Impedance-based Stability Analysis Research Articles

Impedance-Based Stability Analysis of Power System Wideband Oscillations: A Bridge between s Domain and Frequency Domain

Impedance-Based Stability Analysis of Power System Wideband Oscillations: A Bridge between <i>s</i> Domain and Frequency Domain

A Comprehensive Stability Assessment System for EV DC Charging Station Based on Multitimescale Impedance Model

The existing all-in-one impedance-based stability analysis only qualitatively reveal the instability factors by the graphic Nyquist criterion while the stability margin is not considered. In this article, a design-oriented multiattribute and multidimensional based comprehensive assessment system (MAMD-CAS) is proposed to evaluate the stability quantitatively and guide the parameter design as well as ensure the desired dynamic response and stability margin. This MAMD-CAS mainly includes the loop-gain-based multi-timescale impedance estimation to analyze the low-frequency oscillation (LFO), phase margin (PM) calculation of different timescales and dynamic performance indicators as the time-domain quantitative expression of impedance estimation. In detail, the multi-timescale impedance model is established and its loop-gain representation is deduced to implement the impedance estimation. Combined with the known PM, the influence of the parameters on dynamic performance and stability margin can be comprehensively evaluated, then the conflict between dynamic performance and stability margin is explored. It is found that the voltage-loop parameters do not have the coupling problem between dynamic performance and stability margin while <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vir</sub> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">svr</sub> present a conflicting effect between the inertia-loop LFO dynamic performance and stability margin and their interaction affects the severity of inertia-loop LFO. The appropriate control parameters can be thus selected for a good stability margin while suppressing the impedance peak. This MAMD-CAS analysis result is verified by simulation and experiment and this assessment system provides theoretical fundamental for the online stability monitor of multi-timescale power electronics system.

Impedance-Based Stability Analysis: Nodal Admittance or Bus Admittance?

Impedance-based stability analysis is widely adopted for small-signal stability demonstration of power electronics dominated power systems. Stability assessment can be performed using either nodal admittance or bus admittance (i.e. equivalent admittance of a network viewed from a specific bus). This paper demonstrates that stability analysis using the bus admittance may not always produce correct results, even though it is easier to implement. Unstable multi-bus systems can be wrongly identified as stable by the single-bus analysis, in the cases where other buses play a dominant role in causing instabilities. A detailed comparison between nodal and bus admittance stability analysis is presented, leading to recommendations for their practical use. A phase-based method is proposed to facilitate the acquisition of eigenloci encirclement around the critical point, which can be used in the stability analysis based on either nodal or bus admittance. Following the conclusion of our work, we recommend multi-bus analysis in white-box model applications for instability mode analysis and stability-oriented design. Single-bus analysis is preferable in black-box model applications due to its simplicity. It is also suggested to select a bus for analysis from those connected to a high share of inverter-based resources, to ensure the correctness of results.

Revisit Impedance-Based Stability Analysis of VSC-HVDC System

According to different partitioning styles, there exist different impedance-based stability analysis methods for complex systems such as voltage source converter (VSC)-based high-voltage direct current (HVDC) systems. Thus, the determination of the partitioning method is of importance in impedance-based stability analysis. However, how to partition a complex system is not paid much attention in the past. In this paper, the partitioning problems are revisited and a set of practical partitioning principles are proposed. Based on the principles, the VSC-HVDC system is partitioned into five parts, satisfying simplicity and integrity. In addition, the methods to form the equivalent circuits of the sub-systems are given and the equivalent circuits of the sub-systems are built, which is helpful to obtain the input-output models of the sub-systems. Furthermore, a stability criterion by directly applying the argument principle is used instead of the generalized Nyquist criterion (GNC), which could avoid the calculation of eigenvalue transfer functions, especially when a large number of sub-systems are involved. Finally, the correctness of the impedance-based stability analysis method is verified by control hardware-in-loop (CHIL) experimental results.

Enhancing Stability of Grid-Supporting Inverters from an Analytical Point of View with Lessons from Microgrids

The central components influencing future grid stability in the future are inverters and their controllers. This paper delves into the pivotal role of inverters and their controllers in shaping the future stability of grids. Focusing on grid-supporting inverters, the study utilizes a microgrid test setup to explore their impact on overall grid stability. Employing impedance-based stability analysis with the Nyquist criterion, the paper introduces variations in internal inverter parameters and external grid parameters using pole-zero map considerations. The inverter’s control structure, resembling standard generators with droop control, facilitates the application of grid operators’ knowledge to inverter control. Mathematical insights into stability principles are provided, highlighting the influence of poles related to the phase-locked loop and the strategic placement of additional poles for enhanced stability. Furthermore, the paper evaluates the effects of rotating inertia, revealing that a 50% increase in system inertia can stabilize unstable microgrid behavior, enabling grid-supporting inverters to actively contribute to grid reliability.

Impedance-Based Stability Analysis and On-Site Stability Evaluation of Three-Phase Active Voltage Conditioner Embedded System

Impedance-Based Stability Analysis and On-Site Stability Evaluation of Three-Phase Active Voltage Conditioner Embedded System

Impedance-Based Stability Analysis of Grid-Connected Inverters under the Unbalanced Grid Condition

As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments.

Multi-vehicle accessed railway vehicle-grid system stability analysis and optimization based on OLTC

The interaction between Electric Multiple Units (EMUs) and the traction network can lead to oscillation problems due to electrical mismatch. The stability between the EMUs and the traction network is difficult to ensure because of the multiple operation points and variable operation modes of EMUs. To analyze the system stability, impedance-based methods are commonly used. However, existing impedance-based stability analysis methods require identifying system transfer functions, which can introduce under- or over-fitting problems. To address this issue, this paper introduces an optimized open-loop based stability analysis method for multi-vehicle accessed vehicle-grid system, which effectively assesses the impact of vehicle operating points and modes on system stability. In addition, we propose an On-Load Tap Changer based method to enhance the voltage stability of railway traction networks. By optimizing traction network voltage, the impedance characteristics of vehicles are also modified, thus enhancing system stability. Finally, we validate the efficacy of the proposed method through case studies based on an actual railway train schedule diagram.

Oscillation Suppression Strategy of Three-Phase Four-Wire Grid-Connected Inverter in Weak Power Grid

As the penetration of renewable energy increases year by year, the risk of high-frequency oscillation instability increases when a three-phase, four-wire split capacitor inverter (TFSCI) is connected to the grid with complementary capacitors in weak grids. Compared to the three-phase, three-wire inverter, the TFSCI has an additional zero-sequence current loop. To improve the accuracy of the modeling and stability analysis, the effect of the zero-sequence loop needs to be considered in the impedance-based stability analysis. Therefore, a correlation model considering multi-perturbation variables is first established, based on which the inverter positive, negative, and zero sequence admittance models are derived, solving the difficult problem of impedance modeling under small perturbations. Secondly, an admittance remodeling strategy based on a negative third-order differential element and a second-order generalized integrator (SOGI) damping controller is proposed, which can improve the stability of positive, negative, and zero-sequence systems simultaneously. Finally, the effectiveness of the oscillation suppression strategy is verified by simulation and experiment.

Framework to assess the stable operation of commercially available single-phase inverters for photovoltaic applications in public low voltage networks

This paper presents a framework to assess the grid compatibility of single-phase inverters connected to public low voltage network, which is characterized by a stable operation at reasonable emission. The assessment is based on considering emission, immunity and stability. The state of the art for commercially available devices relies only on the classical, impedance-based stability analysis based on the Nyquist criterion. However, experiences have shown that this is not sufficient for a statement towards the stable operation of an inverter, since the stable operation can also be affected by other factors than the network impedance, e.g. a background voltage distortion. Exemplary laboratory measurements of two commercially available single-phase PV inverters are presented to validate the statement by showing that despite the impedance-based stability criterion is met, inverters can still trip in presence of a high background voltage distortion. The paper concludes that the immunity of the inverter with regard to the voltage distortion at the point of connection (PoC) is additionally of importance for its stable operation.

Impact of DFIG impedance model precision on stability analysis

Impedance-based stability analysis (IBSA) is an effective method to analyze the interaction problem between the doubly-fed induction generator-based wind park (DFIG-WP) and series compensated or weakly tied AC grids. The analytical impedance model of DFIG has evolved over the years for better precision. This paper presents a precision comparison of those analytical models where the reference is obtained through EMT-level frequency scanning simulations. Moreover, representative IBSA is also performed with those models on typical test systems in which the DFIG adversely interacts with the series compensated grid and weakly tied AC grid in sub- and super-synchronous frequency ranges, respectively. The common modeling approach, which disregards the coupling between the rotor side converter (RSC) and grid side converter (GSC) at the DC-side, reduces the accuracy of IBSA and may lead to incorrect stability analysis results.

A new stationary frame multi-input multi-output EMT-level frequency scanning method for inverter based resources

Impedance-based stability analysis (IBSA) is an effective method to identify subsynchronous interaction (SSI) problem between the inverter-based resources (IBRs) and series compensated or weakly tied AC grids. The electromagnetic transient (EMT) level positive sequence and dq-frame frequency scanning methods (p-scan and dq-scan, respectively) are used to obtain the sequence single-input single-output (SISO) and dq multi-input multi-output (MIMO) impedance of IBRs, respectively. The dq MIMO impedance usage in IBSA provides more accurate results compared to the sequence SISO impedance. This paper proposes an EMT-level αβ-frame frequency scanning method (αβ-scan) to obtain the αβ MIMO impedance and its usage in IBSA. The αβ-scan requires significantly less time compared to dq-scan for the convergence of MIMO IBR impedance representation and offers similar accuracy with dq-scan in IBSA. The accuracy of the proposed αβ MIMO IBSA is validated by comparing with dq MIMO IBSA and EMT simulations on series capacitor SSI cases with different type IBRs (Doubly-fed induction generator (DFIG)-based wind park (WP) and full-scale converter (FSC)-based WP). This paper also uses a multivariable structure function(MSF)-based method for the first time in IBSA of SSI to achieve Bode plot-based analysis for providing better visualized presentation of resonance frequency and stability margins compared to generalized Nyquist criterion.

Settling Angle-Based Stability Criterion for Power-Electronics-Dominated Power Systems

Impedance-based analysis methods are widely applied to the small-signal stability analysis of grid-connected converters. As the initial step to carry out the impedance-based stability analysis, it is critical to select whether to represent the converter as a Norton or Thevenin equivalent circuit. However, there is lack of definition on the representation of converters, and inappropriately selected impedance model choice leads to improper stability analysis. Moreover, existing impedance-based stability analysis methods, e.g., return-ratio matrix (RRM)-based method, only apply to minimum phase systems where the RRM does not contain right-half-plane poles. In complex and power-electronics-dominated power systems, interactions between multiple converters lead to nonminimum phase power systems, where current methods can no longer be directly applied. To address these problems, a stability criterion is proposed by introducing the concept of settling angle. As the main contribution of this article, the settling angle of total admittance is proven as the intrinsic hallmark of power systems and directly reflects the system stability. The proposed settling-angle-based stability criterion is validated by control hardware-in-the-loop experimental results for a three-terminal system that integrates grid-forming and grid-following converters through a common bus.

Stability and Sensitivity Analysis of Multi-Vendor, Multi-Terminal HVDC Systems

Multi-terminal HVDC projects are increasingly developed in recent years to enhance the flexibility of energy transmission. Differing from the point-to-point HVDC systems, it is more challenging to design the multi-terminal HVDC system and ensure stable interoperability among converter systems, especially when the converters are manufactured from different vendors. Although impedance-based stability analysis allows for analyzing such systems based on black-box models, it is still difficult to utilize those black-box models to identify the root cause of potential instability. To tackle this challenge, this paper proposes a multi-level sensitivity analysis approach using frequency-domain sensitivity functions based on the impedance-based stability criterion. The proposed method differs from the classical sensitivity analysis based on state-space or transfer-function models, as it is purely based on black-box impedance models. Case studies on a four-terminal HVDC system are carried out for stability and sensitivity analysis based on the impedance measurement in PSCAD, through which the most sensitive HVDC station can be identified. The proposed theory and the analyzed results are finally validated by electromagnetic transient simulations.

Output Impedance Derivation and Small-Signal Stability Analysis of a Power-Synchronized Grid Following Inverter

In recent years, grid-following inverters (GFLIs) and grid-forming inverters (GFMIs) have established their position as the mainstream synchronization techniques for the grid integration of inverter-based resources into power systems. However, both of these integration techniques have their shortcomings in weak, strong, and/or series-compensated grids. Recently, in the literature, a power synchronized GFLI has been proposed that does not suffer from the issues exhibited in GFLIs and GFMIs. This article provides an analytical output impedance of this power-synchronized GFLI that uses a linear parameter-varying controller (LPV-PSGFLI). This impedance is then used for impedance-based stability analysis via the Nyquist stability criterion. In addition, the derived impedance is validated via system identification, and a comparison between a conventional GFLI and an LPV-PSGFLI is made under various system strengths. It is seen that the LPV-PSGFLI can inject power into the grid, whereas the conventional GFLI fails when both are integrated into a very weak grid. Finally, the accuracy of the impedance-based stability analysis using the derived output impedance is validated in Matlab/PLECS and in experiments in various scenarios.

Stability analysis of virtual synchronous generator control in a high-voltage DC transmission system using impedance-based method

Numerous distributed generators (DGs), which often include renewable energy sources, are connected to modern power grids through grid-connected inverters. Conventional linear model approximation methods may not be sufficient to accurately analyze the dynamic response of DGs due to the harmonics and nonlinear distortions generated by power-electronic devices. Therefore, an impedance-based stability analysis method has been adopted and applied in high-voltage direct current (HVDC) power transmission systems as a practical data-driven alternative to the linear model approximation method. However, the presence of multiple AC/DC converters and the non-negligible ground capacitance of DC transmission lines increases the difficulty of analyzing the entire HVDC system. Previous studies have mostly focused on the stability of either the generator-side system or the load-side AC system. In this study, impedance-based analyses were performed on the generator-side AC system, DC transmission line, and load-side AC system to evaluate the entire HVDC system when the generator-side AC system was weak. Additionally, an advanced inverter control method called the virtual synchronous generator (VSG) control method, which can result in grid stabilizing effects, was introduced to the load-side AC system. The analysis results demonstrate that the VSG control significantly enhances the stability of HVDC transmission systems as compared with the conventional power control methods.

Stability Assessment of Modular Multilevel Converters Based on Linear Time-Periodic Theory: Time-Domain vs. Frequency-Domain

The periodic characteristic of modular multilevel converter (MMC), which originates from the multi-harmonic couplings among internal dynamics, results in challenges to develop the linear time-invariant (LTI) model of MMC. The linearization of MMC is inherently around time-periodic equilibrium trajectory. In this paper, two different methods to assess small-signal stability of MMC are compared. Both are based on the linear time-periodic (LTP) systems theory, but one is in the time domain (TD) and the other is in the frequency domain (FD). The LTP model of MMC is derived from the linearized arm averaged model. Then, an LTI model for the LTP system is constructed in the FD through the harmonic state-space method. Small-signal stability analysis based on Floquet theory and generalized Nyquist criterion, that accompany TD and FD, are introduced and compared. It is demonstrated that models developed in both domains can effectively capture the small-signal behavior of MMC. Third and higher-order harmonic components of the states have significant effect on the impedance-based stability analysis of MMC around mid-frequency range. Analytical results are validated by electromagnetic transient simulations based on the MMC aggregated model.

Analysis and Design of PLL Less Current Control for Weak Grid-Tied LCL-Type Voltage Source Converter

For a weak grid-tied <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LCL$ </tex-math></inline-formula> -type converter, the conventional current control interacts with a phase-locked loop (PLL) through the voltage at the point of common coupling (PCC). Thus, the dynamics of PLL deteriorate converter stability, hence leads to system instability issues. To avoid the instability issues due to PLL, a PLL less current control is proposed for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LCL$ </tex-math></inline-formula> -type grid-connected converter with capacitor-current-feedback active damping. The analysis and design of the proposed PLL less current control is presented in this article, and the performance of the proposed control is compared with conventional current control (i.e., PLL without bandpass (BP) filter) and improved conventional control (i.e., PLL + BP filter). A small-signal model is developed by considering the dynamics of the PLL and BP filter to show the impact of the current control parameters on converter output impedance. An impedance-based stability analysis is performed to show the system stability against short circuit ratio (SCR) variation for three different current control scenarios, such as proposed PLL less, PLL with a BP filter, and PLL without BP filter. The proposed current control works in both stiff grid and weak grid environments. It has strong robustness against a wide range of variation in grid impedance and more adaptable to grid frequency changes. The performance of the proposed control is verified during grid voltage harmonics, unbalanced voltage, and grid voltage variations and further validated by comparing with the conventional control. In addition to the features mentioned above, the proposed current control is able to operate stably at SCR = 1. Finally, the experiment shows the superiority of the proposed control over conventional control.

Analysis of multi-converter network impedance using MIMO stability criterion for multi-loop systems

This work presents a novel method of simplifying multi-converter systems containing complex grid-forming and grid-following controllers for stability analyses. Analysis is conducted via the equivalent converter output impedance. Important points for impedance-based stability analysis of larger networks are considered, including impedance rotations, proper combination of sources and correctly obtaining a minimum system realisation with appropriate tolerances. The proposed method is used to conduct a sensitivity analysis of different grid-forming and grid-following converter control parameters to determine tuning recommendations for the modern electricity network. To achieve this, complex control structures including power/voltage control, negative sequence regulation and synchronous machine emulation are included. Network stability is found to be sensitive to current control, active power control and frequency-based components such as PLLs. However, voltage control exhibits a smaller effect on stability for a range of short circuit ratios. Some recommendations are provided on when the simplified method can be utilised and how to ensure correct application.

Control-Based Two-Layer Protection for Short-Circuit Fault at an LVDC Feeder Branch

Low-voltage dc distribution offers high efficiency for grid integration of dc-based technologies such as photovoltaic and battery storage systems and new loads such as charging stations for electric vehicles due to reduced number of conversion stages. However, the selection of protection devices, protection coordination and selectivity is still subject to research. This work proposes to use a two-layer protection technique utilizing the control capability of power converters in case of a short-circuit fault at branch level of a low voltage dc feeder. The first layer is limiting the bus current using a virtual resistance in the droop control to avoid tripping of the grid-forming converter. The second layer implements a soft fuse tripping technique for selectivity. The control concept is presented and the system stability is analyzed using impedance-based stability analysis. Experimental results on a hardware-in-the-loop setup verify the findings.