Analysis Of Low-frequency Oscillations Research Articles

SISO Stability Criterion Derived from a Three-Port Admittance Model of Train-Network System and Its Applications in Low-Frequency Oscillation Analysis

SISO Stability Criterion Derived from a Three-Port Admittance Model of Train-Network System and Its Applications in Low-Frequency Oscillation Analysis

Non-Invasive Continuous Optical Monitoring of Cerebral Blood Flow after Traumatic Brain Injury in Mice Using Fiber Camera-Based Speckle Contrast Optical Spectroscopy.

Neurocritical care focuses on monitoring cerebral blood flow (CBF) to prevent secondary brain injuries before damage becomes irreversible. Thus, there is a critical unmet need for continuous neuromonitoring methods to quantify CBF within the vulnerable cortex continuously and non-invasively. Animal models and imaging biomarkers can provide valuable insights into the mechanisms and kinetics of head injury, as well as insights for potential treatment strategies. For this purpose, we implemented an optical technique for continuous monitoring of blood flow changes after a closed head injury in a mouse model, which is based on laser speckle contrast imaging and a fiber camera-based approach. Our results indicate a significant decrease (~10%, p-value < 0.05) in blood flow within 30 min of a closed head injury. Furthermore, the low-frequency oscillation analysis also indicated much lower power in the trauma group compared to the control group. Overall, blood flow has the potential to be a biomarker for head injuries in the early phase of a trauma, and the system is useful for continuous monitoring with the potential for clinical translation.

Identification and Analysis of Low-Frequency Oscillation in a Multi-Grid-Forming-VSC Grid-Connected System

The existing low-frequency oscillation analysis method of a multi-grid-forming-VSC (voltage source converter) is greatly affected by modeling accuracy, and its oscillation mode can only be determined by acquiring the control parameters of the system. Therefore, a method of identifying low-frequency oscillation characteristics of multi-VSC based on VMD (variational mode decomposition) and a Prony algorithm was proposed in this paper. The Prony algorithm is sensitive to noise, and its identification accuracy is greatly affected by noise. Thus, the VMD algorithm was utilized to denoise the measured data. Then, the Prony algorithm was applied to analyze the low-frequency oscillation of the measured data of single VSC and multi-VSC grid-connected systems, and its applicability to different grid-forming VSCs was verified. The error comparison results showed that the proposed low-frequency oscillation identification method had high accuracy. Furthermore, the influence of the number of parallel VSCs, grid strength and active output on the low-frequency oscillation of the system was investigated. Finally, the effectiveness of the proposed low-frequency oscillation method was verified by building a physical experimental platform.

Impedance Modeling and Mechanism Analysis of Low-Frequency Oscillations in Single-Phase MMC-RPC Integrated Vehicle-Grid Coupling System

The single-phase modular multilevel converter-based railway static power conditioner (MMC-RPC) has significant advantages in governing the power quality problems in the traction power supply system. The mechanism analysis of low-frequency oscillations (LFOs) in the MMC-RPC integrated vehicle-grid coupling system when electric multiple units are put into operation is a critical issue, which has been investigated in this article. The third-order ac admittance models of single-phase MMC-RPC and vehicle rectifiers are developed for the first time. To comprehensively study the small-signal stability of the MMC-RPC integrated vehicle-grid coupling system, this article proposes a modal analysis method based on modal phase margin and parameter sensitivity and combined with the generalized Nyquist stability criterion. It is found that LFOs around 10 Hz or 48 Hz are prone to occur due to the interactions of MMC-RPC or vehicle rectifiers with the traction power grid. To reveal the LFO mechanism, dominant modes and key parameters leading to LFOs in different working scenarios are clarified, and a series of guidelines are proposed for LFO elimination. Furthermore, the effects of control loops and power flow of MMC-RPC on system stability are revealed in detail. Finally, real-time hardware-in-the-loop experimental results validate the theoretical analysis.

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.

Revamped Sine Cosine Algorithm Centered Optimization of System Stabilizers and Oscillation Dampers for Wind Penetrated Power System

The mapping of damping ratios and damping factors by Sine-Cosine Algorithm (SCA) is significant in the analysis of low frequency oscillations generated in an integrated network having multiple conventional and renewable energy sources. Multiple random models with unknown search spaces and uncertain conditions and constraints, which incorporate the fluctuation of solutions towards or outwards at the initial stage for solving real-time problems can be analyzed by a revamped sine-cosine algorithm (RSCA) model. In this paper, the SCA has been revamped to explore the stability threshold for a stable system under dynamic nonlinear operating conditions. It is achieved with the infusion of suitable mathematical functions for optimizing the parameters of Power System Stabilizers (PSSs) and Doubly Fed Induction Generator (DFIG) system-based oscillation dampers to enhance the Small Signal Stability of power systems through effective damping of low-frequency oscillations (LFOs). These LFOs weaken the effective power generation and demand management cycle in conventional power systems when the system faces conditions like intermittent renewable energy sources, overloading conditions, impulsive faults etc. The small-signal and transient stability studies for various disturbances and different operating conditions are investigated, and the performance of the proposed RSCA for optimized parameter tuning of system stabilizers and oscillation dampers are analyzed on the modified benchmarking systems with wind generators using MATLAB Ⓡ simulations. The efficiency and robustness of the proposed algorithm has been verified under selective critical operating conditions, line outages, and load uncertainties to prove that the low frequency modes are damped with an elevated positive damping ratio and rapid settling time with reduced oscillations. The application of system stabilizers and oscillation dampers optimized through the proposed RSCA shows a reduced settling time in the LFOs created and improved damping ratio of 0.22 for an increase in 20% loading and 50% of wind power generation in the case study of Two Area Four Machine System.

Development of methods for visual representation of low-frequency oscillation parameters in power systems

The development of wide area measurement system (WAMS) expands the analysis capabilities of the Unified power system based on computational processing of synchronized phasor measurements (SPM). The analysis of low-frequency oscillations (LFO) in the power system is one of the most relevant applications of WAMS data. The task of locating the source of forced LFO in real-time is highlighted. Due to the increasing complexity and heterogeneity of real power systems, a definitive solution to this problem does not currently exist. However, there are SPM data analysis methods that provide a high probability of identifying the source of oscillations. Informative representation of measurement signals, intermediate, and final LFO analysis results can serve as the basis for decision support tools for operational dispatch personnel. Direct visualization of raw data and computed parameters, such as a set of time function graphs, is inefficient due to the large volume. Therefore, compact high-level representations are in demand. This paper proposes some approaches to visualizing SPM data, computed LFO parameters, and the results of applying various oscillation source detection methods. The presented data visualization methods have been implemented by the authors in a LFO analysis software system.

Low-Frequency Oscillation Analysis of Grid-Connected VSG System Considering Multi-Parameter Coupling

With the increasing integration of new energy generation into the power system and the massive withdrawal of traditional fossil fuel generation, the power system is faced with a large number of stability problems. The phenomenon of low-frequency oscillation caused by lack of damping and moment of inertia is worth studying. In recent years, virtual synchronous generator (VSG) technique has been developed rapidly because it can provide considerable damping and moment of inertia. While improving the stability of the system, it also inevitably causes the problem of active power oscillation, especially the low mutual damping between the VSG and the power grid will make the oscillation more severe. The traditional time-domain state-space method cannot reflect the interaction among state variables and study the interaction between different nodes and branches of the power grid. In this paper, a frequency-domain method for analyzing low-frequency oscillations considering VSG parameter coupling is proposed. First, based on the rotor motion equation of the synchronous generator (SG), a second-order VSG model and linearized power-frequency control loop model are established. Then, the differences and connections between the coupling of key VSG parameters and low-frequency oscillation characteristics are studied through frequency domain analysis. The path and influence mechanism of a VSG during low-frequency power grid oscillations are illustrated. Finally, the correctness of the theoretical analysis model is verified by simulation.

Application of Hilbert Spectrum based on SWT to Low-Frequency Oscillation Analysis

Low-frequency oscillation (LFO) appears in power systems with fast excitation of a unit or large-scale connections. An LFO signal exhibits typical nonstationary and time-varying characteristics. The paper proposed an LFO analyzing technique through the Hilbert spectrum of stationary wavelet transform (SWT). The SWT-based Hilbert spectrum contains time-varying and frequency information of LFO. The analytic framework is introduced, SWT is formulated to decompose an LFO signal into the sum of several coefficient components, the instantaneous parameters of each coefficient are then individually calculated, the complete time-frequency distribution is combined, and finally, the time-varying oscillations characteristics parameters are extracted. The simulation shows that the proposed method effectively reveals time-frequency features of the LFO signal.

Modeling and Analysis of Low-Frequency Oscillation for Electrified Railway under Mixed Operation of Passenger and Freight Trains

Addressing the shortcomings of existing low-frequency oscillation research on electrified railways, which has mainly focused on single-type trains and lacks the accurate modeling of traction inverter systems, in this paper we modeled and analyzed low-frequency oscillations in an electrified railway passenger and freight mixed-operation vehicle–grid system. First, an equivalent model of the DC side of the traction inverter was established, with the inverter system being equivalent to the parallel connection of the load resistance and the current source, and the specific mathematical expression was determined and verified by impedance measurement. Secondly, based on the equivalent model of the DC side of the traction inverter, a small signal model of the vehicle–grid system under the mixed operating conditions of CRH5 and HXD2B considering the inverter system was established. The generalized Nyqusit criterion was used to study the low-frequency oscillation characteristics under mixed transportation conditions. The accuracy of the established model and the correctness of the theoretical analysis were verified based on Matlab/Simulink. Finally, using the dominant pole theory to analyze the low-frequency stability conditions, the relationship between the number of mixed trains and the minimum short-circuit ratio was obtained, and the simulation verification was carried out.

Low-frequency oscillation analysis of two-stage photovoltaic grid-connected system

The low-frequency oscillation (LFO) problem of photovoltaic (PV) grid-connected systems has been a critical concern for safe operation, whereas the impact of dc-side components of PV plants are always ignored and single-stage PV plant is used. This paper performs a comprehensive analysis of the LFOs in the two-stage PV grid-connected system. The complete small-signal model of the two-stage PV system is built. On this basis, the LFO modes and high-frequency oscillation (HFO) modes are calculated and related participating components are determined. Then, the impact of key parameters on the LFO characteristics is investigated with the root locus analysis. The theoretical analysis is verified through PSCAD/EMTDC simulations.

Analysis of low-frequency oscillation in power system with renewable energy sources

The development of electric power systems determines the growing probability of low-frequency oscillations, which can be reason of system faults. Traditionally, the task of damping low-frequency oscillations is assigned to synchronous generators, by appropriate setting of the automatic voltage regulator parameters. However, as the installed capacity of renewable generation units increases, research aimed to analyse the impact of these generation units on the power oscillations in the electric power system is becoming more relevant. Moreover, an evaluation of the potential of renewables to solve the problems of power oscillation damping seems necessary to expand the operation functions of the these generation units and to increase the stability of the electric power systems. This paper presents an analysis of renewable energy plants, in particular photovoltaic stations, on damping of these power oscillations. Achieving such damping function is possible via upgrading the automatic control system of photovoltaic stations by using a synthetic inertia block and the possibilities of the “underload” mode. Different scenarios, including small disturbances and severe fault condition for strong and weak grids depending on the location and capacity of photovoltaic station were considered. To evaluate the impact of renewable generation unit to the damping properties of electric power system, the transient damping ratio was calculated. The calculation was carried out in accordance with the guidelines in case of three-phase short-circuit for a different penetration level of renewable generation unit, as well as with and without the synthetic inertia block.

Low-Frequency Oscillation Analysis of Virtual-Inertia-Controlled DC Microgrids Based on Multi-Timescale Impedance Model

Virtual inertia and damping control (VIDC) improves the stability of DC microgrid (DC-MG). However, the potential positive feedback aggravates low-frequency oscillation induced by the interaction insides control loops, which is explained and solved in this paper. The multi-timescale impedance modelling framework is established to clarify stability mechanism of VIDC and the low-frequency oscillation of VIDC controlled DC-MG. Control loops of different timescales are visualized as independent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">loop virtual impedance</i> (LVI) elements to form an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">impedance circuit</i> considering the constant power load (CPL), rather than an all-in-one impedance as the external dynamic representation of power converters. Concrete impedance analysis is performed on LVI to reveal the impedance-shaping effect of control loops intuitively, the physical impedance nature of control parameters and the interaction among different timescale, which illustrates the stability mechanism of VIDC. The low-frequency oscillation ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> impedance interaction) in voltage- and inertia-loop is elaborated by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> circuits of LVIs. The potential instability factors, resulting in poor damping against voltage oscillation, are also revealed. Thus, dynamic stability enhancement method is further proposed to compensate for the negative damping caused by positive feedbacks of VIDC and CPL, and super-capacitor is added to alleviate rapid voltage changes. Accordingly, the passivity property of system impedance is strengthened and the stability can be evaluated by Nyquist plot. Finally, the simulation and experiment results have validated the low-frequency oscillation analysis and stability enhancement method.

A Hybrid Technique for Analysis of Low-Frequency Oscillation in Power System

Estimating the low-frequency oscillation in an interconnected power system is the most important requirement to keep the power system in a stable operating condition. This research work deals with a hybrid robust and accurate approach using a combination of Estimation of signal parameters via rotational invariant techniques (ESPRIT) and Prony algorithm to extract the low-frequency oscillatory modes present in the power system. The observation inspires the hybrid method that the true modes of the signal are present in any signal processing technique (for example, Prony algorithm) along with other fictitious modes regardless of the order of the power system. Moreover, this research obtained true modes by calculating Euclidean distance and applying the threshold value concept. The proposed technique is tested with different noise conditions and varying sampling rates of Phasor Measurement Unit (PMU) to check the proposed hybrid technique’s robustness compared to Prony and the multiple ESPRIT method. Finally, the proposed method is applied to the real signal obtained from the Western Electricity Coordinating Council (WECC) network, and it estimates accurate and precise parameters compared to other methods. The accuracy for estimation of frequency and attenuation factor is calculated for the three-mode synthetic signal at a noise level of 10dB by the hybrid algorithm, multiple ESPRIT, and Prony algorithm, which shows that hybrid algorithm has minimum percentage error. Thus, the proposed hybrid algorithm accurately estimates the parameters of low-frequency oscillation as compared to other existing methods without involving any fictitious modes.

Low-Frequency Oscillation Analysis of VSM-Based VSC-HVDC Systems Based on the Five-Dimensional Impedance Stability Criterion

Virtual synchronous machine (VSM) based high voltage dc systems enhance the inertia of the power system. However, the dynamic interactions between the VSM-based rectifier station, the inverter station, and the grid could induce the system oscillation, which has been investigated in this article. At first, the hybrid ac–dc impedance models of the VSMs considering the coupling between the ac and dc dynamics are established. Then, the relationships between the dc impedance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -frame impedance, and the hybrid ac–dc impedance are presented. It is found that the dc impedance of the VSM-based inverter station and the d-d channel impedance of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -frame impedance of the rectifier station behave as negative resistors in the low-frequency range. Moreover, a five-dimensional impedance stability criterion based on the hybrid ac–dc impedance and generalized inverse Nyquist criterion is proposed to assess the system stability. The analysis results show that the low-frequency oscillation occurs when the grid short-circuit ratio of the rectifier station is small. Finally, the simulation and experimental results verify the impedance models and the stability criterion.

Impacts of Quadrature Signal Generation-Based PLLs on Low-Frequency Oscillation in an Electric Railway System

The low-frequency oscillation (LFO) issue has occurred frequently in single-phase electric train and traction network interactive systems (hereinafter train-network systems). On a single-phase electric train, the quadrature signal generation-based phase-locked loop (QSG-PLL) has been widely used to achieve unit power factor operation. The bandwidth of the single-phase PLL is close to the frequency of the LFO, but its impacts on the LFO are not considered fully in previous works. In this article, three typical QSG-PLLs are studied in depth, and their unified model is derived in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> frame. Furthermore, the impacts of the QSG-PLL structure and parameters on the LFO are revealed. The analysis results indicate that the QSG part plays an important role in the LFO analysis, but the parameters of the PLL part have slight impacts on the train’s impedance under the low-power operation mode. Three different QSGs can all be regarded as providing a second-order low-pass filter (LPF) to generate the virtual <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> component in the single-phase system. The higher damping ratio of the second-order LPF can increase the magnitude of the train’s impedance, which is beneficial to enhance the stability of the train-network system. Finally, experimental results via hardware in loop (HIL) are employed to verify the correctness of the theoretical analysis results.

Low Frequency Oscillations in a Hydroelectric Generating System to the Variability of Wind and Solar Power

The penetration of multiple integrated renewable energies to the power grid are relevant for decision making in energy policy, environment and business. Such an electricity penetration is affected by the intermittent and volatile characteristics of integrated energies, mostly significantly related to the safe and stable electricity production and supply in real world. Here, this paper focuses on the low frequency oscillation analysis of the hydropower generation response to the wind and solar variability. To enable this analysis, a hybrid model of hydropower system integrating with the wind and solar power system is presented. The Nyquist and root-locus stability methods are used to investigate the sensitivity performance of the hydropower governor to the fluctuation of the integrated renewable energies. Additionally, to quantify the risk of the hybrid system, the low frequency oscillation response of hydropower system to wind/solar/hydropower quota and transmission line distance ratio is extensively investigated in this study. The results show that under the case of the wind, solar and hydropower ratio is 40:1:150, the optimal values for maximally reducing hydropower low frequency oscillation are finally determined as kp = 0.8, ki = 0.25 and kd = 0.5. Regarding a certain wind/solar/hydropower quota, it is a promising strategy to increase the solar-load transmission line in order to achieve the safe and stable operation of the hybrid system and a relatively excellent dynamic regulation capacity of the hydropower governor. The model, methods and results implemented in this study are exploited to markedly improve new knowledge applications, policy management, low carbon emissions and investment competitiveness of future energy systems.

Reduced-Order Analytical Models of Grid-Connected Solar Photovoltaic Systems for Low-Frequency Oscillation Analysis

Low-frequency oscillations have been observed in a real-world solar photovoltaic (PV) farm. The goal of this research is to build a simplified analytical model in the synchronous frame for large-signal simulation and small-signal analysis. The latter, e.g., eigenvalue analysis and participation factor analysis, can reveal influencing factors of the oscillations. Two simplified analytical models are proposed, ignoring PV dc-side dynamics (e.g., dc/dc boost converter control and maximum power point tracking), while preserving the grid-side converter (GSC) controls and electromagnetic dynamics of the grid interconnection. The first model assumes the input power from PV's dc side known and constant. The second model assumes that PV's dc side is represented by a constant dc voltage behind an impedance. The simplified models are compared with an electromagnetic transient (EMT) testbed with full details on time-domain simulation results, admittance frequency-domain responses, and eigenvalue-based stability analysis results. The second simplified model is found as capable of accurately predicting oscillation stability.

A Novel ESPRIT Algorithm for Analysis of Low Frequency Oscillations in Power System

With rapidly increasing load and randomly varying load scenario in a densely connected power system may lead to low-frequency oscillations which can further make a power system unstable. To keep the power system in stable operating limits identifying such dominant low-frequency oscillations is essential. Numerous signal processing techniques are used to detect low-frequency oscillations in a power system. Different techniques have their advantages and disadvantages. Estimation of signal parameters via rotational invariance technique (ESPRIT) is a signal processing technique by which low-frequency oscillations can be identified even under noisy conditions . In this paper, a novel ESPRIT algorithm for identifying low-frequency oscillations is proposed. This methodology is based on the ESPRIT algorithm, whose key concept is that real modes existing in oscillations emerge consistently regardless of the algorithm's order. The performance of this algorithm is verified through a set of synthetic signals generated in MATLAB with different noise levels and varying PMU rates and compared with traditional Prony algorithm. The performance of the proposed algorithm is also verified on real-time test data obtained from the Western Electricity Coordinating Council (WECC). This technique performs fairly well in finding low-frequency oscillation characteristics in the power grid.

Specific Features of Using the Linearization Method for the Analysis of Low-Frequency Oscillations of a Towed System

The results of experiments and numerical calculations in the low-frequency range of oscillations of the power and geometric characteristics of a towed system (TS) are presented. The hypotheses used in the linear amplitude-frequency analysis are verified with the use of a discrete model. The limits of applicability of the finite-difference method for numerical TS simulation are determined on the basis of a continuous hyperbolic model that takes into account varying lengthwise tension and finite speed of longitudinal and transverse (configurational) waves. The total error of numerical simulation does not exceed 15–20%. There is a certain delay both in the angle of TS deflection from the vertical and in the maximum horizontal component of the tensile force at its root point. It may be one of the causes of breakage of TS in certain conditions of oscillations and at a certain towing speed, when the tugboat and the TS oscillate in antiphase.