System Fundamental Frequency Research Articles

Analytical solution of serial ferroresonance triggered by circuit breaker operation in solidly grounded power grids

Ferroresonance can be induced by Circuit Breaker (CB) switching operations in neutral point solidly grounded power grids with matching parameters. No complete time domain analytical solution of ferroresonance has been developed in previous research, which is inconvenient for further analysis of this phenomenon. To solve this problem, a commonly accepted circuit model for Serial Ferroresonance (SF) in solidly grounded power grids is used and then validated. Piecewise linearization method is used to process the potential transformer nonlinear excitation inductance considering the gradual decrease of change rate of the characteristic B-H curve. Then the analytical solutions of the excitation inductance flux in underdamped and overdamped operation conditions are expressed. It is found that the response is composed of the steady-state component caused by system fundamental frequency excitation and the transient component determined by the initial energy storage of the system elements. Simulation is done to verify the analytical expression of SF, which lays the foundation for subsequent research on the analysis, detection, and suppression of ferroresonance.

Harvesting energy from shock environments via functionally graded magneto-electro-elastic materials

Given the fact that the environmental kinetic energy may appear in the form of shock pulse excitation, this paper aims to investigate the response of a shock excited cantilever beam equipped with two symmetric functionally graded magneto-electro-elastic layers. To this end, employing a hybrid procedure including the Ritz method together with the geometric nonlinear Euler-Bernoulli beam theory, the coupled magneto-electro-mechanical reduced equations of motion are obtained. The model predictions are compared and successfully validated by those available in the literature. Having the vibration frequency of the system, which is obtained by the method of multiple time scales, the optimal duration maximizing the influence of shock pulse acceleration is predicted using the power shock spectrum introduced in this study for the first time. The results reveal that the harvested power maximizes when the system fundamental frequency becomes 1.36 times the equivalent shock frequency.

Full-scale experimental study on dynamic behaviors of a three-cable network with a pretensioned cross-tie

A cable network of cables interconnected with cross-ties and attached with dampers represents the generalized solution for vibration mitigation of stay cables. It is of significant interest as completely suppressing vibrations of long cables vulnerable to various excitation mechanisms is still challenging. Although many theoretical studies on cable networks exist, large-scale and full-scale experimental validations and investigations are lacking. Therefore, this study first presents a full-scale experiment setup for experimental studies on cable networks, which consists of at most three cables with adjustable length and the maximum length is 41.35 m. The experimental setup is subsequently used for studying effects of a pretensioned cross-tie on cable network dynamics, with the focus placed on the pretension, location and anchoring form of the cross-tie. The experimental results are then discussed in detail with reference to a theoretical model of a three-cable network with cable sag and cross-tie pretension accounted. It is found that the experimental results on system frequencies and mode shapes are consistent with those predicted using the analytical model. Particularly, both the pretensioned cross-tie induced increase and decrease in cable network frequencies have been validated by the experiments. Furthermore, the grounded cross-tie is found to significantly improve the system fundamental frequency, but the increase in frequencies of other local vibration modes is limited. Besides, the test results have validated that a rigid cross-tie has very limited damping effect on the cable network.

Online-Harmonic-Detection-Based System Stabilization Function for Grid-Forming Inverters Under Various Grid Conditions

In power systems with grid-forming inverters (GFMs), small-signal instability issues could occur due to harmonic excitation, impedance interactions, and poor inverter control design. There mainly exist two types of stability issues based on the frequency range. One is the low-frequency resonance (0 – 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f₀</i> Hz) and the other is the high-frequency harmonics (above 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f₀</i> Hz), where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f₀</i> is the system fundamental frequency. By assuming that the low-frequency related controls are well designed, this paper addresses the high-frequency harmonic issues. The goal is to develop a system stabilization function (SSF) to eliminate any high-frequency stability issues under various grid conditions without affecting predefined low-frequency behaviors. The idea is to conduct the inverter passivation test at the system harmonic resonant frequency so that the corresponding harmonic instability can be removed. To achieve this, the resonant frequency of the harmonic instability is detected first, and then if the magnitude of the resonant component exceeds the threshold value, the proposed SSF will be enabled, thus the system would be stabilized. Both simulation and experimental tests are conducted to validate the effectiveness of the proposed approach.

Enhancement of the performance of nonlinear vibration energy harvesters by exploiting secondary resonances in multi-frequency excitations

This study is concerned with utilizing secondary resonances in order to harvest energy from low-frequency excitations. Nonlinearities give rise to secondary resonances, which can potentially activate large-amplitude responses when the excitation frequency is a fraction of the fundamental frequency of the system. Such resonances offer an untapped and unique opportunity for harvesting vibratory energy from excitation sources with low-frequency components. This issue has propelled the current study. Based on multi-frequency excitation, we develop a novel theoretical framework for a piezomagnetoelastic energy harvester to enhance its performance. The proposed scheme is implemented in both monostable and bistable piezomagnetoelastic under low-frequency excitations. It is shown throughout the paper that when the excitation frequencies are certain fractions of the system's fundamental frequency, the combination and simultaneous resonance activate large-amplitude responses. Another advantage of the scheme is that the energy could be harvested from low-frequency ambient vibrations, which is a considerable concern in this field of study. Different responses of the system, such as low-amplitude and high-amplitude limit-cycle oscillations and chaotic motions, are studied through perturbation theory and numerical techniques. Various numerical tools, including phase portrait, Poincare section, and Lyapunov exponent, are used to explore complex dynamical behavior of the system. The performance of the harvester is also compared in different regions. Numeral simulations clearly confirm that the proposed framework dramatically enhances the performance of the energy harvester.

Modeling and Initialization of a Virtual Synchronous Machine for Power System Fundamental Frequency Simulations

Modeling and Initialization of a Virtual Synchronous Machine for Power System Fundamental Frequency Simulations

Improving high precision cam mover’s stiffness

Pre-alignment is a key challenge of the Compact Linear Collider (CLIC) study. The requirement for CLIC main beam quadrupole (MBQ) alignment is positioning to within 1 μm from target in 5 degrees of freedom (DOF) with ± 3mm travel. After motion, the position should be kept passively while the system's fundamental frequency is above 100Hz. Cam movers are considered for the task. Traditionally they are used for the alignment of heavier magnets with lower accuracy and stiffness requirement. This paper presents a new CLIC prototype cam mover with design emphasis on the fundamental frequency. A finite element method (FEM) model predicts the mode shapes and eigenfrequencies of the system and can be used for further improving the design. Experimental modal analysis (EMA) of the prototype shows that the prototype's fundamental frequency is at 44Hz. It also validates the FEM model.

Harmonic Phasor Estimation With Flat-Top FIR Filter

The IEEE Std C37.118.1(a) describes synchrophasor measurement by a phasor measurement unit (PMU) for the system fundamental frequency. Harmonic synchrophasor, i.e., synchrophasor measured for harmonic frequencies, is not considered in the standard. Harmonic synchrophasor is useful for harmonic state estimation, power quality (PQ) monitoring, and harmonic power flow analysis. In this paper, we investigate the usability of the standard basic synchrophasor estimation model for the estimation of harmonic phasor (HP) up to the 50th harmonic as advised by the IEC Std 61000-4-7. For the estimation of HPs, an application of the flat-top (FT) finite-impulse-response (FIR) filter is proposed. Results for the maximally flat differentiator and the interpolated discrete Fourier transform (DFT) are also presented, confirming the superior performance of the proposed FT filter approach. HP estimation is verified with extended tests of the IEEE Std C37.118.1(a), including steady-state and dynamic conditions with additive 60-dB noise.

Small-Signal Modeling and Stability Prediction of Parallel Droop-Controlled Inverters Based on Terminal Characteristics of Individual Inverters

Parallel droop-controlled inverters with renewable energy sources are widely employed in islanded ac microgrids, where dynamic interactions among them may cause small-signal stability issues. Since the active power-frequency droop scheme is applied, the dynamic interactions among inverters exist not only in bus voltage and transmitted current, but also in variable system fundamental frequency. This paper introduces a novel small-signal terminal characteristic model for droop-controlled inverter. Besides conventional impedance and admittance, a new set of terminal characteristics is proposed to characterize the dynamics of fundamental frequency. Furthermore, the small-signal model of parallel inverters is constructed based on the terminal characteristics of individual inverters. Covering the fundamental frequency interactions, a stability prediction approach based on generalized Nyquist criterion is proposed for parallel droop-controlled inverters. Besides the product of impedance and admittance, an additional term is added in the system return ratio, which consists of the proposed terminal characteristics associated with the fundamental frequency. Finally, experimental results validate the effectiveness of this proposed stability prediction approach.

A simplified method for analyzing the fundamental frequency of monopile supported offshore wind turbine system design

Preliminary design of offshore wind turbines requires high precision simplified methods for the analysis of the system fundamental frequency. Based on the Rayleigh method and Lagrange’s Equation, this study establishes a simple formula for the analysis of system fundamental frequency in the preliminary design of an offshore wind turbine with a monopile foundation. This method takes into consideration the variation of cross-section geometry of the wind turbine tower along its length, with the inertia moment and distributed mass both changing with diameter. Also the rotational flexibility of the monopile foundation is mainly considered. The rigid pile and elastic middle long pile are calculated separately. The method is validated against both FEM analysis cases and field measurements, showing good agreement. The method is then used in a parametric study, showing that the tower length Lt, tower base diameter d0, tower wall thickness δt, pile diameter db and pile length Lb are the major factors influencing the fundamental frequency of the offshore wind turbine system. In the design of offshore wind turbine systems, these five parameters should be adjusted comprehensively. The seabed soil condition also needs to be carefully considered for soft clay and loose sand.

Optimal layout method of distributed locking device of satellite based on plant root growth theory

The method of determining the optimal direction of satellite locking point is extended from the mechanical stability principle of plant roots growth under external loads. The method of topological optimization of the number and location of satellite locking units was proposed based on the adventitious root growth pattern of monocotyledons. Inspired by the fibrous root growth rhythm, the method for topological optimization of the effective contact interface shape of the satellite locking units is presented. A satellite finite element model and three-dimensional spring support model are established to lay the foundation for system frequency analysis. Parallel algorithm is used to optimize the position of the main locking points. One-dimensional search method is adopted to select the growth positions of the secondary locking points with the goal of maximizing fundamental frequency of the system. The relationship between the locking stiffness and system fundamental frequency is explored. Finally, the optimization results of this method are compared with those of conventional methods; the comparison demonstrated that the fundamental frequency of the locking system is significantly enhanced by the proposed method.

Islanding Detection Technique based on Karl Pearson’s Coefficient of Correlation for Distribution Network with High Penetration of Distributed Generations

Abstract This article proposes a new Karl Pearson’s coefficient of correlation (‘r’) based islanding detection scheme which utilizes negative sequence voltage and voltage unbalance signal. In order to check the legitimacy of the proposed technique, large numbers of non-islanding and islanding events are generated by modeling IEEE 34-bus network. This scheme detects islanding situation even under 0 % power mis-match condition and thus, reduces the non detection zone (NDZ). Furthermore, the proposed technique detects islanding situation quickly as well as remains stable during the critical non-islanding situation like faults on adjoining feeder having varying location and fault resistance. Moreover, the proposed technique remains immune to variation in external system condition and fundamental frequency. The performance of the proposed technique is comprehensively compared with the schemes currently reported in the literature. This comparison apparently demonstrates the benefits of the proposed technique over existing schemes.

Rate-independent linear damping in vehicle suspension systems

Over the past few decades, several semi-active controllers have been proposed for vehicle suspension systems. Skyhook and groundhook controllers are well-studied and very effective in isolating vibrations. However, these controllers mitigate either the sprung or unsprung mass response at the expense of the other. Moreover, there is no sensor to directly measure the absolute velocity of components in the suspension system (and estimates are subject to error), making it challenging to implement skyhook and groundhook controllers in practical cases. To overcome these limitations, there is a need for a type of damping that mitigates both sprung and unsprung mass responses and also can be implemented using simple local sensors. This paper proposes the use of rate-independent linear damping (RILD) for vehicle suspension systems. RILD provides direct control over displacement; beneficial for low-frequency dynamic systems such as suspension systems that are subject to high frequency vibrations (relative to the system fundamental natural frequency). RILD directly attenuates displacement responses with low damping forces, producing low acceleration responses. The RILD damping force is proportional to the displacement advanced in phase π/2 radians, which makes it noncausal. In this study, a modal causal filter-based approach is proposed to mimic the ideal noncausal response of the RILD model. Acceleration measurements of the sprung mass are used with a Kalman filter to estimate the displacements needed for the algorithm. Numerical analyses were conducted to demonstrate performance of the proposed model in matching noncausal RILD responses. Additionally, the advantages of the proposed model over well-known skyhook and groundhook controllers are studied.

Dynamic soil-structure interaction in offshore wind turbines on monopiles in layered seabed based on real data

The present paper studies the soil-structure interaction (SSI) effects on the dynamic properties of offshore wind turbines (OWT) founded on monopiles. For that purpose, a three degrees-of-freedom substructuring model based on modal parameters is proposed. The whole superstructure is reduced to a punctual mass by its fundamental modal mass and height, while the pile-soil stiffness is represented by the corresponding impedance functions. The proposed model, together with characteristic relations between the fixed-base fundamental frequency and the modal parameters obtained from data of existent OWTs found in the literature, is used to analyse the influence of the superstructure and foundation dimensions and soil profile on the magnitude of the SSI phenomena. The obtained results confirm the relevance of including the foundation stiffness in the design stage of OWT systems, as variations in the fundamental frequency close to 15% can be produced. The homogeneous assumption, even if cs,30 mean values are assumed, yields to misleading results if the actual soil profile presents properties that vary with depth. The superficial layers of the soil profile are found to play a major role in the estimation of the OWT system fundamental frequency and damping when the SSI phenomena are included.

Effects of Machine Tool Spindle Decay on the Stability Lobe Diagram: An Analytical-Experimental Study

An analytical-experimental investigation of machine tool spindle decay and its effects of the system’s stability lobe diagram (SLD) is presented. A dynamic stiffness matrix (DSM) model for the vibration analysis of the OKADA VM500 machine spindle is developed and is validated against Finite Element Analysis (FEA). The model is then refined to incorporate flexibility of the system’s bearings, originally modeled as simply supported boundary conditions, where the bearings are modeled as linear spring elements. The system fundamental frequency obtained from the modal analysis carried on an experimental setup is then used to calibrate the DSM model by tuning the springs’ constants. The resulting natural frequency is also used to determine the 2D stability lobes diagram (SLD) for said spindle. Exploiting the presented approach and calibrated DSM model it is shown that a hypothetical 10% change in the natural frequency would result in a significant shift in the SLD of the spindle system, which should be taken into consideration to ensure chatter-free machining over the spindle’s life cycle.

Resonant–Repetitive Combined Control for Stand-Alone Power Supply Units

This paper investigates a combined resonant–repetitive (RR) control structure for a three-phase four-leg dc/ac converter power supply. The RR control configuration is composed by a resonant controller tuned at the system fundamental frequency working in conjunction with a plug-in-type repetitive controller. The resonant part of the control scheme is used to assure prompt tracking of the inverter output voltage and to achieve as fast as possible system response to load variations; to this purpose, it is tuned at the fundamental frequency. At the same time, the resonant controller is able to stabilize the system without the necessity of any further additional controller; the repetitive part of the scheme is implemented for the fine regulation at the system harmonic frequencies. The proposed control configuration is used to regulate the power supply output voltage, providing very good tracking of the output voltage reference even in the presence of a nonlinear load. Experimental validation from a 40-kVA converter prototype is presented to validate the operation of the proposed converter and control.

Digital proportional multi-resonant current controller for improving grid-connected photovoltaic systems

This paper presents the modelling and design steps of a digital proportional multi-resonant controller used in a grid-connected photovoltaic (PV) system. It is shown that the use of only one Proportional-Resonant (PR) compensator, tuned to the system fundamental frequency, may have its effectiveness compromised due to nonlinearities in the system components. To overcome this drawback and improve the system's output current waveform, a multi-resonant controller is introduced. The performance of the discrete-time designed controller is tested on a grid-connected photovoltaic power plant. Experimental results obtained with the operation of a 30 kWp PV system connected to a distribution network, using only the leakage inductances of a connection transformer as passive filter are presented and discussed to demonstrate the performance of the designed control strategy.

Design of an Almost Harmonic-free TCR

In this study, the traditional thyristor controlled reactor is conditioned to be an almost harmonic-free inductive static Var compensator. The proposed configuration is constructed of a traditional TCR shunted by a parallel resonance circuit and the parallel combination is connected in series to a series resonance circuit. The parallel and series resonance circuits are tuned at the power system fundamental frequency. The series resonance circuit offers almost short circuit to the AC source current fundamental, while it offers very high impedance to the harmonic current components released by the TCR. The parallel resonance circuit offers very high impedance to the AC source current fundamental, while it offers almost short circuits to the harmonic current components released by the TCR. The two circuits operate coherently such that negligible current harmonics are permitted to flow in the AC source side. This type of harmonic treatment is not sensitive to other harmonic sources in the power system network, where this compensator is installed. The no load operating losses of this compensator are negligible compared to its reactive power rating. The proposed compensator is designed and tested on PSpice.

Interharmonics analysis of power signals with fundamental frequency deviation using Kalman filtering

In this paper a spectral decomposition-based method for interharmonic computation is proposed for power systems where the fundamental frequency fluctuates significantly. In the proposed method, the frequency domain components of the voltage waveform are obtained by Kalman filtering. Both the system fundamental frequency and the correct spectrum of the voltage waveform, and hence the exact interharmonics are obtained. The proposed method is tested with both simulated and field data obtained from different electric arc furnace (EAF) plants, where the system frequency deviates continuously due to the fluctuating load demands. Since the interharmonic frequencies are obtained by using Kalman filtering, no leakage effect of the DFT-based methods is involved in case of frequency deviations, which is an important advantage of the proposed method.

Power system frequency estimation using supervised Gauss–Newton algorithm

A supervised Gauss–Newton (SGN) algorithm for power system frequency estimation is presented in this paper. Taking the signal amplitude, the frequency and the phase angle as unknown parameters, the Gauss–Newton algorithm is applied to estimate the frequency for high accuracy. Meanwhile, a recursive DFT method and a zero-crossing method are used to compute the amplitude and the frequency approximately, so that the parameters can be initialised properly and the updating steps can be supervised for fast convergence of Gauss–Newton iterations. With this combined approach, both high accuracy and good tracking speed can be achieved for power system fundamental frequency estimation.