Harmonic Resonance Conditions Research Articles

Steady-state interfacial gravity waves with one-dimensional class-IV triad resonance

Steady-state interfacial waves under a one-dimensional (1-D) class-IV exact triad resonance are investigated in a two-layer fluid with a free surface upper boundary. Four groups (G1–G4) of convergent series solutions are obtained by the homotopy analysis method. Though the harmonic resonance conditions are contained in the class-IV resonance criteria, the influences of 1:2 harmonic resonances on the energy spectrum could be neglected. Unlike former steady-state resonant interfacial wave spectrum where all the components joining the resonance are significant, the energy of one primary component can be ignored for two groups (G2 and G4) of wave solutions obtained in this paper. It is found that a little energy induced from the external environment might greatly change the energy spectrum for G1. However, the energy introduced from the outside cannot vary the wave energy distribution for G2. The reason for the extremely high crests on the instantaneous profiles of free surfaces of G2 and G4 is that the peaks of the class-IV exactly resonant and some trivial components momentarily overlap at some special horizontal positions. The class-IV exact triad resonance curve could be divided into four pieces containing the existence ranges of G3 and G4 and two regions with no solution found. One of the regions without convergent solutions results from an infinite number of singularities or small divisors caused by infinite exact or near resonances. Our results indicate that steady-state interfacial waves with class-IV triad resonance interactions among one surface and two internal wave modes could exist.

Optimal allocation of power quality monitors considering short-duration voltage variations and parallel harmonic resonance conditions in power distribution systems

The proposed allocation methodology of Power Quality Monitors (PQMs) allows optimal monitoring of short-duration voltage variations and potential harmonic resonance conditions by defining strategic nodes in a Power Distribution System (PDS). The allocation methodology combines the Fault Position Method (FPM) and Harmonic Resonance Modal Analysis (HRMA) to obtain a binary covering matrix. The optimization process lately uses this matrix to determine the best installation nodes of the minimum number of PQMs that observe the considered power quality disturbances. From FPM, the remaining nodal voltages are studied for different short-circuits, which cause voltage sags and or swells. HRMA is used to calculate the modal impedances related to the critical modes and identify the respective harmonic frequencies of the PDS. The allocation problem is set as integer linear programming performed using a Branch and Bound algorithm. The proposed methodology was tested for 15 nodes PDS based on a CIGRÉ network and 24 nodes PDS derived from the IEEE 34 nodes test system. Results show that 2 to 4 PQMs are required for the 15 nodes PDS and 2 to 9 PQMs for the 34 nodes PDS to thoroughly observe the considered power quality disturbances.

Optimal Positioning of Power Quality Meters for Monitoring Potential Conditions of Harmonic Resonances in a MV Distribution System

This research proposes an optimized allocation methodology of power quality (PQ) meters in medium voltage (MV) distribution system (DS), considering the potential harmonic resonance conditions. The allocation methodology uses the harmonic resonance mode analysis (HRMA) to calculate the critical modal impedances and identify the harmonic resonance frequencies. Thereby, using the HRMA, it is possible to build a binary observability matrix, which contains the information of nodes' observability for potential harmonic resonance frequencies. The allocation problem is modeled as a constraint integer linear programming that minimizes the number of necessary PQ meters, ensuring the complete observation of the determined harmonic resonance frequencies. The final feasible solution indicates the best locations to install the PQ meters, considering the harmonic resonance conditions, which include distinct operation scenarios of the DS, regarding the capacitor banks of the customers for power-factor correction. The allocation algorithm was applied in two test DSs, based on a CIGRÉ MV network and on the IEEE 34-node test feeder. The results show that four PQ meters are required to completely monitor the potential harmonic resonance frequencies in both the test DSs. It is also shown that the final allocation solution is applicable even for certain variability of the considered capacitor banks.

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.

Harmonic Sequence Impedances: A Tool for the Three-Phase Frequency Scan Technique

In this paper, the harmonic response of an electric system under imbalance conditions is established. Symmetrical harmonic components are proposed to give a new way of interpreting resonance occurrence in three-phase power systems. A three-phase harmonic bus impedance matrix (THBIM) for a simple distribution system is derived using analytical procedures. The development of frequency scans for the THBIM elements in both phase and sequence reference frames is carried out. Simulation results show the benefits of the harmonic sequence components for characterization of the harmonic resonance conditions in unbalanced distribution systems, and for characterizing the effectiveness of the mitigating techniques. This method offers a new way to conduct harmonic analysis and diagnosis in unbalanced power systems.

Effects of grounding on distribution system harmonic resonance conditions

An analytic model is presented which predicts the impact of soil resistivity, grounding, and electric load on power system resonance characteristics. A parametric study is reported which illustrates the significance of these parameters and provides a quantitative evaluation of their effects. The predictions of the model are compared with experimental data obtained from an actual 12 kV power distribution system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>