Positive Sequence Impedance Research Articles

Impedance stability analysis and impedance remodelling of matrix converter grid‐connected system

Matrix converter has become one of the research hotspots of power electronic converter due to its excellent input and output characteristics and adjustable power factor. To study the stability of the matrix converter grid-connected system, the harmonic linearisation method is adopted to model the positive and negative sequence output impedance models of the matrix converter grid-connected system. The stability of the system is analysed by judging whether the plot of the ratio of the input impedance to the positive and negative sequence output impedance satisfies the Nyquist stability criterion. Also, an impedance remodelling method based on the positive sequence impedance is proposed to improve the stability of the system. Finally, the simulation verification is carried out by MATLAB/Simulink. The simulation results prove the correctness of the theoretical analysis and the feasibility of the impedance remodelling method.

Impedance Analysis of Voltage Source Converter Using Direct Power Control

The impedance analysis has been proposed and proved to be an effective way to analyze the grid-connected stability of Voltage Source Converter (VSC) based energy conversion systems. Most of the existing impedance analyzes are discussed based on vector oriented control, while there are few discussions about the impedance analysis of Direct Power Control (DPC). In this paper, an impedance modeling approach of VSC using the DPC is firstly proposed and analyzed, which fills the gap of impedance analysis of the DPC based converters and provides a basis for studying the corresponding grid-integration stability problems. Since there is no need for PLL and Park transformation, the impedance matrix is built directly using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha \beta$</tex-math></inline-formula> reference frame and features symmetrical characteristics. The proposed impedance matrix can be transformed into a positive-sequence impedance and analyzed by using SISO Nyquist criteria. The stability of a weak-grid connected VSC using DPC is analyzed in this article. The main factors affecting system stability, including the grid and control parameters, are considered in the analysis. The effectiveness of the proposed method is demonstrated by the simulations carried out in the Matlab/Simulink Simscape Power Systems as well as a hardware-in-loop system.

Sequence Impedance Modeling and Stability Analysis for Load Converters With Inertial Support

Load converters with inertial support are used to enhance the system inertia. However, these converters may fail to operate stably in the weak grid. In this article, sequence impedance modeling and stability comparison analysis are proposed for the load virtual synchronous machine (LVSM) and the load converter with virtual inertia control (LCVIC). First, the universal sequence impedance formulas are derived by considering dc-link voltage dynamics and frequency-coupling effects. Then, the precise sequence impedance models are built for impedance characteristics analysis of LVSM and LCVIC. The analysis shows that the positive-sequence impedance of LVSM is generally inductive in the middle-frequency band, which is basically consistent with the grid impedance. In contrast, the positive-sequence impedance of LCVIC is negative-resistive-capacitive (i.e., phase angle is between -180° and -90°) in the middle-frequency band, which may lead to harmonic oscillation in the weak grid. Furthermore, the effects of grid impedance, load power, and other control parameters on the stability are analyzed for the two load converters based on the derived model and Nyquist stability criterion. The analysis results reveal that LVSM has better stability than LCVIC in the weak grid. Finally, the experimental results validate the correctness of the theoretical analyses.

Applicability Analysis of Directional Components in AC/DC Hybrid System

AC/DC hybrid power grids are more and more widely used in China, and the traditional relay protection directional components have experienced multiple misoperations. The adaptability of traditional directional components in AC / DC hybrid power grids is studied. Traditional direction components are based on fault sequence component network analysis. During the fault, the positive and negative sequence impedance of the AC-DC hybrid power grid is quite different, and the impedance angle of the line impedance and the equivalent impedance of the grid is no longer close to 90°. Misjudgment will occur in the direction component with sudden change, and performance cannot be guaranteed. As a result, directional elements based on the positive and negative sequence current branching coefficients being approximately equal are not suitable for AC/DC hybrid power grids. As for the directional element of the zero sequence principle, since the zero sequence network on the inverter side is relatively stable, its performance is reliable and it can operate correctly.

Sequence Impedance Modeling and Stability Assessment for Load Converters in Weak Grids

Load converter operating in the weak grid potentially suffers harmonic oscillation problems due to the impedance interaction. In this article, considering dc-link voltage dynamics and frequency-coupling effects, the precise sequence impedance models are derived for the traditional load converter (TLC) and the load virtual synchronous machine (LVSM). Based on the derived models, their sequence impedance characteristics are analyzed and compared. The analysis shows that the positive-sequence impedance of the LVSM is generally inductive in the middle- and low-frequency bands, which is basically consistent with the grid impedance characteristics. In contrast, the positive-sequence impedance of the TLC is negative-resistive-capacitive (i.e., phase angle is between -180° and -90°) in the middle- and low-frequency bands and its amplitude-frequency curve is easy to intersect with the amplitude-frequency curve of the grid impedance, which may lead to harmonic oscillation in the weak grid. Furthermore, based on the derived model and Nyquist stability criterion, the effects of the grid impedance and load power on the stability are analyzed for TLC and LVSM, which indicates that the LVSM has better stability in the weak grid than the TLC. Finally, the experimental results validate the correctness of the theoretical analyses.

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.

Examination of the effect of the reactive power control of photovoltaic systems on electric power grids and the development of a voltage-regulation method that considers feeder impedance sensitivity

When relatively high-capacity renewable photovoltaic (PV) systems are connected to a grid, they can increase or decrease the voltage along feeders because of reverse power flow, even exceeding ± five percent of the rated voltage. Nowadays, grid-connected inverter-based PV systems that can control reactive power can alleviate such an increase or decrease in voltage by adjusting the reactive power, which is referred to as Volt/Var control and management. Therefore, the objective of this paper is to (a) perform case studies to analyze the steady-state response of a large distribution network (i.e., with more than 1000 buses) with high-capacity PV systems that can control Volt/Var (i.e., either producing or consuming reactive power) and (b) present a Volt/Var-control method for three-phase voltage regulation that uses the positive-sequence sensitivity impedance matrix with power-factor constraints. This method is verified in the IEEE 34-bus test feeder. Thus, the proposed methods can be used to regulate the voltage of a bus to which a PV system is connected if the system controls reactive power. These proposed methods can also be used for various impact studies for the operation or planning of distribution systems with such PV systems.

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.

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.

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.

Impedance Matrix and Parameters Measurement Research for Long Primary Double-Sided Linear Induction Motor

Static longitudinal end effect caused by truncated iron and coil windings is the inherent characteristic of linear motors. For multisegment long primary double-sided linear induction motors (DLIMs), subsection power supply mode results in longer iron than excited coil windings, which aggravates the static longitudinal end effect. First, the characteristics of the DLIM impedance matrix are researched through experiments. The impedance matrix is calculated by the measured amplitude and phase of the three-phase voltage and current. Unlike the traditional rotating induction motor, the matrix of DLIM is not a traditional cyclic symmetric matrix. Positive-sequence impedance, which is defined and obtained based on the impedance matrix, could be used to measure parameters by open-circuit and short-circuit experiments. The parameters measurement method is validated more accurate than the traditional average phase impedance. The research results, which are validated by test data from the long primary DLIM system capable of producing 400 kN of force, operating at the 100-MW peak power level, could be the reference for accurate description of the dynamics motor model and parameter measurement.

A New Method for Dimensioning and Designing the Zero-Sequence Electromagnetic Filter Considering System Displacement Power Factor

This paper proposes an innovative method for dimensioning and designing the zero-sequence electromagnetic filter applied to three-phase four-wire distribution power systems. As premises, the optimum ratio between zero-sequence and positive-sequence impedances of the filter must be established in order to potentiate the filtering percentage of zero-sequence currents and ensure the quality of the supply system displacement power factor. The calculations are based on the sequential harmonic transmittances of the equivalent circuit reduced to the coupling point of the electromagnetic filter. To validate the proposed method, the results obtained with the application of the electromagnetic filter designed in a test system using the MATLAB software are compared to the results of the system modeled in the PSIM software.

A Robust Fault Detection and Discrimination Technique for Transmission Lines

The complex and large power systems of modern time with distributed generation are more prone to the faults. Conventionally, the zone based primary and backup protection relies mainly on the information of positive sequence impedance sensed by the relay to protect these lines. The phenomena such as power swings, load encroachment, etc., can also result into low impedance and can trigger the cascade tripping of relays. In this paper, we proposed a robust fault detection and discrimination (RFDD) technique for transmission lines, which utilizes a robust method of phasor estimation to compute accurate fault impedance along with a feature value extracted from the samples of voltage and current signals. The effectiveness of the proposed RFDD technique has been tested and validated on IEEE 14-bus system, six generator 23-bus system and reduced NEREB 29-bus Indian power system with distributed generation using Siemens PSS/Sincal software. The results from simulation explore that RFDD technique can enhance the capability of distance protection relays for the future electric grids.

A New Directional Element for Microgrid Protection

With protective relays exclusive for microgrid applications yet to be developed, microgrids are currently limited mostly to directional overcurrent relays (DOCRs) for protection. This paper unveils that the long-known small fault current of electronically coupled distributed generation (DG) units is merely one of several phenomena that DOCRs suffer from; the current magnitude in microgrids with DG units may even provide misleading indications of fault conditions. More important, commercial-grade torque- and impedance-based directional elements are shown to be adversely affected by the fault behavior of DG units. The misoperation may include incorrect fault direction identification or deactivation of directional elements by false detection of loss-of-voltage condition, ruling out existing impedance relays as workable solutions for microgrid protection as well. This paper also devises a new directional element that addresses these problems. The proposed element detects the direction of asymmetrical faults using the magnitude and angle of the superimposed negative-sequence impedance. For symmetrical faults, the proposed directional element uses the magnitude of superimposed positive-sequence impedance along with the positive-sequence current and torque angle. PSCAD/EMTDC simulation studies verify the performance of this new method.

Rules to estimate the expected values of zero-sequence impedances in 3-phase core-type transformers

Simple rules to estimate the expected values of zero-sequence impedance measurements for 3-phase core-type transformers are shown. The proposed rules are based on the analysis of magnetic circuits. Due to this fact, a conceptual description about zero-sequence impedances of these transformers is included. The rules were verified with measurements on fifteen transformers, and these measurements were used for refining the rules. In case of magnetizing zero-sequence impedances, the presence or not of magnetic shunts on tank walls defines the details of these rules. In case of short-circuit zero-sequence impedances, only the positive-sequence transformer impedances are necessary to apply the proposed rules. These rules are important in order to reduce the probability of errors during the tests. Some rules related to the resistive part of the impedances are also presented.

On the Equivalence and Impact on Stability of Impedance Modeling of Power Electronic Converters in Different Domains

Small-signal analysis of power electronic converters and systems is often carried out by impedance-based methods. At the core of these methods lies the impedance modeling, which can either be obtained through analytical calculations, simulations, or measurements. The impedance models can be obtained into two main domains: the dq -domain and the sequence domain. In the dq -domain, the impedance model is a $2\times 2$ matrix, while in the sequence domain, it is composed by the positive and negative sequence impedance. Recently, a third domain called the modified sequence domain was defined as an extension to the sequence domain, but also with clear similarities to the dq -domain. The objective of this paper is to unambiguously relate to each other the impedances in these three domains, and to show how this equivalence translates into their respective stability assessments. It is also proven that the sequence domain impedance has the same marginal stability condition as the dq -domain impedance matrix. The three-phase voltage source converter is used as an example converter in this paper, as its impedance model in all three domains is well established and reported by previous research. The results in this paper show that the modified sequence domain model can be derived from the dq -domain model (and vice versa), and that the stability analysis will be identical in these two domains. It is also shown how the original sequence domain model can be derived from the two other models through a model reduction. However, a small discrepancy between the two Nyquist plots is observed in the presence of components such as phase-locked loop or dc-link control.

Fault location and classification of combined transmission system: Economical and accurate statistic programming framework

An effective statistical feature extraction approach of data sampling of fault in the combined transmission system is presented in this paper. The proposed algorithm leads to high accuracy at minimum cost to predict fault location and fault type classification. This algorithm requires impedance measurement data from one end of the transmission line. Modal decomposition is used to extract positive sequence impedance. Then, the fault signal is decomposed by using discrete wavelet transform. Statistical sampling is used to extract appropriate fault features as benchmark of decomposed signal to train classifier. Support Vector Machine (SVM) is used to illustrate the performance of statistical sampling performance. The overall time of sampling is not exceeding 1¼ cycles, taking into account the interval time. The proposed method takes two steps of sampling. The first step takes ¾ cycle of during-fault and the second step takes ¼ cycle of post fault impedance. The interval time between the two steps is assumed to be ¼ cycle. Extensive studies using MATLAB software show accurate fault location estimation and fault type classification of the proposed method. The classifier result is presented and compared with well-established travelling wave methods and the performance of the algorithms are analyzed and discussed.

A novel 4‐limb earth fault compensation reactor for distribution network

Summary This paper presents a novel earth fault compensation solution, which presents high positive sequence impedance and magnetically controllable zero sequence impedance. A 4-limb reactor is introduced to compensate earth fault currents in three-phase power distribution networks without the need of neutral point in substation transformer or separate earthing transformer. This results in considerably lower costs in implementing earth fault current compensation with much faster operation, making it possible to tune for 100% compensation during fault thus improving the probability of arc suppression. The presented reactor is analyzed analytically, and its performance is validated by simulations. The presented solution can significantly improve the reliability of the supply network.

Design and Implementation of an Algorithm for Diagnosis of Load Encroachment in EHV Lines

Zone-3 mal-operation of distance relays was one of the important cause for many of blackouts in worldwide. The one of the root cause for the mal-operation is encroachment of load into the Zone-3 characteristics. Such zone-3 mal-operations can be prevented by improvising the zone-3 characteristics which eventually avoids cascaded line tripping. This paper proposes and validates a new algorithm based on the total DC component and Phase angle of the positive sequence impedance to prevent its operation during the load encroachment conditions. Based on the proposed algorithm, improvement in the operation of Zone-3 element can be achieved. The relay can differentiate between actual system faults and load encroachment and thus ensure the security of the system. The proposed algorithm supplements the Zone-3 operation by introducing the ability to identify a load encroachment condition, and thus can avert the possibility of blackouts.

Adaptive distance protection for grounded fault of lines connected with doubly‐fed induction generators

Crowbar circuit is a preferred solution to maintaining wind generators connected to the grid during a disturbance. However, the activation of crowbar protection will lead to an obvious difference between the positive sequence impedance of wind generators and the negative sequence one. This study analyses the influence of this unique fault characteristic of doubly-fed induction generators (DFIGs) on the three zones of distance relays. When the transmission line emanates from a DFIG-based wind farm, there exists a high probability that the conventional protective zones of distance relays fail to operate. Hence, an adaptive branch coefficient is proposed to calculate the zone 2 setting according to the fault type and equivalent sequence impedances of wind generators. The proposed adaptive setting principle realises a better coverage of zone 2 and enhances the reliability and sensitivity of the relays. Simulation results verify the improvement of the protective zone of distance relays.