Low Frequency Oscillation Modes Research Articles

Analysis and Suppression of Oscillations in Doubly Fed Variable Speed Pumped Storage Hydropower Plants Considering the Water Conveyance System

The doubly fed variable speed pumped storage (DFVSPS) system is a hydraulically, mechanically, and electrically coupled system, and the characteristics of the components from the water conveyance system to the transmission line need to be fully considered in the oscillation analysis. Hence, the model of the water conveyance system is included to investigate the oscillation characteristics of the DFVSPS connecting to the grid via a series-compensated line. A small-signal state-space model of the DFVSPS system in the generation mode is first established. The oscillation characteristics of the DFVSPS are studied, and the dominant state variables for each oscillation mode are identified. The impact of system parameters on oscillations is further studied, and simulations are carried out to validate the accuracy of the model. The results indicate the oscillation mode of the DFVSPS comprises the electrical sub-synchronous oscillation (SSO) mode and the hydraulically, mechanically coupled low-frequency mechanical oscillation modes. When the series compensation level is high, the SSO becomes divergent, and the system is more likely to be unstable. Optimizing the rotor-side control parameters and the governor control parameters, sub-synchronous and low-frequency oscillations could be effectively suppressed, respectively. This study provides reference suggestions for the development and use of the future DFVSPS system.

Modelling and analysis of a coal-fired thermal power plant to identify physically observable dominant low-frequency oscillatory modes

Modelling and analysis of a coal-fired thermal power plant to identify physically observable dominant low-frequency oscillatory modes

Identification of power grids low-frequency oscillations through a combined MEEMD-Prony method

Currently, the primary focus of power systems is to enhance precision and resilience against interference in identifying low-frequency oscillation modes. This research proposes a new method combined with ensemble empirical mode decomposition (MEEMD) to improve the sensitivity of traditional Prony to noise in parameter analysis of low-frequency oscillation signals. The method decomposes the measurement signal into intrinsic mode functions (IMF) using MEEMD, introduces permutation entropy to detect randomness, and reconstructs the remaining IMF components. The reconstructed signal was analyzed using the Prony method to extract the characteristic parameters associated with the low-frequency oscillation frequency. Simulations using numerical signals and the EPRI-36 node system confirm the method effectively suppresses modal mixing, mitigates noise interference, and accurately identifies low-frequency oscillation parameters. This approach offers advantages over traditional methods, including enhanced resistance to noise and increased accuracy.

Effects of inflow Mach numbers on shock train dynamics and turbulence features in a backpressured supersonic channel flow

Investigations on shock train dynamics and relevant turbulence features in a backpressured supersonic channel flow are carried out using direct numerical simulation for three inflow Mach numbers of Ma0= 1.61, 2.0, and 2.45. As Ma0 increases, the shock train undergoes a structural change characterized by the leading shock which changes from the symmetric “λ” (Ma0=1.61) to the symmetric “X” (Ma0=2.00) and then to the asymmetric “X” pattern (Ma0=2.45). The symmetry breaking of shock structures induces asymmetric separation, which significantly alters the distribution characteristics of wall variables such as wall pressure and friction. To examine the unsteady behaviors of the shock train, a mode decomposition technique, namely, reduced-order variational mode decomposition [Liao et al., J. Fluid Mech. 966, A7 (2023)], is adopted taking its merit of adaptively extracting time-frequency features of dynamic systems. The modal analysis reveals that the shock train system exhibits significant centralization of low-frequency energy. Specifically, two basic types of low-frequency oscillation modes dominate the unsteady motion of the shock train: one depicts overall translating oscillation while another represents accordion-like oscillation. The analysis of turbulent kinetic energy shows that turbulence amplification is mainly dominated by the interaction of the decelerating mean flow with streamwise velocity fluctuations in the vicinity of the leading shock for all three cases, which is unaffected by the symmetry breaking of shock structures.

PMU-Based Power System Stabilizer Design Using Coati Optimization Algorithm

Low-frequency oscillation modes can destabilize the power system if they do not have adequate damping rates. The interconnection of large power systems and the complexity of operation has caused the increase in these modes and conventional control techniques have difficulty guaranteeing adequate damping rates. This article proposes a design method for a Power System Stabilizer damping controller using data from Phasor Measurement Units (PMUs) to ensure adequate damping rates for the modes even in the event of PMU data failures. Case studies were simulated and analyzed using the IEEE 68-bus system.

A Multistage Algorithm for Estimating Electromechanical Modes of Power Systems

Low-frequency oscillation modes of electromechanical origin, when they have low damping rates, can affect the stability of power systems. The Identification of these electromechanical modes is essential to preserve the continuous and safe operation of power systems. This paper proposes a multistage algorithm to determine the electromechanical modes of signals collected by Phasor Measurement Units (PMUs) in power systems. The proposed algorithm is composed of four processes and at each stage an electromechanical mode is estimated and evaluated. Case studies of a real PMU signal were conducted and discussed.

Robust multi-machine power system stabilizer design using bio-inspired optimization techniques and their comparison

This paper reports a comparative study among four bio-inspired meta-heuristic techniques i.e. Sooty-Tern Optimization (STO), Grey Wolf Optimization (GWO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) to tune the robust Power System Stabilizer (PSS) parameters of the multi-machine power system. These approaches are successfully tested on two bench-mark systems: sixteen-machine, sixty-eight-bus New England Extended Power Grid (NEEPG) and three-machine, nine-bus Western System Coordinating Council (WSCC). The efficacy of planned PSS via STO and GWO is validated by extensive non-linear simulations, eigenvalue analysis, and performance indices for numerous operating conditions under decisive perturbations, and outcomes are matched with those of GA and PSO techniques. In addition, the robustness is also tested for these algorithms. The results indicate that the PSS design using STO and GWO improves the small-signal stability and damping performance for mitigating inter-area and local area modes of low-frequency oscillations compared to GA and PSO.

A feature-state observer and suppression control for generation-side low-frequency oscillation of thermal power units

To construct a new energy system during the low-carbon transition, renewable energy sources (RESs) are increasingly being installed on a large scale worldwide which require thermal power units to operate at low loads and respond quickly to compensate for frequency fluctuations of the power grid during deep peak shaving and frequent load changes. While coal-fired thermal power plants operate under the deep-peak shaving process, low-frequency oscillation (LFO) accidents from the generation side have occurred constantly. According to our investigation, the reasons are the overlook of the nonlinearity of control valves is obviously highlighted under low load, and the preset parameters of the original control device can not match the flow characteristics, which may seriously cause a recurrence of LFOs. This paper focuses on generation-side LFO caused by the prime mover and its governor under all operating conditions constructing a novel nonlinear model and designing an oscillation feature observation matrix to identify the LFO modes, and a hierarchy feature-state observation classification method preventing LFO on the generation side is proposed. The results show that the proposed method can suppress the LFOs ahead, and this approach can weaken the oscillation amplitude by 85% and reduce the oscillation duration by 30 s.

Ambient oscillatory mode assessment in power system using an advanced signal processing method

Estimation of electromechanical mode properties is crucial in modern power systems for providing the operators with an adequate indication of the stress in the system. Measurement-based approaches use signal processing algorithms for mode identification and parameter estimation. This paper presents a novel framework for the assessment of low-frequency oscillation modes using real-world synchrophasor data with minimum computational effort. A nonstationary approach known as Time-Varying Filter based Empirical Mode Decomposition (TVF-EMD) technique is used to identify the dominant low-frequency modes present in the ambient PMU data. The combination of TVF-EMD with Teager Kaiser Energy Operator (TKEO) precisely estimates the instantaneous mode parameters, such as frequency, amplitude, and damping ratio. The efficacy of the proposed approach is demonstrated by applying it in a synthetic signal, simulated data of a standard IEEE test system, and in real-world PMU data of the Indian power grid. The proposed method is compared with the existing methodologies and the observations reveal that the proposed method has robust performance in estimating the instantaneous mode features in the power system with less computational complexities.

Effect of Direction and Frequency of Skull Motion on Mechanical Vulnerability of the Human Brain.

Strain energy and kinetic energy in the human brain were estimated by magnetic resonance elastography (MRE) during harmonic excitation of the head, and compared to characterize the effect of loading direction and frequency on brain deformation. In brain MRE, shear waves are induced by external vibration of the skull and imaged by a modified MR imaging sequence; the resulting harmonic displacement fields are typically "inverted" to estimate mechanical properties, like stiffness or damping. However, measurements of tissue motion from MRE also illuminate key features of the response of the brain to skull loading. In this study, harmonic excitation was applied in two different directions and at five different frequencies from 20 to 90 Hz. Lateral loading induced primarily left-right head motion and rotation in the axial plane; occipital loading induced anterior-posterior head motion and rotation in the sagittal plane. The ratio of strain energy to kinetic energy (SE/KE) depended strongly on both direction and frequency. The ratio of SE/KE was approximately four times larger for lateral excitation than for occipital excitation and was largest at the lowest excitation frequencies studied. These results are consistent with clinical observations that suggest lateral impacts are more likely to cause injury than occipital or frontal impacts, and also with observations that the brain has low-frequency (∼10 Hz) natural modes of oscillation. The SE/KE ratio from brain MRE is potentially a simple and powerful dimensionless metric of brain vulnerability to deformation and injury.

Wide-Area Measurement-Based Two-Level Control Design to Tolerate Permanent Communication Failures

The operation of modern power systems must meet stability requirements to guarantee the supply of electrical energy. One of these requirements is to ensure that the low-frequency oscillation modes have high damping ratios to avoid angular instability and future power system blackouts. Advances in phasor measurement units (PMUs) have contributed to the development and improvement of wide-area damping controllers (WADCs) capable of increasing the damping rates of the oscillation modes of the system, especially the inter-area modes. Nevertheless, the operation of WADCs is vulnerable to communication failures and cyber-attacks, and if not properly designed the WADC can affect the stability of the entire system. This research proposes a procedure for designing a WADC robust to permanent communication failures using a linear quadratic regulator (LQR) and genetic algorithms. Case studies conducted on an IEEE 68-bus test power system show the effectiveness of the WADC designed by the proposed procedure even when communication failures are occurring in the system. The use of genetic algorithms improves the convergence and results of the LQR-based method.

Comparison of Deformation Patterns Excited in the Human Brain In Vivo by Harmonic and Impulsive Skull Motion.

Noninvasive measurements of brain deformation in human participants in vivo are needed to develop models of brain biomechanics and understand traumatic brain injury (TBI). Tagged magnetic resonance imaging (tagged MRI) and magnetic resonance elastography (MRE) are two techniques to study human brain deformation; these techniques differ in the type of motion and difficulty of implementation. In this study, oscillatory strain fields in the human brain caused by impulsive head acceleration and measured by tagged MRI were compared quantitatively to strain fields measured by MRE during harmonic head motion at 10 and 50 Hz. Strain fields were compared by registering to a common anatomical template, then computing correlations between the registered strain fields. Correlations were computed between tagged MRI strain fields in six participants and MRE strain fields at 10 Hz and 50 Hz in six different participants. Correlations among strain fields within the same experiment type were compared statistically to correlations from different experiment types. Strain fields from harmonic head motion at 10 Hz imaged by MRE were qualitatively and quantitatively similar to modes excited by impulsive head motion, imaged by tagged MRI. Notably, correlations between strain fields from 10 Hz MRE and tagged MRI did not differ significantly from correlations between strain fields from tagged MRI. These results suggest that low-frequency modes of oscillation dominate the response of the brain during impact. Thus, low-frequency MRE, which is simpler and more widely available than tagged MRI, can be used to illuminate the brain's response to head impact.

Design of a Wide-Area Power System Stabilizer resilient to permanent communication failures using bio-inspired algorithms

The operation of power systems requires a set of requirements and studies to ensure the continuous and safe supply of electricity to consumer centers. In small-signal stability studies, low-frequency oscillation modes need to be evaluated as they can compromise the operation of power systems if they are not properly damped. Many structures and control devices have been proposed to mitigate these oscillation modes and the Wide-Area Power System Stabilizers (WAPSSs) have proven to be effective in improving the damping rates of these modes as they use remote system signals from Phasor Measurement Units (PMUs). However, cyber-attacks and communication failures can affect WAPSS communication channels and affect its operation in the power system. This article proposes a method based on a multiobjective optimization model for WAPSS design that is robust to the permanent loss of one WAPSS communication channel. Bio-Inspired Algorithms are applied and compared to solve the optimization problem. A set of case studies were conducted and discussed for the IEEE 68-bus system through modal analysis and time domain simulations. The achieved results showed the need for a fault-robust damping controller and the WAPSS-type controller was able to guarantee good dynamic performance regardless of permanent communication failures. Furthermore, different bio-inspired algorithms provided different results for the closed-loop control system when applied to the proposed optimization model.

A Novel Subspace Decomposition with Rotational Invariance Technique to Estimate Low-Frequency Oscillatory Modes of the Power Grid

This paper proposes modified Karhunen–Loeve transform with total least square estimation of signal parameters using rotational in-variance technique (MKLT-TLS-ESPRIT) to approximate the low-frequency oscillatory modes. MKLT decreases the impact of highly correlated additive colored Gaussian noise (ACGN) from the signal by differentiating the correlation matrix w.r.t from the final time instance. A quantitative study of the suggested method with other estimation methods is used to evaluate the effectiveness of the proposed method. Monte Carlo simulations with 50,000 runs are conducted to test the robustness of the estimation scheme for MKLT-TLS-ESPRIT. The evaluation of the efficiency of the proposed method in real-time perspective, the two-area system, and New England sixty-eight bus test system has been considered. The analysis shows that the suggested methodology correctly measures the interarea modes and lowers their mean and standard deviation to a minimum value.

Performance analysis of modeling scale on multiband oscillations in grid-connected wind farm

Grid-connected permanent magnet synchronous generator (PMSG) wind farms may be susceptible to oscillation when connected to weak grids. This paper explores the root causes of the oscillations from two perspectives: the model and the oscillation frequency band. First, the small signal model of PMSG wind farm grid-side system is established, and the small disturbance comparison with the PMSGA full-order electromagnetic transient model in MATLAB/Simulink is carried out. Then, we calculatue the eigenvalues of the small signal model and use model analysis techniques such as participation factors calculation and root locus method to identify the critical factors that cause the oscillation modes to be dominant. Finally, time-domain simulation is used to verify the theoretical analysis. Two dominant modes are identified: the subsynchronous oscillation mode and the low-frequency oscillation mode. The subsynchronous oscillation mode is closely related to the direct current (DC) voltage control and the dynamics of DC link. The low-frequency oscillation is significantly weakened with the decrease in grid strength, and it is closely related to the phase-locked loop (PLL) control. The conclusions can provide a reference for tuning the control parameters of PMSG converter.

Design of a Wide-Area Power System Stabilizer to Tolerate Multiple Permanent Communication Failures

Wide-Area Power System Stabilizers (WAPSSs) are damping controllers used in power systems that employ data from Phasor Measurement Units (PMUs). WAPSSs are capable of providing high damping rates for the low-frequency oscillation modes, especially the inter-area modes. Oscillation modes can destabilize power systems if they are not correctly identified and adequately damped. However, WAPSS communication channels may be subject to failures or cyber-attacks that affect their proper operation and may even cause system instability. This research proposes a method based on an optimization model for the design of a WAPSS robust to multiple permanent communication failures. The results of applications of the proposed method in the IEEE 68-bus system show the ability of the WAPSS design to be robust to a possible number of permanent communication failures. Above this value, the combinations of failures and processing time are high and they make it difficult to obtain high damping rates for the closed-loop control system. The application and comparison of different optimization techniques are valid and showed a superior performance of the Grey Wolf Optimizer in solving the optimization problem.

Identification and damping of low-frequency oscillations based on WAMS data and the revisited residue method – part I

The results of low-frequency oscillations identification in the Republic of Kazakhstan power grid by using a Wide Area Measurement System are presented and an algorithm for damping low-frequency oscillations is proposed in this paper. Analysis of weakly damped inter-area low-frequency oscillations revealed a constant mode with a frequency range of 0.3‒0.4 Hz. It was determined that at these low-frequency oscillations, the amplitude of active power fluctuations along the transmission line was 150 MW with a duration of 9 minutes. The modal analysis calculation of the Republic of Kazakhstan power system model in the «DigSilent Power Factory» software shows the dangerous low-frequency oscillation modes having a damping ratio is 2.2 % and an eigenfrequency 0.328 Hz. These oscillation modes identified by the real data and in the developed model indicate the incorrect tuning of power system stabilizer parameters at power plants. It is necessary to retune the power system stabilizer parameters whenever changing the system’s and mode’s configurations. An analysis of existing power system stabilizer tuning methods was performed, and revisited residue method was determined as sufficiently effective. Thus, the developed algorithm for identification and damping of low-frequency oscillation consists of three tasks. The first task is data collection from the Wide Area Measurement System and Supervisory Control and Data Acquisition system and updating the calculation model based on the current status of equipment (generators, transformers, transmission lines, etc.). The second task is the identification of dangerous electromechanical oscillations and modal analysis based on information obtained in real-time. The third task is tuning the power system stabilizer parameters for damping dangerous low-frequency oscillation modes based on the revisited residue method

Damping of Inter-Area Oscillations Using TCPS Based Delay Compensated Robust WADC

Low-frequency oscillations (LFOs) pose a significant obstacle in achieving optimal power flow and utilizing transmission corridors in large interconnected power systems. In this study, linear matrix inequality (LMI) base robust wide-area damping controller (WADC) is introduced to effectively address critical LFOs. The proposed WADC utilizes wide-area signals, which modulate the phase angle of a thyristor-controlled phase shifter device. To ensure that the concerned modes of LFOs lie in left half of the complex plane, a D-space sub-region approach is applied. However, using wide-area signals introduces time delays, which negatively impact the efficacy of the WADC; hence, a time delay compensator (TDC) is incorporated into the feedback path of the signals. The proposed approach involves four key steps: selecting feedback signals using a combined modal transformation and geometric approach, designing an appropriate TDC, building a generalized plant with mixed sensitivity weights, and solving the LMI. The dynamic efficacy is verified on IEEE 4-machine 11-bus system, and 10-machine 39-bus system. Poorly damped single and multiple critical modes are placed in the D-space region of interest with specified damping ratios viz. 10% and 15%. Furthermore, damping ratios of critical modes are maintained with TDC based proposed WADC while deteriorating with other counterparts.

Enhanced Visualization and Characterization of Low Frequency Oscillations in Power System

Real-time monitoring ofoscillation events provides enhanced wide-area situational awareness to the system operator. This article focuses on visualizing low frequency oscillatory modes, their detection, and classification following an event. The significant oscillatory modes present in the signal are extracted through a novel energy preserving, nonredundant “frequency partition based mode extraction (FPBME)” algorithm. These modes are analytically deduced and classified as governor mode, interarea mode, and local mode through a novel “energy based mode detection and classification (EBMDC)” algorithm. This article proposed method introduces the concept of “visualization” that is highly operator-friendly through the time domain plots of extracted modes. Time-domain plots of mode’s instantaneous frequency and instantaneous energy, which are considered fundamental characterization of low-frequency oscillations, are also portrayed through the developed method. The proposed method is validated through various scenarios of Kundur’s two-area system and IEEE-39 bus system. A practical test case on the ISO-NE system is also verified through the suggested scheme. Comparison of the proposed method in the context of visualization with other methods such as the Hilbert–Huang technique and continuous wavelet transform is also discussed in this article. The comparative assessment demonstrates the superior performance of the proposed method.

Modeling and Low-Frequency Oscillation Analysis of an Asymmetrical Traction Power System Connected to Power Grid

The traction power system is supplied by three-phase power grids in China, forming an asymmetrical system. However, current research on wideband-oscillation analysis of the traction power supply system assumes that vehicles in a feeding section are supplied by a single-phase ideal voltage source. Meanwhile, the existing vehicle impedance models are inapplicable for the stability analysis of this asymmetrical system. In this article, a single-input and single-output impedance of the vehicle is derived and the corresponding admittance can be directly used to form the system node admittance matrix and to analyze system stability by the modal analysis. The node admittance matrix of this asymmetrical system is established by putting the derived vehicles’ admittance into the node admittance matrix of two feeding section traction networks, the traction transformer and the equivalent circuit of power grids. Then, the modal analysis method is used to obtain the low-frequency oscillation modes of this asymmetrical system and to analyze the sensitivities of different parameters to the oscillation mode. The interaction between the two feeding sections and their interaction with power grids is studied. Finally, the correctness of theoretical findings is verified by simulation in MATLAB/Simulink and experiment in Starsim/HIL.