Low-frequency Stability Research Articles

Low Frequency Stability of AC Railway Traction Power Systems: Analysis of the Influence of Traction Unit Parameters

Dynamic interactions between AC railway electrification systems and traction unit power converters can result in low frequency oscillation (LFO) of the contact-line voltage amplitude, which can lead to a power outage of the traction substation and the shutdown of train traffic. Several system parameters can influence the low frequency stability of the railway traction power system, including contact-line length and traction unit parameters such as transformer leakage inductance, DC-link capacitance, control bandwidths and synchronization systems. This paper focuses on the influence of these parameters on the LFO. The methodology is based on a frequency-domain analysis. Nyquist and Bode diagrams are used to determine the stability limit. The validation of the method is performed through the use of time-domain simulations.

Interactions analysis and quadrature voltage compensation control for stabilizing LCC-HVDC system with multiple STATCOMs

Instability may occur in LCC-HVDC system when multiple STATCOMs operate simultaneously at the inverter station. To deeply investigate this problem, firstly a structured linear model of LCC-HVDC system with STATCOMs is presented. Then, a single-input single-output (SISO) form of the model is obtained. Based on the movement of dominant poles (MODPs) of the SISO model, the interactions at the receiving end of the system are investigated. The results reveal that the interactions between LCC and STATCOMs mainly affect the high-frequency (HF) characteristics of the system. With the increase in the number of online STATCOMs, the negative effects of the interactions on the system HF stability gradually increase, while that on low-frequency (LF) stability become weaker. In order to improve such negative interactions, a quadrature voltage compensation control (QVCC) of STATCOM is proposed in this paper. This method introduces the q-axis AC voltage into the constant AC voltage control (CAVC). The theoretical analysis indicates that the QVCC can enhance the stability of the LCC-HVDC system with multiple STATCOMs, which is verified by the simulation results conducted in PSCAD/EMTDC. Finally, the intuitive and physical explanations on the mechanism of instability caused by increasing number of online STATCOMs are given from two perspectives.

Analysis of noise during unbalanced braking of disc brake friction plates

The non-equilibrium contact phenomenon caused by the time difference between the friction plates on both sides and the brake disc during the braking process of the disc brake was analyzed. The brake noise problem in this non-simultaneous clamping condition was studied. Then a three-dimensional assembly model was established and the finite element method was used to find the complex mode and its instability coefficient under different operating conditions when t h e b r ak e w as in u n b al an ce d con ta ct. T he r esults s how th at during non-equilibrium braking, the inherent frequency and low-frequency stability of the braking system decreases, the instability modes increase significantly, and the shorter time difference leads to a strong tendency of whistling.

Microstructure and dielectric properties of (Ba0.6Sr0.4)TiO3/PEEK functional composites prepared via cold-pressing sintering

Ceramic/polymer dielectric functional composites have attracted extensive attention because of their applications in portable electronic devices, filters and other fields. However, the high dielectric loss and the attenuation of dielectric constant with frequency limit the applications. Here, (Ba0.6Sr0.4)TiO3/PEEK (BST/PEEK) composites with high frequency stability of the dielectric constant and low dielectric loss were prepared via cold-pressing sintering. The dielectric frequency stability of BST/PEEK composites was assessed by employing the frequency dispersion factor F(x). The results showed the BST/PEEK composites possessed the optimal properties with a permittivity of 23, a loss of 0.0065, an F(x) of <5%, and a dielectric tunability of 11.9% when the BST concentration was 40 vol% and the composites were sintered at 360 °C for 1 h. In addition, the numerical fitting results of dielectric constant of composites showed that the Yamada model with a shape factor n of 9.5 would obtain the best simulation result by keeping the relative error lower than 2%. This work provides the idea for obtaining a new composite with low loss and high frequency stability.

A New Tool to Assess Maximum Permissible Solar PV Penetration in a Power System

With diminishing fossil fuel resources and increasing environmental concerns, large-scale deployment of Renewable Energy Sources (RES) has accelerated the transition towards clean energy systems, leading to significant RES generation share in power systems worldwide. Among different RES, solar PV is receiving major focus as it is most abundant in nature compared to others, complimented by falling prices of PV technology. However, variable, intermittent and non-synchronous nature of PV power generation technology introduces several technical challenges, ranging from short-term issues, such as low inertia, frequency stability, voltage stability and small signal stability, to long-term issues, such as unit commitment and scheduling issues. Therefore, such technical issues often limit the amount of non-synchronous instantaneous power that can be securely accommodated by a grid. In this backdrop, this research work proposes a tool to estimate maximum PV penetration level that a given power system can securely accommodate for a given unit commitment interval. The proposed tool will consider voltage and frequency while estimating maximum PV power penetration of a system. The tool will be useful to a system operator in assessing grid stability and security under a given generation mix, network topology and PV penetration level. Besides estimating maximum PV penetration, the proposed tool provides useful inputs to the system operator which will allow the operator to take necessary actions to handle high PV penetration in a secure and stable manner.

Сучасні проблеми низькочастотної динаміки рідинних ракетних двигунних установок

One of the key problems in liquid-propellant rocket engine (LPRE) design is to provide the stability of LPRE working processes, in particular low-frequency stability. In LPRE experimental tryout, every so often there occur situations where the development of divergent oscillations set up in some of the LPRE loops or units results in contingencies: exceeding the engine ultimate strength, pump stall, chamber ignition, etc. Such contingencies may lead to grave consequences, including engine and bench equipment failure. Because of this, mathematical simulation is one of the main tools that allow one to predict he dynamic performance of an LPRE both in its steady operation and in transients and its startup operation features at the design and tryout stage. This paper overviews and analyzes scientific publications for the past 15 years concerned with the study of the dynamics and low-frequency stability of advanced LPREs and units thereof along different lines. This analysis made it possible to identify problems in low-frequency stability prediction and assurance for liquid-propellant rocket propulsion systems (LPRPSs) under design, to cover new research results (experimental and theoretical) on the origination and development of all-engine low-frequency oscillations and low-frequency oscillations in LPRPS systems and units and to identify new approaches to the mathematical simulation and study of low-frequency processes in LPRPSs and promising lines of investigation. The man lineы of the analysis are as follows: the low-frequency dynamics of cavitating inducer-equipped centrifugal pumps and LPRE gas paths, LPRE thrust control problems, the interaction of launch vehicle airframe longitudinal oscillations with low-frequency processes in the sustainer LPRPS, dynamic processes during an LPRE startup/shutdown, and low-frequency in-chamber oscillations.

Research on the FM control for hydraulic wind turbine based on virtual inertia compensation control method

Wind has been admitted as one of the most promising renewable energy resources in multinational regionalization policies. However, the intermittent wind energy volatility and the weak coupling between traditional wind generators and the power grid all influence the electrical grid frequency stability. The hydrostatic transmission wind turbine (HWT) is taken as the research object, and the hydraulic energy storage system (HESS) is introduced into HWT to improve the frequency regulation capability. First, the mathematical models of rotor, hydraulic power main transmission system, and the excitation synchronous generator are established. Then, the HWT frequency modulation characteristics are analyzed under different amplitude of load frequency fluctuation. In view of the HWT limited frequency modulation capability, the frequency modulation control strategy based on virtual inertia compensation is proposed with the HESS. Under the condition of maximum power point tracking, the effectiveness is verified. The simulation and experimental results show that the control strategy has a good control effect, and the HESS dynamic response characteristic satisfies the wind power–frequency regulation. The research results will be helpful to make wind power become grid-friendly power and solve the problem of electrical grid low frequency stability.

Low-Frequency Stability Analysis of Vehicle-Grid System With Active Power Filter Based on dq-Frame Impedance

To eliminate the low-frequency oscillation (LFO) phenomenon in the vehicle-grid system of high-speed railways, a single-phase cascaded H-bridge multilevel active power filter (APF) directly accessed to the 27.5-kV traction network is proposed in this article, which can provide the dynamic reactive and interharmonic compensation. To explore the mechanism of APF on LFO suppression, the dq-frame impedance model of vehicle-grid system with APF is established first. The impact of the second-order generalized integrator model and the duty ratio model on the impedance accuracy is discussed in detail. Then, based on the generalized Nyquist stability criterion and system power consumption criterion, the stability of vehicle-grid system and its sensitivity to parameters in different cases are compared. The results indicate that the proposed APF can significantly improve the low-frequency stability of vehicle-grid system and owns much better performance than the STATCOM proposed in previous literatures. Finally, the time-domain simulations in MATLAB and the experiments on the controller hardware in the loop platform are implemented, which further validate the accuracy of theoretical analysis and the superior performance of APF in LFO elimination.

An Active Voltage Stabilizer for a DC Microgrid System

This paper analyzes the low-frequency stability challenges that exist in a complex DC microgrid (MG) system. The converters that belong to a DC MG are categorized into different groups based on their control approach. The small-signal model of the DC MG is presented, and the conditions for system stability are derived. In some DC MG applications, there is the possibility of installing off-the-shelf converters with little flexibility and access for controller auto-tuning. To tackle this, a hardware-based active voltage stabilizer solution is proposed to stabilize the DC MG. The active stabilizer's functionality, based on an isolated bidirectional DC-DC converter, is elucidated, and a suitable control strategy is proposed. The active stabilizer and its associated control configuration involve only local voltage sensing and are non-intrusive. A dual active bridge (DAB) converter-based active stabilizer is implemented, and hardware-based steady-state and transient experimental results from a DC MG test-bench are provided to validate the functionality and effectiveness of the proposed active stabilizer.

Colossal permittivity of (Gd + Nb) co-doped TiO2 ceramics induced by interface effects and defect cluster

Material with high dielectric constant plays an important role in energy storage elements. (Gd + Nb) co-doped TiO2 (GNTO) ceramics with giant dielectric permittivity (>104), low dielectric loss, good temperature and frequency stability in broad range of 30–150 °C and 102–106 Hz have been systematically characterized. Especially, a low dielectric loss of 0.027 and a giant dielectric permittivity of 5.63 × 104 at 1 kHz are attained for the composition with x = 0.01. Results of complex impedance spectroscopy, I–V curve and frequency dependent dielectric constant under DC bias indicate that internal barrier layer capacitance (IBLC) effect, electrode effect and electron-pinned defect-dipole (EPDD) effect contribute to the colossal permittivity (CP) property simultaneously.

Multi-longitudinal mode fiber laser digital vibration-sensing system based on a multi-carrier modulation/demodulation technique.

A multi-longitudinal mode fiber laser sensor (MLMFLS) system based on a digital modulation/demodulation technique is proposed. To the best of the authors' knowledge, this is the first digital vibration-demodulation system ever reported by a MLMFLS system. Multiple beat frequency signals (BFS) generated by the MLMFLS work as signal carriers of applied vibration signals. The vibration signals modulated on several BFS at different frequencies are simultaneously demodulated based on a multi-channel digital down-conversion technique by utilizing the digital universal software radio peripheral (USRP). The demodulated vibration signals from different signal channels are superposed by the USRP. Signal-to-noise ratio (SNR) of output vibration signal is highly improved, which increases sensing stability and accuracy of the system. This is really important for sensing of vibration signals that have an extremely low frequency or weak energy. Measurement results demonstrate that the sensing system has an excellent low frequency vibration-sensing capability, simple structure, high SNR, stability and accuracy.

Low-Frequency Stability Analysis of Inverter-Based Islanded Multiple-Bus AC Microgrids Based on Terminal Characteristics

For system planning of three-phase inverter-based islanded ac microgrids, the low frequency instability issue caused by interactions of inverter droop controllers is a major concern. When internal control information of procured commercial inverters is unknown, impedance-based small-signal stability criteria facilitate prediction of resonances in medium and high frequency ranges, but they usually assume the grid fundamental frequency as constant and thus they are incapable of analyzing the low-frequency oscillation of the fundamental frequency in islanded microgrids. Aiming at solving this issue, this paper proposes two stability analysis methods based on terminal characteristics of inverters and passive connection network including the dynamics of the fundamental frequency for analysis of low-frequency stability in islanded multiple-bus microgrids. Based on the Component Connection Method (CCM) to systematically separate inverters from the passive connection network, a general approach is developed to model the microgrid as a multiple-input-multiple-output (MIMO) negative feedback system in the common system d-q reference frame. By applying the generalized Nyquist stability criterion (GNC) to the return-ratio and return-difference matrices of the MIMO system model, the low-frequency stability related to the fundamental frequency can be analyzed using the measured terminal characteristics of inverters. Analysis and simulation of a 37-bus microgrid verify the effectiveness of the proposed stability analysis methods.

High‐power microwave generation by double‐anode virtual cathode oscillator

AbstractThe virtual cathode oscillator (vircator) is one of the promising devices to oscillate high‐power microwaves. Simplicity and high‐power capability are advantages. However, the low efficiency and frequency stability are serious problems. In this article, we dealt double anode to strengthen the microwave interactions. The measurement result shows that the output of the virtual cathode oscillator can be progress by using the double‐anode.

Comparative analysis of probabilistic and deterministic approach to tune the power system stabilizers using the directional bat algorithm to improve system small-signal stability

The modern power system consists of a large mixture of renewable energy sources (RES), varying and flexible loads, and is also experiencing a situation where a significant number of conventional generators are being replaced by power electronics based sources. All of these factors may lead to a decrease in the small-signal stability (SSS) margin of the system which in turn can cause power system instability. Power system stabilizers (PSSs) are widely used to improve the low-frequency oscillatory stability of power systems. Currently, there are two popular methods to coordinate multiple PSSs to improve SSS: deterministic and probabilistic method. This paper first formulates the problem of coordinating multiple PSSs to improve SSS as a deterministic and a probabilistic optimization problem which is then solved using the new directional bat algorithm. A detailed comparison between the two design methods under different scenarios based on obtained results is carried out afterward. All of the analysis was carried out on a modified IEEE 68 bus system. The obtained results provide key insights as well as the advantages and limitations of the probabilistic and deterministic approach to optimize the PSS parameters.

Effect of Reactive Power Characteristic of Offshore Wind Power Plant on Low-Frequency Stability

Oscillation phenomena of offshore wind power plant (OWPP) in a wide frequency range can be caused due to impedance interactions between grid-connected inverters (GCIs) and transmission cables. In this article, impedance model of GCI with outer power control loop, inner current control loop and phase-locked loop is first established in dq reference frame. The correctness is validated by frequency scanning method. Then, the effects of active and reactive power/current references on dq impedance characteristics of GCI with/without consideration of power control loop are investigated using complex space vectors and complex transfer functions. Furthermore, RLC circuit model of transmission cable considering frequency-dependent characteristics is also established for dq-domain IBSC. On the basis of them, it's found that low-frequency oscillation phenomena of OWPP under power control mode may occur if active power reference exceeds a certain threshold value, which can be mitigated by injecting a certain amount of negative reactive power. Impacts of PLL parameters, length of transmission cable and number of paralleled GCIs on required negative reactive power for low-frequency stabilization are further investigated. Both Matlab/Simulink-based simulation and OPAL-RT-based real-time verification are implemented in an OWPP with four permanent magnet synchronous generators to validate the correctness of the reactive power characteristic analysis results and the feasibility of mitigating low-frequency oscillation phenomena by negative reactive power injection.

Multi-Area Automatic Generation Control Scheme Considering Frequency Quality in Southwest China Grid: Challenges and Solutions

Southwest China Grid (SCG) is one of the hydropower-rich power grids around the world. SCG has recently been into asynchronous operation mode, it is expected to face challenges in low inertia and frequency stability issues caused by the hydraulic turbine governing system (HTGS), which brings profound changes to the validity and stability for the multi-area automatic generation control (AGC) power systems. This article analyzes the frequency control problems of SCG according to the operation data from asynchronous operation tests. To overcome the large overshoot and reverse regulation for external disturbances, frequency-based segment values of frequency bias for areas under TBC mode are developed considering multi-deadband effects, and a switching method of control modes for supporting large-disturbance recovery is proposed. Based on the complex and nonlinear of AGC systems, a fuzzy PD+I controller is proposed to reduce the excessively large overshoot. Furthermore, the rule for tuning D gain is established by the sign of change of area control error (ACE), and flexible I-part is applied to the control process based on the relationship between ACE and frequency. Then, we also provide filter-based control strategies with adaptive parameters to effectively coordinate hydropower and thermal power generators. The filter coefficients are computed considering various delays within AGC systems. Some case studies and actual operating conditions demonstrate the efficiency and accuracy of the proposed ideas compared with current control strategies.

Low-Frequency Instability Induced by Hopf Bifurcation in a Single-Phase Converter Connected to Non-Ideal Power Grid

With the high-density operation of China Railways High-speed (CRH) series vehicles in railways, a large number of power electronic converters are connected to the traction network. Due to the nonlinear characteristics of power electronic converter, it is easy to cause the low-frequency oscillation (LFO) in the single-phase vehicle-grid system of high-speed railways when the converter is connected to a non-ideal power grid. In order to solve this problem, the time domain nonlinear dynamic average model is proposed in this paper. Given Jacobian method to probe into the low-frequency stability of single-phase vehicle-grid system based on Hopf bifurcation, the characteristics and applicability of this method is summarized. The effects of electrical and control parameters can be analyzed with this model. In addition, with the emergence of LFO, the stability boundary leading to catastrophic bifurcation is discussed in detail. In the end, theoretical analysis results are verified by simulations and hardware-in-the-loop (HIL) platform.

A well-posed surface currents and charges system for electromagnetism in dielectric media

The free space Maxwell dielectric problem can be reduced to a system of surface integral equations (SIE). A numerical formulation for the Maxwell dielectric problem using an SIE system presents two key advantages: first, the radiation condition at infinity is exactly satisfied, and second, there is no need to artificially define a truncated domain. Consequently, these SIE systems have generated much interest in physics, electrical engineering, and mathematics, and many SIE formulations have been proposed over time. In this article we introduce a new SIE formulation which is in the desirable operator form identity plus compact, is well-posed, and remains well-conditioned as the frequency tends to zero. The unknowns in the formulation are three dimensional vector fields on the boundary of the dielectric body. The SIE studied in this paper is derived from a formulation developed in earlier work by some of the authors~\cite{ganesh2014all}. Our initial formulation utilized linear constraints to obtain a uniquely solvable system for all frequencies. The new SIE introduced and analyzed in this article combines the integral equations from \cite{ganesh2014all} with new constraints. We show that the new system is in the operator form identity plus compact in a particular functional space, and we prove well-posedness at all frequencies and low-frequency stability of the new SIE.

Low-Frequency Noise Evaluation on a Commercial Magnetoimpedance Sensor at Submillihertz Frequencies for Space Magnetic Field Detection.

The purpose of this study was to measure the low-frequency noise and basic performance of a commercial magnetoimpedance (MI) sensor at sub-millihertz frequencies for use in space missions. Normally, space missions require measuring very weak magnetic fields with a long integration time, such as the space gravitational wave detection mission requiring sub-millihertz frequencies. We set up a platform for measuring the performance on this MI sensor, including low-frequency noise, measurement limit, linearity, and temperature stability. The results show that the low-frequency noise of the MI sensor is below 10 nT/√Hz at 1 mHz and below 100 nT/√Hz at 0.1 mHz; its measurement limit is 600 pT. The MI sensor is characterized by high precision, small size, and low noise, demonstrating considerable potential for application in magnetically sensitive experiments requiring long integration time. This is an effect way to solve the problem that there is on one suitable magnetic sensor at space magnetic field detection, but the sensor requires improvements in temperature stability.

Different Influence of Grid Impedance on Low- and High-Frequency Stability of PV Generators

Recently, the stability issues when renewable energy sources are connected to the weak grid have obtained great attention. The popular view thinks that the grid impedance is adverse to the system stability. However, in this paper, it is first found that for the photovoltaic (PV) generator, the grid impedance has different influence on the system stability depending on the frequency range when the complete model of the PV generator is taken into consideration. That is, the increase of grid impedance can suppress the low-frequency ( 300 Hz) stability. Concretely, for the low-frequency range mainly dominated by the power loop and voltage loop of the PV generator, the describing function method is adopted to overcome discontinuity and nonlinearity of the power loop. Then, the low-frequency dynamics such as power oscillation can be analyzed accurately. For the high-frequency range mainly dominated by the phase-locked loop and current loop of the PV generator, the impedance analysis method is adopted to reveal the high-frequency instability mechanism. Through these analyses, the different influence of grid impedance on the low- and high-frequency stability of PV generators can be clearly distinguished. All the conclusions are verified through the real-time hardware-in-loop tests.