This course teaches the theory and application of immittance-based frequency-domain methods for the modeling, stability analysis, and design of converter-interfaced resources and future grids dominated by such resources. The materials are derived from the instructor’s research in the subject area over 20 years as well as first-hand experiences from direct involvement in solving real-world stability problems in renewable energy, HVDC transmission, and critical power systems. Presentation of the materials emphasizes fundamental concepts, engineering insights, and practical applications to make the course most valuable to working professionals.

To give some flexibility for registration and attendance, the course is divided into two parts each consisting of nine (9) three-hour lectures.

Part I: Immittance-Based Stability Modeling and Analysis

Starting from the basic concepts of immittance and converter control, Part I of the course first introduces the definition of small-signal sequence immittances and their modeling in both analytical and numerical forms. Mathematical development is combined with engineering judgement to create simple models that are intuitive and easy to use. In additional to the modeling of voltage-source converters with control functions that are common for grid applications, this part also includes immittance modeling of synchronous generators, loads and other types of converters that are important for practical system studies but are often ignored in research papers.

Following the modeling at the converter level, Part I teaches the development of system-level models for different application scenarios with increasing complexity. Besides mathematical formulation to explain the general theory, practical methods and algorithms to obtain network and system models are also presented. Frequency-domain stability analysis by applying Nyquist and generalized Nyquist criteria to the developed models are then explained. Below are the topics of the nine lectures of Part I.

1. Circuits and Control of Converters for Power System Application
2. Frequency-Domain Modeling and Analysis of Converters
3. Modeling of Voltage-Source Converters with Constant DC Bus Voltage
4. Modeling of Voltage-Source Converters with DC Bus Dynamics
5. Immittance Modeling by Frequency Scan and Measurement
6. Modeling of Generators, Loads, LCC and Grid-Forming Converters
7. Stability at Converter-Grid Interface
8. Stability of Power Systems with Grid-Following and Grid-Forming Converters
9. Stability of DC and Hybrid AC-DC Grids; Other Applications

(Click here to see a detailed list of topics and subtopics of each lecture)

Part II: Instability Modes, Root Causes and Mitigation

Part II applies the modeling and analysis methods presented in Part I to identify common instability modes, their root causes, as well as practical solutions. To that end, the analytical models presented in Part I are examined first to give insights into how each control function of a converter affects the immittance. The general converter models are then used to develop specific immittance models for PV inverters, type-III and type-IV wind turbines, and HVDC converters. The models are presented such that they can be used directly to represent different practical designs. The models are also used to identify features that are important for systems stability, giving attendees the ability to “read” immittance responses and make judgements about their effects on system stability without a complete system model.

Built on these insights and intuitions, the remaining 2/3 lectures of Part II are devoted to understanding the common modes of system instability as well as their root causes and practical solutions. Much of the materials covered in these lectures are based on the instructor’s first-hand experiences and are not publically available. The ongoing development of immittance-based standards and product specifications that can ensure system stability is also reviewed. Below are the topics of the nine lectures of Part II.

1. Immittance Responses and Effects of Control
2. PV Inverter and Wind Turbine Immittances
3. HVDC Converter Immittances
4. High-Frequency Instability – Modes and Root Causes
5. High-Frequency Instability – Solutions
6. Low-Frequency Instability – Modes and Root Causes
7. Low-Frequency Instability – Solutions
8. Multi-Converter System Instability
9. Design for System Stability; Future Development

(Click here to see a detailed list of topics and subtopics of each lecture)