Frequency Variations in Power Systems

Modeling, State Estimation, and Control

Federico Milano, Alvaro Ortega Manjavacas

• Publisher: Wiley-IEEE Press
• Year: 2020
• ISBN:
  9781119551874
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Energy

Frequency Variations in Power Systems: Modeling, State Estimation and Control presents the Frequency Divider Formula (FDF); a unique approach that defines, calculates and estimates the frequency in electrical energy systems. This authoritative book is written by two noted researchers on the topic. They define the meaning of frequency of an electrical quantity (such as voltage and current) in non-stationary conditions (for example the frequency is not equal to the nominal one) and pose the foundation of the frequency divider formula. The book describes the consequences of using a variable frequency in power system modelling and simulations, in state estimation and frequency control applications.

In addition, the authors include a discussion on the applications of the frequency divider in systems where part of the generation is not based on synchronous machines, but rather on converter-interfaced energy resources, such as wind and solar power plants. This important book:

• Offers a review that clearly defines and shows how the Frequency Divider Formula can be applied
• Discusses the link between frequency and energy in power systems
• Presents a unified vision that accurately reveals the common thread that links modelling, control and estimation
• Includes information on the many implications that "local frequency variations" have on power system dynamics and control
• Contains several numerical examples

Written for researchers, academic staff members, students, specialised consultants and professional software developers, Frequency Variations in Power Systems questions the conventional transient stability model of power system and proposes a new formulation.

Part I
Background

Chapter 1
Frequency in Power Systems

1.1. Conventional Definitions

Frequency is a fundamental quantity used in several fields of science and engineering and is utilized to characterize a huge variety of oscillatory and periodic phenomena. These include mechanical vibrations, sound, radio waves, and light.

Frequency is usually denoted as f [Hz] and is defined in the dictionaries as the number of occurrences of a repeating event per unit of time. This definition implies that, whatever is the event to be counted, the frequency cannot be measured until such an event has repeated at least twice. This definition is thus not adequate for transient phenomena and, apparently, indicates that the frequency cannot be defined for “fractions” of an event. The definition above is generally coupled with that of period, T [s], which is the duration of time of one cycle in a repeating event, thus T = 1/f.

The definition of frequency above is only adequate in stationary conditions, where events (or signals) repeat forever. This is sometimes called stationary frequency or Fourier frequency.

In electrical engineering, it is more useful to define an instantaneous angular frequency, ω [rad/s], as the rate of change of the phase, ϑ [rad], of a sinusoidal wave [12, 20]. If one has a signal:

(1.1)

the relationship between ϑ, ω, and f is:

(1.2)

and, consequently, also the period becomes time-varying:

(1.3)

Finally, the rate of change of frequency (RoCoF) [Hz/s] is defined as:

(1.4)

To properly interpret (1.2) is not always trivial. If the angular frequency is constant, the definition is also consistent with the intuition. In fact, if ϑ is:

(1.5)

where ω_o and θ_o are constant, then, as expected, the angular frequency is ω_o. However, if ϑ is:

(1.6)

...

Table of contents

• Cover
• Table of Contents
• List of Figures
• List of Tables
• Preface
• Acknowledgments
• Acronyms and Abbreviations
• Notation
• Part I: Background
• Part II: Theory
• Part III: Applications
• Appendices
• Bibliography
• Index
• End User License Agreement