unmeasured locations by learning a physical system’s non-linear relationships. This article examines a new flexible, close-to-real-time concept of harmonic state estimation using synchronized measurements processed in a neural network. A physics-aware approach enhances a data-driven model, taking into account the structure of the electrical network. An OpenDSS simulation generates data for model training and validation. Different load profiles for both training and testing were utilized to increase the variance in the data. The results of the presented concept demonstrate high accuracy compared to other methods for harmonic orders 1 to 20.

Time-domain harmonic state estimation of three-phase power networks including wind generation sources

Time-domain harmonic state estimation of three-phase power networks including wind generation sources

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.

Harmonic State Estimation in Power Systems Using the Jaya Algorithm

The increasing use of nonlinear loads in power systems introduces voltage and current components at non-fundamental frequencies, leading to harmonic distortion, which negatively impacts electrical and electronic devices. A common mitigation strategy involves identifying harmonic sources and installing filters nearby. However, due to the high cost of power quality (PQ) meters, comprehensive harmonic level monitoring across the entire power system is impractical. To address this, various methodologies for Harmonic State Estimation (HSE) have been developed, which estimate distortion levels on unmonitored system buses using data from a minimal set of monitored ones. Many HSE techniques rely on optimization algorithms with numerous tuning parameters, complicating their application. This paper proposes a novel methodology for fundamental frequency power flow and harmonic state estimation using the Jaya algorithm, which is characterized by fewer tuning parameters for easier adjustment. It also introduces a strategy to determine the minimal number of buses that need monitoring to achieve system observability. The methodology is validated on the IEEE-14 and IEEE-30 bus systems, demonstrating its effectiveness. The results of the proposed methodology are compared with those obtained using Evolutionary Strategies (ESs), highlighting its enhanced accuracy and computational efficiency.

Confinement Effects of Two-dimensional Surfaces on Water Adsorption and Dissociation over Pt(111).

It has been established that the confined space created by stacking a two dimensional (2D) surface atop a metal catalyst serves as a nano-reactor. According to recent research, when a graphene (Gr) overlayer encloses a Pt catalyst from above, the activation barrier for the water dissociation reaction, a process with major industrial significance, decreases. In order to investigate how the effect of confinement varies among different two-dimensional (2D) materials, we study the adsorption and dissociation barriers of water molecule on Pt(111) under graphene, hexagonal boron nitride (h-BN), and heptazine-based graphitic carbon nitride (g-C3N4) layers using density functional theory calculations. Our findings reveal that the strength of adsorption does not decrease consistently with a reduction in the height of the 2D overlayer. Furthermore, a smaller barrier is not always the consequence of poorer adsorption of the reactant. We also examine the effect of confinement on the shape of the reaction path, on the frequencies of vibrational modes, and on the rate constants derived using the harmonic transition state theory. Overall, all three of the 2D surfaces cause a decrease in barrier height and a weakening of adsorption, though to differing degrees due to a mix of mechanical, geometric and electronic variables.

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.

Flat-topped optical spectrum as a specific marker of multi-pulse grouping in a soliton fiber laser.

We report the experimental observation of a stable generation regime in a soliton fiber laser, characterized by a distinct flat-topped optical spectrum. Notably, in multi-pulse generation, this specific spectrum shape prevents the harmonic mode-locking state, instead connecting the solitons into bound complexes or tight chaotic bunches. Physically, this suggests that in the observed regime, long-range attractive forces dominate over the inter-pulse repulsion across the entire laser cavity. Our experimental findings align with numerical simulations, which demonstrate that the predominance of a long-range inter-pulse attraction is due to a complex interaction mechanism. This mechanism combines the generation of dispersive waves with dissipative forces arising from gain depletion and recovery.

Plasmon‐Enhanced Circular Polarization High‐Harmonic Generation from Silicon

AbstractHigh harmonics of circular polarization can be directly generated by monochromatic circularly polarized incident light owing to the high density and stable structure of crystal media. If the arrangement of multiple coplanar atoms in the unit structure of the crystal exhibits rotational symmetry, the polarization state of the high harmonics generated from the crystal follows specific selection rules that have been observed in the 2D crystal medium. In addition, the geometric symmetry of the coplanar atom distribution is related to the orientation of cubic crystals. This implies that only the polarization along a specific crystal orientation can achieve a selection of high‐harmonic polarization states. However, this is a very weak process in cubic crystals owing to the attenuation of crystal anisotropy to circularly polarized light and the dependence of the electron transition rate on the crystal orientation. In this study, plasmonic nanoantennas are designed on silicon crystal films to enhance this process. The harmonic emission is more than ten times brighter than that without nanoantennas and conformed to the selection rules for high harmonics. The research results offer a new approach for deep­ultraviolet space filtering, carrier control, and the development of compact extreme­ultraviolet light sources.

Generation of squeezed high-order harmonics

For decades, most research of high harmonic generation (HHG) considered matter as quantum but light as classical. Recently, HHG driven by quantum states of light such as bright squeezed vacuum was predicted to reach beyond the classical HHG cutoff. Moreover, in squeezed coherent illumination, it was shown that the underlying dynamics are significantly modified by the photon statistics effective force. Here we show that HHG driven by quantum light results in quantum high harmonics. We derive a formula for the quantum state of the high harmonics, when driven by arbitrary quantum light states, and then explore specific cases of experimental relevance. Specifically, for a moderately squeezed pump, HHG driven by squeezed coherent light results in squeezed high harmonics. Harmonic squeezing is optimized by syncing ionization times with the pump's squeezing phase. Beyond this regime, as pump squeezing is increased, the harmonics initially acquire squeezed thermal photon statistics, and then occupy an intricate quantum state which strongly depends on the semiclassical nonlinear response function of the interacting system. Our results pave the way for generation of squeezed extreme-ultraviolet ultrashort pulses, and more generally, quantum frequency conversion into previously inaccessible spectral ranges, which may enable ultrasensitive attosecond metrology. Published by the American Physical Society 2024

Quantum gravity signatures in gravitational wave detectors placed inside a harmonic trap potential

In this work, we consider a general gravitational wave detector of gravitational waves interacting with an incoming gravitational wave carrying plus polarization only placed inside a harmonic trap. This model can be well acquainted with the description of a resonant detector of gravitational waves as well. The well-known detector-gravitational wave interaction scenario uses the method of a semiclassical approach where the detector is treated quantum mechanically but the gravitational wave is considered at a classical level. In our analysis, we use a discrete mode decomposition of the gravitational wave perturbation which results in a Hamiltonian involving the position and momentum operators corresponding to the gravitational wave and the harmonic oscillator. We have then calculated the transition probability for the harmonic oscillator-gravitational wave tensor product state for going from an initial state to some unknown final state. Using the energy flux relation of the gravitational waves, we observe that if we consider the total energy as a combination of the number of gravitons in the initial state of the detector then the transition probability for the resonant absorption case scenario takes the analytical form which is exactly similar to the semiclassical absorption case. In the case of the emission scenario, we observe a spontaneous emission of a single graviton which was completely absent in the semiclassical analog of this model. This therefore gives a direct signature of linearized quantum gravity. Published by the American Physical Society 2024

Explicit n-particle harmonic oscillator states in products of SU(1,1) representations

In this paper, we present a simple algorithm for the explicit construction of [Formula: see text]-particle harmonic oscillator states simultaneously belonging to irreducible representations of [Formula: see text] (or [Formula: see text]) and [Formula: see text]. For degenerate representations, the construction can be done using generating functions or hyperspherical harmonics. The cases with [Formula: see text] and [Formula: see text] are investigated at greater length. The analysis is extended to nondegenerate states, although the states are not so easily obtained as in the degenerate case. Finally, we briefly touch on the [Formula: see text] structure of Bell states.

Harmonic State-Space Modeling and Closed-Loop Control of Single-Stage High-Frequency Isolated DC–AC Converter

The port harmonic features of the single-phase single-stage high-frequency isolated dc-ac converter is not analyzed so far and the corresponding theoretical basis for improving the current quality is still a research gap. In this paper, a linear model in frequency domain of the single-stage high-frequency isolated dc-ac converter is originally derived based on the combined harmonic state space and extended description function modeling technique. The systematic modeling process is analyzed and the accuracy of the modeling is verified by the simulation results. Combined with the model analysis, the harmonic coupling characteristics between the ac side and the dc side are clearly presented. On this basis, this paper proposes a closed-loop control strategy to reduce the decrease of the dc-side and ac-side current quality caused by the harmonic coupling at the control level. Furthermore, this paper constructs the compound controllers based on the P-type iterative learning to suppress the harmonic currents of the dc side and the ac side, respectively. The composite controller does not distinguish the harmonic frequency. Hence, the proposed controller achieves the effective suppression of the harmonic currents in real time. The effectiveness and feasibility of the proposed control strategy are verified by the experiments.

Harmonic Interaction Analysis of Inverters Based on Harmonic State-Space Model Considering Dead-Zone Effect

In the context of increasing device switching frequencies year by year, non-ideal factors such as dead-zone effects in inverters not only cause output waveform distortion, but also generate harmonics that make the interaction between inverters and power grids more complex. In order to accurately describe and analyze this phenomenon and establish a more practical grid-connected inverter model, this paper proposes and establishes a three-phase LCL grid-connected inverter harmonic state space model that considers dead-zone effects. By incorporating dead-zone effects into the modeling process, the system transfer function matrix is derived to quantify the harmonic interaction coefficient between the inverter and the power grid, and the influence mechanism of dead-zone effects on the harmonic interaction process at high switching frequencies is analyzed in depth. The necessity of considering dead-zone effects is illustrated through simulation, and the effectiveness and accuracy of the inverter HSS model considering the effects of dead-zone effects are verified through experiments.

Real-time harmonic state estimation of power systems using optimal placement of measurement devices through RT-LAB implementation

Real-time harmonic state estimation of power systems using optimal placement of measurement devices through RT-LAB implementation

Period-multiplying pulses generation by total self-mode-locking of Nd:YVO4 lasers

We experimentally demonstrated the phenomenon of period-multiplying pulses in the self-mode-locking Nd:YVO4 laser. With a fixed cavity length of 50 mm and the input mirrors in the resonator with radii of curvature of 100 mm, 200 mm, and 500 mm, the mode-locked pulses with pulse periods 4 times, 6 times and 10 times the fundamental mode-locked pulse period are observed respectively. Besides, by tilting the angle of the output mirror to control the spatial distribution of transverse modes, the switching between the period-multiplication state and its harmonic self-locking state can be achieved. Numerical simulations further confirm that this period-multiplying phenomenon results from the simultaneous locking of multi-longitudinal and multi-transverse modes. This study is of great significance for understanding the complex transverse dynamics in the self-mode-locking lasers.

A quantum mechanical example for Hodge theory

On the basis of (i) the discrete and continuous symmetries (and corresponding conserved charges), (ii) the ensuing algebraic structures of the symmetry operators and conserved charges, and (iii) a few basic concepts behind the subject of differential geometry, we show that the celebrated Friedberg-Lee-Pang-Ren (FLPR) quantum mechanical model (describing the motion of a single non-relativistic particle of unit mass under the influence of a general spatial 2D rotationally invariant potential) provides a tractable physical example for the Hodge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism where the symmetry operators and conserved charges lead to the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. We concisely mention the Hodge decomposition theorem in the quantum Hilbert space of states and choose the harmonic states as the real physical states of our theory. We discuss the physicality criteria w.r.t. the conserved and nilpotent versions of the (anti-)BRST and (anti-)co-BRST charges and the physical consequences that ensue from them.

A Novel Series 24-Pulse Rectifier Operating in Low Harmonic State Based on Auxiliary Passive Injection at DC Side

To reduce the current harmonics on the input side of a multi-pulse rectifier, this paper proposes a low harmonic current source series multi-pulse rectifier based on an auxiliary passive injection circuit at the DC side. The rectifier only needs to add an auxiliary passive injection circuit on the DC side of the series 12-pulse rectifier, which can change its AC input voltage from 12-step waves to 24-step waves. We analyzed the working mode of the rectifier, optimized the optimal turn ratio of the injection transformer from the perspective of minimizing the total harmonic distortion (THD) value of the input voltage on the AC side, and analyzed the diode open circuit fault in the auxiliary passive injection circuit. Test verification shows that, after using the passive harmonic injection circuit, the THD value of the input voltage of the AC side of the rectifier is reduced from 14.03% to 4.86%. The THD value of the input current is reduced from 5.30% to 2.16%. The input power factor has been increased from 98.86% to 99.83%, and the power quality has been improved.

Passively harmonic mode-locked erbium-doped fiber lasers based on PbSnS2 saturable absorbers

The two-dimensional (2D) material PbSnS2, a type of transition metal dichalcogenides (TMD), is a highly anisotropic layered compound with potential applications in ultrafast optics. We prepared PbSnS2 nanosheets by liquid phase exfoliation, attached them to microfibers to fabricate saturable absorbers (SAs) by optical deposition method, and successfully applied them to a passive erbium-doped fiber laser (EDFL). In addition, the saturable absorption properties of PbSnS2-based SA were confirmed using a balanced two-detector measurement system. The results demonstrate that the PbSnS2-based SA can realize different stable mode-locked states in the same EDFL cavity, including fundamental frequency conventional soliton and 15th harmonic mode-locked states. Among them, the laser produced fundamental frequency mode-locked state with a signal-to-noise ratio of 59.51 dB (6.58 MHz repetition frequency). The HML pulse with a maximum repetition frequency of 98.71 MHz (corresponding to the 15th harmonic) was obtained. The results demonstrate that PbSnS2 is a candidate material for generating ultrafast pulses and has excellent potential for application in ultrafast lasers.

Sculpting harmonic comb states in terahertz quantum cascade lasers by controlled engineering

Optical frequency combs (OFCs), which establish a rigid phase-coherent link between the microwave and optical domains of the electromagnetic spectrum, are emerging as key high-precision tools for the development of quantum technology platforms. These include potential applications for communication, computation, information, sensing, and metrology and can extend from the near-infrared with micro-resonator combs, up to the technologically attractive terahertz (THz) frequency range, with powerful and miniaturized quantum cascade laser (QCL) FCs. The recently discovered ability of the QCLs to produce a harmonic frequency comb (HFC)—a FC with large intermodal spacings—has attracted new interest in these devices for both applications and fundamental physics, particularly for the generation of THz tones of high spectral purity for high data rate wireless communication networks, for radio frequency arbitrary waveform synthesis, and for the development of quantum key distributions. The controlled generation of harmonic states of a specific order remains, however, elusive in THz QCLs. Here, and by design, we devise a strategy to obtain broadband HFC emission of a pre-defined order in a QCL. By patterning n regularly spaced defects on the top surface of a double-metal Fabry–Perot QCL, we demonstrate harmonic comb emission with modes spaced by an (n+1) free spectral range and with an optical power/mode of ∼270µW.

Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates

We investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.