Frequency Characteristics Of Systems Research Articles

Analysis of frequency characteristics of power system with wind farm-energy storage coordinated inertial control

With the increasing penetration level of wind power in the power system, the decoupling of wind turbine rotor speed and system frequency has led to the loss of the inertia of wind farms (WF), which can no longer be neglected. With the continuous development of energy storage (ES) technology, WF-ES coordinated inertial control has attracted attention as an effective means for wind turbines (WT) to participate in inertia response. How to build a WF-ES coordinated inertial control strategy and analyze system frequency characteristics has become a key research issue. In this paper, the frequency response model of a power system with WF-ES is established using the system frequency characteristic analysis method. The wind speed zones of the WF are taken into account, and different WF-ES control schemes are adopted under different wind speeds, aiming to ensure the active participation of WTs in the system frequency process across all wind speed conditions and effectively prevent frequency secondary drop. Finally, a power system frequency response simulation model is built in Matlab/Simulink to analyze the frequency characteristics of the power system with WF-ES coordinated inertial control and verify the feasibility of the proposed WF-ES coordinated inertial control strategy under various wind speeds.

Investigating Small Disturbance Stability in Wind Farm Grid-Connected Systems: A Data-Driven Approach

The presence of unknown synchronization characteristics, unclear instability mechanism, and various fault mode evolution laws, lacking corresponding theoretical support and analysis methods and instability criteria, are defined with clear physical concepts. It is still impossible to systematically understand the transient synchronization mechanism of the wind power grid-connected system from the perspective of the whole fault stage. Therefore, this study uniformly reveals its temporary synchronous stability problem and proposes a large/small disturbance adaptive synchronous stability control method, which improves the dynamic characteristics of the wind turbine through the control of the inverter itself to improve the system stability—using different scenarios, such as single doubly-fed wind turbines. The experimental results show that the small disturbance on the AC side significantly impacts the system characteristics, followed by a bit of annoyance on the DC side. The DC side fault will cause a change in system frequency characteristics, especially at the receiving end. However, compared with the Voltage Source Converters-High Voltage Direct Current (VSC-HVDC)system, Modular Multilevel Converters-High Voltage Direct Current (MMC-HVDC) systems operate at a much higher frequency and produce less low-frequency harmonics. This makes them less likely to induce subsynchronous oscillations in the system.

Frequency Control and Optimal Operation of Low-Inertia Power Systems With HVDC and Renewable Energy: A Review

With the integration of large-scale renewable energy sources (RES) and high voltage direct current (HVDC) based inter-regional transmission, modern power systems are facing low-inertia issues and poor frequency regulation capabilities. This paper conducts a comprehensive review on frequency control and optimal operation methods in this context. First, the frequency characteristic of a low-inertia power system is analyzed covering the whole frequency response process. Secondly, the impacts of RES and HVDC integration on system inertia and frequency performance are studied, and the system frequency characteristics considering RES and HVDC are analyzed. Then, the frequency response modes of various frequency regulation resources are compared from the perspective of “source-grid-load-storage”, including their basic control principles and frequency control strategies. Further, from the operation dispatch perspective, the frequency security-constrained power system optimal operation methods are reviewed. Finally, future research trends in this area are discussed.

Transient energy dissipation control of energy storage devices in wind power generation systems

The transient stability of power systems with high penetration of wind power generation can be significantly improved through the utilization of variable virtual inertia if the energy source of rotational inertia can be expanded by energy storage devices (ESDs). This paper first establishes the relationship of energy conversion between ESD and mechanical kinetic energy inside a synchronous generator (SG). Then, the impact of the controllable inertia on system frequency characteristics and power angle oscillation is analyzed using the small-signal model corresponding to this system. Based on the analysis of the change of transient energy at different stages in the transient process, the control of transient energy dissipation is proposed employing ESDs for reliable inertia support. Finally, a typical simulation system with high penetration of wind power generation is carried out to demonstrate the viability of the proposed control scheme. The test results show that the fluctuation of SG’s power angle and system frequency can be reduced by regulating the variable inertia in transient events, significantly improving the reliability of the inertia support provided by the ESDs.

INFLUENCE OF EXTERNAL CUBIC VISCOSITY ON THE DYNAMICS OF A CANTILEVER ROD LOADED WITH A TRACKING FORCE

The analysis of the influence of external nonlinear cubic viscosity on the behavior of a cantilever rod loaded with a compressive tracking force is performed. The Bernoulli – Euler beam model is used for the describing of the rod bending deformations. After the transition to dimensionless variables, we obtained the form of notation in which the coefficients of the equation do not depend on the coefficient of cubic viscous friction. This indicates the independence of the critical load and system frequency characteristics from the level of nonlinear attenuation. Using the standard procedure of the Bubnov – Galerkin method, taking into account the first two forms of eigen oscillations, the problem is reduced to the analysis of a fourth order nonlinear system of ordinary differential equations with respect to generalized coordinates and generalized velocities. For the linear version of the equations with low attenuation, the values of the critical load are obtained in dependence on the ratio of the damping coefficients of the eigenforms. The behavior of the system is analyzed taking into account the considered cubic nonlinearity using the method of nonlinear normal forms. The problem is reduced to the analysis of a nonlinear dynamical system with one degree of freedom. There are constructive analytical methods of qualitative and approximate quantitative research for this class of problems. The critical value of the compressive force was determined by the analysis of the dependence of the first Lyapunov magnitude on the load parameter. It turned out to be less than the value corresponding to the system without damping (the destabilizing effect of external nonlinear friction). A bifurcation occurs in the system at the critical load value. Therefore, the zero equilibrium becomes an unstable complex focus of the first order and a limit cycle is born. The function of the self-oscillations amplitude of the load magnitude is constructed using the harmonic linearization method.

Stages and main tasks of the century-long control theory and system identification development

The article provides a review of the mathematical description of the dynamics of continuous and discrete linear stationary systems and objects, used at the development stage of the classical theory of automatic control in the form of mathematical models of the «input-output» type. The time and frequency characteristics of continuous and discrete control systems are described, typical links of stationary systems are considered, parametric discrete models of objects as part of typical digital control loops are presented. Stochastic discrete autoregressive models of stationary time series used to describe the dynamic objects in the synthesis of digital control systems are considered. A review of standard control laws for the implementation of continuous and discrete controllers has been completed. A method for synthesizing discrete controllers for multidimensional controlled objects with different, unknown and changing delays is considered, through which variable delays are compensated in the characteristic equation of a closed-loop control system. A common technique for synthesizing one-dimensional and multidimensional controllers for stochastic objects with delays based on ARMAX models is considered. An analysis of approaches to identifying delays in controlled objects is carried out and a method for identifying delays when using input-output models is considered, based on the calculation and comparison of impulse responses for extended and non-extended models of the controlled object. An analysis of the advantages and disadvantages of «input-output» type models is given, as well as the possibilities of their application for solving various classes of control theory problems.

Stochastic generation maintenance scheduling with inertia-dependent primary frequency regulation constraints

The problem of insufficient inertia and frequency security becomes a critical concern in generation maintenance scheduling due to the increasing penetration of renewable energy sources (RESs). To address the issue, this paper presents a stochastic generation maintenance scheduling with inertia-dependent primary frequency regulation constraints. First, inertia-dependent primary frequency regulation constraints consisting of the minimum inertia requirement, frequency nadir, and quasi-steady-state frequency deviation are formulated based on the dynamic frequency characteristic of power systems in response to large disturbances. Then, a two-stage stochastic optimization model for generation maintenance scheduling including frequency security constraints is proposed. Finally, a solution methodology based on Benders decomposition (BD) is used to promote the calculation speed of the proposed model. Numerical simulations demonstrate that the proposed generation maintenance scheduling could address the potential frequency security issues and promote integration of RESs associated with calculation speed.

A Meander Delay System Design Using Caps-Triple GAN Optimized with the Remora Optimization Algorithm for IOT Application

In this manuscript, a Meander Delay System design using Caps-Triple GAN optimized with the Remora Optimization Algorithm (ROA) is proposed for the Internet of Things (IoT) application. For designing the Meander Microstrip Delay Line (MMDL) Antenna, the Capsule Triple generative adversarial network (Caps-Triple GAN) is used. The Caps-Triple GAN error and delay parameters are optimized using the ROA. Hence, the designed MMDL Antenna is available in the IoT application. The proposed method is executed in the commercial Sonnet software package. The performance of the proposed method is examined under performance metrics, such as delay time with resistance characteristic, one-step delay time resistance characteristic, delay time, one-step delay time, error, and speed. The prediction results of the proposed MMDL-CAPS-Triple GAN-ROA method predict lower delay times of 14.77%, 15.89%, and 11.50%, higher speed of 32.57%, 16.25%, and 8.44% compared with the existing methods, such as Prediction of the meander delay system parameters for internet-of-things devices utilizing a Pareto-optimal artificial neural network and multiple linear regression (MDS-ANN-MLR), Predicting the frequency characteristics of hybrid meander systems utilizing the feed-forward back propagation network (MDS-FFBPN), Frequency Characteristic Analysis of Meander Structures with Different Connecting Electrodes (MDS-MoM), respectively.

LABVIEW IN THE RESEARCH OF FRACTAL PROPERTIES OF THE TOPOLOGY OF NETWORKS AND STOCHASTIC PROCESSES

The advancement and utilization of computer technologies for studying and diagnosing the technical state of dynamic systems are closely linked to scientific and technological progress. Among these technologies, fractal technologies hold a prominent position [1]. Time series data, which record changes in controlled parameters over time, are commonly used for diagnosing technical objects and systems. The use of fractals will also be of interest in assessing the resonant frequency characteristics of oscillatory systems [3]. The informational characteristics of topologically distributed networks (e.g., computer, cellular) significantly depend on their geometry, node placement, and inter-node distances. The fractal dimension, a fundamental characteristic of networks, plays a crucial role in this context [2]. The research paper presents a methodology for modeling and synthesizing large networks using the node density function, which follows a power function with a fractal dimension. This characteristic aligns with Zipf's law of population distribution around urban centers. The paper also provides fractality degree indices for the network diagram. Software tools such as LabVIEW play a significant role in scientific research and experiment automation.

Virtual Admittance Reshaping Based Input Current Phase Shift Suppression Method for Totem-Pole Bridgeless PFC Converter

Grid-side current phase shift (GCPS) is an important issue in totem-pole bridgeless power factor correction (TBPFC) converters. In this article, a virtual admittance reshaping based GCPS suppression method is proposed based on the establishment of the admittance model of the TBPFC converter including the EMI filter. The virtual admittance reshaping does not need additional current and voltage sensors and can realize complex admittance through a control algorithm. Thus, the current phase error can be adjusted to zero with the optimal design. The inherent admittance of the system is analyzed from the perspective of system frequency characteristics to extract leading-phase admittance. Then, the parallel admittance is produced through the inductance current for canceling it. The current reference and the modulation voltage are combined to realize obtaining the equivalent virtual admittance and meanwhile reduce the burden of the current regulator. The sensitivity of the system parameters is analyzed, and the saturation effect of the inductor and the error of the EMI filter parameters have little effect on admittance reshaping. Besides, the research method does not need to adjust parameters according to the load. The effectiveness of the proposed method is verified by experiments on a TBPFC converter platform.

Factors affecting public transport performance due to the COVID-19 outbreak: A worldwide analysis

In this paper we investigate the public transport trip frequency variations, as well as the reasons that led to the shift away from public transport means, due to the COVID-19 pandemic. We studied relevant data from the Moovit platform, and we compared operational and trip frequency characteristics of public transport systems before and after the outbreak of the pandemic in 87 cities worldwide. On average, waiting times at public transport stops/stations increased while trip distances decreased, apparently due to the mobility restriction and social distancing measures implemented in 2020. Most of the Moovit users who said that they abandoned public transport in 2020 were found in Italy and Greece. We developed linear regression analysis models to investigate (among the 35 variables examined in the study) the relationship between public transport abandonment rates and socioeconomic factors, quality of service characteristics, and indicators of pandemic's spread. Empirical findings show that public transport dropout rates are positively correlated with the COVID-19 death toll figures, the cleanliness of public transport vehicles and facilities, as well as with the income inequality (GINI) index of the population, and thus reconfirm previous research findings. In addition, the waiting time at stops/stations and the number of transfers required for commute trips appeared to be the most critical public transport trip segments, which significantly determine the discontinuation of public transport use under pandemic circumstances. Our research findings indicate specific aspects of public transport services, which require tailored adjustments in order to recover ridership in the post-pandemic period.

Optimization of the structure of filter-compensating devices in networks with powerful non-linear power consumers based on fuzzy logic

<span lang="EN-US">The article presents a solution to the problem of optimizing the structure of filter-compensating devices (FCD) when installed in high-voltage mine networks with powerful nonlinear electrical receivers. The urgency of the problem of choosing a rational structure of the FCD. The problem of choosing the design and installation location of the FCD is presented. The main technical means of compensation of higher harmonics of currents and voltages in high-voltage networks with powerful nonlinear electrical receivers are considered. Analysis of different types of passive filters (PF) and their frequency properties showed that the choice of specific types of PF refers to the multi-criteria optimization problem. The main methods of optimization of FCD design are considered. The variant of FCD construction based on the solution of multi-criteria optimization problem with the use of fuzzy sets is proposed and justified. To this end, the calculation of PF parameters and frequency characteristics of equivalent systems of the "filter-external network" type for four possible combinations of PF is performed. The optimal is a FCD with two resonant PF tuned to the 11<sup>th</sup> and 13<sup>th</sup> harmonics, and a second-order broadband PF tuned to compensate harmonics starting from the 23<sup>rd</sup> and above. The analysis of simulation results showed effective compensation of higher harmonic currents and voltages.</span>

Equivalent Inertia Estimation of Asynchronous Motor and Its Effect on Power System Frequency Response

With the increase in renewable energy penetration, the traditional synchronous generator is gradually replaced, resulting in the decrease in system inertia level and the weakening of frequency modulation capability. In addition to synchronous inertia, load inertia of asynchronous motors also widely exists in power systems, but its effect on system frequency stability has not been fully studied. To this end, based on the detailed model of asynchronous motor, the amplitude–phase motion equation based on potential after transient reactance is proposed, and then the phase motion equation of potential after transient reactance is derived to evaluate the equivalent inertia of asynchronous motor under electromechanical time scale. The equivalent inertia of asynchronous motor is studied theoretically by building the system frequency response model. The results show that the equivalent inertia of asynchronous motor can essentially improve the system frequency stability, while showing time-varying characteristics due to the combined effect of slip frequency and rotor speed. The analyses are validated with time-domain simulation results. The proposed method lays a foundation for mechanistic understanding of the frequency characteristics of the equivalent inertia of asynchronous motors affected by active and reactive power and its influence on the system frequency characteristics.

Common-Mode Frequency in Converter-Integrated Power Systems: Definition, Analysis, and Quantitative Evaluation

As synchronous generators (SGs) are extensively replaced by converter-based generators (CBGs), modern power systems are facing complicated frequency stability problems. Conventionally, the frequency nadir and the rate of change of frequency (RoCoF) are the two main factors concerned by power system operators. However, these two factors heavily rely on simulations or experiments, especially in a power system with high-penetration CBGs, which offer limited theoretical insight into how the frequency response characteristics are affected by the devices. This paper aims at filling this gap. Firstly, we derive a formulation of the global frequency for a CBG-integrated power system, referred to as common-mode frequency (CMF). The derived CMF is demonstrated to be more accurate than existing frequency definitions, e.g., the average system frequency (ASF). Then, a unified transfer function structure (UTFS) is proposed to approximate the frequency responses of different types of devices by focusing on three key parameters, which dramatically reduces the complexity of frequency analysis. On this basis, we introduce two evaluation indices, i.e., frequency drop depth coefficient (FDDC) and frequency drop slope coefficient (FDSC), to theoretically quantify the frequency nadir and the average RoCoF, respectively. Instead of relying on simulations or experiments, our method rigorously links the system's frequency characteristics to the characteristics of heterogeneous devices, which enables an in-depth understanding regarding how devices affect the system frequency. Finally, the proposed indices are verified through simulations on a modified IEEE 39-bus test system.

Robust control for a tracking electromechanical system

<p>A strategy for the design of robust control of tracking electromechanical systems based on 𝐻∞ synthesis is proposed. Proposed methods are based on the operations on frequency characteristics of control systems designed and developed using the MATLAB robust control toolbox. Determination of the singular values for a transfer matrix of the control system reduces the disturbances and guarantees its stability margin. For selecting the weighted transfer functions, the basic recommendations are formulated. The efficiency of the proposed approach is verified by robust control of an elastically coupled two-mass system whose parameter values are adjusted by matching them with the parameters of one of the supplied robots. The simulation results confirm that the proposed strategy of design of robust control of two-mass elastic coupling system using the 𝐻∞ synthesis is very efficient and significantly reduces the perturbation of parameters of the controlled plant.</p>

Frequency regulation control strategy of wind farms based on temporal and spatial uncertainty

The Frequency regulation capability of a double-fed induction generator (DFIG) in a large wind farm is influenced by its operating state and installation position, as well as the wind speed (size and direction) at which it is located, resulting in temporal and spatial uncertainties. First, to simplify control difficulty and optimize frequency regulation increment allocation, model predictive control(MPC) and k-means clustering method are used for spatial optimal grouping of DFIG in wind farms based on the uncertainties of DFIG installation location and wind direction. Second, a timing coordinated control strategy is proposed based on the uncertainties of the DFIG operation state and wind speed. The strategy allows the DFIG to enter and exit the frequency regulation system based on wind speed, active power increment, and sustainable time and then reduces the negative effect of the DFIG exiting the frequency regulation system. Finally, based on temporal and spatial optimization, a coordinated control strategy based on temporal and spatial uncertainties is proposed to optimize the overall frequency regulation capability of wind farms. Simulation examples show that the time–space coordinated control strategy treats each group as an independent DFIG control, which not only simplifies the control problem but also fully utilizes the DFIG frequency regulation capacity and effectively improves the system frequency characteristics.

FREQUENCY FEATURES OF THE NUMERICAL METHOD SAMPLING OF DIGITAL CONTROL SYSTEMS

Context. The studies of the frequency properties of the explicit multistep numerical integrators which use for sampling of continuous transfer function in the digital control systems, are conducted in this article. Numerical integrators in such systems implement as an integral parts of the digital regulators. Objective. The goal of this research is an analysis of the behavior of explicit numerical integrators of different orders, which areused to discretize continuous systems, in order to study their impact on the properties of the synthesized digital system. Method. Numerical methods of integration are considered as digital filters, the behavior of which is studied by the frequency characteristics method. To do this, the z-transform apparatus was used. Integrators’ discrete transfer functions were found for frequency analysis using the Control Systems Toolbox package of the mathematical application MATLAB. For further analysis, two closed feedback test structures were used: with integrators in the forward channel and in the feedback loop. Both variants of structures were studied by the frequency characteristics method for sampling using numerical integrators of 1st–6th orders. Results. The inefficiency of using high-order numerical integrators for continuous systems’ discretization is shown. Given the behavior of the frequency characteristics of test systems, the most rational is the use of low-order integrators, namely – the first and second orders. Establishing the cause of this phenomenon requires additional research, in particular, to identify the possible impact of additional zeros and poles of discrete transfer functions of the numerical integrators. Conclusions. The use of low-order integrators, namely the first and second orders, is the most rational for sampling of digital control systems and the inefficiency of using high-order numerical integrators to sample continuous systems is proven.

Research on source-load frequency response control strategy of distributed generation system

Abstract Distributed power generation, as an effective form of new energy power generation, has attracted extensive attention. However, due to the lack of physical inertia support, the stability of the distributed power supply system is threatened. Aiming at the problem of low inertia and weak damping in distributed systems, a source-load frequency response control strategy is proposed in this paper. Firstly, this paper introduces the structure and working mode of the distributed power generation system, and the system frequency characteristics are theoretically analyzed. Then, based on the operating characteristics of the conventional power system, the generator is simulated through the distributed power generation, the load-side converter is coupled to the grid frequency and further the source-load frequency response control strategy is achieved that taps the potential of frequency adjustment capability of the load side through frequency coupling control to provide auxiliary inertia support for the system, and this paper illustrates the source-load frequency adjustment response mechanism in detail. Compared with the conventional single frequency response control, the control strategy proposed in this paper can effectively alleviate the frequency adjustment pressure of distributed units, reduce the capacity of energy storage equipment due to frequency adjustment and improve the efficiency of system operation. Finally, through the simulation analysis of the distributed power generation system, the effectiveness of the control strategy proposed in this paper is verified.

Checking the adequacy of the method for generating a random process of disturbance of oscillations of rail carriages according to the impulse response of the forming filter

Usually, to study the vibrations of rail carriages, the equivalent geometric unevenness of the track obtained as a result of processing the records of the track measuring car is taken as a disturbance. Such a record contains a certain set of irregularity wavelengths, for example, 50, 25 and 12.5 m. However, when it is used to simulate disturbances at different operation speeds, these wavelengths will correspond to frequencies depending on the given speed of motion, which is not permissible, since a stable frequency range from 0.2 to 10 Hz is required to excite the vibrations of all the bodies included in the carriage. To eliminate this drawback, in the previously performed works it was proposed to generate a random process of geometric irregularities for a given operation speed by changing the set of wavelengths included in the irregularities. In this paper, based on the study of random oscillations of a simplified model of a rail carriage, as a system with one degree of freedom, the adequacy of the method for generating a random disturbance process is verified in two ways. In the first method, it was found that the characteristics of random oscillations of such a model, obtained in the time domain on the basis of numerical integration of the equation of motion when specifying the generated disturbance, have satisfactory convergence with similar characteristics found by the frequency method using Shannon's formula. In the second verification method, the cross-correlation function and the mutual spectral density between the disturbance and the bouncing oscillations were determined from the generated disturbance realization and obtained by numerical integration of the vibration process realization. Then, using the method of identifying the dynamic system, experimental amplitude and phase frequency characteristics were found, which showed satisfactory convergence with the corresponding calculated characteristics obtained by numerically solving the equation of oscillations of the model under study. On the basis of the results obtained, it was concluded that the considered method of generating a random process of disturbance is sufficiently adequate and that it can be applied to solve problems of the dynamics of rail carriages.

Quasi-Static Time-Series Power Flow Solution for Islanded and Unbalanced Three-Phase Microgrids

Recent advances in inverter-based distributed energy resources (DERs) allow microgrids to operate in grid-connected and islanded modes with ease. However, determining a steady-state load flow solution of a real-world unbalanced and islanded three-phase microgrid remains a challenge. Existing methods are either unsuitable, labor-intensive or computationally demanding for a long-term analysis of islanded microgrids. To address these issues, we propose a practical solution framework that employs externally-updated system frequency, power quantities, and droop characteristics governing the voltage and phase angle of DERs in every iteration as inputs to an off-the-shelf open-source multi-phase, multi-wire, unbalanced power flow software tool to solve an islanded-microgrid power flow. Using our framework, users only need to implement a set of droop equations and update system variables. The power flow solution is accomplished entirely by an off-the-shelf power flow tool, e.g., OpenDSS. Our proposed framework can model a microgrid of any arbitrary configuration and operating condition. We demonstrate and validate the proposed method’s efficacy by comparing its results with those modeled using a time-domain simulation with PSCAD/EMTDC. Finally, an example of a quasi-static time-series study is presented to better illustrate the application of such a tool.