High-order Harmonic Resonance Research Articles

High-Order Harmonic Elimination and Resonance Damping Based on Inductive-Filtering Transformer for Electrified Railway Transportation System

This article focuses on the high-frequency resonance and harmonic elimination in the electrified railway transportation system. The high-order harmonic currents, which are generated by the grid-side converter in the locomotives' drive system, will inject into the traction power supply system (TPSS). These injected harmonic currents are harmful to electrical equipment along the transmission line in the TPSS, causing vibration, overheating, increased losses of the traction transformer, and deteriorating the power quality of TPSS. Even worse, these harmonics can be amplified in the locomotive-TPSS coupling system when their frequency matches the inherent frequency of TPSS, resulting in system resonance. To absorb the high frequency and avoid the resonance phenomenon, an inductive-filtering-based onboard traction transformer (IFTT) is proposed. The IFTT is designed for the restricted installation space by adding extra filtering windings to a convention onboard traction transformer. A detailed design process of the harmonic low-impedance loop is provided, which is the precondition of inductive filtering. Simulation and experimental results are shown to verify the feasibility of the proposed method.

Influence of the Catenary Distributed Parameters on the Resonance Frequencies of Electric Railways Based on Quantitative Calculation and Field Tests

High-order harmonic resonance is a key issue in the traction power supply systems (TPSS) of electric railways for safe operation. The effective evaluation of the resonance frequency is critical for taking measures to suppress harmonic resonance. In this paper, the influence of the distributed parameters of traction networks on resonance frequencies based on accurate calculation is proposed. The quantitative assessments of the distributed impedance and admittance are investigated. Furthermore, the theoretical calculation is directly verified using field tests at a high voltage level equal to 25 kV. The results show that the resonance frequencies of the TPSS are mainly affected by the distributed parameters, including the self-admittance and self-impedance of the contact wires, and the self-admittance of the positive feeders. In addition, the admittance connected in parallel has a greater effect than the series-connected impedance. The calculation method is also adapted to TPSS connected to renewable energy.

Long period fibre gratings inscribed by sinusoidal intensity modulated femtosecond laser

To the best of our knowledge, this is the first study to propose and verify a novel and simple direct inscription method for long-period fibre gratings (LPFGs) with an arbitrary grating period using a sinusoidal intensity modulated femtosecond laser. This method induces a sine refractive index modulation, which makes the LPFGs have no higher-order harmonic resonance that exists in the normal square-wave modulation method. This is beneficial for reducing the insertion loss of the LPFGs and optimising the transmission spectrum. Using this method, we also conveniently realise the inscription of superimposed, apodised, and chirped LPFGs. This work presents a simple but effective inscription scheme for various types of LPFGs using a femtosecond laser.

Geometric phase and non-adiabatic resonance of the Rabi model

We investigate the effects of counterrotating terms on geometric phase and its relation to the resonance of the Rabi model. We apply the unitary transformation with a single parameter to the Rabi model and obtain the transformed Hamiltonian involving multiple harmonic terms. By combining the counter-rotating-hybridized rotating-wave method with time-dependent perturbation theory, we solve systematically time evolution operator and then obtain the geometric phase of the two-level system. Our results are beyond adiabatic approximation and rotating-wave approximation (RWA). Higher-order harmonic resonance happens when driving frequency is equal to higher-order subharmonic of the Rabi frequency. In comparison with numerically exact results, our calculated results are accurate over a wide range of parameters space, especially in higher-order harmonic resonance regimes. In these regimes we demonstrate geometric phases change dramatically while those of the RWA are smooth. The RWA is thoroughly invalid even if the driving strength is extremely weak. We find it is the higher-order harmonic terms that play an important role on the cyclic state and demonstrate the characters of geometric phase in higher-order harmonic resonance regime. We also present analytical formalism of the change rate of geometric phase and quasienergies, which agree well with numerically exact ones even in the strong driving case. The developed method can be applied to explore the dynamics of strongly driven qubits and physical properties of higher-order harmonic processes.

Field Tests for Evaluating the Inherent High-Order Harmonic Resonance of Traction Power Supply Systems Up to 5000 Hz

The inherent resonant frequency of a traction power supply system (TPSS) needs to be accurately identified in order to provide crucial information for resonance suppression, safe operation, and system optimization of electrified railways. In this paper, implementation of experiments was carried out in actual railway systems to evaluate the inherent harmonic resonances of the TPSS. The field tests were based on a harmonic generator (HG) constructed with cascaded H-bridge converters (CHBCs). Compared to other experimental setups, the field tests of this paper, which were performed in the 25kV practical system, can provide straightforward results in a wide frequency range up to 5000 Hz. Such a wide frequency range is necessary for assessing and taking effective measures to address the harmonic resonance problem. The results of this paper will supply valuable data for the modeling of TPSSs and the stability analysis of train converters contributing to improvement of the power quality of electric railways.

Assessing High-Order Harmonic Resonance in Locomotive-Network Based on the Impedance Method

Many new types of locomotives are put to use in electric railway systems, resulting in instability problems such as high-order harmonic resonance occurring as a consequence of the interaction between the electrical locomotive (including electrical multiple units) and the traction network. In order to investigate this problem, this paper adopts the impedance-based approach to analyze the stability properties of the system interaction. The detailed impedance of the traction network is obtained by taking its distributed parameters into account. Then the locomotive converter with single-phase transient current control algorithm (TCCA), which can represent the locomotive when performing the impedance-based stability analysis, is modeled as the dq-frame impedance by single-phase dq decomposition. By plotting bode diagrams of the impedance for the traction network and the locomotive separately, and calculating the phase margin at the intersection point of the magnitude of the two impedances, the stability of the locomotive-network system is evaluated and thus the high-order harmonic resonance can be predicted. Moreover, a time-domain model of locomotive-network systems is established in this paper, which can reproduce the high-order harmonic resonance in the time domain as a first validation step of the analysis. Finally, a field test in a traction substation of the Beijing-Harbin Railway is carried out to finally validate the effectiveness of the proposed method. The stability analysis method in this paper is simple and effective without the need for a complex calculation of some norms or Eigenvalues. As a result, the high-order harmonic resonance can be predicted before a new type of locomotive is put into use.

Resonant frequency identification based on harmonic injection measuring method for traction power supply systems

Accidents related with high-order harmonic resonance seriously threaten the safety and stable operation of traction power supply systems (TPSSs). Generally, the resonant frequency of a TPSS, which is the crucial information for resonance suppression, cannot be accurately obtained through model-based methods due to the TPSS complexity. This study proposes a direct measuring method that harmonic currents at different frequencies and amplitudes are injected into the TPSS by a harmonic generator (HG). Then, the resonant frequency can be identified by measuring the harmonic response. The HG based on a single-phase cascaded H-bridge converter and its control algorithms are developed. Both simulations on a railway system model and experimental results on an equivalent resonant circuit are carried out to validate the feasibility and effectiveness of the proposed method.

Design and Analysis of Ag-<formula formulatype="inline"><tex Notation="TeX">${\rm Fe}_{3} {\rm O} _{4}$</tex> </formula> Films as a Multi-Harmonic Suppressor in Wideband Bandpass Filters

This letter proposes a novel method of designing wideband bandpass filters (BPFs) that contain high-frequency harmonic suppression. Ag-Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> films are used as harmonic suppression materials in such filters to replace the current general suppressing circuits. The wideband BPF can be designed using distributed highpass filters are equipped with two short-circuited stubs, and Ag-Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> films are combined with the harmonic suppression mechanism. Several high-order harmonic resonance bands may be suppressed using a wide stopband by adjusting the thickness of the Ag-Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> films appropriately. The stopband of the proposed wideband BPF is extended to 20 GHz, which result in a rejection level higher than 15 dB.

2309 Vibration Affected by Contact Radius and Sinusoidal Wavy Workpiece to Explain Initial Resonance Growth in Turing

Before occurrence of self-excited chatter, initial resonance has to be grown in turning. In this study, despite external forced vibration, we explain occurrence and growth of SDoF tool oscillation from the trajectory of the tool nose contacting with wavy cylindrical workpiece. By regarding the deviation of the workpiece as a simple sinusoidal function and local contact of the tool with finite radius, we showed the trajectory excites the oscillator under high-order harmonic resonance conditions. The amplitude of the resonance is affected from local contact radius against that of workpiece. From damping effect these resonance conditions are expanded. The growth of the initial resonance would cause either forced or self-excited chatters in afterwards. The occurrence of chatter during wear and the existence of ultra-precision machining are explained from these properties.

Simple-structured capillary-force-dominated tunable-focus liquid lens based on the higher-order-harmonic resonance of a piezoelectric ring transducer

This paper proposes a tunable-focus liquid lens implemented with a simple cylindrical container structure and liquid as the lens material. The cylindrical container was constructed using a Pb [Zr(0.52)Ti(0.48)]O(3) (PZT) ring transducer and a polydimethylsiloxane membrane that was attached to a flat side of the transducer. The free surface of the liquid in the cylindrical container can be driven as a static-like convex lens with different curvatures because the higher-order harmonic resonance of the PZT transducer was electrically controlled. Based on a capillary-force-dominant design, the activated liquid lens maintained surface curvature in an arbitrary orientation without a gravitational effect. Profiles of the liquid lenses were characterized with the driving voltages of the transducer ranging from 12 to 60 V peak-to-peak (Vpp) at a resonant frequency of 460 kHz. The temperature effects on the lenses caused by the continuous operation of the transducer were measured. Images showed the various curvatures of the lenses with a range of actuation voltages. A change in focal length of eight times (5.72 to 46.03 cm) was demonstrated within the 10 Vpp variation of the driving voltage. For the characterized liquid lenses, the distortion was less than 2%, and the modulation transfer function reached 63 line pairs per mm (lp/mm) using ZEMAX analysis.

Calculation of high-order harmonic generation spectrum and Floquet resonance states using the dynamical symmetry

The Floquet resonance states of a periodically driven system are obtained using a special weighted power method which forces the dynamical symmetry into regular wave propagation methods. We demonstrate the utility of this method for the calculation of high harmonic generation spectra in rare gases. By using this method the resonance Floquet state which dominates the spectrum is obtained directly at a low computational cost. This may allow the calculation of resonance Floquet states in parameter regimes not accessible before. Implementation involves only slight adjustments to the standard wave propagation codes. The method's unique advantage is explained and demonstrated.

Guided-Wave EO Intensity Modulator Using Coupled Microstrip Line Electrode of Higher-Order Harmonic Resonance Combined with Polarization-Reversed Structure

A novel structure of a resonator type guided-wave electrooptic intensity modulator is introduced that uses a higher-order harmonic resonant electrode of coupled microstrip lines combined with polarization-reversed structure. The light modulation cancellation caused by the light transit-time effect in the resonant electrode, which is longer than the wavelength of the standing wave, is compensated for to enhance modulation efficiency. The modulator for 26 GHz operation was designed and fabricated with a LiTaO 3 substrate. The modulation electrode is 9.03 mm long for seventh order harmonic resonance by RF signal. The workability of the modulator was confirmed by experiments with 1.3 μm wavelength light.

PZT bimorph actuated atomizer based on higher order harmonic resonance and reduced operating pressure

This paper presents the design, fabrication and testing of a PZT bimorph actuated atomizer. The atomizer with the size of 43 mm × 37 mm × 7 mm is composed of a PZT bimorph actuator, which is sandwiched by top and bottom flow channel plates and cover shields. The micronozzle plate is attached onto the top cover shield. UV laser machining and micro electrical discharge machining (μEDM) are applied to fabricate the micronozzles with different geometry. The experimental results indicate that we can justify the frequency response of flow rate by acoustic pressure analysis. The peak flow rates occur at higher order resonances, and the operating pressure is less than 0.1 MPa, which is much lower than that of existing atomizers. Also, the influence of flow rate by changing the distance between the PZT bimorph and the nozzle plate, as well as the flat plate on the bottom cover shield are discussed. The maximum flow rate of 8 ml/min is obtained by using the μEDM-made micronozzle plate, when the atomizer is driven with square pulses at 7 kHz with 50% duty cycle and 27 V peak-to-peak.

Clarification and measurements of high frequency harmonic resonance by a voltage sourced converter

This work presents the clarification and measurements of a high-order harmonic resonance phenomenon for voltage sourced converters. When a voltage sourced converter is connected to a power system through a cable, there is a possibility that small, high frequency, harmonic voltages due to the converter are magnified by series and parallel resonances. The cause of the high-order harmonic resonance is investigated and clarified in this paper by analysis using EMTP. It is shown that this high frequency phenomenon can be strongly attenuated and will not cause any problems in a field installation if measures are taken a priori to avoid its impacts. Additionally, the phenomenon is verified by field tests of an actual installation showing that high-order harmonic resonance can occur and is a practical matter to be dealt with. The measurements for the resonance phenomenon are included in this paper. Furthermore, it is shown that this high-order harmonic resonance can be predicted by power system analysis in advance. The procedure of the analysis is investigated and presented here.

Resonant electrode guided-wave electro-optic phase modulator using polarisation-reversal structures

Guided-wave electro-optic phase modulators with long resonant electrodes and polarisation reversals are proposed and experimentally demonstrated. Adopting polarisation-reversal structures to electro-optic modulators with standing-wave resonant electrodes operated in a higher-order harmonic resonance mode, high-efficiency optical modulation is obtained by compensation of the transit-time effect.

A Study for High-Order Harmonic Resonance Phenomena of Voltage Sourced Converter in Cable System

This paper presents high-order harmonic resonance phenomena of voltage sourced converter (VSC). When a voltage sourced converter is connected to power system with cables, there is possibility that minute high-order harmonic voltages of a voltage sourced converter are magnified by a series resonance and a parallel resonance, and high-order harmonic resonance phenomena are found by this study. The cause of high-order harmonic resonance phenomena is investigated and figured out by the analysis using EMTP. In addition, it is verified that high-order harmonic resonance phenomena occur as a practical matter.

High-order harmonic resonance phenomena of a voltage-sourced converter in cable system

This paper presents high-order harmonic resonance phenomena of voltage-sourced converters (VSC). When a voltage-sourced converter is connected to a power system with cables, there is a possibility that minute high-order harmonic voltages of a voltage-sourced converter are magnified by a series resonance and a parallel resonance, and high-order harmonic resonance phenomena are determined by this study. The cause of high-order harmonic resonance phenomena is investigated and elucidated by the analysis using EMTP. In addition, it is verified that high-order harmonic resonance phenomena occur as a practical matter. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(3): 26–35, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20054

Higher order harmonic resonance of electrons with electromagnetic waves propagating through magnetoplasma

The effect of higher order cyclotron harmonic resonance of electrons with the propagating electromagnetic wave through the magnetoplasma is considered. It is shown that the synchronous energy gain for m=1 and n=1 becomes oscillatory at higher harmonics (m not=1,n=D). The expressions for the time period of energy oscillations and maximum energy gain during an oscillation are derived. The nature of pseudo-potential, maximum energy gain and the time period of energy oscillation are shown graphically.