Research and education in power system dynamics


With increasing penetration of distributed and renewable sources into power grids, and with increasing use of power electronics based devices, the dynamic behavior of modern power systems is becoming increasingly complex. Several systematic issues are active power balancing, reactive power balancing, reduced system inertia, fast transients, stability, frequency regulation, and inter‐area oscillations. Stability and dynamic responses of power systems are often studied by means of time‐varying phasors, under the assumption that the system is quasi‐static. However, with increasing integration of fast renewable and distributed sources, this assumption is becoming increasingly inaccurate.

One of the barriers for integration of renewable sources today is that the impact of these sources on the system dynamics and stability is not yet fully understood. In many cases the need to preserve the system reliability and stability is a bottleneck, which practically prevents the use of such sources, despite their positive environmental impact and low cost. In this light, our research group is studying dynamic problems using the tools provided by the dq0 transformation. By exploring broad classes of systems from the perspective of dq0 based model, we expect to gain a better understanding of the nonlinear dynamics associated with complex power systems. This web page offers lectures and software tools reflecting this approach.

Lectures on power system dynamics
  1. This lecture is an introduction to the topic of power system dynamics. We discuss different approaches for modeling dynamic phenomena, and explain how to construct models based on time-varying phasors.
  2. This lecture discusses the center of inertia (central angle) reference frame, and introduces the aggregated swing equation. We show how these concepts allow analysis of global system properties with minimal data and computational effort.
  3. This lecture introduces the Direct-Quadrature-Zero (DQ0) transformation, and shows how it is applied to general linear networks. We discuss the advantages and disadvantages of dq0 based models, and explain how this transformation is used to analyze complex transients and fast dynamic phenomena.
  4. In this lecture we discuss the dynamics of the synchronous machine. We present a dq0 model of the machine, and demonstrate how to use it in power system simulations. We also show how to describe systems that include several machines, and explain the relations between the machine's dq0 model and time-varying phasors model.
  5. This lecture is a short introduction to the dynamics and control of Switched Power Converters. We show a general technique for analyzing the converter dynamics based on the idea of average signals, and present a basic method for designing the control loop.
  6. This lecture outlines the design principles of three-phase inverters, focusing on their control. We introduce the concepts of grid forming, grid feeding, and grid supporting inverters, and explain how they are used in specific applications, such as renewable energy systems and microgrids. We also present a basic control scheme for a Permanent Magnet Synchronous Motor (PMSM).
  7. This lecture focuses on management and control of energy storage devices. We mainly consider high capacity storage devices, and explain how they may be used for energy balancing, load leveling, peak shaving, and energy trading. We also discuss the crucial role of storage in integration of renewable energy sources.

... more to come ...


This is a free software tool for analyzing the dynamics of power systems based on dq0 signals. It is designed to simulate and analyze power systems that include several generators and loads, and possibly a large transmission network. The software provides tools for constructing dynamic models of the system components, and enables analysis in the frequency domain or the time domain. The manual (including tutorial) and software provide simple explanations and examples that can help one get started, even if one has no prior knowledge.

  1. Download the software files from MATLAB Central, and copy them to a directory of your choice, e.g., C:\DQ0 dynamics.
  2. Setup the directory in your MATLAB path. In the MATLAB, go to File > Set Path... and click on Add with Subfolders.... Now, select the directory that contains the DQ0 dynamics folder.
  3. Save the path for future MATLAB sessions (usually administrator privileges are necessary).
  4. For more advanced installation options please see the MANUAL.
Contact (✉)
Yoash Levron
The Andrew and Erna Viterbi Faculty of Electrical Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
E-mail: Send Mail
  Juri Belikov
Department of Computer Systems,
Tallinn University of Technology,
Akadeemia tee 15a, 12618 Tallinn, Estonia
E-mail: Send Mail