Tutorial: Immittance and Frequency Response of Inverter-Based Resources


Tuesday afternoon
11 October 2022
09:00 – 13:00


The Frequency Responsoe tutorial will be held both on-site and online.

On-site participation
The on-site Frequency Response tutorial will be held at the workshop venue, the The Hague Conference Centre in Room 2.3.

Please come to the main registration desk to collect your conference badge before going to the tutorial.

Online participation
Please log into the virtual conference room at least 5 minutes before the start of each session to avoid potential connection issues. It is requested that the participants mute their microphones during the session unless addressing the speakers.


Background and Objectives

The term immittance, combining the concept of impedance and admittance, was created by Hendrik W. Bode. Input and output immittances of a converter are a type of transfer functions that define the converter’s frequency response to external disturbances. Immittance modeling and analysis of converters in ac power systems was initially motivated by the need to study converter-based power system stability for electric ship and more-electric aircraft development. The rapid development of renewable energy and HVDC transmission in recent years created an opportunity as well as a need to apply the methods to utility power grids. As a result, a large body of knowledge and a wealth of practical experiences have been developed. Immittance-based frequency-domain modeling now provides a comprehensive framework to study the stability of inverter-based resources (IBRs) and systems. It also enables design engineers to optimize IBRs and their control design for stable operation with/in the grid. New immittance-based IBR performance specifications and system study procedures/tools are also being developed.

Tutorial lecturer: Prof. Jian Sun
Rensselaer Polytechnic Institute, USA

This tutorial presents an overview of the theory and different applications of immittance-based frequency-domain modeling and analysis techniques for converters in the grid, with a focus on IBRs such as renewable power generation and HVDC transmission.

Target Audience

This is an intermediate-level tutorial and assumes knowledge of converter circuits and control for IBR applications. The targeted audience includes:

  • Electrical engineers involved in the design, characterization, testing and system integration of wind turbines, PV inverters and HVDC converters;
  • System engineers responsible for grid system design and planning, IBR interconnection study, as well as performance specification and grid code development for IBRs;
  • Hardware and software engineers involved in the development of test equipment and software tools for IBR-related and future power system applications;
  • Researchers and PhD students wishing to learn about practical applications of the theory and contribute to its future development.


Preliminary Agenda

08:00 – 09:00

Check in

09:00 – 09:50

Lecture 1 (45 min.)
Basic Concepts and Applications

We start the tutorial by discussing the importance of immittance in power systems and the difficulty to define it for converters. After a brief review of different definitions attempted in the early days of research in this field, small-signal sequence immittance is introduced as a natural extension to the existing definition of immittance for transformers, transmission lines, generators and other components common in power systems. Practical methods to determine frequency responses of small-signal sequence immittances by frequency scan based on laboratory measurement and numerical simulation are then presented. Requirements for the laboratory setup and simulation models/algorithms to ensure reliability of scan results are also explained. The lecture concludes with the formulation of an immittance-based IBR-grid system model for frequency-domain stability analysis based on the classical Nyquist stability criterion.

Discussion (5 min)

09:50 – 10:40

Lecture 2 (45 min.)
IBR Immittance Models and Characteristics

This lecture reviews the development and use of immittance models in analytical form for PV inverters, type-III and type-IV wind turbines, as well as HVDC converters. The mathematical principle and process to develop such models are explained in sufficient detail to allow those interested in analytical work to apply the technique to IBRs that have not been modeled in the literature. The remaining of the lecture focuses on practical applications and uses the analytical models to explain the effects of IBR design on its immittance responses and characteristics. For this purpose, the overall frequency spectrum is divided into low, medium and high frequency ranges. The effects of different control functions, including PLL, ac current and voltage control, as well as dc bus control in each frequency range are explained to provide insights into their design tradeoffs and shed lights on possible ways to shape the immittance responses for the benefit of system operation and stability.

Discussion (5 min)

10:40 – 11:00

Coffee Break

11:00 – 11:50

Lecture 3 (45 min.)
System Models and Stability Analysis

Formulation of system models based on immittance for stability analysis is treated systematically in this lecture. A large class of practical IBR stability problems can be studied by using a system model that resembles the model of a single-input-single-output (SISO) feedback loop. This SISO formulation can be used to study grid integration issues of individual IBRs. Through aggregation, it can also be applied to multiple IBRs operating in parallel, such as wind or PV farms. For more complex systems, a multiple-input-multiple-output (MIMO) formulation is introduced to account also for possible interactions among different IBRs. Both grid-following and grid-forming controls are considered. Frequency-domain stability analysis of MIMO systems based on the generalized Nyquist criterion is also explained. Practical applications of the MIMO formulation includes power systems with multiple renewable power plants in different locations, multi-terminal HVDC, as well as future hybrid ac-dc grids.

Discussion (5 min)

11:50 – 12:40

Lecture 4 (45 min.)
Modes and Mitigation of System Instability

The component and system immittance models introduced in early lectures are used to explain typical modes of instability and resonance in different types of IBR systems, including onshore and offshore wind farms, as well as HVDC converters operating with overhead lines, cables and renewable sources. The instability modes are classified according to their frequency ranges and each is identified with certain root causes related to different design aspects/parameters or characteristics of the IBR and the grid. Practical methods to damp and avoid instability are also reviewed and categorized as control tuning, active damping, and passive damping in general. Design of each of these methods, their pros and cons, as well as possible unintended consequences are discussed according to the type of system and the frequency range in which they are applied.

Discussion (5 min)

12:40 – 13:00

Future Development

The following topics will be briefly discussed to highlight some of the opportunities for future development:

  1. Electromagnetic transient (EMT) simulation (including hardware-in-the-loop simulation) and its relationship to immittance-based frequency-domain modeling and analysis;
  2. Development of immittance-based IBR performance specifications (standards) to guarantee system stability in at least certain frequency range to reduce the number of system studies;
  3. Development of integrated software tools to support immittance-based frequency-domain modeling and analysis of large IBR systems and future converter-based grids.
13:00 – 14:00

Lunch (included in participation fee)



  • The Tutorial on Immittance and Frequency Response of Inverter-Based Resources is not included in the general participation fee of the 21st Wind & Solar Integration Workshop.
  • As the number of participants for this Tutorial is limited, tickets are available on a first come, first served basis.
  • The Tutorial can be canceled if less than 10 participants register.
  • The participation fee includes a coffee break and lunch.
  • The following table shows both the gross prices (incl. 21% Dutch V.A.T. | marked in bold) as well as the net prices (excl. V.A.T.).




Early Bird

04 Aug 2022

435.00 €
359.59 €

300.00 €

Mid Registration

08 Sep 2022

485.00 €
400.83 €

350.00 €

Late Registration

09 Oct 2022

555.00 €
458.68 €

400.00 €

On-site Registration

09 Oct 2022

600.00 €
495.87 €


330.00 €
272.73 €

220.00 €