Impedance-based Stability Analysis Research Articles

Fast and accurate grid impedance estimation approach for stability analysis of grid-connected inverters

Interactions between grid-connected inverters and the equivalent grid impedance seen at their point of common coupling have been identified as one of the main causes of instability problems. Therefore, the need for real-time monitoring tools to identify grid impedance variations cannot be underrated. Even though existing techniques have shown to estimate the grid impedance accurately, several concerns have remained unsolved. These include the trade-offs between the estimation accuracy and the magnitude and the time duration of the injected disturbance(s). Hence, this paper proposes a fast and accurate grid impedance estimation approach for the application of online impedance-based stability analysis of grid-connected inverter systems. First, the wideband grid impedance is estimated online based on the injection of two triangular pulses, allowing fast and multiple-input multiple-output (MIMO) identification in the synchronous (dq) reference frame. Then, curve fitting of the estimated wideband grid impedances is applied to obtain their parametric models. Afterward, the stability analysis is performed in the dq reference frame based on the generalized Nyquist criterion. The proposed algorithm allows accurate stability analysis over all frequencies as it relies on the parametric impedances. Most importantly, to optimize the trade-offs between the power quality and accurate stability analysis, the proposed algorithm is executed again and injects the two pulses disturbances to the grid only if the system operating conditions change (e.g., variations of the grid impedance). It is also applicable to perform the stability analysis while the inverter is still in standby mode. The simulation and experimental results of a 3-phase grid-connected inverter are presented to validate the efficacy of the proposed technique.

A Magnetic-Sensing-Based Wide-Bandwidth Grid Impedance Measurement Technique With Small Perturbation Injection

Grid impedance is an important parameter in the impedance-based stability analysis method for analyzing the interaction between the power electronic inverters and the power grid. However, the existing measurement technique is deteriorated by narrow-bandwidth sensors, large perturbation injections, and inaccurate response components extraction based on the fast Fourier transform (FFT) algorithm. To overcome these problems, a magnetic-sensing-based wide-bandwidth grid impedance measurement technique with a small perturbation injection is proposed in this article. A novel impedance extraction algorithm based on the quadrature delay estimator (QDE) is developed to overcome the spectral leakages and frequency aliasing effect of the existing FFT-based impedance extraction algorithm. The proposed grid impedance measurement technique is implemented on a digitally controlled inverter system, and its effectiveness is verified through the experimental results.

DC‐link capacitor current observation based stability enhancement control for back‐to‐back converter

This article presents a stability enhancement control scheme applied in the three-phase back-to-back (BTB) converters with L filter. The stability enhancement control scheme is concocted using the feedback of DC-link capacitor current without additional sensors. Both grid-side converters are equipped with this control scheme, which can also be called the coordinated compensation control scheme. In this article, DC terminal impedance models of two converters before and after optimization and stability criterion are introduced. Furthermore, means of impedance analysis, including Bode plot and Nyquist curve, are discussed to categorize the causes of BTB converter instability caused by the increased power. The coordinated scheme is compared with the conventional scheme for revealing the theoretical basis. The proposed method is capable of optimizing the disturbance suppression capability of DC-link voltage, which would potentially reduce capacitor volume and physical size of the DC-link. The impedance-based stability analysis indicates that the controllability and stability of the BTB converter is enhanced with the proposed DC-link capacitor current coordinated control. Furthermore, the proposed control scheme is implemented in the MATLAB/Simulink environment. Moreover, for further validation, the feasibility of the coordinated control scheme is verified with the experimental results.

Systematic Procedure for Mitigating DFIG-SSR Using Phase Imbalance Compensation

Replacing conventional generation by power electronics based generation changes the dynamic characteristics of the power system. This results among others in the increased susceptibility to sub synchronous oscillations (SSO). This paper proposes a systematic procedure for mitigating the interactions between a DFIG and a series compensated transmission line using the phase imbalance compensation (PIC) concept. The impact of the series and parallel PIC on the resonance behaviour of the grid is first thoroughly investigated. Then, the influence of the system strength on the capabilities of the PIC to mitigate DFIG-SSR is assessed. Based on the findings a design framework which enables the systematic assessment of the series and parallel PIC for mitigating DFIG-SSR is developed and successfully implemented in the modified IEEE 39 bus system. Comparison between both concepts reveals that the parallel PIC is better suited to mitigate DFIG-SSR. The impedance based stability analysis and detailed time domain electromagnetic transient (EMT) simulations are used to respectively screen and validate the results.

A Potential Issue of Using the MIMO Nyquist Criterion in Impedance-Based Stability Analysis

The impedance-based stability criteria are widely adopted for small-signal stability analysis of power systems. Among them, the determinant-based multi-input multi-output (MIMO) Nyquist criterion is particularly attractive since it simplifies the stability determination process without calculating the eigenvalues of MIMO systems. However, it is found in this letter that the determinant-based Nyquist criterion can potentially result in incorrect stability analysis results with pure inductance models in the MIMO models of the power network. This letter illustrates the issue and its root cause through mathematical derivation and numerical analysis. Then, the issue is demonstrated through an example system, and the corresponding solutions are provided as well.

Extended Nodal Admittance Matrix Based Stability Analysis of HVDC Connected AC Grids

Motivated by emerging oscillation issues of high-voltage direct-current (HVDC) transmission system resulted from the interaction with AC grids, impedance-based stability analysis becomes an attractive approach in the de-risking studies due to the capability of black-box modelling and clear physical meaning. However, impedance-based stability assessment of HVDC is typically conducted either from the AC side or from the DC side, without fully considering both AC and DC grid dynamics, thus impairs evaluation accuracy. In this paper, the nodal admittance matrix based resonance mode analysis method is extended to include both AC and DC dynamics through formulating a hybrid AC-DC admittance matrix. To achieve this goal, HVDC interfacing-converters are modelled as three-port admittance networks with one DC port and two AC ports (in dq-frame) integrating both the AC side frequency coupling and the AC-DC dynamic coupling. In contrast to the widely adopted Nyquist-based methods, the proposed method does not requires knowing the number of right half-plane poles of system minor-loop gain, thus simplifies stability analysis, and moreover, the participation factors of both AC and DC grid nodes in critical resonance modes can be identified through eigenvalue-decomposition analysis, which is in favor of the design of mitigation measures. The effectiveness of the proposed method is validated by EMT-simulations in MATLAB/Simulink.

SISO Impedance-Based Stability Analysis for System-Level Small-Signal Stability Assessment of Large-Scale Power Electronics-Dominated Power Systems

To address the growing dynamic issues in the power electronics-based power system, this paper proposed an enhanced impedance-based stability analysis which can not only obtain the global view of system dynamics, but also provide a tailor-made stabilization solution by the direct use of the measured black-box models. With the proposed method, the dynamic interactions at selected multiple ports of the system are translated as multiple decoupled single-input single-output (SISO) minor loops in the frequency domain, of which the stability can be readily assessed by the SISO Nyquist stability criterion. Moreover, the oscillation mode shapes, i.e., the relative magnitude and phase of oscillated voltages and currents at the selected ports, are derived mathematically. Furthermore, the frequency-domain participation factor is defined to identify the most contributive components for the oscillations; Through impedance shaping solution of the corresponding oscillatory mode, it also provides the most effective system stability enhancement solution. EMTDC/PSCAD time-domain simulation results from an 800 MW offshore wind energy system with a realistic complexity confirm the effectiveness of the proposed method.

Comparison of PLL-Based and PLL-Less Control Strategies for Grid-Following Inverters Considering Time and Frequency Domain Analysis

This article presents a comprehensive comparison of three control strategies used for grid-following inverters (GFLIs). The first strategy is the phase-locked loop (PLL)-based vector current control (VCC), and the other two PLL-less controllers are the voltage-modulated direct power control (VMDPC) and the linear-parameter-varying power-synchronized control (LPV-PSC). The VCC relies on the PLL to synchronize with the grid frequency to control the exchanged real and reactive power with the grid, which may result in instability issues under weak grid conditions. To prevent this, the VMDPC and LPV-PSC are proposed recently as PLL-less approaches to overcome the difficulties of the VCC in weak grid conditions. The performance of the VCC, VMDPC, and LPV-PSC are comprehensively reviewed in this article, considering the operations of the GFLIs under both strong and weak grids. In each operation mode, the provided tests investigate: 1) step response of active and reactive power, 2) frequency jump in the grid voltage source, 3) phase jump in the grid voltage source, and 4) voltage sag in the grid voltage source. In addition to evaluating the three controllers in the time domain, the frequency domain impedance-based stability analysis based on the generalized Nyquist criterion is also considered, which confirms the time domain findings in terms of accurate predictions of the stable/unstable operations of the GFLIs that are equipped with these controllers. It is found that, compared to the conventional VCC and the VMDPC, the LPV-PSC has promising performance under various test conditions in both strong and weak grids, which may be a future solution for weak-grids connection of GFLIs.

Controller design-oriented analysis of grid-forming converters for stability robustness enhancement

Grid-forming converters can suffer from control interaction problems in grid connections that can result in small-signal instability. Their inner-loop voltage controller tends to interact with the outer-loop power controller, rendering the controller design more difficult. To conduct a design-oriented analysis, a control-loop decomposition approach for grid-forming converters is proposed. Combined with impedance-based stability analysis, the control-loop decomposition approach can reveal how different control loops affect the converter-grid interaction. This results in a robust controller design enabling grid-forming converters to operate within a wider range of grid short-circuit ratios. Finally, simulation and experimental results, which validate the approach, are presented.

Impedance Modeling and Stability Analysis of VSG Controlled Type-IV Wind Turbine System

In order to realize the grid-friendly wind turbine system (WTS), applying of the virtual synchronous generator (VSG) control strategy to WTS has become a trend of research, and it is also required to analyze the grid-connected operation characteristics of the VSG controlled WTS. In this paper, the impedance modeling and impedance-based stability analysis of the VSG controlled type-IV WTS are carried out. Different from existing impedance modeling method that the WTS is modeled by a high dimensional impedance model with complex expressions, a model to describe the shaping effects of dc-link dynamics is proposed, and combined with the space vector diagram to analyze the system impedance characteristics. It is found that the impedance of the VSG controlled type-IV can be capacitive below the fundamental frequency, which is inherited from its GSC impedance and the capacitive characteristics has been weakened by the influence of dc-link dynamics. Instable risk has also been found between the VSG controlled type-IV WTS and the connected weak grid, and the instability can be avoided if the capacitive characteristics of the VSG controlled type-IV WTS are weakened by reshaping its GSC impedance or by enhancing the dc-link dynamics. Experiments are also carried out as verifications.

Identification of Grid Impedance by Broadband Signals in Power Systems with High Harmonics

Grid impedance is an important parameter and is used to perform impedance-based stability analysis for the operation of grid-connected systems, such as power electronics-interfaced solar, wind and other distributed power generation systems. The identification of grid impedance with the help of broadband signals is a popular method, but its robustness depends strongly on the harmonic disturbances caused by non-linear loads or power electronics. This paper provides an in-depth analysis of how harmonics affect the identification of grid impedance while using broadband measurements. Furthermore, a compensation method is proposed to remove the disturbing influences of harmonics on broadband impedance identification. This method is based on exploiting the properties of the used maximum-length binary sequence (MLBS). To explain the methodology of the proposed method, the design basis for the excitation signal is discussed in detail. The analysis from simulations and a real measurement in an industrial power grid shows the effectiveness of the proposed method in compensating the disturbing influences of harmonics on broadband impedance measurements.

Impedance-Based Stability Analysis of Grid-Tied Photovoltaic System With Superconducting Magnetic Energy Storage System

As the deployment of superconducting magnetic energy storage (SMES), the characteristic of grid-tied photovoltaic system becomes more complicated. However, existing research of the grid-tied photovoltaic system takes no account of the effects of SMES system. Hence, an investigation is made on the effects of digital control delay of SMES converter on the stability of system in this paper. The modelling of grid-tied photovoltaic system is proposed based on impedance modelling method, where the digital control delay of SMES converter system is considered. It is shown that the digital control delay of SMES converter deteriorates system stability and even leads to instability. Meanwhile, the stable grid-connected capacity of photovoltaic system is also reduced due to the weaken of system stability. The simulations are performed to validate that SMES's digital control delay has a significant impact on system.

Modeling and frequency characteristic analysis of DSOGI-PLL in dq reference frame

Dual second-order generalized integrator phase-locked loop (DSOGI-PLL) is widely used in grid-connected system for grid synchronization because of its simple implementation and good filtering capability. However, the frequency characteristics of DSOGI-PLL affect the impedance modeling of the system, which in turn affect the impedance-based stability analysis. In order to improve the accuracy of system modeling, in this paper, the equivalent transfer function of positive-sequence calculator (PSC) block constructed in αβ reference frame in DSOGI-PLL is presented in dq reference frame, where the relationship between DSOGI-PLL and traditional synchronous reference frame PLL (SRF-PLL) small-signal model is investigated. Then, based on the established model, DSOGI-PLL and SRF-PLL are compared from the tracking characteristics and robustness characteristics. It is further demonstrated that DSOGI-PLL is able to improve the robustness performance of PLL while maintaining the same tracking performance as SRF-PLL. Finally, simulation results are presented to validate the established model and frequency characteristic analysis.

New analysis on two‐variable converter impedance model in grid‐connected systems

This paper presents an in-depth analysis for the two-variable impedance model of a grid-connected system. The two-variable model describes the impedance using the frequency as well as the operating point variable. The impedance-based stability analysis method cannot be directly applied because the conventional models are derived for a specific steady-state operating point and the operating point varies during operation. Thus, this paper develops a new analysis method to shed light on the role the two-variable model plays instability analysis. The proposed method not only analyzes the system stability at different operating points, but also enables the controller design to ensure system stability. Experimental results are presented to demonstrate the effectiveness of the proposed method.

Impedance Modeling and Stability Analysis of DFIG-Based Wind Energy Conversion System Considering Frequency Coupling

Impedance-based stability analysis is an effective method for addressing a new type of SSO accidents that have occurred in recent years, especially those caused by the control interaction between a DFIG and the power grid. However, the existing impedance modeling of DFIGs is mostly focused on a single converter, such as the GSC or RSC, and the influence between the RSC and GSC, as well as the frequency coupling effect inside the converter are usually overlooked, reducing the accuracy of DFIG stability analysis. Hence, the entire impedance is proposed in this paper for the DFIG-based WECS, taking coupling factors into account (e.g., DC bus voltage dynamics, asymmetric current regulation in the dq frame, and PLL). Numerical calculations and HIL simulations on RT-Lab were used to validate the proposed model. The results indicate that the entire impedance model with frequency coupling is more accurate, and it is capable of accurately predicting the system’s possible resonance points.

Impedance-Based Stability Analysis of Less Power Electronics Integrated Electric Shipboard Propulsion System Considering Operation Mode, PLL, and DC-Bus Voltage Control Effect

A doubly-fed induction machine (DFIM) is a promising choice for the shipboard propulsion system (SPS) of a more-electric ship (MES) to increase the system safety level by employing less power electronics. In this paper, the detailed impedance model of DFIM-SPS is established, with a salient-pole synchronous generator (SPSG) acting as the power source and a DFIM functioning as the propulsion load. The impedance modelling of DFIM is carried out from the aspect of ac coupling between the stator and rotor circuits, which is easy for physical understanding. In addition, the back-to-back power converter (BTBPC) is regarded as controlled voltage sources with impedances in the equivalent circuit. The phase-locked loop (PLL) is a key element in influencing the system stability, and it is integrated to upgrade the system dq impedance model. Moreover, the impedance shaping effect caused by dc-bus voltage control is investigated. Nyquist stability criterion is employed for system small-signal stability analysis, which is implemented with respect to the DFIM operation mode and PLL controller effect, and the time-domain simulations are carried out to verify the stable operation of a 5 MW DFIM-SPS in Matlab/Simulink. Furthermore, the experimental verification is done on a 1.5 kW DFIM electric drivetrain platform.

Two-Port Characterization and Transfer Immittances of AC-DC Converters–Part II: Applications

This two-part paper presents a general method to model three-phase ac-dc converters as two-port networks for power system stability studies. Part I of the work has developed the two-port network models and identified two types of transfer characteristics that are unique to ac-dc converters and important for system stability. Part II presents the applications of the developed models in stability analysis of different power systems that use ac-dc converters, including grid integration of converter-based generation from wind, PV and other renewable sources, grid-connected dc microgrids and dc distributed power systems, high-voltage dc transmission, as well as hybrid ac-dc power systems. While impedance-based stability analysis has been studied for each of these systems, the new two-port models, especially the transfer immittance models, make it possible and easy to formulate more complete system models to include dynamics and coupling effects that have been ignored or impossible to consider in the past. The methods to study the stability of each type of systems are explained and illustrated by case studies that also highlight the effects of coupling modeled by the transfer immittances on system stability. Each case study also exemplifies a practical stability concern in converter-based power systems.

Two-Port Characterization and Transfer Immittances of AC-DC Converters—Part I: Modeling

This two-part paper presents a general method to model three-phase ac-dc converters in the frequency domain for power system stability studies. In the developed approach, an ac-dc converter is treated as a two-port network connecting an ac and a dc power system, and is characterized by a set of self and transfer immittances. The transfer immittances describe two types of small-signal coupling that are unique to three-phase ac-dc converters: The first type describes the coupling between the ac and dc port and involves a frequency shift by the fundamental; the second type models the coupling over frequency in the ac port current response and involves a frequency shift by twice the fundamental. Together with the self-immittances of each port, the developed models can be used as building blocks to support impedance-based stability analysis of various power systems that involve such converters, including ac, dc, and hybrid ac-dc power generation, transmission and distribution systems. Part I of the paper explains the two-port modeling approach and develops the associated models for a two-level voltage-source converter. Part II presents applications of the developed models for stability analysis of different systems.

Analysis of online impedance measurement range based on voltage disturbance injection

The harmonic injection method is often used to measure the impedance of grid-connected inverter, which is necessary for impedance-based stability analysis of grid-connected systems. This paper proposes an online impedance measurement range analysis method that takes into account the grid impedance, electrical signal measurement range, and the upper limit of safety response of the equipment under disturbance in online measurement. This method provides a basis for the verification of impedance measurement results. It also can guide the design of the amplitude of the injected disturbance. The method helps to provide more accurate impedance measurement results, which is important for impedance-based stability analysis. Finally, this paper verifies the proposed impedance measurement range through simulation.

An Integrated Method for Generating VSCs’ Periodical Steady-State Conditions and HSS-Based Impedance Model

An integrated method for generating the system's periodical steady-state (PSS) conditions and the harmonic-state-space (HSS)-based impedance model is presented, referred to as the automatic-model-generation (AMG) method. This method is efficient for parametric impedance-based stability analysis, since it can precisely take the varying PSS into account and the presented algorithm can be readily implemented by the frequency-domain iteration. Application of this AMG method to the impedance acquisition and stability analysis of a single-phase grid-tied voltage-source-converter (VSC) along with experimental verifications is presented as an example. The presented results demonstrate how the AMG method can facilitate parametric stability assessments (e.g., under varying control parameters) in an efficient and accurate manner.