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Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To address the challenge of solving the zero-pole of transcendental equation for distributed power station with simultaneous consideration of two factors， i.e.， dq-axis coupling and line distribution parameter， an impedance model for distributed power station considering the two factors is established. This paper proposes a matrix-determinant zero-pole solution method for transcendental equation using Padé approximation and provides detailed steps for calculating the zero-pole distribution of the transfer function. Furthermore，it analyzes the impact of the two factors on harmonic instability analysis in the system under different scenarios. The research demonstrates that the proposed method can accurately analyze harmonic instability issues when these two factors are considered simultaneously. And ignoring one of the two factors may result in the misjudgment of stability， and considering the line distribution parameter is a necessary prerequisite for solving the amplification point of high-frequency harmonics. The effectiveness of the proposed method is verified by simulation.

Copyright of Zhejiang Electric Power is the property of Zhejiang Electric Power Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The distributed parameter model of the transmission line is a necessary premise for accurately analysing the harmonic instability of the wind farm. However, when the model is used for harmonic instability analysis, it causes difficulties in solving the zero and pole distributions of the transcendental equation of the system. Given this, the impedance model of the wind farm considering the line distribution parameters is established and verified. Next, a method based on Pade approximation to solve the zero and pole distributions of the transcendental equation is proposed. The exponential function is approximated to the rational fraction only by selecting the order of the rational fraction, without fitting coefficients. Further, the influence of different transmission line models on the harmonic instability under different line lengths and grid strengths is analyzed. Finally, the effectiveness of the proposed method is verified by the simulation case. The results show that the effect of distribution parameters cannot be ignored, otherwise, it may lead to the inaccurate analysis of stability and deviation or even omission of harmonic amplification points in the high-frequency band. The proposed method can not only accurately evaluate the stability of the system, but also analyze the harmonic amplification points.

Copyright of Electric Power Engineering Technology is the property of Editorial Department of Electric Power Engineering Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In power systems with grid-forming inverters (GFMs), small-signal instability issues could occur due to harmonic excitation, impedance interactions, and poor inverter control design. There mainly exist two types of stability issues based on the frequency range. One is the low-frequency resonance (0 – 2f0 Hz) and the other is the high-frequency harmonics (above 2f0 Hz), where f0 is the system fundamental frequency. By assuming that the low-frequency related controls are well designed, this paper addresses the high-frequency harmonic issues. The goal is to develop a system stabilization function (SSF) to eliminate any high-frequency stability issues under various grid conditions without affecting predefined low-frequency behaviors. The idea is to conduct the inverter passivation test at the system harmonic resonant frequency so that the corresponding harmonic instability can be removed. To achieve this, the resonant frequency of the harmonic instability is detected first, and then if the magnitude of the resonant component exceeds the threshold value, the proposed SSF will be enabled, thus the system would be stabilized. Both simulation and experimental tests are conducted to validate the effectiveness of the proposed approach.

[Introduction] The paper aims to effectively suppress the disturbance of non characteristic harmonics to the power grid in the tokamak power supply system, the paper studies the mechanism of low-frequency harmonics in the tokamak power supply system. [Method] By introducing an improved switching function model, selected ITER fusion device as an example and established its corresponding AC/DC equivalent circuit model combined with its corresponding parameters, the corresponding output second harmonic was obtained through calculation and simulation. [Result] The ratio of output to input is calculated, and the stability factor value almost tends to zero. [Conclusion] It is determined that the DC bias of rectifier transformer do not cause harmonic instability of the system.

Pole-zero cancellation technique has drawn much attention to tackle the filter resonance of the LCL-type grid-connected inverter for simplifying the stability-oriented design. However, its potential stability risk was rarely concerned. As one representative of this technique, the weighted average current (WAC) control is assessed. It is found that the LCL resonance in the state variable WAC is cancelled out by pole-zero cancellation, but the ones in some uncontrollable or unobservable state variables such as the grid current are still inherited, resulting in harmonic instability. From this perspective, this article appeals that this technique should be cautiously used or even avoided. An extended WAC control which avoids pole-zero cancellation is proposed accordingly. The theoretical expectations are finally validated by simulation and experimental results. [ABSTRACT FROM AUTHOR]

Copyright of Southern Energy Construction is the property of Southern Energy Construction Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Power electronic (PE) penetration in energy networks has been increasing rapidly in recent years due to the campaign to rely on distributed generation as a clean, sustainable energy source. This increase leads to new challenges and stability problems occurring because of the increase in the harmonic current injected into the power network. To study and address such issues, accurate and computationally efficient models are required. In this article, a Hammerstein–Wiener-based approach is proposed to develop black-box models for PE devices capable of capturing the devices’ harmonic characteristics. A novel method based on magnitude square coherence is also proposed to compare the results of different models in the frequency domain. The method is implemented in a simulation environment and was further tested and validated through laboratory measurements. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The high-frequency negative damping characteristics of the electric train and the traction network interaction system may excite harmonic instability issues. This paper proposes a detailed impedance model and a simplified method in the αβ-frame for investigating the high-frequency impedance characteristic of the electric train. Meanwhile, the impedance model is validated by means of the frequency sweeping method. Based on the αβ-frame impedance model of the train, the negative damping range is mathematically expressed. It is helpful for analyzing the impacts of controller bandwidths and network impedances on the harmonic instability. In addition, a voltage feedforward filter combining its transfer function is proposed to enhance the system stability. Taking advantages of the proposed voltage feedforward filter, the output impedance of the train can maintain passive characteristics well in a specific high-frequency range, effectively avoiding harmonic instability issues. Simulation and experimental results validate the effectiveness of the proposed harmonic instability analysis and suppression methods. [ABSTRACT FROM AUTHOR]

Compared with the conventional power systems, large-scale power electronics based power systems present a more complex situation, where harmonic instability may be induced by the mutual interactions between the inner control loops of the converters. This paper presents an approach to locate which power converters and buses are more sensitive and have a significant contribution to the harmonic instability. In the approach, a power electronics based system is introduced as a multi-input multi-output (MIMO) dynamic system by means of a dynamic admittance matrix. Bus participation factors (PFs) are calculated by the oscillatory mode sensitivity analysis versus the elements of the MIMO transfer function matrix. The PF analysis detects which power electronic converters or buses have a higher participation in harmonic instability excitation than others or at which buses such instability problems have a higher impact. In order to confirm the effectiveness of the presented approach, time-domain simulation results are provided for a 400-MW wind farm in PSCAD software environment. [ABSTRACT FROM AUTHOR]

This paper presents an impedance-based method to systematically investigate the interaction between multiple trains and a traction network, focusing on evaluating the harmonic instability problem. First, the interaction mechanism of the multitrain and the traction network is represented as a feedback interconnection of the two subsystems, i.e., an equivalent output impedance of the traction network and an equivalent input admittance of the multitrain. Then, the harmonic instability is evaluated through a series of pole-zero diagrams drawn from the closed-loop transfer matrix of the multitrain and network system. The interaction system is unstable, and the harmonic instability will happen if there are some high-frequency poles of the closed-loop system locating in the right-half plane. This method is used for analyzing the harmonic instability phenomena, the characteristics, influential factors, and potential mitigation schemes. The theoretical results are further validated by the simulations and experiments. [ABSTRACT FROM AUTHOR]

Low-frequency oscillation (LFO), harmonic resonance, and harmonic instability phenomena in high-speed railways (HSRs) result from the interactions between multiple electric trains and the traction network. A train–network interaction system and a unified impedance-based model are therefore presented to reveal the mechanism of these three phenomena in Part I of the two-part paper. Part II of the paper presents and compares the detailed simulation and experiment results to investigate the available possible influential factors, verifications, and discussions of the three phenomena. The influential factors include the following: 1) four-quadrant converter (4QC) parameters involving the control parameters of the current controller (CC), the voltage controller (VC), and the phase-locked loop (PLL); 2) network parameters involving the utility power system, traction transformer, primary/secondary supply lines, catenary lines, and autotransformers (ATs); and 3) different numbers and positions of trains and railway lines will also be considered and discussed. In order to validate the theoretical results, the time-domain simulation and experiment system have been conducted. Finally, the differences and the relations among the three phenomena are discussed. [ABSTRACT FROM AUTHOR]

This paper presents an impedance-based model to systematically investigate the interaction performance of multiple trains and traction network interaction system, aiming to evaluate the serious phenomena, including low-frequency oscillation (LFO), harmonic resonance, and harmonic instability. The train–network interaction mechanism is therefore studied, and one presents a detailed coupling model for investigating the three interactive phenomena and their characteristics, influential factors, analysis methods, and possible mitigation schemes. In Part I of the two-part paper, the measured waveforms of such three phenomena are first characterized to indicate their features and principles. A unified framework of the train–traction network system for investigating the three problems is then presented. In order to reveal the interaction mechanism, all-frequency impedance behaviors of the electric trains and traction network are equally modeled. In which, an impedance-based input behavior of the train is fully investigated with considering available controllers and their parameters in DQ-domain. The entire traction network, including traction transformer, catenary, supply lines, is represented in a frequency-domain nodal matrix. Furthermore, the impedance–frequency responses of both electric train and traction network are measured and validated through frequency scan method. Finally, a generalized train–network simulation and experimental system are conducted for verifying the theoretical results of the two-part paper. [ABSTRACT FROM AUTHOR]

Harmonic stability of double-fed induction generators (DFIGs) now has become a significant topic because of its harmful impact on power quality issues of the system. Since the double pulse width modulation (PWM) converter is one of the main harmonic sources in DFIGs, it may cause harmonic instability with increasing harmonic contents. Thus, the modeling and stability analyses of PWM converters in DFIGs are essential steps to assess the harmonic stability of DFIGs. Aiming at dual PWM converters, which include the grid side converter (GSC) and the rotor side converter (RSC), this paper divides converters into two parts: circuit modules and control modules. Closed-loop input impedance models of each module are then derived by means of transfer functions. Hence, the stability of the system can be readily predicted through Nyquist diagrams. The contributions of parameters to the system’s harmonic stability are also identified. Finally, time-domain simulations are conducted in a real-time digital simulation (RTDS) system. Simulation results confirm that the established impedance model can effectively reveal the stability of the DFIG-based system and can give critical conditions for the occurrence of harmonic instability.

For the efficiency and simplicity of electric systems, the dc power electronic systems are widely used in a variety of applications such as electric vehicles, ships, and aircraft and in homes. In these systems, there could be a number of dynamic interactions and frequency coupling between network and loads and other converters. Hence, time-domain simulations are usually required to consider such a complex system behavior. However, simulations in the time domain may increase the calculation time and the utilization of computer memory. Furthermore, frequency coupling driven by multiple converters with different switching frequencies or harmonics from ac–dc converters makes that harmonics and frequency coupling are both problems of ac system and challenges of dc system. This paper presents the modeling and simulation methods of a large dc system by using the harmonic state space (HSS) modeling. Through this method, the required computation time and CPU memory can be reduced, where this faster simulation can be an advantage of a large network simulation. Besides, the achieved results show the same results as that of the nonlinear time-domain simulation. Furthermore, the HSS modeling can describe how the frequency components are coupled with each other through the different switching frequency of each converter. [ABSTRACT FROM PUBLISHER]

This paper presents a harmonic instability analysis method using state-space modeling and participation analysis in the inverter-fed ac power systems. A full-order state-space model for the droop-controlled distributed generation (DG) inverter is built first, including the time delay of the digital control system, inner current and voltage control loops, and outer droop-based power control loop. Based on the DG inverter model, an overall state-space model of a two-inverter-fed system is established. The eigenvalue-based stability analysis is then presented to assess the influence of controller parameters on the harmonic instability of the power system. Moreover, the harmonic-frequency oscillation modes are identified, where participation analysis is presented to evaluate the contributions of different states to these modes and to further reveal how the system gives rise to harmonic instability. Based on the participation analysis, a reduced-order model for harmonic instability analysis is also proposed. The experimental results are presented for validating the theoretical analyses. [ABSTRACT FROM PUBLISHER]

To investigate the harmonic resonance, harmonic instability and low-frequency oscillation phenomena in high-speed railways, this paper proposes a full-frequency impedance model of the train-traction network system (simplified as ‘train-network’) based on d-q coordinates system. Compared with traditional models which deal with only the grid-side converter, the proposed model also includes its load models—the inverter and the traction motor. It also reflects complete control scheme of grid-side converter, which makes it easier to analyze unstable phenomena mentioned above. Moreover, this paper improves the impedance modeling of the network by taking the network impedance and admittance into detailed consideration. In addition, based on the proposed train-network model, the 3D figure and zero-pole diagram are also presented for the analysis of the stability of the integral system. Simulation and experiment results verify the accuracy of the model.

The increasing number of renewable energy sources in the distribution grid is becoming a major issue for utility companies since grid-connected converters are operating at different operating points due to the probabilistic characteristics of the renewable energy. Usually, the harmonics and impedance from other renewable energy sources are not taken carefully into account in the installation and design of the systems. It can bring an unknown harmonic instability into a multiple power-sourced system and makes the analysis difficult due to the complexity of the grid network. This paper proposes a new model of a single-phase grid-connected renewable energy source by using the harmonic state-space modeling approach, which can identify such problems. The model can be extended to a multiple connected converter analysis. The modeling results show the harmonic impedance matrixes, which represent the harmonic coupling characteristic, as well as different dynamic characteristics. The theoretical modeling and analysis are verified by simulations, as well as experimental results. [ABSTRACT FROM PUBLISHER]

This paper reveals the existence of poorly damped resonant modes in the modular multilevel converter (MMC) that can result in harmonic instability. A small-signal model based on dynamic phasors is introduced which takes into consideration the dynamics of internal variables, such as circulating arm currents, which have a tendency for a large second harmonic component and module capacitor voltage ripple, which has other harmonic components. The small-signal model is validated by comparison with the electromagnetic transient simulation of a detailed model. It is shown that the use of an active circulating current suppressing scheme can effectively improve the damping of internal harmonic modes in comparison with a passive filter used for the same purpose. The damping of internal harmonic modes has been shown to be significantly impacted by the gains of the MMC's outer-loop controller but is less sensitive to the ac system strength or the gain of the phase-locked loop. A larger arm resistance also increases the damping of these internal modes. [ABSTRACT FROM PUBLISHER]

Static var compensator (SVC) is used to maintain constant load voltage by compensating the var required by poor power factor loads. The SVC is also used to balance the unbalanced three phase loads. The side effect of the SVC is the generation of harmonic components. Under certain conditions, one of the harmonic components generated by the SVC becomes magnified. This magnified harmonic component leads to a time-bifurcation instability in the thyristor controlled reactors (TCR). This paper shows the effect of the SVCs inductor on harmonic magnification and the time-bifurcation. The experimental results are reported, and the time-bifurcation of the TCR current is generated. [ABSTRACT FROM AUTHOR]

Harmonic stability of double-fed induction generators (DFIGs) now has become a significant topic because of its harmful impact on power quality issues of the system. Since the double pulse width modulation (PWM) converter is one of the main harmonic sources in DFIGs, it may cause harmonic instability with increasing harmonic contents. Thus, the modeling and stability analyses of PWM converters in DFIGs are essential steps to assess the harmonic stability of DFIGs. Aiming at dual PWM converters, which include the grid side converter (GSC) and the rotor side converter (RSC), this paper divides converters into two parts: circuit modules and control modules. Closed-loop input impedance models of each module are then derived by means of transfer functions. Hence, the stability of the system can be readily predicted through Nyquist diagrams. The contributions of parameters to the system's harmonic stability are also identified. Finally, time-domain simulations are conducted in a real-time digital simulation (RTDS) system. Simulation results confirm that the established impedance model can effectively reveal the stability of the DFIG-based system and can give critical conditions for the occurrence of harmonic instability. [ABSTRACT FROM AUTHOR]

To investigate the harmonic resonance, harmonic instability and low-frequency oscillation phenomena in high-speed railways, this paper proposes a full-frequency impedance model of the train-traction network system (simplified as ‘train-network’) based on d-q coordinates system. Compared with traditional models which deal with only the grid-side converter, the proposed model also includes its load models—the inverter and the traction motor. It also reflects complete control scheme of grid-side converter, which makes it easier to analyze unstable phenomena mentioned above. Moreover, this paper improves the impedance modeling of the network by taking the network impedance and admittance into detailed consideration. In addition, based on the proposed train-network model, the 3D figure and zero-pole diagram are also presented for the analysis of the stability of the integral system. Simulation and experiment results verify the accuracy of the model. [ABSTRACT FROM AUTHOR]