Low Frequency Oscillation Modes Research Articles

Impact of high-depth penetration of wind power on low-frequency oscillatory modes of interconnected power systems

This paper investigates impact of high-depth penetration of wind power, i.e., up to 30%, on low-frequency (0–2 Hz) oscillatory modes of interconnected power systems. The wind power is integrated as large Wind Power Plants (WPPs) based on Type-3 and Type-4 wind units represented by enhanced generic nonlinear and linearized models. The studies are based on eigen analysis of the 16-machine/68-bus NPCC equivalent system with multiple WPPs added to it. The case studies consider different ratios of Type-3/Type-4 WPPs to investigate impact of interaction between WPPs adopting different technologies on power system low-frequency dynamics. The studies reveal that WPPs can (i) noticeably impact the damping ratios of existing inter-area oscillatory modes at low-depth penetrations more than at high-depth ones, (ii) introduce new low-frequency oscillatory modes and (iii) cause instability by interacting with existing controllers in the system.

Coordinated Tuning of the Parameters of PSS and POD Controllers Using Bioinspired Algorithms

This paper presents a technique based on the novel bat algorithm (NBA) for the design of the parameters of power system stabilizers and the generalized Unified power flow controller-power oscillation damping in a multimachine power system. The objective is to ensure minimal damping rates to low-frequency electromechanical oscillation modes. Simulations were carried out on the New England system to compare the performance of the NBA with three other techniques: particle swarm optimization, bacterial foraging optimization oriented by particle swarm optimization, and the bat algorithm. For the cases analyzed in this paper, the NBA produced results superior to other techniques. Moreover, the proposed methodology was able to obtain solutions with high damping levels, which showed to be robust when a wide range of loading conditions of the power system were considered.

A Virtual Synchronous Generator Control Strategy for VSC-MTDC Systems

With the rapid increase of renewable energy sources and power electronic converters in the power system, the inertia of the power system is declined and the stability problem is more serious than ever before. In this paper, a virtual synchronous generator (VSG) control strategy is proposed to enable the voltage-source converter-based multiterminal high-voltage direct current (VSC-MTDC) system to damp the low-frequency oscillation modes. Both rotational inertia part and governor part are modeled in the VSG controller. The $V^2-P-\omega$ characteristic is developed based on the $V^2-P$ droop control to emulate the action of the speed governor when the frequency of ac grid deviates from the nominal value. The virtual inertia part is used to emulate the inertia response of the synchronous generator. The communication between VSC stations is unnecessary with the autonomous power allocation ability of the $V^2-P-\omega$ characteristic. Modal analysis is utilized to test the system stability and optimize the controller parameters. Two test systems which include offshore wind farms, VSC-MTDC systems, and onshore power grids are built in the DIgSIENT/PowerFactory. The simulation results verify the effectiveness of the proposed VSG strategy.

A New Design of Wide-Area MIMO Coupling Robust HVDC Supplementary Controller

A new multi-input multi-output (MIMO) robust coordination approach for the controller design of multi-infeed high voltage direct current (HVDC) system is proposed. This design will enhance the damping of certain low frequency oscillation mode. The dominant mode ratio (DMR) is applied to choose the appropriate feedback signals, while time delay of wide-area signals is considered. The Total Least Squares-Estimation on Signal Parameters via Rotational Technique (TLS-ESPRIT) algorithm serves in identifying the MIMO system model. To reach the best control effect and disturbance suppression level, the mixed H2/H∞ robust theory with regional poles placement is introduced to design the controller. The new MIMO design approach avoids system decoupling in complex situation, and it uses the interactions of different control loops to enhance the system's stability when most MIMO HVDC controllers are designed by decoupling strategy. Simulation results of a multi-infeed HVDC system validate the control effect and robustness of the proposed method.

Extracting Low-Frequency Spatio-Temporal Patterns in Ambient Power System Data Using Blind Source Separation

Wide-area techniques provide a powerful tool to extract spatio-temporal patterns from high-dimensional datasets and can be used for event detection and visualization, data fusion, stability assessment, and coherency analysis. In this paper, a novel blind source separation-based approach for extracting low-frequency spatio-temporal patterns from measured ambient power system data is proposed and a spatio-temporal visualization index is also suggested. This methodology combines a nonlinear hierarchical neural network with a Blind Source Separation (BSS) technique. The neural network allows reducing noise and removing the nonlinear relations among data (preserve dynamic features of interest), while the BSS technique permits extracting spatial and temporal patterns. In addition, the proposed approach takes advantage of the latest techniques in nonlinear estimation of non-stationary time series. Finally, application examples of the proposed framework on real test cases recorded from an actual power system by Phasor Measurement Units (PMUs) are presented. The obtained results show that the temporal patterns can be used for extracting and identifying the low-frequency oscillation modes and the spatial patterns can be used for identifying modes with the most contribution in original data. Compared to other BSS approaches, the proposed method has shown to be better for the analysis of real ambient data.

Identification of Dominant Low Frequency Oscillation Modes Based on Blind Source Separation

On-line monitoring and analysis of low frequency oscillation (LFO) are important for stability and security of a power system. This paper proposes a blind source separation (BSS) based method for LFO modal analysis of one-channel measured signal, which consists of a second-order blind identification (SOBI) algorithm and the Hilbert transform (HT) technique. This is the first time when a BSS technique is applied as a modal decomposition tool in this field. The proposed SOBI-HT based dominant mode identification method combines an iteration procedure with an identification procedure to determine the model order, and then identify dominant modes. The performance of the proposed method is evaluated on numerical simulation signals and a record of real data, verifying its effectiveness and accuracy.

A method for the identification of low frequency oscillation modes in power systems subjected to noise

The high penetration of renewable energy sources and the consequent integration of such distributed energy generation systems into the grid have significantly increased the interaction between power sources, which can result in low frequency oscillations. Different control techniques are proposed in literature to suppress low frequency oscillations, but the first step to attenuate such oscillations is to characterize them in terms of their dominant modes. This paper combines different results from literature to propose a unified two-step methodology for the mode characterization of low frequency oscillations based on the signals acquired by wide area measurement systems. Since the measured signals typically contain noise, the first stage of the proposed method uses the basis pursuit denoising method combined with a Tunable Q-factor wavelet transform to increase the signal-to-noise ratio and improve the identification results. In a second stage, an improved version of the matrix pencil algorithm, as proposed in this paper, is used to identify the parameters of low frequency oscillation dominant modes. Both simulation and experimental results show that the proposed method has better characterization accuracy than traditional methods, especially when Gaussian noise is considered in the measurements. In addition, the processing time has proven to be reasonable for online identification and characterization of low frequency oscillations.

Resonant tidal excitation of oscillation modes in merging binary neutron stars: Inertial-gravity modes

In coalescing neutron star (NS) binaries, tidal force can resonantly excite low-frequency (< 500 Hz) oscillation modes in the NS, transferring energy between the orbit and the NS. This resonant tide can induce phase shift in the gravitational waveforms, and potentially provide a new window of studying NS interior using gravitational waves. Previous works have considered tidal excitations of pure g-modes (due to stable stratification of the star) and pure inertial modes (due to Coriolis force), with the rotational effect treated in an approximate manner. However, for realistic NSs, the buoyancy and rotational effects can be comparable, giving rise to mixed inertial-gravity modes. We develop a non-perturbative numerical spectral code to compute the frequencies and tidal coupling coefficients of these modes. We then calculate the phase shift in the gravitational waveform due to each resonance during binary inspiral. We adopt polytropic NS models with a parameterized stratification. We derive relevant scaling relations and survey how the phase shift depends on various properties of the NS. We find that for canonical NSs (with mass M = 1.4M_sun and radius R = 10 km) and modest rotation rates (< 300 Hz), the gravitational wave phase shift due to a resonance is generally less than 0.01 radian. But the phase shift is a strong function of R and M, and can reach a radian or more for low-mass NSs with larger radii (R > 15 km). Significant phase shift can also be produced when the combination of stratification and rotation gives rise to a very low frequency (< 20 Hz in the inertial frame) modified g-mode. We also find that some inertial modes can be strongly affected by stratification, and that the m = 1 r-mode, previously identified to have a small but finite inertial-frame frequency based on the Cowling approximation, in fact has essentially zero frequency, and therefore cannot be excited.

Design of the PI–UPFC–POD and PSS Damping Controllers Using an Artificial Bee Colony Algorithm

This paper presents two variations of the artificial bee colony (ABC) algorithm, the classical and a modified version, called GBest, for the design of the proportional–integral and supplementary damping controllers: power system stabilizers and the unified power flow controller (UPFC)–power oscillation damping set. The objective is to insert additional damping to the low-frequency oscillation modes present in multimachine electrical power systems, to guarantee the small-signal stability of the system considering different loading conditions. A new current injection formulation for the UPFC is proposed and incorporated into the current sensitivity model used to represent the dynamical operation of the electric power system. Static and dynamical analysis were performed for the New England system to validate the proposed formulation and to evaluate the performance of the optimization algorithms. The results indicate that the modified version of the ABC algorithm has superior performance for this problem, providing robust solutions, that ensure the stability of the system even when small variations of the load are considered.

Mode identification of low‐frequency oscillations in power systems based on fourth‐order mixed mean cumulant and improved TLS‐ESPRIT algorithm

Wide area monitoring systems (WAMS) provide effective support for online identification of low-frequency oscillations in power systems. The WAMS signal is sensitive to the surrounding environment, and it contains Gaussian white noise. The Gaussian white noise will produce Gaussian coloured noise through the filter, which will bring some errors to the mode identification. In order to solve the above problem, this study proposes a method to identify the low-frequency oscillation modes of a single-channel measurement of the power system based on the combination of the fourth-order mixed mean cumulant and the improved TLS-ESPRIT (total least square-estimation parameter space rotation invariant technique). The actual signal is replaced by the processed signal using the fourth-order mixed mean cumulant mathematical statistical method, thereby the Gaussian coloured noise is suppressed effectively; then, TLS-ESPRIT algorithm is used to identify the signal, which is used to identify the low-frequency oscillation of each mode. A novel relative change rate of singular value was also introduced in order to avoid the artificially threshold-setting error. The simulation results show that the proposed method has better anti-noise performance and higher accuracy of fitting than other methods reported in literature, besides being easy to be implemented and suitable for performing on-line identification.

Identification method for power system low‐frequency oscillations based on improved VMD and Teager–Kaiser energy operator

An improved variational mode decomposition (VMD) method is introduced into the mode recognition of low-frequency oscillation of power system in this study. First, fast Fourier transform is used to determine the number of VMD components, and the approximate fitting formula of the best balancing parameter α is obtained by a large number of tests. The original signal is decomposed into several modes via improved VMD (IMVD) method. Then, Teager–Kaiser energy operator is applied on the fitting of each component to get the amplitude, frequency, and damping factor of it. By the constructed test signals, the proposed method is compared with the methods of non-parametric VMD, empirical mode decomposition, total least-squares estimation of signal parameters via rotational invariance techniques, and Prony on the performance of mode parameter identification. Results show that the IVMD method effectively overcomes the shortcomings of those methods mentioned above in dealing with mode mixing, noise sequence, and non-stationary signals. Finally, the feasibility of the proposed method in extracting the low-frequency oscillation mode parameters of power system is verified by the simulation signals of the IEEE two-area four-generator power system and the New England 39-bus system.

Instabilities in flexible channel flow with large external pressure

We examine the stability of laminar high-Reynolds-number flow through an asymmetric flexible-walled channel driven by a fixed upstream flux and subject to a (large) uniform external pressure. We construct a long-wavelength, spatially one-dimensional model using a flow profile assumption, modelling the flexible wall as a thin tensioned membrane subject to a large axial pre-stress. We numerically construct the non-uniform static shape of the flexible wall and consider its stability using both a global eigensolver and numerical simulation of the nonlinear governing equations. The system admits multiple static solutions, including a highly collapsed steady state where the membrane has a single constriction which increases with increasing external pressure. We demonstrate that the non-uniform static state is unstable to two distinct (infinite) families of normal modes which we characterise in the limit of large external pressure. In particular, there is a family of low-frequency oscillatory modes which each persist to low membrane tensions, where the most unstable mode has an oscillating membrane profile which is outwardly bulged at the centre of the domain with a narrow constriction at the downstream end. In addition, there is a family of high-frequency oscillatory modes which are each unstable beyond a critical value of the tension within a two-branch neutral curve. Unstable modes along the lower branch of the neutral curve are sustained by a leading-order balance between unsteady inertia and the restoring force of membrane tension along the channel. In addition, we elucidate the mechanism of energy transfer to sustain the self-excited oscillations: oscillations decrease the mean maximal constriction of the channel over a period, which reduces the overall dissipation of the mean flow and releases energy to sustain the instability. Fully nonlinear simulations indicate that as the Reynolds number increases these unstable normal modes can grow supercritically into sustained large-amplitude ‘slamming’ oscillations, where the membrane is periodically drawn very close to the opposite rigid wall before recovering.

An Improved IRA Algorithm and Its Application in Critical Eigenvalues Searching for Low Frequency Oscillation Analysis

On the basis of implicitly restarted Arnoldi (IRA) method, an improved algorithm is proposed, in which the dimension of Krylov subspace is dynamically increased to compute eigenvalues in specified circle. First, the radius of searching circles is dynamically expanded through automatically increasing the number of eigenvalues and the dimension of Krylov subspace, based on the locking mechanism. Second, the region where the low frequency oscillation modes located is divided into small independent computing units, which are covered by specified searching circles. Third, the independent computing units can be calculated simultaneously with no effects on each other. The proposed method can avoid eigenvalues missing caused by inappropriate resetting of search number in equidistant-searching IRA method. Furthermore, no manual intervention is needed in the proposed method. Two systems with 570 and 5272 state variables are tested in this paper, and the results indicate that the proposed method is efficient, reliable, and practical.

Dynamics of laminar separation bubble over NACA-0012 airfoil near stall conditions

In this paper, we investigated the dynamics of laminar separation bubble over an airfoil near stall conditions. Large eddy simulation of flow around NACA-0012 airfoil was conducted at an angle of attack α=11.5∘ for a Reynolds number Rec=1.3×105 and Mach number M∞=0.4. A self-sustained low-frequency flow oscillation was observed and its life cycle was described and analyzed. The computed Strouhal number of the oscillation was in good agreement with the experimental data. The flow oscillation was due to quasi-periodic bursting and reforming of the laminar separation bubble. The size of the computed bubble was twice that of the experiment and resulted in 19% difference between the computed and the experimental lift coefficients. The average of the maximum reverse velocity percentage inside the bubble, during attached phase, was 23.4%. The characteristics of the transition in the separated shear layer changed through the low-frequency cycle in which the turbulent kinetic energy was maximum when the bubble is at its shortest length. Dynamic mode decomposition analysis of the computed flow identified two dominant modes; the low-frequency oscillation mode and a high frequency mode representing trailing-edge shedding. The reconstructed flow of the DMD modes produced two distinct events, i.e., (1) fully separated flow with intense shedding at the trailing-edge and (2) a fully attached flow with no apparent vortex shedding at the trailing-edge. The DMD results suggest a critical role of acoustic feedback from the trailing edge in promoting earlier transition and forcing the separated flow to reattach.

Distributed Electromechanical Oscillation Mode Online Estimation

For the existence of low frequency oscillation phenomena in the interconnection power systems, a new style of distributed algorithm for detecting the low frequency oscillation modes was proposed to avoid the disadvantages of previous methods that require large amount of concentrated computation and communication. The whole structure of oscillation detection contains two levels, namely the substation level and control center level. In the substation level, damped sinusoid model based on atomic decomposition is employed to represent atomic library. Using the power angle trajectory, the modal parameters were identified from the atomic library by atomic decomposition method and atomic decomposition energy entropy was calculated during the identification process. In the control center level, the oscillation detection result of the substations are uploaded and combined to generate overall oscillation frequency and damping ratio by a weighted linear function. The results of a simulation case show that this algorithm can quickly detect the oscillation mode and the simulation results are identical to that of the normal form theory, and the accuracy and effectiveness of the proposed method were validated.

Identification of low frequency oscillation modes in large transmission systems

Existe un comportamiento dinamico tipico asociado a todo sistema. Las oscilaciones son fenomenos inherentes a los sistemas dinamicos, por lo que el analisis de estos resulta fundamental para entender el comportamiento dinamico de un sistema en particular. El conocimiento de la frecuencia de oscilacion y su correspondiente razon de amortiguamiento, asociados con los modos naturales del sistema, resulta fundamental para inferir el comportamiento dinamico del sistema despues de que ha experimentado un disturbio. En un sistema electrico de potencia los cambios topologicos en la red de transmision son bastante comunes debido a los requerimientos operativos. Esto ocasiona cambios en los valores tanto de la frecuencia de oscilacion como el amortiguamiento de los modos naturales del sistema. En el pasado, cambios normales en la condicion de operacion del sistema mexicano han dado como resultado la aparicion de oscilaciones de potencia no amortiguadas, por esta razon el conocer el amortiguamiento asociado con los modos criticos del sistema resulta de vital importancia. Este articulo reporta la aplicacion del analisis modal y simulaciones en el dominio del tiempo para el rastreo de las oscilaciones de baja frecuencia dominantes, tambien conocidas como modos inter-area, en el sistema electrico mexicano durante diferentes condiciones de operacion. Los resultados obtenidos permiten identificar a las variables del sistema de potencia mas importantes sobre las oscilaciones de baja frecuencia.

A self-tuning NeuroFuzzy feedback linearization-based damping control strategy for multiple HVDC links

This research work proposes a multi-input multi-output (MIMO) online adaptive feedback linearization NeuroFuzzy control (AFLNFC) scheme to improve the damping of low frequency oscillations (LFOs) in an AC/DC power system. Optimized NeuroFuzzy identification architecture online captures the oscillatory dynamics of the power system through wide area measurement system (WAMS)-based measured speed signals of machines. Based on the identified power system model, the appropriate control law is derived through feedback linearization control with a self-tuned coefficient vector. The generated control signal modulates the real power flow through a high voltage direct current (HVDC) link during perturbed operating conditions and enhances system stability. The effectiveness of the proposed control strategy is demonstrated through different contingency conditions of a multi-machine test power system with multiple HVDC links. The results validate the significance of the proposed control strategy to improve the capability of HVDC links to damp inter-area modes of LFOs. The proposed MIMO AFLNFC performance is bench-marked against conventional PID based supplementary control.

Power oscillation damping control by PSS and DFIG wind turbine under multiple operating conditions

Multiple operating conditions in power systems including wind power sources significantly affect the damping of low frequency oscillation modes due to diverse generating and loading conditions, random wind speeds, line outage contingencies, etc. To cope with multiple operating conditions, this paper proposes the new parameter optimization technique of the power system stabilizer (PSS) and the doubly-fed induction generator (DFIG) wind turbine with the power oscillation damper (POD) based on the probability method. Different operating conditions are randomly generated by Monte Carlo simulation. Under the generated operating points, the particle swarm optimization of PSS and POD parameters is carried out to achieve the highest probability that the damping ratios of all oscillation modes are greater than the desired damping ratio for all operating points. Study results in the IEEE New England 39-bus system indicate that under the occurrence of faults, the PSS and POD optimized by the proposed method yield better stabilizing performance than the conventional PSS and POD over a wide range of operating points.

Torsional vibration characteristic study of the grid-connected DFIG wind turbine

This paper studies the torsional vibration characteristics of the grid-connected doubly-fed induction generator (DFIG) wind turbine by small signal analysis method. Firstly a detailed small-signal stability union model of the grid-connected DFIG wind turbine is developed, including the mechanical system and electrical system. To study the dynamic characteristic of the blade, gearbox, low speed and high speed shafts, a three mass shaft model for the mechanical system is adopted. At the same time, small signal models of DFIG, the voltage source converter (VSC) and the transmission line of the electrical system are developed respectively. Then, through calculating the eigenvalues of the state matrix A and the corresponding participation factors, the modal analysis is conducted in the shaft torsional vibration issues. And the impact of the system parameters including the series compensation capacitor, the flat-wave reactor, the PI parameters, especially the speed controller of generator rotor on shaft torsional vibration are discussed. The results show that the speed controller strengthens association between the mechanical system and the electrical system, and also produces a low-frequency oscillation mode.

Power system low frequency oscillation mode estimation using wide area measurement systems

Oscillations in power systems are triggered by a wide variety of events. The system damps most of the oscillations, but a few undamped oscillations may remain which may lead to system collapse. Therefore low frequency oscillations inspection is necessary in the context of recent power system operation and control. Ringdown portion of the signal provides rich information of the low frequency oscillatory modes which has been taken into analysis. This paper provides a practical case study in which seven signal processing based techniques i.e. Prony Analysis (PA), Fast Fourier Transform (FFT), S-Transform (ST), Wigner-Ville Distribution (WVD), Estimation of Signal Parameters by Rotational Invariance Technique (ESPRIT), Hilbert-Huang Transform (HHT) and Matrix Pencil Method (MPM) were presented for estimating the low frequency modes in a given ringdown signal. Preprocessing of the signal is done by detrending. The application of the signal processing techniques is illustrated using actual wide area measurement systems (WAMS) data collected from four different Phasor Measurement Unit (PMU) i.e. Dadri, Vindyachal, Kanpur and Moga which are located near the recent disturbance event at the Northern Grid of India. Simulation results show that the seven signal processing technique (FFT, PA, ST, WVD, ESPRIT, HHT and MPM) estimates two common oscillatory frequency modes (0.2, 0.5) from the raw signal. Thus, these seven techniques provide satisfactory performance in determining small frequency modes of the signal without losing its valuable property. Also a comparative study of the seven signal processing techniques has been carried out in order to find the best one. It was found that FFT and ESPRIT gives exact frequency modes as compared to other techniques, so they are recommended for estimation of low frequency modes. Further investigations were also carried out to estimate low frequency oscillatory mode with another case study of Eastern Interconnect Phasor Project (EIPP) data with the seven signal processing techniques (FFT, PA, ST, WVD, ESPRIT, HHT and MPM). It was found from the simulation results of EIPP data that two low frequency oscillatory mode (0.51Hz, 0.2Hz) exist.