Sequence Impedance Research Articles

Impedance Modeling and Stability Analysis of the IMAF-PLL-Based NPC Three-Level LCL Grid-Connected Inverter

The phase-locked loop of grid-connected inverters affects their output impedance characteristics and stability. Based on the NPC, three-level LCL grid-connected inverter, this article first analyzes the frequency characteristics of the improved moving average filter phase-locked loop (IMAF-PLL). Then, analyzing the influence of the neutral point control on the inverter impedance modeling, the harmonic linearization impedance modeling method combined with the symmetrical component method is used to establish a positive and negative sequence impedance model of the NPC three-level LCL grid-connected inverter. Furthermore, the frequency characteristics of the IMAF-PLL and the impedance model of the NPC three-level LCL grid-connected inverter are verified by simulations. Finally, the impedance-based analysis method is used to study the stability of the grid-connected system under different grid impedance conditions when using different phase-locked loops, and the theoretical analysis was validated experimentally.

Development and Application of Type-III Turbine Impedance Models Including DC Bus Dynamics

Several small-signal impedance models have been reported for type-III wind turbines for use in impedance-based system stability studies. Common to these models is the assumption that the dc bus between the rotor- and stator-side converters is an ideal voltage source. Under this assumption, there is no dynamic coupling between the two converters and the turbine can be represented by the impedance of the stator-side converter in parallel with the impedance of the induction generator with the rotor-side converter behind it. The assumption is well justified above the second harmonic frequency but introduces considerable error at lower frequencies, especially within 20–30 Hz of the fundamental frequency in which dc bus voltage control is active and dc bus capacitor impedance is high. This paper presents the development and application of full-order sequence impedance models for type-III turbines that include dc bus dynamics. The new models also consider the coupled current responses created by each of the converters as well as their coupling across the dc bus. Inclusion of these additional dynamics leads to more accurate prediction of turbine impedance responses and turbine-grid system stability. A comparison with existing models is presented to show the utility and limitation of each model. A practical resonance problem is also presented to demonstrate the application.

Sequence Impedance-Based Stability Analysis of AC Microgrids Controlled by Virtual Synchronous Generator Control Methods

In this paper, sequence impedance-based modelling is applied to two different grid-forming converters which are based on virtual synchronous generator (VSG) concepts including a dual loop voltage control. The considered controls only differ in the feedback design (PLL-driven or not) of the power-related control loop. In general, impedance modelling is a suitable method to analyse stability issues related to converter controls for use in larger power networks. In this work, the analytical model of a voltage-controlled converter is illustrated first. Sequence impedance models are then proposed, which do not only predict the effect of two different VSG controls on the systems stability, but also reveal its frequency coupling effect and analogy to the classical droop control. In addition, a small power system consisting of VSG-controlled converters is analysed by their equivalent output impedances. These models and the stability of the converter cluster are validated by time-domain simulations and laboratory experiments. The close correlation between sequence impedance model, time-domain simulation and experimental results confirms the effectiveness of the derived models.

Impedance modeling and stability analysis of PV grid-connected inverter system considering frequency coupling

Impedance analysis is an effective method to analyze the oscillation issue associated with grid-connected photovoltaic systems. However, the existing impedance modeling of a grid-connected photovoltaic inverter usually only considers the effect of a single perturbation frequency, ignoring the coupling frequency response between the internal control loops of a grid-connected inverter, which severely affects the accuracy of the stability analysis. Hence, a method of impedance modeling and stability analysis for grid-connected photovoltaic inverters considering cross-coupling frequency is proposed in this paper. First, the generation mechanism of frequency coupling in grid-connected photovoltaic inverters, and the relationship between the coupling frequency and perturbation frequency are analyzed. Secondly, a sequence impedance model of grid-connected photovoltaic systems considering the coupling frequency is established by using the harmonic linearization method. The impact of DC bus voltage control strategy on frequency coupling characteristics of a grid-connected photovoltaic system is evaluated, and the impact of a coupling frequency term on system stability is quantitatively analyzed. Finally, the advantages of the proposed method are verified by several simulations. The results show that the proposed impedance model can accurately predict the potential resonance points of the system, and the coupling frequency characteristics will become much stronger with smaller DC bus capacitance or larger bandwidth of the DC bus controller.

Methods to aggregate turbine and network impedance for wind farm resonance analysis

Small-signal sequence impedance models have been developed for different types of wind turbines and used in industry to study wind farm and high-voltage direct current (HVDC) system harmonics and resonances. Compared to other small-signal methods, a major advantage of system modelling and analysis based on sequence impedance is its scalability: an equivalent impedance model can be easily built for any complex system by aggregating the impedance of individual turbines and the network. A recent development in the small-signal sequence impedance theory is the modelling of frequency coupling to improve the accuracy of system analysis and explain a common characteristic of harmonics created by system resonance. In light of this new development, this study presents and compares different aggregation methods to build farm-level impedance models in the presence of coupling in individual turbine responses. The objective is to identify practical methods that can meet the needs of different system analyses and are easily to use. Experiences of China State Grid and TenneT with the application of sequence impedance models in renewable energy and HVDC system resonance and harmonic analysis are also discussed, along with an overview of their ongoing efforts to develop new grid codes and system analysis tools based on sequence impedances.

Harmonic Transfer-Function-Based Impedance Modeling of a Three-Phase VSC for Asymmetric AC Grid Stability Analysis

Impedance modeling and stability analysis of a grid-voltage source converters (VSC) system under symmetric ac grids have been extensively discussed in the literature, where the dq domain impedances are usually adopted. As for asymmetric ac grids, impedance modeling is no longer straightforward in the dq domain due to the presence of negative sequence components, where the linearization will result in a linear-time-periodically-varying system, making the frequency-domain analysis intractable. One way to address this issue would be the harmonic-transfer-function (HTF) approach. Although this method is conceptually clear, its application to the stability analysis of an unbalanced grid-VSC system is still challenging and an effective model is missing here, therefore this paper aims to bridge this gap. First, the sequence impedances of an unbalanced grid-VSC system is modeled in the HTF framework. Then the HTFs are truncated into four-by-four matrices by exploiting the property of frequency couplings. Based on this, the equivalent source and load model for Nyquist-based analysis are established, and they are thoroughly verified by impedance measurements as well as the accuracy on stability analysis. Finally, several stability concerns of the unbalanced grid-VSC system, as well as the feasibility of symmetric models for asymmetric ac grid stability analysis are discussed and clarified.

Influence of Inverter-Interfaced Renewable Energy Generators on Directional Relay and an Improved Scheme

Renewable energy sources are typically interfaced to the grid using power electronics, which can cause their fault current characteristics to display significant low-frequency harmonics and unbalanced sequence impedances. Such current characteristics can lead to the operation failure of fault-component-based directional relays. To demonstrate the influence of inverter-interfaced renewable energy generators (IIREGs) on directional relays in detail, analytical expressions for the IIREG equivalent positive- and negative-sequence superimposed impedances are derived in this paper. Considering various factors, the angular characteristics of the sequence superimposed impedances are investigated. Based on these attributes, it can be concluded that fault-component-based directional relays may be unable to operate in some circumstances. A novel high-frequency impedance-based protection scheme is proposed to manage the adaptability problem by determining the fault direction due to a stable impedance angle. The theoretical analysis and the proposed scheme are tested and verified through real time digital simulation and field testing data.

Modelling and Stability Analysis of Wind Power Plants Connected to Weak Grids

It is important to develop modelling tools to predict unstable situations resulting from the interactions between the wind power plant and the weak power system. This paper presents a unified methodology to model and analyse a wind power plant connected to weak grids in the frequency-domain by considering the dynamics of the phase lock loop (PLL) and controller delays, which have been neglected in most of the previous research into modelling of wind power plants to simplify modelling. The presented approach combines both dq and positive/negative sequence domain modelling, where a single wind turbine is modelled in the dq domain but the whole wind power plant connected to the weak grid is analysed in the positive/negative sequence domain. As the proposed modelling of the wind power plant is systematic and modular and based on the decoupled positive/negative sequence impedances, the application of the proposed methodology is relevant for transmission system operators (TSOs) to assess stability easily with a very low compactional burden. In addition, as the analytical dq impedance models of the single wind turbine are provided, the proposed methodology is an optimization design tool permitting wind turbine manufacturers to tune their converter control. As a case study, a 108 MW wind power plant connected to a weak grid was used to study its sensitivity to variations in network short-circuit level, X/R ratio and line series capacitor compensation (Xc/Xg).

Analysis and suppression of high-frequency oscillation between converter-based source and loads in an island power system

In island power system with strong mutual interaction of power electronic devices, stability problems such as high-frequency oscillation are prone to occur. Firstly, a small-signal sequence impedance model of an island power system is built by harmonic linearization method. It is found that the output sequence impedance of the source PWM inverter in the system is not affected by the stable operating point, but the input sequence impedance of the load PWM rectifier will decrease with the increase of power. Then, based on the sequence impedance model and Nyquist stability criterion, the influence of load type and load power on stability of the island power system is analyzed, which can reveal that high-frequency oscillation occurs when the source PWM inverter interacts with the load PWM rectifier. The essential reason of the high-frequency oscillation is that the capacitive output impedance of the source PWM inverter does not match the inductive output impedance of the load PWM rectifier at high-frequency areas. Aiming at this issue, an impedance reconstruction control for the source PWM inverter is proposed, which improves the phase of the output sequence impedance of the source PWM inverter at high-frequency areas to effectively suppress the high-frequency oscillation of the system. Finally, experiment results verify the correctness of analysis and effectiveness of the proposed control strategy.

A new developed smart grid protection technique with wind farms based on positive sequence impedances and current angles

The wind farms penetration in power systems has an adverse impact on transmission lines system protection due to the characteristics of wind farms that are different from the conventional sources during fault occurrence. Different factors such as the distributed generation concept, the own behavior of the wind generator, variation of wind farm impedance during faults inside the farm, and varying wind speed arise different challenges regarding the behavior of the relay protection. The paper introduces a novel protection technique based on total positive sequence impedance and positive sequence current angles through wide area monitoring system. A new protection-setting contour with an efficient and capacity to identify the faulted zone during different fault conditions is developed. The proposed protection scheme tripping action has to fulfil the fault ride through capability (FRT). The results showed a simple and robust new protection system for such smart grid configuration system with wind farms.

Sequence Impedance Modeling and Stability Comparative Analysis of Voltage-Controlled VSGs and Current-Controlled VSGs

The premise that the virtual synchronous generator (VSG) can actively support the weak grid is that the VSG can operate stably. In this paper, the small-signal sequence impedance models of the voltage-controlled VSG and the current-controlled VSG are built and the sequence impedance characteristics of these two types of VSGs are compared and analyzed. The sequence impedance of the voltage-controlled VSG, being consistent with the grid impedance characteristics, is generally inductive. By contrast, the sequence impedance of the current-controlled VSG is mainly negative impedance in the middle- and high-frequency area and the impedance amplitude is quite low. Based on the built sequence impedance models and the impedance stability criterion, the influence of the weakness of the grid on the stability of these two types of VSG grid-connected system is analyzed. The results of stability analysis show that the current-controlled VSG is prone to instability while the voltage-controlled VSG remains stable. Therefore, the voltage-controlled VSG is more suitable than the current-controlled VSG for grid-connected renewable energy generation in an ultraweak grid from the point of view of system stability. Finally, experiment results validate the stability analysis.

Improvement in Recloser–Fuse Coordination Technique Based on Modification Factor

This paper presents a new adaptive technique to restore coordination between recloser and fuse of a distribution network in presence of distributed generations (DGs). The proposed technique is based on the derivation of modification factor (MF) which is defined as the ratio of the preset value of positive sequence impedance seen by a recloser (Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1preset</sub> ) to its calculated value (Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1cal</sub> ). Based on the value of MF, the recloser fast time- current characteristic is altered. The value of Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1cal</sub> is obtained by acquiring samples of currents and voltages at the location of the recloser. Performance of the proposed scheme has been evaluated by modeling IEEE 34-bus network in real time digital simulator (RTDS)/RSCAD environment. At the same time, appropriateness of the proposed scheme has been verified on a practical setup developed in the laboratory. The results obtained from simulations as well as from the laboratory prototype indicate that the proposed scheme is able to restore coordination between recloser and fuse with a high as well as a low penetration of DG. At the end, a comparative analysis of the proposed scheme with the previously published schemes proves its superiority in restoring the recloser-fuse coordination.

Accurate aggregated modelling of wind farm systems in modified sequence domain for stability analysis

With the wind power penetration rate continuously rising, a suitable wind farm model considering both accuracy and simplicity is required for power system stability analysis. To accomplish this goal, an accurate aggregated modified sequence impedance model of the wind farm is established in this paper. The modified sequence impedance model of wind turbine generator is established, which considers the coupling between the positive- and negative-sequence impedances. The modified sequence impedances of the ac collection system, transformers, and ac grid are also derived. In this way, the impedance network of the entire wind farm system can be formed and simplified to acquire the accurate aggregated modified sequence impedance. Furthermore, the proposed model is compared with the traditional single-machine aggregated model which shows the necessity of establishing the accurate aggregated model. It is worth noting that the differences among each wind turbine generator’s operation points can be included in the proposed model. Compared with the results of impedance measurements of a target wind farm, the accuracy of the proposed aggregated sequence impedance model of the wind farm is verified in frequency domain. The application of the proposed model in the stability analysis of a grid-connected wind farm is also presented with consideration of the ac grid strength. What is more, the effect of the inertial controller on the wind farm system stability is also analyzed to make the impact of this study much more appealing and up to date.

Incorporating network uncertainties in voltage dip state estimation

The magnitudes of voltage dips on non-monitored buses can be estimated by applying Bayes’s theorem with measured voltage dips on a limited number of monitored buses. Bayes’s theorem is used to obtain the grid conditions, including the network impedance, load, distributed generation vector, and short-circuit location, from which the voltage magnitudes along the feeder can be calculated. In order to implement this approach effectively, it is necessary to understand which parameters among the grid conditions are more significant for the estimation performance and how the uncertainties associated with these parameters affect the estimation results. Moreover, since the measurement structure provides observations to calculate the posterior distribution from the prior distribution of the grid conditions. The measurement parameters, quantities, and accuracy levels are varied in simulations to obtain an optimum measurement structure balancing between the cost and the measurement performance. This paper presented the results of the sensitivity studies which have been done on the IEEE 13-Bus and 123-Bus test systems. The results shows the performance of the voltage dip state estimation approach is less sensitive to the uncertainty level of the load while more sensitive to those of the DG, the short-circuit power, the zero sequence impedance of the cable and the short-circuit resistance. The voltage measurement accuracy is more important than that of current and phase angles. The proposed method shows much stronger robustness compared to the conventional one and the estimation performance can be improved through several measures, e.g. adding more measurement points.

A Configurable Virtual Impedance Method for Grid-Connected Virtual Synchronous Generator to Improve the Quality of Output Current

There are two significant problems for the virtual synchronous generator (VSG) under the nonideal grid, including power coupling and current distortion. Although the virtual impedance (VI) is often used to decouple the control of active power and reactive power, it can neither suppress current harmonics nor solve current imbalance caused by the nonideal grid. Therefore, this paper proposes the configurable virtual impedance (CVI) approach to improve both the power coupling and the output current quality. The proposed methodology could aid the independent design of the virtual sequence impedance (VSI) for any harmonics, of which the virtual fundamental positive sequence impedance can be used to realize power decoupling, and the other VSI is designed to mitigate current aberration. Due to the requirements of VSI, the novel harmonic extraction algorithm (NHEA) based on the state space model is presented to separate the positive-sequence component (PSC), negative-sequence component (NSC), and zero-sequence component (ZSC) in the fundamental and harmonic current. Then, under this harmonic extractor, 90° phase lead for each SC can be easily achieved by means of simple vector rotation. Excellent extraction performance of the NHEA and remarkable ability of current quality control and power decoupling regarding CVI are demonstrated by simulations and experiments.

Sequence Impedance Modeling and Analysis of MMC in Single-Star Configuration

This paper presents sequence impedance modeling and analysis of modular multilevel converters (MMCs) in a single-star configuration for static VAR compensation (STATCOM) application. Prior work on impedance modeling of MMC is limited to the double-star configuration for high-voltage dc transmission applications. Compared to that, single-star configuration uses only a single arm of switching modules in each phase, eliminating the second-harmonic circulating current and the need for the associated circulating current control. On the other hand, the lack of connection to a stiff dc bus makes it essential to include module capacitor voltage control in the model. A special form of the multi-harmonic linearization method is applied to take advantage of the simpler harmonic spectra and to reduce the complexity of the resulting models. The developed models are verified by simulation and experiment, respectively, and used to understand the similarities and differences in the impedance characteristics of the two configurations as well as the effects on stability. A representative wind power plant is presented as an example to demonstrate the application of STATCOM impedance models on the system stability analysis.

ANALISIS GANGGUAN HUBUNG SINGKAT PADA JARINGAN PEMAKAIAN SENDIRI PLTU BOLOK PT. SMSE (IPP) UNIT 3 DAN 4 MENGGUNAKAN SOFTWARE ETAP 12.6.0

Bolok Steam Power Plant has its own 6.3 kV usage network to service loads such as Feed Water Pump and Circulating Pump Feed. This self-use network is expected to supply unit loads at the Bolok coal-fired steam power plant without any interference. The presence of disturbances such as short circuit in the electric power system can cause problems such as damage to electrical equipment and the emergence of a power outage. Therefore problems that arise like this require an analytical study to determine the short circuit current that will occur while reducing the consequences that arise.&#x0D; This study aims to determine the largest short circuit fault current with the help of ETAP 12.6.0 software. Short circuit simulation results with ETAP 12.6.0 will be compared with manual calculations based on positive, negative and zero sequence impedance values from the point of disturbance location. &#x0D; Based on the results of the research that has been done, it is known that the type of two-phase short circuit interference to the ground is the largest type of interference, which is equal to 10,615 kA on the generator bus. Whereas for the smallest type of short circuit interference is the type of disturbance one phase to the ground that is equal to 3,967 kA on the OutGoing II bus. From the results of the simulations conducted, it can also be seen that changes in the value of short circuit fault currents are affected by changes in the number of operating loads. The more load that operates the positive and negative sequence impedance the smaller and the value of the short circuit current will be greater, while the zero sequence impedance does not affect the amount of load operating, as well as the opposite.

A Theory for Harmonics Created by Resonance in Converter-Grid Systems

This letter presents a theory for the creation of harmonics by resonance in converter-grid systems. A harmonic of this type is usually not present or observable under normal operation, but may suddenly appear, with a growing magnitude and at a frequency that coincides with a system resonance frequency. The growth may be unbounded, leading eventually to a shutdown of the converter or other components in the system due to protection or physical damage, but often it stops after certain time and the harmonic sustains itself at a constant magnitude. The latter is the focus of this work and is identified as a result of system operation changing from an initially unstable mode to a critically stable mode achieved via a self-adjusting process. Small-signal sequence impedance models are used to explain this self-adjusting process and to determine the resulting harmonic responses. Experimental measurements are presented to validate the theory and to demonstrate the characteristics of this new type of harmonics.

Sequence-Impedance-Based Stability Comparison Between VSGs and Traditional Grid-Connected Inverters

Traditional grid-connected inverters (TGCI) could suffer from small-signal instability owing to the dynamic interactions among inverters and a weak grid. In this letter, the small-signal sequence impedance model of the virtual synchronous generator (VSG) is built, and the sequence impedance characteristics of the VSG and the TGCI are compared and analyzed. The sequence impedance of the TGCI is mainly capacitive in the middle-frequency area, and the impedance amplitude is quite high. By contrast, the sequence impedance of the VSG, being consistent with the grid impedance characteristics, is generally inductive, and the impedance amplitude is quite low. Based on the sequence impedance model and the Nyquist stability criterion, the influence of the grid stiffness, the number of paralleled inverters, and the phase-locked loop (PLL) bandwidth on the stability of the VSG and the TGCI systems is analyzed. The stability analysis results show that the TGCI loses stability easily, whereas the VSG still works well without PLL restrictions under an ultraweak grid or with a large number of inverters connected to the grid. Therefore, the VSG is more suitable than the TGCI for achieving high penetration of renewable energy generation in an ultraweak grid from a system stability viewpoint. Finally, the experimental results validate the sequence impedance model and the stability analysis.

Subsynchronous oscillation of PV plants integrated to weak AC networks

The grid-connected photovoltaic (PV) power is booming, and large-scale PV power is mostly integrated to grid through long transmission lines; however, PV systems may face the threat of subsynchronous oscillation (SSO) when AC system strength is weak. This study establishes the sequence impedance model of grid-connected PV system; mechanism and characteristic of SSO in PV plants integrated to weak AC networks are delved into through impedance-based analysis method. The results show that, under certain conditions, the impedance of PV system is capacitive in the subsynchronous frequency domain, when the networks are weak and the PV capacity is high, the resonance may occur between the capacitive PV system and inductive AC grid. In addition, a smaller proportional gain of current loop may increase the risk of SSO; however, a larger proportional gain and integral gain of phase-locked loop can ease the SSO. Finally, time domain simulation based on PSCAD/EMTDC is conducted to validate the results of the impedance-based analysis. The research here can provide guidance to the project of scaled PV plants integrated to weak AC networks in some sense.