A Survey on Impedance-Based Dynamics Analysis Method for Inverter-Based Resources

Impedance-based method has been increasingly adopted to assess the stability of inverter-based resources (IBRs). To get a better view of the state-of-the-art and challenges for implementing the impedance-based dynamic analysis, a survey with general/specific questions has been initiated by IEEE Task Force on Frequency-Domain Modeling and Dynamic Analysis of High-Voltage Direct Current (HVDC) and Flexible AC Transmission System (FACTS). The feedbacks are collected from universities, national labs, transmission system operators (TSOs), power plant developers, as well as IBR vendors. It is interesting to note that while many common understandings have been established in practices, certain gaps still exist among different stakeholders. This article intends to bridge this gap by sharing a summary of the survey, including questionnaires, responses from different stakeholders, and the analysis of survey results. The challenges for different stakeholders using impedance-based method are identified, which shed a light on the future research work.


Introduction
The legacy power grids that are dominated by electrical machines are gradually evolving as power-electronic-based power systems with high proportion of IBRs and active loads.The multi-timescale control dynamics of IBRs may interact with one another and with grid dynamics, leading to resonances and instabilities in a wide frequency range [1], [2].Addressing these challenges call for new methods and tools for dynamics analysis of IBR-dominated power systems.
The impedance-based dynamics analysis method is increasingly used to screen stability risks of IBRdominated power systems, mainly due to its advantage of dealing with black-box models [3], [4], as shown in Figure 1.Over past years, numerous efforts have been devoted, from both academia and industry, to advance this technology [5], [6].However, certain gaps persist among different stakeholders.An over-simplified IBR-grid system with a few or even single IBR is often used by academia for the impedance-based dynamic analysis.Such a simplified system may not be capable of reflecting all practical challenges in complex electrical systems, where thousands of IBRs can be configured in meshed and radial network structures.On the other hand, practicing engineers may not be aware of the latest advances in the impedance modeling theory and dynamics analysis.
To bridge the gaps, the joint IEEE Power Electronic Society (PELS) and IEEE Power and Energy society (PES) Task Force on Frequency-Domain Modeling and Dynamic Analysis of High-Voltage Direct Current (HVDC) and Flexible AC Transmission System (FACTS) made a questionnaire survey on the impedance-based dynamics analysis, aiming to obtain insights into the latest state-of-the-art and challenges of using this method.The survey got 46 responses from a diverse range of participants (54% from academia and 46% from industry), including universities, national labs, transmission system operators (TSOs), power plant developers, as well as IBR vendors across the globe.More detailed statistics of the survey participants are given in Tables 1 and 2.
This article intends to share the survey results and summarize both common and unique challenges for different stakeholders in implementing impedance-based method, which shed a light on the future research work in this direction.

Questionnaire and Responses
The questionnaire is designed with five general questions and six specific technical questions, the details of which are described by Q1-Q12 as follows.The corresponding response to those questions are given by Figures 2-13.-Table 1. Respondent sector statistics.

Respondent Sector Number
Academia University 25

Industry
National lab 3 TSO 5 Power plant developer 1

Geographic Location Number
North America 8 Europe 23 Asia/Pacific 15 Q5 What need to be further developed for using impedance-based method?A) Defining clear specifications on impedance profiles of IBRs.B) Improved efficiency and accuracy of impedance measurements in offline EMT simulations.C) Impedance-measurement tools in controller-hardware-in-the-loop tests.D) Impedance-measurement tools in field tests.E) Impedance-based stability and sensitivity analysis methods for multi-IBR systems.Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

B. Technical Questions
Figure 2 clearly demonstrates that almost all respondents have used or intend to use the impedance-based method for dynamic analysis.There is also an increasing awareness on how the method should be correctly implemented.As indicated in Figure 9, the vast majority of respondents recognize the necessity of employing multiple-input multiple-output (MIMO) impedance matrices, rather than single-input singleoutput (SISO) impedance transfer functions, for the accurate stability assessment in both αβ or dq frame [6].
While most respondents express confidence in the effectiveness of impedance-based method, industry respondents exhibit lower levels of confidence compared to their academic counterparts (see Figure 3).This disparity may be attributed to the fact that industries tend to encounter more complex electrical systems, which increases the likelihood of divergence between impedance-based predictions and EMT simulations/field measurements results.

B. Challenges for the Industry
Based on the response of Q3 and Q4 (Figures 4 and 5), both the unique and common challenges faced by TSOs/power plant developers and IBR vendors in implementing impedance-based dynamic analysis are summarized as follows: Unique Challenges for TSOs/Power Plant Developers: It can be seen from Figure 4 that the lack of the automated impedance measurement toolbox is one of most significant challenges for TSOs/power plant developers.The impedance measurement tools have been developed, both in simulation software and hardware, for measuring impedances of single or a few IBRs [7], [8], [9], [10].However, TSOs/power plant developers are dealing with large and complex electrical systems that may include thousands of IBRs, which imposes more stringent requirements on the time efficiency of the automated impedance measurement tools.A recent attempt can be found from Aalborg University and Ten-neT TSO that has developed the impedance measurement toolbox and tested in a multi-terminal HVDC system [8], as shown in Figure 14.National Renewable Energy Laboratory (NREL) [9] as well as Electric Reliability Council of Texas (ERCOT) [10] have also developed similar toolboxes that are tested in wind power plants.Yet, more efforts are still expected to further improve the computational efficiency and accuracy.
Figure 4 indicates another challenge for TSOs/power plant developers, which is the difficulty of verifying the accuracy of the impedance measurement.This challenge arises because TSOs/power plant developers work with black-boxed simulation models of IBRs, as the IBR vendors cannot disclose the control algorithms of IBRs due to intellectual property (IP) concerns.Consequently, TSOs/power plant developers cannot theoretically derive the impedance models to check with the measured results.A few TSOs/ power plant developers have asked IBR vendors to provide black-boxed, theoretically-derived impedance models for cross-validation with the measured impedances [11].However, this requires IBR vendors to have adequate expertise in impedance modeling of IBRs, and hence, it is still not a common practice at the current stage.
Unique Challenges for IBR Vendors: Based on Figure 5, the lack of impedance specifications poses a significant challenge for IBR vendors.Given the fact that the impedance matrix of IBR can be simplified to a SISO form in the high-frequency range, its real part is required to be non-negative by some grid codes for the guarantee of high-frequency stability [12].However, there are currently no specifications for impedance matrix of IBR in the low-frequency range, where its original MIMO form should be adopted for stability assessment.This is mainly due to the absence of a straightforward link between the low-frequency stability margin and the dynamic properties of impedance matrix, which makes it difficult to establish the impedance specifications.Moreover, the missing of such a direct link also poses a challenge for IBR vendors in obtaining analytical insights into controller design from the impedance-based dynamic analysis, as indicated by Figure 5.
Common Challenges: It can be seen from Figures 4  and 5 that TSOs/power plant developers and IBR vendors have expressed their concerns in using impedance-based dynamic analysis for multi-IBR systems.This concern can be further broken down into two questions: 1) how to aggregate impedance models of IBRs and 2) how to deal with multiple operating points of a complex electrical system, which are indicated by Q11-Q12.The industry's responses to the former question, as given by Figure 12(b), suggest that they are skeptical to the capability of aggregated impedance model of multiple IBRs in reflecting the control interactions therein.Further, their response to the latter question reflects a lack of an appropriate method for dealing with multiple operating points, i.e., they either attempt to cover as many operating points as possible, or select multiple operating points based on practical experiences or operational guidelines but are not sure if the selected operating points can cover the worst-case scenarios, as illustrated in Figure 13(b).

FIG 15
Open issues with impedance-based dynamics analysis methods.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

C. Gap Between Academia and Industry
It is quite interesting to see from Figures 12 and 13 that academia and industry hold quite different opinions on impedance-based dynamic analysis for multi-IBR systems.By comparing Figure 12(a) and (b), it is found out that although both groups acknowledged that the control interactions of IBRs is the primary cause of inaccuracy of the aggregated impedance model, academia additionally identifies different operating points of individual IBRs as an important contributor, while industry attributes the inaccuracy to different controller and circuit parameters.This disparity may stem from the fact that academia often examines homogeneous multi-IBR systems, where IBRs have identical controller and circuit parameters, and thus fails to capture the impact of heterogeneous IBRs on the accuracy of impedance aggregation.
Moreover, Figure 13(a) indicates that around 30% of academic researchers are confident to cover the worst-case scenarios by following certain guidelines, whereas this confidence is not agreed by the industry, as indicated in Figure 13(b).
In a nutshell, the results of Figures 12 and 13 clearly indicate the gap between understandings of academia and industry on the challenges of using impedance-based method, and highlight the importance of academia-industry collaboration in developing effective impedance aggregation methods for multi-IBR systems.

Future Development of Impedance-Based Dynamic Analysis
Based on the challenges identified in Section "Key Results and Analysis," and the response to Q5, several open issues with the impedance-based analysis method are summarized as follows, which are also outlined in Figure 15.Addressing these issues require collaborative research and development efforts of academia and industry.1) Dynamic Specifications for MIMO Impedance Matrix: Control theories that can link dynamic properties of MIMO impedance matrix to low-frequency stability margin, as well as linking the characteristics of each element of impedance matrix to specific controllers need to be developed.Such links would not only aid TSOs/power plant developers in developing clear specifications and requirements on the impedance matrix of IBRs, but also offer insights for IBR vendors in shaping control dynamics of IBRs.2) Impedance Measurement Toolbox: An automated impedance measurement toolbox with high measuring accuracy and high time efficiency should be developed and tested in large and complex electrical systems.3) Impedance-Based Analysis of Multi-IBR System: A solid theoretical framework of implementing impedance-based dynamic analysis should be developed for heterogeneous multi-IBR systems in complex electrical networks.This framework should be able to accurately aggregate impedance models of IBRs and address the challenges related to multiple operating points.

Conclusion and Future Action
The results of the survey on impedance-based dynamics analysis method have identified gaps and challenges faced by different stakeholders, based on which, several emerging topics in this direction are summarized.In the future, IEEE Task Force on Frequency-Domain Modeling and Dynamic Analysis of HVDC and FACTS will organize more technical activities to facilitate the collaborations between academia and industry in addressing the challenges, which can hopefully advance the technology for stability analysis of future power systems.

About the Authors
Heng Wu (hew@energy.aau.dk) is an Assistant Professor with the Department of Energy, Aalborg University, Denmark.
Fangzhou Zhao (fzha@energy.aau.dk) is an Assistant Professor with the Department of Energy, Aalborg University, Denmark.
Xiongfei Wang (xiongfei@kth.se) is a Professor with the Division of Electric Power and Energy Systems, KTH Royal Institute of Technology, Sweden, and a part-time Professor with the Department of Energy, Aalborg University, Denmark.

FIG 11 FIG 12 FIG
FIG 11 Response to Q10.(a) Response from academia.(b) Response from industry.

Q1 Do you use the impedance-based (frequency scan) method for dynamics analysis
? A) Yes B) No C) Not yet, may use it in the future Q2 What

Q6 How do you select frequency range and frequency resolution for impedance measurement
? A) Nyquist frequency of IBRs.B) Based on specific frequency range of oscillations.C) The maximum frequency of a black-box model specified by vendors.D) No clear guideline.Q7 Do

you use the multiple-input multiple-output (MIMO) impedance matrix for dynamics analysis
? A) Yes, because the accurate impedance model of three-phase balanced IBR is a 2 × 2 matrix.
) Yes, but the MIMO impedance matrix can be reduced to SISO impedance transfer function beyond certain frequency.C) No, because no efficient tool for measuring impedance matrix is available.D) No, only the single-input single-output (SISO) impedance transfer function is used for dynamics analysis.Check if the marginally stable case predicted by the impedance model agree with EMT simulation tests.B) Check if the step response of impedance model match with that of EMT simulation model.C) Compare the measured impedance data with theoretically derived impedance model.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.BQ9 How do you verify the measured impedance model?A)