Power System Grounding and Transients

An Introduction

A.P. Sakis Meliopoulis

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351423106
• Edition: 1
• Topic: Technologie et ingénierie
• Subtopic: Ingénierie de l'électricité et des télécommunications

""This authoritative work presents detailed coverage of modern modeling and analysis techniques used in the design of electric power transmission systems -- emphasizing grounding and transients. It provides the theoretical background necessary for understanding problems related to grounding systems, such as safety and protection.

1
Power Transmission Systems

1.1 Introduction

This book addresses the topics of power system grounding and transients. The two topics are as old as power engineering itself. Since the early days of power system engineering, the two topics were investigated experimentally and appropriate solutions were invented which resulted in established practices. As power systems grew in size and complexity, it became necessary to reevaluate present practices and to improve design procedures of grounding systems and protection against transient overvoltages. Recent technology advancements coupled with research efforts resulted in improved models for the analysis of grounding systems and analysis of transient phenomena in power systems. The improved analytical models are the cornerstone for better designs of power systems apparatus and installations.

Analytically, the two topics are closely interrelated. Specifically, the theoretical bases for building analytical models for the study of these phenomena are similar. In subsequent chapters we introduce the modeling procedures and examine specific applications, such as design of grounding systems, protection against electrical transients, and so on. In this chapter we introduce basic definitions and nomenclature and discuss the general characteristics of the systems and phenomena to be studied in this book.

1.2 Basic Definitions and Nomenclature

In this section we introduce basic definitions and nomenclature that will be utilized throughout the book. First, instantaneous values of voltages and currents will be denoted by lowercase letters. for example, v(t) and i(t) denote the instantaneous value of voltage and current, respectively, as a function of time.

Many power system analysis problems deal with the power system operating under steady-state conditions. The generating units of the system generate nearly sinusoidal voltages and currents. In this case the voltage or current at any point of the system is varying sinusoidally with time. In general, the sinusoidally varying voltage or current is expressed as follows:

v(t)=2Vcos(ωt+ϕ)⁢(1.1a)

i(t)=2Icos(ωt+θ)⁢(1.1b)

where

V or I = rms value of the voltage or current

ω = angular frequency

φ, θ = phase angles

The sinusoidal voltage or current of (1.1) can also be represented with phasors. The phasors are complex numbers and provide an alternative way for representing sinusoidal waveforms. The phasors will be denoted by uppercase letters with a “~” above them. Thus the voltage and current phasors representing Eqs. (1.1) are denoted by V˜ and Ĩ, respectively. The instantaneous values of the voltage or current is by definition

v(t)=Re⁡{V˜ejωt}⁢(1.2a)

i(t)=Re{I˜ejωt}⁢(1.2b)

where Re{Z} means the real part of the complex number Z. By equating Eqs. (1.1) and (1.2), it is apparent that

V˜=Vejj⁢(1.3a)

I˜=Iejθ⁢(1.3b)

The majority of power systems comprise three-phase arrangements. It is expedient to introduce terms and definitions that will be used extensively in describing these systems.

In general, a three-phase system is constructed with single elements that are connected in a three-phase arrangement. Examples are electric loads, transformers, and motors. The elements may be connected in a delta or a wye configuration or any combination of these two. The delta and wye connections are illustrated in Fig. 1.1. For the description of three-phase systems, the following definitions are introduced:

Definition 1.1: Balanced Set of Three-Phase Voltages. A set of three-phase voltages, v_a(t), v_b(t), v_c(t), is called balanced if and only if :

The voltages vary sinusoidally with time.

The amplitudes of the voltages are equal.

There is a 120° phase difference between any two.

As an example, the following set of three-phase voltages is balanced:

va(t)=2Vcos(ωt+ϕ)⁢(1.4a)

vb(t)=2Vcos(ωt−120°+ϕ)⁢(1.4b)

vc(t)=2Vcos(ωt−240°+ϕ)⁢(1.4c)

In Eqs. (1.4), the phase difference between the phase a voltage and the phase b voltage is 120° and positive. This phase relationship among the three phases will be called the positive phase sequence. A three-phase generator generates a set of three-phase voltages that are nearly balanced and of the positive phase sequence. It is expedient to introduce the concept of an ideal three-phase source, which is illustrated in Fig. 1.2. An ideal three-phase source generates a set of balanced three-phase voltages of the positive or negative phase sequence. It is apparent that a set of balanced three-phase voltages is completely described with the voltage magnitude V, the angular frequency ω, the phase angle φ, and the sequence. Alternatively, it can be completely defined with the phasor of the phase a voltage, V˜a=Vejϕ, and the sequence. Throughout the text, when...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• 1. POWER TRANSMISSION SYSTEMS
• 2. TRANSMISSION LINE MODELING: LINE INDUCTANCE
• 3. TRANSMISSION LINE MODELING: LINE RESISTANCE
• 4. TRANSMISSION LINE MODELING: LINE CAPACITANCE
• 5. POWER SYSTEM GROUNDING I: MODELING TECHNIQUES
• 6. TRANSMISSION LINE ANALYSIS
• 7. POWER SYSTEM FAULT ANALYSIS
• 8. POWER SYSTEM GROUNDING II: DESIGN PROCEDURE
• 9. POWER SYSTEM TRANSIENTS
• References
• Appendix
• Index